DISSERTAITONES PHYSICAE UNIVERSITATIS TARTUENSIS 16 «.Я? STUDIES OF CRYSTALLINE CELLULOSES USING POTENTIAL ENERGY CALCULATIONS Ph. D. Thesis by Alvo Aabloo TARTU 1994 DISSERTATIONES PHYSICAE UNIVERSITATIS TARTUENSIS 16 STUDIES OF CRYSTALLINE CELLULOSES USING POTENTIAL ENERGY CALCULATIONS Ph. D. Thesis by Alvo Aabloo TARTU 1994 The study has been performed in University of Tartu, Institute of Experimental Physics and Technology, Tartu, Estonia. Supervisors: Raik-Hiio Mikelsaar, Dr. Sei. Alexander I. Pertsin, Dr. Sei. Official j;jponents: Arvi Freiberg, Dr. Sei. (Tartu) Valery Poltev, Dr. Sei. (Puchchino) Raivo Teeäär, Cand. Sei. (Tallinn) The thesis w ill be defended on May 25, 1994 at 2 p. m. in Council Hall of University of Tartu, Ülikooli 18, EE2400 Tartu, Estonia. Secretary of the Council: A. Lushcik The author was born in 1965. He graduated from University of Tartu in 1989. During 1989-1991 he worked as a junior research worker in Institute of Experimental Physics and Technology of University of Tartu. During 1991 -1994 he was a PhD student at the same institute. The permanent address of the author is: University of Tartu, Institute of Experimental Physics and Technology, Tähe 4 Street, EE2400 Tartu, Estonia E-mail: alvo@physic.ut.ee © Alvo Aabloo, 1994 Table of contents 1. Introduction 1.1. Polysaccharides and cellulose as wide-spread biopolymers .... 4 1.2. Survey of crystalline structure crystallographic and modelling methods of saccharides .... 6 1.2.1. Experimental m ethods..................................................................6 1.2.2. Theoretical methods of conformational analyses.....................7 2. Methods 2.1. Molecular m odelling .... 9 2.2. Molecular mechanics and the minicrystal m ethod .....11 2.2.1. Molecular m echanics....................................................................11 2.2.2. Constructing of a minicrystal for M M 3............................... .... 12 2.3. Rigid-ring calculations - advantages and drawbacks .....13 2.4. An implementation of rigid-ring method in cellulose crystal structure refinem ent ..... 16 2.4.1. A force f ie ld ...................................................................................16 2.4.2. X-ray refinem ent...........................................................................17 3. Results and discussion 3.1. Rigid-ring calculations improvement with different glucose rings and force fie ld s ............................................................................19 3.2. Potential energy calculations of the crystalline structure of cellulose I .... 29 3.2.1. Initial conform ations.....................................................................29 3.2.2. Parallel models of cellulose 1 crystalline structure...................30 3.2.3. Antiparallel models of native celluloses....................................31 3.3. The full molecular mechanics (MM3) calculations of cellu loses .....33 3.3.1. Experimental...................................................................................33 3.3.2. Effect of the dielectric constant............................................ ...... 34 3.3.3. Energies of cellulose polym orphs...............................................35 3.4. Discussion over cellulose structure .....37 4. Conclusions 4.1. M ethods .....38 4.2. Structure of cellu loses .... 40 Acknowledgements .....41 References ..... 41 List of publications...................................................................... ..... 45 Tselluloosi kristalsete faaside struktuuri uurimine kasutades energeetilisi arvutusi ............... .....46 - 4 - 1. Introduction 1.1. Polysaccharides and cellulose as wide-spread biopolymers Saccharides are ubiquitous in nature. They occur in all forms of life and, because of their unusual properties, present a unique source of chemicals. Saccharides of living organisms and plants perform a great biological role. They function as structural materials, energy reserves and adhesives. They appear to be essential in the process of infection by certain pathogenic species. Cellulose is chemically a poly-(1-*4)-/?-D- glucopyranose - [(C6H100 5)2]n. A cellulose chain unit consists of two pyranose rings (see Figure 1). The level of polymerization n is between 1000 and 10000, depending on the sample's nature. It is one of the most widely spread biopolymers in the world. A native sample consists of an amorphous phase as well of a crystal phase of cellulose. The latter is made up of microcrystallites. These microcrystals form fibres. This very complicated and dynamical structure makes native cellulose samples extremely Figure 1. The pyranose ring. flexible and strong. An investigation of the structure of this widely spread polymer seems to be important. Notwithstanding multitudinous researches carried out in the past decades, the exact structure of cellulose crystals remains w ithout satisfactory explanation. Pure cellulose crystals exist in various forms, named I to IV, depending on the nature of the sample. Cellulose I, the native cellulose, has recently been recognized to occur as a - 5 - compound of two polymorphs, I a and \ß. These polymorphs occur in different ratios in different native cellulose samples. The most important industrial cellulose is cellulose II, which forms during a mercerization process (treatment in 22% sodium hydroxide) or at crystallization from solution. Cellulose III is the product of celluloses I and II treatment with liquid ammonia. Cellulose IV results from treatment in high temperature. Both phases III and IV have also tw o subclasses depending on their parent structure12. Computational methods used up to now for solving a structure of cellulose crystals have been extremely tremendous3,4. They use too enormous computer resources. It is possible to refine structures with more simple algorithms. These methods will solve a structure even more precisely. There have arisen different questions which require explanations. As the parameters of unit cells of native cellulose phases have been recently recognized5, the first aim of the present paper is to attempt to refine a structure of these phases. A second interesting problem dealt w ith in this paper is the issue of cellulose chains' direction in an unit cell. Cellulose II is considered to have an antiparallel structure8. It is known from experimental data that cellulose la converts into cellulose \ß during annealing78 and cellulose I into cellulose II during mercerization. The question is, how the parallel cellulose I converts into the antiparallel cellulose II; whether cellulose I has an antiparallel structure or whether there exists another option. 2 - 6 - 1.2. Survey of crystalline structure crystallographic and modelling methods of saccharides 1.2.1. Experimental methods The crystal structure analyses are generally routine; to obtain a single crystal of suitable quality may be a serious problem for the majority of saccharides. In fact, the diffraction analyses of a crystalline polymer cannot be approached in the same manner as a classical single crystal analyses. Because of the lack of diffraction data, positions of atoms cannot be determined directly from intensity data. A model analysis technique s>nould be applied to refine the minimized differences between the experimental data and a calculated model. X-ray, electron diffraction and infrared spectroscopy9 are the most powerful diffraction techniques. Recent developments in solid state NMR spectroscopy, particularly the crossed polarization magic angle spinning technique indicate that this could be a very vigorous method to investigate solid state molecular conformations and environments for saccharides10. The high resolution NMR spectroscopy has become the most valuable physical implement for studying conformations of saccharides11 12 ,:i, particularly in solution. Chemical shifts, coupling constants, NOE's (Nuclear Overheimer Effect) and relaxation rates contain detailed information about the conformational structure of saccharides in solution. - 7 - 1.2.2. Theoretical methods of conformational analyses There exist various approaches to theoretical conformational analysis. The classification of these can be made in several ways. One of the possible methods is shown1415 in Figure 1. Direct methods are based on the calculations of total energy of an object which is minimized w ith respect to all or to some of the structural parameters. In indirect methods, on the other hand, conclusions are made on the basis of analyses different experimental data. There are several ways to estimate the total energy of structure in direct methods. Usually there are two or more schemes to estimate the total energy in non-uniform methods. The total energy calculations are split into different interactions. In general, there are different basis to estimate bonded and Figure 2. Classification of theoretical methods of conformational analyses. 2* - 8 - non-bonded terms. Further, non-bonded interactions are divided into different terms. In case of a uniform method there is only one scheme to calculate total energy. This happens when applying quantum mechanical methods in which all electrons or all valence electrons are used. They constitute a group of uniform methods. With neglect of relativistic effects and within the scope of the Born-Oppenheimer approximation, the exact wave function of the structure is derived from the solutions of the Schoedinger equation16. Based on the approximations used in solving the Schoedinger equation, the uniform methods can be classified into tw o groups: ab in itio (non-empirical) and semiempirical. The ab in itio calculations need huge computer resources. Only smaller acyclic and cyclic molecules can be used as models for the structural segment studies of saccharides17. Classical methods originate from vibrational spectroscopy. The system is held together by forces which are described as potential functions of structural features, e. g. bond lengths, etc. A more detailed description of molecular mechanic methods will be given further. There exists one mighty method of structure refinement. The latter is related to non-uniform classical methods of structure refinement and is called molecular dynamics18. It differs from other refinement implements in the sense that the aim of this method is not to minimize the total energy of the system, but to follow the dynamical state of the system. Naturally, the system moves towards its equilibrium. By application of the simulation method of MD, a trajectory (configurations a function of time) of the system can be generated by simultaneous integration of Newton's equations of motion for all atoms (i = 1,2,...,N) in the system d 2r,(t) , — m t F j ( t ) d t2 ' (1) - 9 - where the force affected on atom i w ith mass m( is derived from 6V(r,(t),r2(t)....rN(t)) , ( ) ‘ (2 ) MD methods use a classical mechanical force field as a potential energy term. It means that MD cannot be more precise than the applied force field. MD, in comparison with the standard classical mechanical methods, is more powerful because it does not calculate only a static potential force field but also includes kinetic energy. The latter makes it possible to calculate dynamic states. The issue of minor local minimas is being solved. At the same time the MD requires huge computer facilities. MD is wide-spread in investigations of proteins, nuclein acids, solvations etc. It is used in structure refinement of celluloses19. 2. Methods 2.1. Molecular modelling Despite many powerful computation methods to solve secondary and tertiary structure of biological molecules, the molecular modelling remains one of the most wide-spread methods in structure analyses. First, it has a role of visualization and demonstration of the conformation of biomolecules. Second, it is a powerful method to visualize computational methods. By using molecular modelling, we can add human thought to the refinement of biostructures. We can find the initial structures for calculations and follow the computing output. Molecular modelling can be divided into two main branches: computer graphics modelling and physical modelling. 3 - 10 - Computer graphics modelling. Close to computer calculation facilities. The results of calculations can be directly converted into graphics routine input and vice versa. The results of graphic modelling can serve as an input for calculations. We can also check the calculation process by monitoring intermediate results through graphic output. System modifications can be made easily. There is a lot of software built for computer graphics' modelling. By using computer graphics, we can visually control and improve several configurations of molecules. Shifting the molecules and rotating the side groups makes it possible to follow the most likely models of macromolecule systems. Physical m olecular m odelling.20 Physical models are close to a 3-dimensional reality. Despite the fast development of graphics hardware, the computer image cannot reach the desired quality. Physical models are more handy and more informational, for they give full 3- dimensional properties. They are more convenient for demonstration and study purposes. On other the hand, the main negative qualities comprise technological difficulties of building up a perfect model and making changes in the model. Another type of negative properties concerns remoteness from computer-world. It is hard to convert the results of physical modelling for computer computation purposes and vice versa. We principally only get a basic idea from physical models on which we can build up a computer model. -11 - 2.2. Molecular mechanics and the minicrystal method 2.2.1. Molecular mechanics Molecular mechanics (MM) as a method of conformational analyses21 has a wide usage being a rather simple method of substance structure refinement. We look for a minimal value of energy function. When simulating a molecular system, we postulate an energy function which describes the potential energy of the molecular system as a function of the positions r, of the N atoms labeled by the index i. The minimizing function is the crystal's potential energy, i. e. the steric energy. The aim of this method is to find a energy minimum by changing the conformation of molecules. The MM methods22 are based on the following philosophy: a molecule is regarded as a collection of atoms held together by harmonic forces. These forces can be described by the potential functions of structural features. The main feature is to use a simplified parametric force field instead of solving complicated equations. The need of parametrization results from the enormous amount of calculations needed to solve the conformation of a molecule. Even semiempirical valence-electron approximation16 calculations are too extensive to solve the structure of bigger molecules, not do mention the biological macromolecule and crystal structures. All of the most widely spread force fields use a bond-related ideology - parameters are associated with bonds, bond angles, torsional angles or distances between two atoms. The empirical functions have been suggested in several works23 24. Depending on requirements they can be more complicated w ith more correction members. The values of parameters and formulas of empirical functions are derived from ab in itio calculations, semiempirical calculations and experimental data on the conformations. We used the MM3(90) 3 * - 12 - program25 26 for full molecular mechanics27-28 calculations. A thorough description of this program can be *ound elsewhere2930. 2.2.2. Constructing of a minicrystal for MM3 The MM3 program is able to use a maximum of 800 atoms w ith block diagonal minimization option standard. This limits the construction of crystals. With the number of atoms increased, the minimization requires more time. Each atom adds six more degrees of freedom into conformational space. As MM3 does not have any crystal border effect facilities, it is necessary to construct a minicrystal'. In order to establish a crystal force field for cellulose chains. For this reason we built in the course of the research cellulose chains as cellotetroses (see Figure 3) and arranged seven cellotetroses into crystal packing' in accordance w ith unit cell parameters (see Figure 1.2 and Figure IV.2) refined from experimental diffraction data. We presumed that at this minicrystal case glucose rings that are situated in the central part of a minicrystal should have an average and periodical force field. Figure 3. A cellotetrose of a cellulose chain used in minicrystals. - 13 - This approximation is relatively good as most o f the interactions vanished significantly at distances less than 1 nm. We also added terminating hydrogen atoms in the ends of cellotetroses. This is needed for neutralizing charges that we used for the calculations of electrostatic interaction. The MM3 routine does not use any cuto ff distances in atom-atom interaction calculations. VanderWaal's and electrostatic interactions will be calculated over all atoms. The orientation of terminal hydroxyl groups was random. Their positions optimized during minimization. 2.3. Rigid-ring calculations - advantages and drawbacks Full molecular mechanics calculates potential energy of structures (crystal) including all components of a force field. In theory, we should get a heat of formation of crystal as a result. As it was already mentioned above, conformation of molecules is defined by the following interactions: bond lengths, bond angles, torsion angles, non-bonded (VanderWaal's and electrostatic), and hydrogen bond interactions. Variations in the molecular geometry of molecules are then very simply defined as changes in bond length, bond angle or torsional angle. Application o f a typical force constant o f bond stretching26 and assuming Hook's law dependence indicate, that the distorsion of a single bond of 0.03 Ä would cost about 1.2 kJ/mol. A bond angle bending is less sensitive, and a bond stretch about 0.05 Ä is equal to an angular distorsion of about 10° 15. Torsional changes involve rotation around bond axis. The barrier to rotation around aeingle C-C bond is 12.3 kJ/mol. The barrier to rotation of methoxyl group in dimethoxymetiiane is approximately 4.2 kJ/mol2®. At the same time distorsion of hydrogen bond of 0.1 Ä costs less 4 - 14 - than 0.3 kcal/mol. These values show that different terms in the function of potential energy have different "sensitivity". Sometimes there is no need to calculate full potential energy for solving structures. The structure is determined simply by some components of force field. Other terms are not changing remarkably and only disturbing a minimization process. The crystal structure of celluloses is mostly determined by hydrogen bond and non-bonded interactions between the chains of cellulose. Due to stronger interactions (bond lengths and bond angles of atoms in sugar ring) the geometry of glucose rings is rigid enough. The values of these conformational parameters can be reached by an experiment or by ab in itio and semiempirical calculations of similar and more simple compounds. This is called a linked atom approach31. There are two reasons why the above-mentioned terms disturb structure refinement. First, by excluding these interactions from minimizing functions, we simply decrease the number of variables. By this we make the refinement algorithm more effective. Effectiveness depends on the algorithm we use. Second, these components may be extremely "strong” in comparison with others (see page 14). It means that small changes in conformation cause relatively higher energy changes from equilibrium state. We have a situation where some of the components of a force field are significantly more intensive than others. The minimizing routine traps because of these interactions. It starts to oscillate around the equilibrium states of these components and, minimizing other interactions, remains on the background. On the other hand, these terms are playing a leading role in the formation of the crystals of polysaccharides. If we turn the terms which are more efficient into constants, it is also possible to refine the terms that are weaker but have an important role in structure formation. - 15 - This method has many dangerous 0 6 рдеМ от nuances. When fixing some conformational parameters as bond lengths or bond angles, we must be assured that these parameters would not change remarkably. Moreover, small deviances from the best solution - in force field meaning - do not significally affect the results Figure 4. D i f f e r e n t 0 6 of refinement. Even if we take these values positions (tg.gg and gt) in glucose frorri similar substances, they are not exactly ring. th. e same as in our structure. The geometry of molecules in crystal structure can be different from their equilibrium in a free state, e. g. in solution. The final energy of all crystal structures can even be lower if a molecule has been distorted. For example, it is known from experimental data and theoretical calculations that hydroxymethyl groups of polysaccharide chains are preferable in gg position (see Figure 4). However, as it will be shown later, it seems that in celluloses they are preferably in tg position. At the same time, a glucose ring seems to be extremely stable. Calculations w ith MM3 show32 in 99.99% percent of the cases that a pyranose ring is in the 4C, conformation position (see Figure 5). Figure 5. Some examples of different conformations of a pyranose ring. 4 * 2.4. An implementation of rigid-ring method in cellulose crystal structure refinement 2.4.1. A force field In the following discussion of structure refinement we will apply the rigid-ring refinement method to find the crystal structure of different polymorphs of cellulose. As the structure of native celluloses is not clearly solved yet, this is a good reason to try to improve different models for these phases by rigid-ring calculations. The method to build up cellulose chains from glucose rings using virtual bond33 and a unit cell from these chains is described elsewhere1,34. Measurements of unit cells of native celluloses is taken from Sugiyama et a/6. Experimental data for cellulose II is taken from Ko/pak e t a/35. All calculations have been made in internal coordinates - bond lengths, bond angles etc. - and the program uses the so-called Z-matrix coordinates. As a force field we have used a simple one without an outlined electrostatic interaction term. The electrostatic interaction has been considered in other terms. Avoiding direct electrostatic interaction simplifies the usage of periodic boundary conditions and an infinite chain in calculations. As we did not variate any bond length, this interaction term is not necessary. Bond angle bending potential. In equation (3) в is a bond angle, 0O is a equilibrium bond angle and ke is a force constant. Ев - кв(в -в 0)г (3) Torsional potential.36 In equation (4) w is a torsional angle U0 is a force - 17 - constant. E.. = — (1 +cos3u) 2 (4) Hydrogen bond potential.36 37 A Morse equation was used for hydrogen bond term calculations. In the equation (4) r is a distance between the acceptor oxygen and donor hydrogen atoms. D is a force constant. EH = D[e 6{r ro)- 2e 3M>)] (5) Non-bonded atom-atom potential.38 A Buckingham expression was used for non-bonded interaction modelling. In the equation (6) r is a distance between atoms, A, В and С are force constants. As this term includes VanderWaals', electrostatic and other interactions between two non-bonded atoms, we use different force constants in case of intramolecular interactions and intermolecular interactions39. Ел = -A r* + Be 01 (6 ) This force field is simple compared to the MM3's field. As we do not variate the glucose ring or any bond length, these terms are sufficient enough to express forces in our case. 2.4.2. X-ray refinement The difficulties with cellulose are not unexpected regarding its comparatively poor quality of diffraction pattern from oriented cellulose samples. Typical X-ray diagrams of cellulose II, III and IV contain only a few dozens reflections, which is clearly insufficient to refine all atomic parameters by standard crystallographic 5 - 18 - studies. X-ray data of cellulose I is not available yet, as the phase I a coexists only with the phase \ß. To increase the terms of refinement of the cellulose crystalline structure, we use X~ray diffraction patterns as part of the minimizing function. We compute the objective function Ф U I WR‘ (7) where U is a potential energy, W - a weighing factor, R" - a crystallographic discrepancy factor. /?"-factor is defined by E , r— obs m Fr- R (8 ) E “ J F ‘ m 1 where Fn°bt and Fmcelc are the observed and calculated structure factor amplitudes, uim is the weight factor applied to the m-th reflection. M is the number of observed reflections. Each Fn,cah is a function of the parameters of model and is computed from: f t - * { e [/=;Ге~мг}: (9) The summation in this equation is over all planes hkl, contributing to the m-th reflection, pm is the reciprocal «/-spacing, К is the scale factor. We can see from the equation (7) that the calculated fl"-factor is given a weight of W. The value of W is chosen in order as to make small changes in Ft" and U equal meaning for objective function. The idea is that statistically significant changes in R "-factor should be equal to significant changes in potential energy - 19 - level. A significant level can be obtained from Hamilton' tables40. The latter depends on a number of variables. In potential energy calculations the typical level of accuracy is about 1 kcal/mol41. As mentioned before, we could use this objective function refinement only for the crystal structure of cellulose II. It is not possible in case of native celluloses the X-ray data and we can refine the structure by using potential energy minimization. 3. Results and discussion 3.1. Rigid-ring calculations improvement with different glucose rings and force fields In rigid-ring calculations we used fixed glucose rings and made an attempt to investigate the influence of residue geometry on the resuits of minimization". Using different glucose rings, we found the minimums for several crystalline models of cellulose II described elsewhere41. We improved six different glucose ring conformations42 43, including even o-glucose rings which were converted into /ff-glucose by chiral inversion of residues. All other conformational parameters of minimization were kept the same. Similarly, several minimization technique were used to obtain the best results. All results are presented elsewhere". Tables 1 and 2 show the objective function and the potential energies of the thirteen most probable models of crystalline structure of cellulose II. Consequently, we can see that the best and most important models do not change remarkably. Only one model ( A l l ) was not found in some cases and it was minimized to model A 1 . In 5* - 20 - Table 3 there are presented the mean movements of the models according to Arnott-Scott average ring case. We can see that generally all results of different rings for most models have good accordance with Arnott-Scott ring results. It seems that models with lower energy deviate less during the change of the glucose ring. In Table 4 are presented variable torsion angles as the results of different rigid-ring minimizations w ith different glucose rings. Another attempt to improve the rigid-ring method was made. We built an alternative force field23. As this force field includes an electrostatic equation, due to boundary condition, some virtual hydrogens were included in the boundary glucose rings to correct the charge neutrality problem. Positions of these hydrogens were not minimized. We used an electrostatic constant of 4 IV" as in the case of full minimization technique of MM3. Results of these calculations are shown in Table 5, 6 and 7. We can see that in this case the best models remain in their present positions. The values of energies are different. There exist different reasons for the diverse energy values obtained as a result of crystal energy minimizations are different. The most important of them is that during fixed-ring the minimization we switched off some interactions. If we change the force field, the components of force field act in a different way. The value of crystal energy obtained by the minimization process has minor significant meaning. The analyze is possible by comparing different values and making conclusions at this level. We can see that these results are somewhat dispersed in comparison with different ring calculations, but the best models are in their place. The three last models (A10-A12) were not found in some cases and were minimized to positions of other models. In Table 6 the mean movement was calculated against the conformations that these models had in the initial force field. Similarly to the previous computer experiment, the models which had lower energy terms deviated less during different minimization processes. We can see that values of the mean atomic - 21 - movement are low. According to these calculation experiments we can say that small changes in glucose rings do not remarkably influence the minimization results. Also, having used different force fields that gave us similar results in full minimization process4, we can conclude that all rigid-ring calculations gave the same kind of structures. We also saw that structures w ith lower crystal energy have a iower mean atom movement in different conditions. As the model with the lowest energy is also the most probable model, it depends least of all on minor changes in a glucose ring or on force field deviations. The glucose ring is rigid enough in polysaccharides to omit its degrees of freedom in a energy term function. Components of force field related to bond lengths, bond angles and glucose ring conformations are too efficient in comparison to the components related to torsional angles of side groups and hydrogen bonds. These forces play a leading role in the formation of crystal phases of polysaccharides. By decreasing the amount of degrees of freedom in a minimizing function, we make the minimization process more efficient as we decrease the amount of variables in potential energy function from 285 to 12 (in case of phase la). 6 Table 1. Objective functions of most probable models of cellulose II crystals using different rigid glucose rings. Glucose rings: AS - average Arnott- Scott; CHA2 - cyclohexaamylose; PLA - planteose; GUR - glucose-urea; CBIO - cellobiose; ßGLU - /З-D-glucose. A 1 A 1 2 , P1 - most probable models of the unit cell of cellulose II. Models Objective functions with different glucose rings (kcal/mol) AS CHA2 PLA GUR CBIO BGLU A1 -18.70 -19.75 -18.53 -19.05 -19.94 -18.60 A2 -18.50 -19.31 -19.25 -18.41 -19.72 -18.41 A3 -18.54 -18.00 -17.90. -17.89 -18.60 -19.03 A4 -17.59 -16.88 -15.98 -17.49 -16.97 -18.70 A5 -17.60 -19.10 -18.13 -17.22 -18.99 -17.34 A6 -17.48 -16.90 -18.37 -18.60 -17.21 -18.15 A 7 -17.40 -16.41 -16.53 -17.83 -17.34 -18.06 P1 -16.90 -18.00 -16.67 -15.95 -19.32 -16.43 A8 -16.40 -15.86 -17.00 -16.19 -16.61 -16.80 A9 -15.80 -14.99 -16.41 -16.83 -15.43 -16.63 A10 -15.10 -14.20 -10.03 -12.76 -9.11 -13.01 A11 -8.00 -13.10 -11.50 -9.54 -19.80 -18.64 A12 -7.80 -8.10 -11.83 -14.48 -15.20 -15.11 Table 2. Potential energies of most probable models of the Table 3. The mean atomic movements that result cellulose II crystal using different fixed glucose from the change of glucose ring at rings. AS - average Arnott-Scott; CHA2 - rigid-ring minimization of cellulose II cyclohexaamylose; PLA - planteose; GUR - crystals. For abbrevations see Table 2. glucose-urea; CBIO - cellobiose; ßGLU - The initial glucose ring was the average Д-D-glucose. A1,,.., A12, P1 - most probable Arnott-Scott ring. models of the unit cell of cellulose II. Models Mean movements Models Energies with different glucose rings (kcal/mol) CHA2 PLA GUR CBIO BGLU AS CHA2 PLA GUR CBIO BGLU A1 0.040 0.093 0.081 0.172 0.110 A1 -21.40 -22.62 -21.38 -21.86 -22.89 -21.39 A2 0.057 0.112 0.109 0.157 0.171 A2 -21.20 -22.04 -21.94 -21.49 -22.01 -21.40 A3 0.102 0.054 0.067 0.108 0.146 A3 -21.20 -20.67 -20.66 -20.94 -21.22 -21.89 A4 0.101 0.186 0.101 0.011 0.090 A4 -20.10 -20.06 A5 0.093 0.148 0.092 0.185 0.059-18.91 -20.10 -19.98 -21.89 A6 0.025 0.135 0.190 0.101 0.168 A5 -20.39 -21.80 -20.67 -20.39 -21.52 -20.20 A7 0.086 0.078 0.108 0.169 0.086 A6 -1940 -19.33 -20.49 -20.54 -19.84 -20.57 P1 0.183 0.074 0.201 0.139 0.113 A7 -20.50 -19.40 -20.22 -21.01 -19.82 -21.21 A8 0.139 0.183 0.103 0.137 0.107 P1 -19.40 -21.20 -19.31 -18.52 -18.17 -22.07 A9 0.131 0.203 0.139 0.184 0.118 A8 -18.30 -18.07 -15.86 -18.34 -19.07 -18.75 A10 0.109 0.056 ' 0.087 0.264 0.092 A9 -17.60 -17.32 -18.38 -18.63 -17.68 -18.54 A11 0.299 0.164 0.179 0.214 0.320 A10 -17.10 -14.50 -13.38 -15.28 -11.94 -15.21 A12 0.241 0.203 0.181 0.213 0.248 A11 -9.70 -13.30 -13.51 -11.36 -22.63 -21.47 A12 -9.40 -14.70 -13.87 -16.51 -17.81 -18.11 ТаЫе 4. Variable toouon «ogles of different cellulose II crystal models using several glucose rings. For abbrevation see Table 2. Models Glucose rings T„ T,« T* T22 T» T* " a i CHA2 73 -48 -151 167 74 164 -54 157 PLA 66 -51 -151 174 69 162 -53 163 GUR вв -51 -151 174 69 162 -53 162 BGLU 72 -56 -167 181 71 178 -58 164 CBIO 68 -51 -147 190 74 181 -59 167 AS 66 -51 -151 174 69 162 -53 163 A2 CHA2 73 -48 -152 166 76 103 -56 158 PLA 68 -51 -152 175 70 103 -57 163 GUR 68 -51 -152 176 71 103 -57 163 BGLU 75 -52 -152 -197 76 108 -56 167 CBIO 73 -55 -150 -197 70 115 -62 183 AS 68 •52 -152 -176 71 103 -57 163 A3 CHA2 71 58 -80 175 74 167 -53 173 PLA 65 57 -79 177 71 166 -52 175 GUR 65 57 -79 177 71 166 -52 175 BGLU 65 60 -84 189 72 163 -57 180 CBIO 72 60 -80 189 73 173 -56 191 AS 65 57 -79 177 71 166 -52 175 A4 CHA2 -68 176 -163 173 72 164 -54 158 PLA -63 173 -161 182 69 163 -52 174 GUR -63 173 -161 182 69 163 -52 174 BGLU -63 186 -158 182 69 167 -56 191 CBIO -70 193 -164 181 74 165 -52 174 AS -63 173 -161 182 69 163 52 174 A5 CHA2 71 -48 -152 -54 73 101 56 158 PLA 66 -50 -152 -55 68 102 -56 160 GUR 67 -50 -152 -55 68 102 -56 161 BGLU 69 -53 -166 -56 71 99 -59 163 CBIO 71 -53 -169 -58 72 106 -60 171 AS 67 -50 -152 -55 68 102 -56 161 CHA2 177 165 -97 172 75 161 -57 166 PLA 179 164 -96 164 70 159 -55 164 GUR 173 164 -97 174 72 161 -56 167 BGLU 199 180 -107 179 80 177 -56 173 CBIO 196 182 -95 172 69 180 -59 176 AS 178 164 -97 174 71 161 -56 167 (continuing) Glucose rings T,. T12 T21 *22 T24 A7 CHA2 70 -51 -153 176 74 35 -54 72 PLA 67 -52 153 176 70 34 -54 72 GUR 65 -52 -153 175 70 34 -54 71 BGLU 67 -51 -161 191 70 33 -52 79 CBIO 68 -53 -149 177 75 35 -59 73 AS 67 -52 -153 176 70 34 -54 72 P1 CHA2 72 64 -68 163 177 174 -78 161 PLA 64 64 -70 172 171 175 -77 169 GUR 64 64 -70 172 171 175 -77 169 BGLU 63 68 -78 171 181 175 -77 180 СВЮ 62 71 -76 171 165 185 -81 176 AS 64 64 -70 172 170 175 -77 169 Ae CHA2 174 166 -124 172 75 61 176 166 PLA 174 166 -123 177 64 -65 177 166 GUR 174 166 -123 177 64 -65 177 166 BGLU 195 171 -131 185 66 -65 193 181 CBIO 186 164 -121 196 65 -72 183 172 AS 175 166 -123 177 64 -65 177 106 A9 CHA2 178 166 -110 170 81 171 181 166 PLA 177 162 -109 175 77 172 183 167 GUR 177 162 -109 176 76 172 183 167 BGLU 182 173 -115 188 79 177 195 178 CBIO 191 176 -107 172 81 171 201 176 AS 177 162 -109 176 76 172 183 167 A10 CHA2 -178 208 86 173 -171 -57 -30 166 PLA -199 204 87 174 -170 -57 -28 170 GUR -178 187 88 167 -155 -54 -27 166 BGLU -193 175 93 188 -161 -69 -36 183 CBIO -192 180 90 192 -171 -63 -35 186 AS -178 168 88 174 -164 -62 -35 167 A11 CHA2 77 -52 -164 183 103 171 -55 177 PLA 84 -54 -157 176 109 174 -58 170 GUR 77 -48 -156 173 102 162 -52 160 BGLU 68 -52 -161 189 68 167 -55 168 CBIO 66 -52 -152 181 70 161 -52 159 AS 77 -48 -156 173 102 162 -52 160 7 Table 5. Potential energies of most probable models of the Table 6. The mean atomic movements that result from the cellulose II crystal using different glucose ring and an change of force field at rigid-ring minimization of alternative force field. For abbrevations see Table 2. cellulose II crystals. For abbrevations see Table 2. г----------- Models Potential energies(kcal/tnol) Models Mean movements AS CHA2 PLA GUR CBIO BGLU j AS CHA2 PLA GUR CBIO BGLU 1 AI -22.01 -23.12 -21.91 -22.70 -23.79 -22.58 j A1 0.008 0.067 0.127 0.092 0.103 0.131 A2 -21.95 -22.32 -22.80 -21.92 -22.26 -21.25] A2 0.010 0.076 0.295 0.147 0.092 0.077 A3 -21.20 -20.82 -21.24 -21.49 -21.12 -21.54 A3 0.006 0.114 0.269 0.184 0.219 0.124 A4 -20.67 -19.14 -19.89 -19.70 -19.17 -21.26 A4 0.016 0.066 0.276 0.090 0.195 0.230 A5 -20.13 -19.45 -20.76 -19.58 -20.57 -20.97 A5 0.012 0.147 0.074 0.047 0 175 0.112 A6 -19.80 -19.19 -20.68 -20.78 -19.17 -20.78 A6 0.019 0.128 0.283 0.211 0.195 0.139 A7 -19.30 -19.58 -20.08 -19.39 -18.92 -20.22 A7 0.007 0.059 0.221 0.124 0.250 0.153 PI -18.93 -19.20 -19.72 -18.86 -18.28 -18.07 PI 0.004 0.086 0.186 0.127 0.053 0.105 A8 -17.83 -17.16 -16.69 -18.95 -21.36 -19.23 A8 0.008 0.063 0.293 0.070 0.119 0.203 A9 -18.34 -17.73 -17.81 -18.85 -19.69 -18.08 A9 0.009 0.114 0.213 0.083 0.205 0.075 A10 -16.51 -15.39 -12.92 -15.39 -17.15 -17.77 A10 0.019 0.101 0.259 0.159 0.226 0.134 A ll -8.90 -14.05 -14.49 -11.52 -11.71 -15.35 A ll 0.018 0.081 0.289 0.096 0.166 0.083 A12 -8.82 -14.04 -13.56 -17.39 -22.73 -20.34 A12 0.007 0.086 0.125 0.098 0.128 0.165 Table 7. Variable torsion angles of different cellulose II crystals models using several glucose rings and an alternative force field. For abbrevations see Table 2 and Figure X.2. Models Glucose r i n g s T , ,__________ T j j __________T u,__________т 14_______________________ T 2 2 __________^ 2 3 A1 CHA2 73 -48 -151 163 72 168 -53 156 PLA 66 -50 -149 173 67 158 -54 160 GUR 67 -50 -152 172 67 157 -52 162 BGLU 70 -55 -164 179 70 178 -59 160 CBIO 68 -50 -148 193 72 182 -59 165 AS 66 -52 -152 178 69 163 -52 166 A2 CHA2 72 -48 -149 167 78 104 -54 160 PLA 68 -50 -150 173 68 100 -58 160 GUR 68 -52 -156 171 71 102 -55 168 BGLU 76 -53 -150 -193 75 107 -55 167 CBIO 74 -54 -153 -193 69 113 -64 183 AS 70 -53 -154 -172 70 104 -59 159 A3 CHA2 71 59 -81 179 76 168 -53 170 PLA 64 57 -80 179 72 164 -51 179 GUR 63 58 -78 180 73 169 -52 178 BGLU 65 60 -82 193 73 163 -59 185 CBIO 73 60 -80 189 72 176 -56 196 AS 65 58 -80 174 71 170 -53 174 A4 CHA2 -69 171 -158 175 71 168 -53 154 PLA -61 175 -164 177 69 159 -51 176 GUR -63 176 -163 185 71 162 -52 174 BGLU -64 189 -162 188 69 163 -54 192 CBIO -70 195 -161 180 75 162 -52 175 AS -63 177 -162 187 67 163 -51 174 A5 CHA2 69 -48 -155 -54 74 99 -57 156 PLA 66 -50 -148 -55 68 99 -56 156 GUR 69 -50 -147 -54 69 102 -57 157 BGLU 71 -54 -165 -55 71 97 -58 165 CBIO 70 -54 -171 -56 70 106 -60 167 AS 68 -51 -149 -56 68 100 -58 164 CHA2 172 164 -97 170 78 162 -57 164 PLA 175 166 -95 168 70 162 -55 166 GUR 172 167 -96 177 72 158 -56 168 BGLU 193 178 -109 180 78 178 -58 172 CBIO 196 181 -94 170 71 182 -60 181 AS 180 168 -97 170 73 163 -56 165 7* Table 7. (continuing) Models Glucose rings T, ~A7 CHA2 71 -51 -150 177 75 34 -56 71 PLA 68 -52 157 179 66 34 -54 71 GUR 68 -53 -157 178 70 34 -55 72 BGLU 66 -52 -159 188 70 32 -52 81 CBIO 69 -53 -148 174 74 34 -59 73 AS 68 •53 -154 173 69 33 -54 73 P1 CHA2 74 62 -67 161 176 177 -76 160 PLA 65 62 -68 169 167 173 -75 164 GUR 66 65 -71 174 172 175 -79 169 BGLU 64 69 -79 168 177 177 -75 178 CBIO 63 73 -76 175 169 190 -81 172 AS 63 64 -69 173 170 172 -75 166 AS CHA2 176 166 -122 174 76 62 179 167 PLA 175 164 -121 180 63 -65 179 164 GUR 175 162 -123 173 66 -63 173 163 BGLU 193 171 -128 180 67 -63 189 186 CBIO 184 160 -122 192 67 -73 180 167 AS 172 161 -120 . 181 66 -64 177 161 A9 CHA2 183 161 -108 168 80 167 177 164 PLA 182 163 -110 170 77 171 188 167 GUR 176 158 -112 171 76 175 186 167 BGLU 182 169 -114 192 77 175 197 180 CBIO 189 171 -105 172 60 173 197 174 AS 179 162 -111 180 77 168 183 164 A10 CHA2 -173 212 88 175 -172 -58 -30 168 PLA -194 202 89 172 -166 -57 -28 175 GUR -162 172 76 218 -173 -60 -32 181 BGLU -148 161 78 201 -161 -58 -32 183 CBIO -160 165 80 191 -179 -63 -32 179 AS -174 173 86 179 -166 -63 -36 169 CHA2 74 -52 -162 187 104 174 56 174 PLA 83 -54 -159 176 109 177 -57 167 GUR 79 -48 -154 177 99 165 -52 163 BGLU 71 -44 -126 195 104 153 -60 152 CBIO 78 -48 -137 191 103 148 -57 163 AS 78 -48 -161 178 104 164 -52 156 - 29 - 3.2. Potential energy calculations of the crystalline structure of cellulose I 3.2.1. Initial conformations Besides the problem of a correct force field another major issue in the methods based on molecular mechanics is the problem concerning initial models and local minimas. As we already discussed, in case of MM methods, when calculating only potential energy of crystals we should be aware that the minimization process will not trap into local minima of force field. It is not possible to avoid this problem completely, but we can minimize the probability to pass the global minima. Firstly, our minimizing algorithm should be appropriate for such kind of minimizations. It must be powerful enough to cross small local minimas and at the same time reasonably sensitive to fall into narrow, but deep minimas. We tried several minimization algorithms44,45. Finally, we chose the Powell-Davidson algorithm48 47. Parameters of optimization routine were optimized in each case and we saw that the process was very sensitive even to minor details o f minimization algorithm. For example, parameters depended on a version of Fortran compiler and on an operating system using the same Fortran source code. The considerations in selecting parameters of minimizations are as follows: during the refinement procedure the equilibrium of structure, caused by different forces of force field, must be found. It is clear that this minimum of potential energy is not the equilibrium of different forces. On the one hand, the gradients of forces are remarkable, on the other, the minimization should not pass any significant minima. A first step in estimating initial models for computation is the molecular modelling. Using physical models and computer graphics software we presumed 8 - 30 - all kinds of possible conformations, according to unit cell measures. The chief idea was to avoid bad contacts. Based on this modelling system, the computer generated hundreds of initial models. These models were minimized by using the rigid-ring method. Results of these were checked on the basis of the local minimas reached and also by computer graphics facilities. Correspondingly, to check the results, a new set of initial models were generated and minimized. The results were subjected to yet another graphic check. On the basis of these results some minimization levels were sometimes added. The models obtained have already been •ubject to analysis and conclusions. In some cases an improvement of rigid-ring calculations MM3 calculations followed. 3.2.2. Parallel models of cellulose I crystalline structure Several years ago VanderHart and Atalla48 discovered that all native cellulose I -s are composed of two phases of crystals49 60. Later, Sugiyama et a/.5 described these phases in M icrodictyon tenius. They used electron diffraction technique and solved tw o unit cells: a triclinic one-chain unit cell for phase of la w ith cell parameters a = 6.74 A, b = 5.93 Л, с = 10.36 Ä, a = 1 1 7 ° ,/? = 1 1 3 ° , к = 81°, and a monoclinic two-chain unit cell for phase of \ß w ith cell measures a = 8.01 A, b = 8.17 Ä, с = 10.36 Ä, / = 97.3°. We refined the structures of these phases by using the rigid-ring method. A complete description of that work and its results are given elsewhere,V-V. The structures have similar hydrogen bondings. It is possible to convert the structure of I a into \ß via simple shifting of the chain sheets. The energy barrier calculated by the rigid-ring method is about 9 kcal/mol. This has an extremely high value. Calculations with annealing conditions would probably give less value. This high value can explain why the phase I a does not transform into the \ß phase in normal conditions. Minimized energies are in agreement with - 31 - experimental data51. As cellulose lor converts into the phase \ß during annealing process and cellulose I reforms into the phase II w ith mercerization process, the energy differences of 0.4 kcal/mol between la and \ß and 1.5 kcal/mof between \ß and II are extremely low. The difference between the phases of native cellulose are at the significant level. The hydrogen bond system is the same in native phases, although some investigators have reported changes in the system. From the point of view of energy calculations and modelling, it is hard to find another hydrogen bond system which would enable us to make comparisons with systems found by minimization (see Table IV. 1). This statement is valid only for parallel structures of native celluloses derived from the data reported by Sugiyama et at. 3.2.3. Antiparallel models of native celluloses Recent data of electron d i f f r a c t i o n o f n a t i v e ce llu loses obtained by Sugiyama e t a l are explained as parallel structures. All chains in a unit cell are parallel. In one-chain unit cells there are no other possibilities, however, in the two-chain one, there exists an antiparallel option, too. The issue of parallelity of Figure 6. A conversion of native cellulose into cellulose chains has been cellulose II during a mercerization process. under discussion for several 8* - 32 - decades5263. A number of researchers have given their interpretation, but no satisfactory explanation has been reached yet. According to the diffraction data35 54 and energy calculations66 “ it seems that cellulose II has an antiparallel structure. However, cellulose I was interpreted as parallel structure. During mercerization treatment native cellulose converts into cellulose II forming several intermediate structures. These phases have been thoroughly described by Sarko's group57. They declare that already the first intermediate phase, the so-called Na-cellulose-l (see Figure 6), already has an antiparallel structure. It is extremely difficu lt to explain how it is possible to change the direction of a cellulose chain which has a molecular weight over 10000. Different researchers have elucidated this as interdigitation. There are different microcrystals in a cellulose fibre. Some of them are oriented up, some of them down. During the first step of mercerization process these crystallites w ill mix and form antiparallel structures. This process is complicated and has not been satisfactorily explained. Another way to explain antiparallel cellulose II structures is to presume that cellulose I or at least some phases or components are already by themselves antiparallel. We have also proposed several models for the antiparallel structures of native celluloses. The construction of antiparallel models of unit cells is based on the parameters of unit cells as reported by Sugiyama et al. We constructed eight-chain unit cells68 for both phases of native cellulose and simple antiparallei two-chain unit cell for the phase of \ß. We calculated these models by using the rigid-ring method, improving several initial models by modelling and calculation methods71 VHI. These initial models are thoroughly described invu". Results of these calculations are presented in table VI. 1. An antiparallel two-chain unit cell has a relatively high energy level. At the same time, an eight-chain unit cell for the \ß phase, denoted as A3a (see Figure VI. 10), has a low energy of -21.0 kcal/mol. However, antiparallel eight-chain unit - 33 - cell models for the la phase do not offer good energy results. There exists an explanation why the la phase needs not to be in global minima. A la phase, existing independently from the \ß phase, has not been discovered yet. There appear only mixtures of tw o native cellulose phases. This explains why the la phase can be found in structures which have comparatively higher crystal energies, for example, model A1 a (see Figure VI.4). The model has a different hydrogen bond system from both the mode! P2 (see Figure VI.8) and the A3a (see Figure V I.10). This is in accordance w ith the hydrogen bond change in la to \ß conversion marked by VanderHart and Atalla. 3.3. The full molecular mechanics (MM3) calculations of celluloses 3.3.1. Experimental The starting coordinates of atoms were calculated by the rigid-ring method or taken from literary sources. Cellulose la was described inlv, cellulose \ß inv and crystalline small molecules as a-D and /7-D-glucopyranose in69. Minicrystals were constructed for calculating energies (see p.2.2 and in '). The molecular graphics software and some conversion software were used to construct crystals, to use the PLMR output data, to manipulate the molecules and to prepare MM3 input files. After minimization the initial and final structures were fitted by the least squares procedure. After the fitting procedure the average of the absolute values of differences between the initial and the final coordinates was reported as the mean atom ic movement. This was also used for comparing different results o f PLMR calculations. 9 - 34 - 3.3.2. Effect of the dielectric constant As the MM3 routine use electrostatic interaction to model long term interactions, the value of the dielectric constant used will play an important role in s t r u c t u r e r e f i n e m e n t . F o r t h a t purpose we m o d e l l e d 1 several smaller molecules as IbM an «по** 0в-С #-С *-0€ glucose rings w ith different с values. The Figure 7. 0 6 rotation for /fglucose. 06H orientation is left to optimize. r e s u l t s o f varying the dielectric constant in 'final steric energy' calculations are shown in Figure 1.5. The mean atomic movement is plotted in Figure 1.6. It is evident that the dielectric value close to 4 is the best solution. The latter gives the best agreement with experimental data26. Dielectric values as low as 1.5 produce extreme movement, it even gives the best agreement with 6/31 g* ab in itio studies when e is equal to 1. Figure 7 shows the simplest type of analysis, one for the rotation of primary alcohol group wherein the 06H orientation is left to optimize. We can see that the barrier does not depend much on the value of the dielectric constant. - 35 - 3.3.3. Energies of cellulose polymorphs The starting structures in MM3 calculations were taken from the best models of the PLMR process. The description of minicrystals built for minimization is given in'. The model crystals were optimized with no restrictions of space group. The full molecular mechanics minimization process should be more valid than rigid-residue calculations. There are no restrictions to moving and flexing. The energy values calculated by MM3 are likely to be accurate; the standard deviation in calculated heat formation for 40 isolated alcohols and ethers was 0.38 kcal/mol. Energies of the minicrystals are probably less accurate. The results of MM3 minimization are given in Table V.3 and Table IV. 1. The analysis of these results is described elsewherev. We got the energy of 185 kcal for I a phase and 182 kcal for \ß phase. Analogous values of PLMR were -19.5 kcal/mol and -19.9 kcal/mol. For cellulose II the energy values were 176 kcal by MM3eo and -21.4 kcal/mol by PLMR. These values are in good agreement with the experiment. The energies of both phases of cellulose I are slightly higher than the energy of cellulose II, and the la phase is a bit higher than \ß. The energies of both phases of native cellulose are extremely close. This may explain why they can coexist. The energy values of cellulose III and IV are comparatively higher. To compare the results of PLMR and MM3 we calculated the mean atom movement. These results are presented in Table V.3. Relatively low values show good agreement of both methods. Most of the best models of PLMR remain at their positions also after MM3 minimization. MM3 method found some additional intersheet hydrogen bonds in models of U„3, U04 and 11̂ 6. PLMR did not find these bonds. Actually these models trapped into local minimas of a constrained force field. We also calculated lattice energies using MM3. For this purpose we removed the central chain and calculated energies o f the chain and they remained 6 chains without minimization. These results are in Table 9 * - 3 6 - 8. In comparison w ith other polymorphs, a lattice energy of cellulose IV is low. This means that intramolecular energy is high - the molecule has distorsion from equilibrium. The lattice energies, calculated by MM3, are very Table 8. Energies of cellulose models. close to the values of PLMR, as most of the PLMR energy value Structures Total energy Lattice component is an interchain (kcal/mol) energy (kcal/tetrose) energy. These MM3 values are (/glucose) slightly higher than PLMR Cellulose la 185 -76.1/(-19.0) interchain components. The Cellulose \ß 182 -78.0/И9.5) differences between the full Cellulose II 176 -79.0/И9.8) Cellulose III, 200 -73.4Д-18.3) m o le cu la r m ech an ic and Cellulose IV, 202 -79.6/M9.9) rigid-ring calculations do not Cellulose IV2 232 -79.5/M9.9) render remarkably different results for the cellulose crystal structure. Differences are minor and express in reality, the differences in force fields. Some differences may also occur as a result of the periodic boundary conditions used in rigid-ring calculations. These express more precisely the situation in a crystal. As we can see from the MM3 output, the side chains are in somewhat different conformations than the a central chain (see Figures 11.1 and IV.2), the latter being in the most pseudoperiodic force field conditions. - 37 - 3.4. Discussion over cellulose structure It is clear that the issue of the structure of different cellulose polymorphs is far from being solved. The parallelity of cellulose chains and the structure o f native celluloses remains the most dubious questions. The latter question has been given some light on, but serious problems still exist in the field. It seems that the structure of cellulose II (mercerized) has an antiparallel structure. This is confirmed by different experiments and calculations. At the same time recent experiments reveal that cellulose I has a parallel structure. X-ray diffraction investigations of different intermediate states of mercerization process report that already the Na-cellulose-l has an antiparallel structure. It is explained as an interdigitation of chains, but this is not a very good interpretation. In our opinion the main problem in solving the structure of celluloses is to find the construction of unit cells and to solve the problem of parallelity of cellulose chains. An idea has been put forward that it is likely that native celluloses from different sources have unit cells w ith somewhat different parameter value. As our calculations show, very exact parameters of unit cells are not obvious. The results of the \ß unit cell refinement w ith parameters reported in Pertsin e t a l,61 and the results of the refinement o f ramie celluloses80 62 are extremely close. It is more important to find a symmetry group and positions of cellulose chains. The problem of how to explain the conversion of cellulose I into cellulose II remains to be a common topic. An interdigitation is not a very satisfactory explanation. Atalla proposes that there can be tw o different cellulose II unit cells. This is one way to explain the situation. The other way to explain it is to look for antiparallel native cellulose structures. For these purposes we calculated several antiparallel structures based on unit cell measures reported in Sugiyama et a/6. As we found an antiparallel structure with 10 - 38 - a very good energy, this explanation cannot be overlooked. 4. Conclusions 4.1. Methods Analyzing the material presented in this paper, we can conclude that the structure of cellulose crystallites is mostly determined by hydrogen bonds and non-bonded interactions. Therefore, to refine these structures by using the steric energy minimization technique we can discard some of the components of full steric energy. The glucose ring is rigid enough to assume that it would remain fixed during a cellulose crystal structure refinement. Due to these simplifications, we can investigate the structural properties of cellulose chains in a crystal structure more precisely and faster. Advantages o f the rig id-ring m ethod: By decreasing the number of variables, we make the minimizing routine more efficient, i. e. the process will converge better. By avoiding comparatively strong interactions in potential energy function, we make refinement routine more sensitive against weaker interaction which plays the main role in the formation of cellulose crystals. In fact the minimization process will not oscillate around strong interactions. Drawbacks o f the rig id-ring method-. The force field is deformed and does not correspond to the "real" force field. Values of crystal energies that we get as a result have not enough physical background. It corresponds only to some terms of force field and have no accordance with experimental data. - 39 - Due to distorsions in the force field there are more conformational barriers and local minimums compared to full molecular mechanics which makes the refinement of a global minimum more complicated. We must be certain that the minimization would not remarkably affect the restricted degrees of freedom, and that the refining structure is not very sensitive to minor changes of these terms from equilibrium. It means that molecules in a crystal structure are not far from their conformation of "free" equilibrium. As calculations improve, these simplifications will justify themselves. In the course of the calculations we got the right initial structure of cellulose \ß, which was not achieved by the previous calculation with MM3 mostly due to the lack of complicated minimization functions. Even extremely simple potential energy functions give precise enough results. The rigid-ring method seems to be suitable for fast and powerful research on crystal structures of celluloses and other polysaccharides. Even if the force field is deformed, it will not affect the results. Although this force field has more erroneous local minimas, the best results are easy to refine. It is possible to incorporate X-ray diffraction data for this refinement process, though, it seems that the potential energy calculations are very powerful even without the diffraction data. The construction of minicrystal models for modelling cellulose crystals is valuable, even if it has drawbacks which were mentioned above. Incorporating X- ray data into this minimization technique makes it more awkward. At the same time calculations with full molecular mechanics give us a possibility to compare our results w ith experimental data, i.e. comparison of heat of formation. Similarly, a full molecular mechanics studies may give more detailed information about the structure. For final refinement purposes it would be more useful as it gives more accurate results. Larger crystal models would be better but they need extremely 10* - 40 - large computer resources. However, for structure refinement purposes it suffices w ith the rigid-ring calculations. 4.2. Structure of celluloses As we have mentioned several times, the complete solving of cellulose polymorphs structure is not yet finished. Cellulose II seems to have an antiparallel structure. The crystal energy calculations of both phases of native cellulose give results which are in a good agreement with the experimental data on the conversion lcrH/f-41. Though the results of the parallel structure of native celluloses is very easy to interpret, it is hard to explain the conversion of a parallel structure into an antiparallel structure during mercerization process. According to this we cannot overlook the idea about antiparallel structures of native celluloses. An alternative way is to reinspect the conception of cellulose II. Only further experiments will be able to answer that problem. * * # In the present work the rigid-ring methodology has been developed to refine structures of celluloses and other polysaccharides. 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French, A. D.; Howley, P. S. in Cellulose and Wood - Chem istry and Technology, Ed. Schuerch, C. John Wiley & Sons, New York 1989, 159. - 45 - List of publications I. French, A. D.; Dowd, D.; Aabloo, A. In t J B iol Macromolecules 1993, 15 30-36. II. Aabloo, A.; Pertsin, A. J.; Mikelsaar, R.-H. in Cellulosics: Chemical Biochem ical and M ateria! Aspects, Eds. J. F. Kennedy, G. O. Phillips, P. A Williams, Ellis Horwood Series Polymer Science and Technology, Elli Horwood, New York, 1993, 61-65. III. Mikelsaar, R.-H.; Aabloo, A. in Cellulosics: Chemical, Biochem ical an M aterial Aspects, Eds. J. F. Kennedy, G. 0 . Phillips, P. A. Williams, Elli Horwood Series Polymer Science and Technology, Ellis Horwood, New Yort 1993, 57-60. IV. Aabloo, A.; French A. D. Makromolek Chem, Theory and Sim ulations 199^ 2, in press. V. Aabloo, A.; French A. D.; Mikelsaar, R.-H.; Pertsin, J. Cellulose , in pres VI. Mikelsaar, R.-H.; Aabloo, A. Cellulose, in print. VII. Aabloo, A.; French, A. D.; Mikelsaar, R.-H. in Cellulose Derivates at Related Polysaccharides, Eds J. F. Kennedy et al, Ellis Horwood Series Polymer Science and Technology, in press. VIII. Mikelsaar, R.-H.; Aabloo, A. in Cellulose Derivates and Relati Polysaccharides, Eds. J. F. Kennedy et al, Ellis Horwood Series in Polym Science and Technology, in press. 12 - 4 6 - Tselluloosi kristalsete faaside struktuuri uurimine kasutades energeetilisi arvutusi Tselluloos on üks levinumaid biopolümeere maailmas. Tema struktuuri on uuritud juba aastakümneid, kuid sellest hoolimata leidub veel palju lahendamata probleeme. Kristalne tselluloos esineb erinevates vormides-polümorfides. Looduslik tselluloos (I) koosneb kahest komponendist nn. faasid lo ja \ß. Sõltuvalt päritolust sisaldab looduslik tselluloos neid komponente erinevas vahekorras. Kõige levinum tööstuslik tselluloosi vorm on tselluloos II. Teised faasid on vähem levinud. Tselluloos I kristalsete faaside ühikrakkude ehitus on määratud hiljuti, seetõttu ongi käesoleva töö üheks eesmärgiks nende faaside struktuuri uurimine. Samuti pakume välja mõningaid alternatiivseid ühikraku struktuure, mis seletaksid paremini tselluloosi faaside üleminekuid. Struktuuri määramiseks kasutame kristalli potentsiaalse (steeri/ise) energia arvutusi. Arvutuste käigus me fikseerisime need konformatsioonilised parameetrid, mis minimiseerimise käigus niikuinii oluliselt ei varieeru ning seetõttu ainult segavad arvutusi. Samuti kasutasime kristalli konstrueerimise käigus perioodilisi ääretingimusi jms., mis vastab paremini reaalsele jõuväljale, mille paikneb suhteliselt pikk polümeerahel. Arvutusmetoodikat kontrollisime ka molekulaarmehaanika meetodiga. Tulemused langevad vägagi hästi kokku. Miniature crystal models of cellulose polymorphs and other carbohydrates Alfred D. French* Southern Regional Research Center, PO Box 19687, New Orleans, Lousiana 70179, USA DomM P. Miller Consultant, PO Box 423, Waveland, Mississippi 39576, USA and Alvo Aabloo Department o f Experimental Physics, Tartu University, 202400 Tartu, Estonia (Received 10 September 1992; revised 28 September 1992) Miniature crystal models o f cellulose and other carbohydrates were evaluated with the molecular mechanics program MM3. The models consisted of groups o f 24 to 32 monosaccharide residues, with the models of mono- and disaccharides based on well-established, single-crystal work. Structures o f the cellulose forms and cellotetraose were based on published work using fibre diffraction methods. A structure for the single-chain la cellulose unit cell was also tested. A dielectric constant o f about 4 was best for this type o f work. Calculated intra- and intermolecular energy for glucose agreed with literature values for the heat o f combustion. Cellulose II had the lowest calculated energy for a cellulose form, followed by la, cellulose 111,, ramie I, IV,, and IV,. Optimization o f cellulose IV caused larger mean atomic movements from the original crystallographic positions than the other cellulose forms, and cellotetraose had larger movements than any o f the other structures. Lattice energies for the cellulose forms were about 20 kcal/mol o f glucose residues, with a dominant van der Waals component. Keywords: Cdtukwe; crystal model*; molecular mechanics Introduction energies of the various forms has not been attem pted Pure cellulose crystallizes in various forms, named I to before. Instead, these differences in stability are normally IV, depending on the history of the sample. Cellulose I, ascribed to different intra- and intermolecular hydrogen the m ajor native type, has recently been recognized to bonding schemes, often proposed from X-ray fibre occur mostly as mixtures of the two subclasses, la and diffraction experiments. However, such experiments are l ß l . The two subclasses occur in different am ounts and so difficult that even Ihe chain-packing polarity is often have, respectively, one and two chains per unit cell. not well-determined. Even in the far more accurate X-ray Together' they account for the 8-chain unit cell proposed diffraction studies of single crystals of small molecules, earlier3. Cellulose II results from mercerization (treatment the hydrogen bonding is often difficult to assess. If in 22% sodium hydroxide) or crystallization from accurate positions of hydrogen atoms are needed, low solution. Cellulose III, the product of treatment of temperatures an d /o r neutron diffraction are used. Thus, cellulose I or II with liquid ammonia or other amines, hydrogen bonding schemes resulting from fibre diffraction has two subclasses, III, and III„, depending on the parent studies are speculative. In fibre diffraction work, structure. Finally, cellulose IV results from treatm ent at hydrogen bonding is derived with the aid of computer high temperature (in glycerol at 260°C) of I, II or III, models. These models are necessary components of the with subclasses IV, and IV„ depending on the parent fibre diffraction method, but typically come from structure. Cellulose IV also appears in immature native software that is less well developed than other software samples*. used only for modelling. Researchers have long thought that these various forms In the present work, we have studied the energies of have different relative stabilities, with the most stable small model crystals of most of the cellulose forms, form being cellulose И. Of the native la and \ß forms, using a sophisticated molecular mechanics system, the product of annealing a mixture is pure fß, so Iß is M M 35’®, that was designed to handle a wide variety of thought to have the next lowest energy2. Since the III organic molecules. For comparison, we have modelled and IV forms can revert to their parent I or II forms, several crystal structures of smaller carbohydrate they are thought to have slightly higher energy than the molecules for which good crystal structure data are parent forms. available. A variety of information comes from these As far as we are aware, quantitative comparison of the studies. An approximate lattice energy (or heat of sublim ation) can be determined from the optimized minicrystal by first removing the central molecule. The •To whom correspondence should be addressed. energy of the central molecule and the total energy of This work is the property of ihe US Government and is not subject the surrounding molecules are then calculated (without to copyright further optimization). Their sum exceeds the energy of 0141 -«130/93/010030-07 О 19931 Battcrwofth-Heinemann Limited 30 In t J. BioL Macromol., 1993, Vol. 15, February 12* Crystal models o f cellulose polymorphs: A. D. French et al. ict m inicrystal by the am o u n t o f the lattice energy, when M M 3 results were com pared with crysta l ttice energy can be added to the h eat o f form ation s truc tu res, to m im ic the efTect of crysta lline e nv ironm ents isolated m olecule (calcu lated as a norm al o p tion on isolated m olecules8. H ow ever, we were explicitly (3) giving a to ta l AH, which can be com pared with creating a m in ia tu re c rysta l, and the q u estion therefore ire values for the heat of fo rm ation of solid a rose w hether the op tim um balance betw een the ydrates. dispersive and e lec trostatic forces w ould be o b ta in ed w ith lattice energy can be b roken dow n in to the van 4 or with som e o th er value. lals and ‘d ip o le -d ip o le ' term s. These co rrespond dispersive forces and-the e lectrostatic forces. F rom olubility of cellulosic m olecules in m any solvents, Experimental ■ns th at bo th are relatively stro n g , but we law are of specific p roposa ls o f their relative Starling coordinates udes. W e started with the proposed atomic coordinates of to ta l steric energy reported by M M 3 is a sum of the crystal structures already in the literature, or tables irious a ttrac tio n s and repulsions. It includes deposited with the structure reports. F o r the cellulose olecular term s, such as the b ond s tre tch ing and structures, we chose for internal consistency mostly the ig costs of form ing p yranose and furanose rings, work from S ark o 's group at S yracuse9-12. C ellu lose la I as n o n-bonded forces th a t can apply to bo th was described elsewhere . C rysta lline sm all molecules and in term olecular in teractions. T he m ore stable included a-D-14 and 0-D-glucopyranose15, /i-D-fructo- will have a low er to ta l energy, regard less of pyranosc16, methyl Д-D-galactopyranoside17, sucrose" :r the stab ility com es from a m ore s tab le isolated and /?-D-cellobiose‘\ W e also modelled a crystal of lie o r from a be lte r in term olecu lar arran g em en t. cellotetraose proposed from fibre difTraction studies'*. ;css the stabilities of the various cellulose form s, Som e results of a similar miniature crystal study were ire, the to ta l steric energy term s for each can be reported elsewhere for the tetrasaccharide nystose20. red. If the energy is m uch h igher th an for an o th e r, ly sized g ro u p of m olecules, then the proposed Construction o f m ini-crystals ire may n o t be valid. O u r m odels of the cellulose form s consisted o f seven r the m inicrystals are optim ized , there will have cello te traose m olecules a rran g ed by the ap p licab le om e changes in a tom ic positions from the original sym m etry o p e ra to rs to m ake a pseu d o h ex ag o n al, nates, even when sta rtin g with w ell-determ ined close-packed m in ia tu re crystal ( F ig u re I) . T h e sm all ! structu res. Lii and A llinger, w ho used a special m olecules were sim ilarly a rran g ed (see Figure 2), im (C R S T I.) based on the n o n -b o n d ed term s of depend ing on the crysta l stru c tu re , so th a t a cen tra l for m odelling c ry sta ls1, found ad ju stm en ts of m olecule was su rro u n d ed , in so far as possib le, on all con stan ts of as m uch as 0.28 A for relatively sides. T erm inal hydroxyl hydrogen a to m s o r hydroxyl , h y drocarbon m olecules. T hose differences were gro u p s were ad d ed to the cellulose m odels as needed, ited to lim iting a ssum ptions such as a spherical with the o rien tatio n s o f the new O H g ro u p s being for a tom s. W hile som e m ovem ent is therefore essentially ran d o m . O th e r O H gro u p s o f th e cellulose ed , excessive m ovem ent w ould indicate a defective m odels were o rien ted to build a ne tw o rk of hydrogen sed structu re . bond in g co rresp o n d in g to th e a u th o rs ' p roposa ls. In the choice o f dielectric co n stan t is critical in M M 3 case o f cello te traose, ab sen t a p ro p o sed hydrogen itio n s, wherein it scales the e lec trostatic inter- b ond ing schem e, a n e tw ork was devised. These s relative to the o th er forces. In M M 3 (9 0 ), the m inicrystals were then op tim ized , w ith o u t res tric tions o f -d ip o le energy , used instead o f energy schem es any k ind on the a to m ic m ovem ent. on explicit a tom ic charges in o th er m odelling ire, depends on the d ielectric co n s tan t, as does a Calculations I hydrogen b ond ing term th a t is rep o rted as part T h e ca lcu lations were d o n e w ith 1B M -PC com patib le d ip o le -d ip o le value. A value n ear 4 was suggested 486 and VAX com puters . T he 1990 version o f M M 3 was 1 The minicrystal model of cellulose III,, before (— ) and after (— ) optimization with MM3 Int. J. Biol. Macromol., 1993, Vol. 15, February 31 Crystal models o f cellulose polymorphs: A. D. French et al. r ig u re 2 The starling minicrystal of 7 I) glucopyrnnose with 27 molecules used, with the energy-based ( ra th e r than geom etry- based ) default term in a tio n c riterion th a t depends on the num ber of a tom s in the s tru c tu re (0.05 k ca l/m o l for a 27-m olecule m in ic ry sta l). T h e O H E M -X p ro g ra m 21 was used to construc t the crysta ls, to m an ipu late the m olecules, and to p repare M M ? input files. C H E M -X was also used to fit the initial and final struc tu res by a least squares p rocedure, m inim izing the function where a, and bt are the a to m co o rd in a te s of the ith a to m after and before m in im ization22. After this fitting procedure, (he average of the abso lu te values of the residual differences betw een a, and bi was reported as the m ean a tom ic m ovem ent. It was co m p u ted only for the oxygen and carb o n atom s. Figure 3 Energy minimization of i-n-glucosc at a dielectric constant of 4. The restarts are indicated. After the energy went Lim itations up al the end of the first run. the hydroxyl groups showing maximum movement were rotated and the optimization Several lim ita tions characterize o u r m odels. T he restarted. At the end ofthc second run. there was still substantial num ber of m olecules is sm all, as is the chain length. T he fluctuation of some other hydroxyl hydrogen atoms (see lim its on size arise bccause of the lim it o f 700 a to m s in Figure 4). The energy declined only slightly during the third run the M M 3 program . W hile th a t size lim it is som ew hat artificial, significantly larger m odels w ould requ ire m uch m ore com puter time. F o r exam ple, one m ore layer of m olecules a ro u n d the cu rren t 27-m olecule crystal of severe oscilla tions o f hydroxyl hydrogen a to m s on the glucose w ould add 98 m olecules. T he larger m odel would o u tp u t, as the a to m s w ith m axim um ato m ic m ovem ent, require ab o u t 20 tim es as long to optim ize. show n in Figure 4. T he M M 3 o u tp u t lists, at each five ite rations, w hich a to m w ould be m oved the m ost and Energy increases the pro jected ex ten t of the m ovem ent, based on the In these and o th er m odelling studies o f ca rb o h y d ra te s , derivatives ca lcu lated d u rin g the op tim iza tio n step. The M M 3 often has a p roblem wiih energy increases that a to m ic m ovem ent per ite ra tio n is ac tua lly lim ited to term inate the m inim ization . T his happens only when a b o u t 0.25 A an d does no t occur to th e ex ten t show n in using the block d iagonal least squ ares m inim izer, Figure 4. T h is p rob lem preven ted the full o p tim iza tion necessary for s truc tu res co n ta in in g m ore th an 80 a tom s. o f several o f the m inicrystals, at least un til the indicated Figure 3 show s the energy values d u rin g three separa te hydroxyl g ro u p s were ro ta ted (w ith C H E M -X ) to a m inim ization runs o f the glucose m inicrystal derived from su itab le a lte rn a te staggered o rien ta tio n . After ro ta tio n of the neu tra l d iffraction study. O n the 71st cycle of the hydroxyl g ro u p s, the energy w ould be m om entarily o p tim iza tion , the energy went up slightly. O p tim izatio n s h igher, such as the 5 k c a l/m o l increase show n for of struc tu res th a t yield energy increases a lso ind icate ite ratio n 72 in Figure 3, bu t m in im ization w ould quickly 32 Int. J. Biol. M acrom ol., 1993, Vol. 15, F eb ru ary Crystal models o f cellulose polymorph** A . D . French et al. 21 41 61 61 101 121 14! Figure 5 Plot of the MMJ 'final steric energy' for the Iteration number minicrystal models of ®-i»-glucose at different dielectric Figure 4 The maximum movement by any atom, as indicated constants by MM3. The movement reached a suitable value only during the third run. even though the energy changed only slightly. The atoms are limited to movements of about 0.25 A by the program; they are not actually moved as much as indicated. As in figurcS. the first run ended al 71 iterations, and the second at the I IXth iteration lower the to ta l to a value less than the previous low. T he problem happened often with the som ew hat random o rien tation given to the added hydroxyl g roups at the cello te traose ends, but som etim es it also afflicted o ther g roups on the surfaces of the m inicrystals. T he m axim um m ovem ent of any individual atom indicated in Figure 4 is distinct from the m ean atom ic m ovem ent that we have used to indicate the qua lity of the force field a n d , in the case o f the s truc tu res determ ined Figure ft Plot of Ihe mean atomic movement for the minicrystal models of glucose at different dielectric constants. by fibre d iffraction, the q ua lity o f the s tru c tu re . T he m ean ( 0 ) f»-n glucose; i • ) /(-l)-glucose a tom ic m ovem ent refers to the average o f all the d istances betw een the initial and final positions of each a to m , and is only applied to the carb o n and oxygen a to m s in this w o rk . The m axim um a tom ic m ovem ent refers to the a tom m olecules, the m ean a tom ic m ovem ent d u rin g o p tim iz­ th at is indicated to need to m ove the m ost to low er the a tio n seem s to have a general m inim um centred a ro u n d energy d u rin g m inim ization . The a to m th a t is indicated a d ielectric o f 4, as show n in Figure 6. /?-l)-G lucopyranose to have the greatest m ovem ent is alm ost alw ays a has lower values on e ither side o f 4, bu t they m ay be due hydroxyl oxygen when the problem with energy increase to incom plete m inim ization of those structures. Therefore, d u ring m inim ization occurs. a value of 4 was used on the o th er m odels in this study . W hen this problem causes p rem atu re term in a tio n of D ielectric values as low as 1.5 p roduced extrem e the o p tim iza tion , the differences in the initial and final m ovem ent, even though M M 3 agreed best w ith 6 / 3 1 g* atom ic positions are not as large as if the s tru c tu re were ah initio studies when the dielectric co n stan t was set to fully optim ized . Also, the energy is not as low as when 1,025. W hen condensed phase system s are m odelled w ith the o p tim iza tion has been carried full term after ro ta tio n m olecular m echanics p rogram s using a dielectric of the indicated groups. O f course, p a rt of the increased constan t of I, the resulting im balance betw een the m ovem ent and decreased energy is due to the ro ta tio n electrostatic forces and all o th er energy term s is a likely o f the hydroxyl hydrogen atom s. In a few instances, it source of e rro r. T h is o b serva tion also suggests th a t ab was not possible to find an a lternative position that initio studies and condensed phase experim ents will no t allowed full op tim ization . H ow ever, after several trials, have co m p arab le results. even the s truc tu res that con tinued to term inate with an energy increase were th o u g h t to be reasonably well M ovem ents optim ized T herefore, we reluctan tly accepted these Table I show s the m ean a tom ic m ovem ents th a t result results as the best available. from the o p tim iza tion with M M 3 o f the different crystal s tructures. The struc tu res based on good single crystal R esu lts a n d d iscu ssio n d a ta have a range of 0.09 to 0.21 Ä in the m ean atom ic m ovem ents. T here is a slightly wider range for the Effect o f varied dielectric constant cellulose s truc tu res and a large m ovem ent for cello­ Results of varying the d ielectric co n tan t in the M M 3 tetraose. T he tw o cellulose IV s tru c tu res , in p a rticu la r, calcu lation a re show n in Figures 5 and 6. Figure 5 shows have large m ean m ovem ents. Inspection of the in itial and the varia tion in calcu lated energy. In view of its final s truc tu res show ed th a t the prim ary a lcohol g roups 880 k ca l/m o l range, the im portance of the dielectric in bo th cellulose IV, and 1V„ m oved substan tia lly d u rin g co n stan t w ould be hard to ignore. F o r bo th glucose o p tim iza tion , accoun ting for m uch o f the m ean Int. J. Biol. M acrom ol., 1993, Vol. 15, F eb ru ary 33 Crystal models o f cellulose polymorphs: A. D. French et al. Table I Models, movements (A ) and energies (kcal/mol) for minicrystals Lattice Total energy (kcal) Compounds modelled' Model size Movement energy /tetraose (/glucose) (kcal) Cellulose lot 7 tetramers 0.106 185 Ramie cellulose 1 7 tetramers 0.160 201 — 76.1 / — 19 0 Cellulose II 7 tetramers 0.202 176 - 7 9 .0 / / -19 .75 Cellulose III, 7 tetramers 0.198 200 - 7 3 .4 / - 18 3 Cellulose IV, 7 tetramers 0.255 209 — 79.6/ — 19.9 Cellulose IV„ 7 tetramers 0.254 202 - 7 9 .5 / -1 9 9 Cellotetraose 8 tetramers 0.418 232 Energy/molecule ot-n-Glucose 27 monomers 0 205 68 -3 7 .4 /(-nCilucose 27 monomers 0.211 36 -3 7 .6 /(-n-Fructopyranose 25 monomers 0.118 97 — 35.8 Methyl 0-l>-galactopyranosidc 27 monomers 0 091 114 - 36.1 /(-i)-Cellohiose 16 dimers 0.092 199 -6 1 .0 Sucrose 14 dimers 0.209 296 — 44.5 m ovem ent. T he considerable a to m ic m ovem ent in the respectively. In th a t crysta l s tru c tu re , the p lanes of the celio te traose s tru c tu re suggests th at the p roposed rings are p erpend icu lar to the z-axis, a long which the s tru c tu re m ay not be co rrect, as indicated by the au th o rs . greatest m ovem ent is observed. The confo rm ations o f som e of the m odel cello te traose m olecules changcd to s truc tu res with ap p ro x im ate Energies two-fold screw sym m etry. T hose changes in conform ation , Table / also show s the to ta l s teric energies and heats how ever, could have resulted instead from o u r guesses of fusion (w hen ca lcu lated ). T he energy values for the regard ing the hydrogen bonding in the struc tu re . In different s truc tu res vary w idely, even a cco u n tin g for the retrospect, it seem s that having m ore specific guidance dilTercnccs in the sizes of the c rysta ls needed to provide to the p roposed hydrogen bonding would be w orthw hile, a tota lly su rro u n d ed cen tra l m olecule. As a check on the even though the hydrogen bonding is not rigorously overall validity of these ca lcu lations, we have also de term ined . A result consisten t w ith the orig inal au th o rs ' com puted the heat of fo rm ation of /)-n-g lucose with op in ion would be useful for tests such as the present work MM.V T he isolated /f-D-glucose m olecule in its lowest The m ean a tom ic m ovem ent in the m odel struc tu res energy co n fo rm atio n has a A/ / , o f —265.8 k c a l/m o l. was not iso tropic. Superirnposition o f the optim ized calcu lated at a d ielectric co n stan t of 1.5. W hen added to m odel and intial s tru c tu re show ed that there was very the —37.6 k c a l/m o l of fusion energy , the to ta l o f 303.4 little m ovem ent a long the fibre axis. In the (100) planes equals the lite ra tu re value of —303 k c a l/m o l calcu lated of the ram ie cellulose I, III (see Figure I ) and IV from the heat of com b u stio n for solid g lucose26. The s truc tu res that co n ta in the in ter-chain hydrogen b o nd ing , diclectric c o n ta n t is som ew hat less critical for the there was also little m ovem ent. T he m ajo rity of in tram olecu lar energy. At a d ielectric co n stan t of 4, the m ovem ent was p erpend icu lar to those planes. The (100) iso lated /J-п -glucose m olecule has a AH , o f -260.0 planes were slightly sep ara ted , as if the h y d rophob ic k c a l/m o l, still allow ing a sum reasonab ly close to the bond ing were not pulling (he s tru c tu re together strongly lite ra tu re value. enough. How ever, this m ay be a result o f the small m odel size. T he v iariations in unit cell d im ensions reported for different native celluloses24 m ay be due in part to the Energies o f cellulose polym orphs. O f the cellulose different crystallite sizes found in the different m aterials. s tru c tu res , cellulose II has the lowest energy , resulting Sm all crystallites would give slightly larger unit cells from bo th the low in tram o lecu lar energy , and as show n because of fewer long-range in te rac tions pulling the by the lattice energy, the second-low est in te rm olecu lar struc tu re together. energy. Its an tip ara lle l m odel has four up ( c o rn e r ) chains M ovem ent in the cellulose II lattice was assessed by and three (dow n ) centra l chains. T he co rn e r chains have ro ta tin g the struc tu res 74", so that the planes o f the chains 0 6 in the gl position at slightly low er energy th an the were parallel to the x-axis. T he co m p o n en ts o f m ovem ent Ig p o sition occupied on the cen tra l chains. (T he lower were separated and , again , the m ajo r m ovem ent occurred energy for the gt form is a consequence of the dielectric perpend icu lar to the m ain p lanes of the cellulose chains. c o n s tan t of 4, as w ell.) The energy of the p ack ing m odel The m ovem ent a long the z-axis (the fibre ax is) was with four dow n chains and three up ch a in s sh ou ld also 0.058 A, a long the x-axis was 0.083 A, and a long the be averaged with this one. W hen this is done , the to ta l у-axis of C artesian space it was 0.149 Ä. Because the energy increases ab o u t 5 kcal, still leaving cellulose II lengths in M M 3 for the glycosidic C -l 0 -1 bond are off with the lowest energy. O n ly the ram ie cellulose m odel by as m uch as 0.02 A2', the deficiencies in the z-d irection , differs from expectations, h av ing energy su b tan tia lly to which the glycosidic bond are nearly paralle l, a re small. h igher than the la m odel, equal to the III, m odel. The Sim ilar calcu lations for /?-D -fructopyranose show ed x-, lattice energy of cellulose III, is b roken dow n in Table 2 y- and z-axis m ovem ents o f 0.043, 0 054 and 0.074 A. in to the van der W aals and d ipo le d ipo le term s for the 34 Int. J. Biol. M acrom ol., 1993, Vol. 15, F ebruary Crystal models o f cellulose polymorph:.: A. D. French et al. Г«Ые 2 Breakdown of energy calculations for cellulose 111, 7-tetramer 6 outer 1 inner Lattice energy Energy term minicrystal chains chain /tetraose (/giucose) van der Waals -189.2 -117 .9 -9 .0 -6 2 .3 ( -1 5 .6 ) Other Dipole -dipole -5 8 .7 -4 2 .6 -4 .9 — 11.2 ( — 2.8) Total -7 3 .4 ( -1 8 .3 ) entire m odel, the isolated cen tre m olecule and the C o n c lu sio n s rem aining m odel. It shows th a t, com puted at a dielectric constan t of 4, the m agn itude of the van der W aais T he con stru c tio n of m odel m inicrystals and the a ttrac tio n s (15 k ca l/m o l of glucose residues) is consider­ calcu lation o f their energies seem s to be a valuable type ably larger than the values for e lectrostatic a ttrac tio n of m odelling study. W e have show n th a t it is possible to (3 k ca l/m o l of glucose residues). T hus, in the past, the ob tain nearly q u an tita tiv e values o f the heat of fo rm ation , con trib u tio n s by the hyd ro p h o b ic g roups to crystal an im p o rtan t experim ental qu an tity . Also, the ap p ro ach stability have been underestim ated . H ydrogen bonds provides a useful m eans to determ ine the value of the have bo th electrostatic and van der W aals com ponents. dielectric co n stan t used to scale the e lectrostatic and If the single hydrogen bond in the cellulose III m odel o th er forces in a m olecu lar m echanics force field. T he has an energy of 5 k c a l/m o l, the rem ain ing lattice energy work show ed th a t a value of 4 is a b o u t righ t; the would be ab o u t 13 k c a l/m o l, all arising from van der consequences o f excessive a tom ic m ovem ent and W aals forces. decreased energy from using a value o f 1 o r 1.5 to m odel T he lattice energy of IV, is slightly low er than all the condensed phases are m ade qu ite c lear in this study. o ther form s, while its overall energy is greater. This The m inicrystal m ethod also seem ed to be useful for suggests th a t the in tram olecu lar energy term is higher. testing s truc tu res proposed in fibre d iffraction studies. The proposed s truc tu res of cellulose IV had sub stan tia l M ono- and oligosaccharide energies. The m o n o ­ m ovem ent o f the p rim ary a lcohol g roups and were thus saccharide struc tu res have su bstan tia lly low er (m ore the least com patib le with the M M 3 force field. W e were negative) lattice energies per residue th an the larger also unab le to supplem ent the p ro p o sed c a rb o n and m odels, ow ing to the larger n um ber of in term oiecular oxygen positions for ceilo te traose w ith a hydrogen hydrogen bonds th a t a re possible in m onosaccharides. bond ing schem e th a t avoided su b stan tia l m ovem ent Cellobiose has less stability per residue th an glucose, d u ring o p tim iza tion w ith M M 3. T h e a u th o rs had partly because two of the hydroxyl groups of glucose concluded that the ceilo te traose d a ta were not solved and have been replaced by the glycosidic linkage in the refined to an acceptable degree o f accuracy . Like any d isaccharide. The m odel sucrose d isaccharide has a high m odelling study , the m inicrystal techique c an n o t prove energy com pared with the cellobiose m odel. Since the that a s tru c tu re is co rrect, n o r, because o f the extensive sucrose m odel had only 14 d isaccharide residues in a tim e required for op tim iza tio n , is it useful for finding the structu re with P 2 , sym m etry , the packing in its range of likely possibilities. Instead , it seem s to function m inicrystal was sim ilar to that of the cellulose m odels, as a soph isticated secondary check o f the m odelling except that there were two layers. T herefore , som e of the com ponen t o f s truc tu res derived by fibre d iffraction three-d im ensional cha rac te r of the sinall-m olecule m ethods. struc tu res was lost. A better m odel of sucrose would have This type o f investigation could be im proved in a th ird layer of m olecules above o r below our num erous ways. L arger crystal m odels w ould be better, arran g em en t, bu t this was beyond the capacity of o u r if accom pan ied by significantly faster com puters , o r m ethod. T he high energy can also be a ttr ib u te d to two periodic b o u n d ary cond itio n s could be in co rp o ra ted into o ther factors. O ne is the presence of furanose rings, which M M 3. T he M M 3 (9 2 ) p ro g ram in co rp o rates a test on have significantly higher angle-bending and torsional the angle o f hydrogen bond ing , a lthough the p roblem of energies than pyranose rings (am o u n tin g to several p rem atu re energy term ina tion still exists. T he C R ST L k ca l/m o l per residue). A nother factor is the presence of program allows a m uch larger crystal size to be em ployed, overlapp ing anom eric effects a t the sucrose linkage. for m ore rigorous calcu lations. H ow ever it does not allow O th e r work has shown that M M 3 m ay overestim ate the the m olecules them selves to optim ize, crucial for the study energies of such linkages, a lthough the increase for of the relative stabilities of different form s. sucrose is not as severe as for o th er crysta ls, such as rafiinosc, where the largest problem exists27. In the R efe ren ces m odels of nystosc20, where the sucrose linkage has an M M 3 energy 3 k ca l/m o l h igher th an the global 1 vanderHart, D. L. and Alalia, R. I f . Macromolecules 1984, 17, 1465 m inim um , the m ean atom ic m ovem ent in the m inicrystal 2 Sugiyama, J., Vuong, R. and Chan/.y, H. Macromolecules 1991, was 0.312 A, a lthough the m ovem ent for the central 24, 4108 m olecule in the crystal was sm aller. A p artial reason for 3 Honjo, G. and Watanabe. M. Nature 1958, 181, 326 the sm aller lattice energy in the sucrose m odel com pared * C'han/y, H., Imada. K. and Vuong. R. Protoplasma 1978,94,299 with m ay be th a t crystalline sucrose has tw o in tra ­ Allingcr, N. L., Yuh, Y. H. and L ii, J.-H. J. Am. Chem. Soc.1989, I I I , 8551 m olecular hydrogen bonds, dim inish ing the o p p o rtu n ity (, Allingcr, N. L., Raman, M. and L ii, J.-H. J. Am. Chem. Soc. for in term oiecular hydrogen bonds. 1990, 112, 8293 Int. J Biol. M acrom ol., 1993, Vol. 15, F eb ru ary 35 Crystal models o f cellulose polymorphs: A. D. French et al. ^ l ii. J H and A llinger. N. L J Am. Cli-ni Soc. IP89. I I 1 .8576 19 Henrissat, B.. Perez, S.. Tvaroska, (. and W inter. W. T in 8 French. A I) . Rowland. R S. and Allinger. N. I. in 'Computer T h e Structures of Cellulose: Characterization o f the Solid State'. M odeling o f Carbohydrate Molecules'. ( Fds French, A . D. and (F.d. Atallas, R. H .), ACS Symposium Series no. 340. ACS Brady, J. W I, AC'S Symposium Series 430. ACS Books. Books, W ashington, D C , 1987. p 38 Washington, DC. 1980. p 121 20 French. A. D ., M ohous-R iou, N. and Perez, S. С arhohydr Res 9 W oodcock, C. and Sarko, A. Maeromolft ulr.s 1980, 13, U83 ( in press I 10 Stipanovic, A. J. and Sarko, A. Macroiuolrtulcs 1976. 9. 851 21 C H F M -X is developed and distributed by Chemical Design Ltd. 11 Sarko. A., Southwick, J, and Hayashi, J. M armm oht ales 1976. O xford, England «. 857 22 Ferro. D. R. and Hermans, J. Acta i ryslalloifr 1977, A33.345 12 Ciardiner. F. S. and Sarko. A ' Vm ./. Chem 1985. 63. 173 23 Aabloo, A. and French, A. D. (unpublished) 13 Aablo, A. and French. A. D. M acronwlaulvs (in press) 24 O kano. T. and Koyanagi, A. B io po litu rr .s (9X6. 25, 851 14 B row n.(I. M. and l.cvy. H. A. /irfuCrixtitllotir. 1979. ВЛ5,656 25 Dowd. M . K ., F'rench, A. D. and Reilly. P. J. Corhohydr. Res 15 Chu. S S C. and JelTrry.C». A. Art и ( ’гуш Н щ г. 1968, B24.830 1992 ( in press) 16 Kanters. J. A., Roelofscn. G.. Alblas. В. P. and Meindcrs, I. 26 ‘CRC Handbook of Physics and Chem istry’, 1983. p 1)181 A rm Cn.Molhifr 1977. BJ.1, 665 27 French, A. D .. Schäfer. L and Newton. S. О C m hohutr Rrs. 17 S held rick, B. Aria СгуМаНщг 1977. B33. 3003 (in press) 18 Brown,C5. M. and Levy. I I. A. Aria Cry slather. 1973. B29. 790 36 Int. J. Biol. M acro m o l., 1993, Vol. 15, F eb ru a ry 62 Biosynthesis, Structure and Organisation [PLl probable models of a crystal of cellulose we have minimized the objective function F=UtWR" where U is the potential energy of the system, R" is the crystallographic discrepancy factor based on the cellulose f] intensity data from Kolpak et al [2]. The potential energy consists of 10 in which U „ « is the conformational energy of the monomer residues, Calculations of potential energy of Ц »« 1» the conformational energy between two successive residues along both of the two crystallographically distinct chains, U *., is the the cellulose crystal structure intermoiecular energy which includes non-bonded and H-bond energy between the atoms of different chains. Calculations have been executed Ahro Aabloo, Aleksandr J. Pertsin* and R.-HL MikeUaar** - Tartu University, in internal coordinates. There are two different extents of atomic Department of Experimental Physics, Tähe 4 Street, 202400 Tartu, Estonia. "Institute adjustments that can be used to reduce F. The first possibility is to leave of Element-Organic Compounds, Vavilova 28 Street, GSPI, V-334, 117813 Moscow. ••Tartu University, Institute of General and Moleculai Pathology, Veski 34 Street, all bond lengths etc flexible. The second way is to fix some structural 202400 Tartu, Estonia. components that do not vary much during minimization. This method allows us to decrease the number of variables. In earlier work [3] thirteen most probable models for the cellulose II crystal structure were calculated. ABSTRACT CALCULATIONS OF THE POTENTIAL ENERGY OF THE CRYSTAL STRUCTURE OF CELLULOSE II Many aspects of cellulose crystal structure remain without satisfactory explanation. We have calculated objective functions based on diffraction To learn the importance of variable residue geometry, we have calculated intensities and potential energies of the cellulose П crystal using ‘rigid all thirteen most probable models of cellulose II crystal structure [3] by model' calculations. We used different geometries of the glucose rings the use of the "rigid model" method described in [3,4], applying five and found that this does not shift the results of potential energy different initial glucose rings. We used ß-glucose rings constructed by calculations very much. The second part of this work contains preliminary chiral inversion of residues found in cydohexaamylose-KOAc/CHA2/, results of potential energy calculations for the cellulose la crystal planteose/PLA/ and glucose-urea/GUR/ [5]. We also used reducing ß-D- structure. Models with the lowest energy are in the tg conformation. cellobiose/СВЮ / and ß-D-glucose/ÖGLU/ [6]. We presumed symmetry However, the best gg model has very complicated hydrogen bonding that P2, for the chain of cellulose II. During minimization we fixed the bond includes two hydrogen bonds between sheets. lengths, bond angles and glucose ring geometry. We varied the totsional angles of the hydroxymethyl and three hydroxyl groups and the torsional INTRODUCTION and bond angles describing the junction between two successive monomer residues. We also varied rotations and shift of chains in the unit In recent years there have been only a few attempts to determine the cell w cellulose II [2]. As for the most probable models, their variable structure of cellulose by combined potential energy and X-ray diffraction parameters do not shift remarkably when the “Xxfferent geometries are calculations [1]. A typical X-ray diagram of cellulose contains only few used. The only models that shifted were ones that ranked last in the dozen reflections, a number that is clearly insufficient to refine all atomic Initial preference list [3] (using "average Amott-Scott" ring). When the parameters by standard crystallographic methods. To increase the ratio model A ll was based on PLA and ÖGLU rings, it did not find the same of observations to refineable parameters we have used various energy minimum. Instead the A ll shifted to the A l model. In Figs. 1 and stereochemical and packing constraints and non-bonded contacts 2 we present the value of the objective function and the potential energies calculated by the atom-atom potential method. For calculating the most of the thirteen most probable models of crystal structure П. It can been Ch.10] Calculations of Potential Energy 64 Biosynthesis, Structure and Organisation p u seen that the models of lowest values of energy do not change PRELIMINARY CALCULATIONS OF THE POTENTIAL ENERGY OF remarkably. We deduce that 'rigid" model calculations are quite correct THE CELLULOSE la CRYSTAL STRUCTURE for the initial calculations of cellulose structure. For more exact calculations it is reasonable to use "flexible” methods (as MM3) in which For a long time there were many questions about the structure of "rigid model" results can be used as initial variable sets. crystalline cellulose I. Several authors [7,8] tried to solve the problem, but it has up to now been unsolved. Later, using NMR data [9,10] it was found that the crystal of cellulose I consists of two phases: cellulose [a which must have triclinic symmetry, and cellulose Iß which must have monoclinic symmetry. This year Sugiyama and collaborators [11] reported a new structure of the crystal of cellulose I. They used a new precision electron diffraction apparatus which allows them to apply a very narrow initial electron beam. They found that cellulose la has a one-chain triclinic unit cell with parameters: a=117”, ß=U3°, у=81°, а=6.74А, Ь=5.93А, с=10.3бА. The aim of our work is to examine that unit cell from the energetic viewpoint. Unfortunately, X-ray d;ffraction data of phase la do not exist yet. We have calculated the potential energy of the crystal of cellulose la using "Amott-Scott" glucose ring geometry for "rigid model" Models calculations. This time we presumed symmetry PI for the chain cf cellulose la. We varied torsional angles of the two nydroxymethyl and six ftgnn I. Objective function* of moat probable model* of celluloae П cryiul Glucoac .ings: AS - average AnoO-Scott; CHA2- cydohexsamyloac; PLA - planteose: GUR - glucose-urei; hydroxyl groups and the two torsional and bond angle between two CBIO - cellobioee; ßCLU - ß-D-giucoae. A1_A12.P1 - n u l probable model* of the unit cell successive units along th? chain (Figure 3.). Table 1 shows the 19 models of ccllulose Q [Э]. having lowest energy for phase la. The best "up” model (Ul) has an energy of -19 kcal/mol in tg conformation. It is remarkable that at energies -14 to -16 kcal/mol there exist b "up” models with different hydrogen bonds. The best "down" model (Dl) has an energy of -17 kcal/mol. The best gg model has an energy of -14 kcal/mol. It has very complicated hydrogen bonding. There are two hydrogen bonds between sheets along the a-axis. Models Figure 2. Potential eneigies of moat probable models of the celluloae II crystal. For abbreviation* tee Fig 1. Пциг» X Variable tonloaal and bond angles In tie dials of celluloae la. Ch. 10] Calculaiions of Potential Energy Table 1. Tbe mo« probable models of die cellulose la tridlnic wait cell. U_ * ’up' modele; D_ - ‘down* models; - variable bond and torsional angles (see Fig. 3.); r - angle describing chain rotation; ' - H-boods in a chain; 1 - H-bonds in s sheet <1I0>; 1 - H bonds between sheets <100>. 17S -77 tg < 170 -1 tq I 171 -71 t planes; 3 - H -bonds Mean a to m mo ve m en t betw een sh eets (parallel to the < 1 0 0 > p lanes); * - H -bonds which PLMR ммз w i t h w i t h o u t w ere found by M M 3. H ' s H ' s U1 - 1 9 . 5 185 . 1 7 5 . 1 0 6 up t g D1 - 1 6 . 8 206 . 1 5 8 . 1 0 8 down t g U2 - 1 6 . 3 222 . 1 7 8 . 1 4 8 up t g U l t g 0 5 . НОЗ 1 0 2 Я . О б ' 1 06H. .ОЗ2 из - 1 6 . 2 218 . 1 7 7 . 0 9 2 up t g 0 6 H . . 0 3 f o r m a t i o n D1 t g 0 5 . НОЗ 1 0 2 H . О б ' 1 06H. .ОЗ2 U4 - 1 5 . 7 2 15 . 193 . 0 9 8 up t g 0 6 H . . 0 3 f o r m a t i o n 02 t g 0 5 . H03 1 0 1 ; 0 2 . . H O 6 ' 1 Ü5 - 1 5 . 0 234 . 0 5 6 . 0 3 5 up t g Ü3 t g 0 5 . H03 1 0 2 H . О б ' 1 ОбН. .ОЗ4 U6 - 1 4 . 3 2 10 . 2 5 7 . 1 6 3 up t g 04 t g 0 5 . НОЗ 1 0 2 H . О б ' 1 ОбН. .ОЗ4 D2 - 1 4 . 3 206 . 2 3 2 . 1 5 8 down t g OS t g 02H . 0 6 1 ОЗН. Об2 D3 - 1 4 . 2 213 . 2 7 7 . 2 3 4 down t g 06 t g 0 5 . НОЗ 1 0 6 H . U7 - 1 4 . 1 229 . 4 5 1 . 3 8 4 up g g 02 0 5 . H03 1 0 2 H . О б ' 1 ОбН. .ОЗ2 D3 0 5 . H03 1 0 1 ; 0 2 . . H 0 6 ' 1 07 gg 0 5 . .НОЗ 1 0 2 H . О б ' 1 ОбН. . 0 5 3 rt ft vfl о о 13 T a b le 4. C a r te s ia n c o o rd in a te s o f th e best m odel (U l) o f cellulose Icr. 30 02 * 2 . 2 5 1 3 4 - . 5 0 4 5 8 8 . 6 0 7 1 5 31 0 3 ' 1 . 4 1 1 7 1 - . 6 3 9 4 4 5 . 8 8 9 1 2 T h e a to m s a r e from the c e n tra l tw o res id u es in th e m idd le o f 32 H-C 4 ' - 1 . 1 0 1 0 6 . 0 3 9 2 2 6 . 2 6 0 7 1 th e m in ic ry s ta l. 33 H-C 5 * - . 2 8 9 3 0 2 . 7 2 6 5 3 7 . 5 8 1 0 3 34 H -C l ' . 9 6 5 5 5 1 . 6 4 2 3 1 9 . 2 8 8 9 5 3 5 H -C 2 ' . 3 1 3 7 2 - 1 . 1 6 6 0 2 8 . 1 3 9 6 6 Naa* x<&) y<*> I (A) 36 H-C3' 1 . 7 2 3 4 6 1 . 2 3 8 6 8 6 . 7 8 6 0 5 37 0 6 ' - 2 . 4 0 7 4 5 3 . 2 5 9 7 8 6 . 1 5 0 4 1 1 04 .00000 .00000 .00000 38 H-C6 a' - 3 . 0 1 7 4 1 1 . 4 1 9 6 1 6 . 9 2 7 4 4 2 C4 . 2 1 1 4 2 . 7 5 4 1 7 1 . 2 0 3 1 7 39 H-C6b' - 2 . 8 0 8 8 9 2 . 7 2 8 1 7 8 . 1 2 5 5 0 3 C5 . 7 2 7 9 7 - . 1 8 6 7 0 2 . 2 9 6 2 2 40 H - 0 6 ' - 3 . 2 0 9 8 8 3 . 7 6 0 2 5 6 . 2 3 7 2 0 4 05 . 8 1 1 2 7 . 5 4 1 8 2 3 . 5 1 6 8 1 41 H - 0 2 ' 2 . 1 9 9 2 7 - . 8 8 6 9 2 9 . 4 7 4 7 1 5 C l - . 4 6 4 4 8 . 9 7 2 2 8 3 . 9 8 6 0 0 42 H - 0 3 ' 1 . 5 0 3 2 7 - . 2 5 6 0 2 5 . 0 2 6 9 7 6 C2 - 1 . 0 2 5 1 4 1 . 9 7 5 3 0 2 . 9 8 2 4 0 7 СЭ - 1 . 1 4 7 3 4 1 . 3 2 9 0 7 1 . 6 0 4 8 8 8 C6 2 . 1 3 8 7 7 - . 6 9 3 1 5 2 . 0 1 5 9 4 9 0 4 ' - . 3 0 1 6 0 1 . 6 7 4 0 8 5 . 1 9 6 7 7 10 02 - 2 . 3 4 4 9 0 2 . 3 1 5 0 6 3 . 4 2 4 3 2 11 03 - 1 . 5 0 4 2 6 2 . 3 5 0 8 2 . 6 6 1 6 8 12 H-C4 . 9 4 0 9 4 1 . 5 7 6 5 7 1 . 0 2 3 9 8 13 H-C5 . 0 4 3 3 6 - 1 . 0 5 5 2 1 2 . 4 1 7 7 6 14 H -C l - 1 . 1 5 3 7 2 . 1 1 0 6 5 4 . 1 0 3 4 4 15 H-C2 - . 3 8 3 3 5 2 . 8 8 2 7 5 2 . 9 2 7 6 9 16 H-C3 - 1 . 9 2 1 4 4 . 5 2 8 2 2 1 . 6 2 4 2 1 17 06 2 . 1 4 3 2 1 - 1 . 5 0 4 9 8 . 8 3 4 8 3 18 H -C6a 2 . 8 3 9 7 5 . 1 5 6 3 9 1 . 8 8 7 0 9 19 H -C 6b 2 . 4 9 7 7 9 - 1 . 2 8 9 4 3 2 . 8 8 0 3 6 20 H -0 6 2 . 9 7 1 2 8 - 1 . 9 6 7 5 8 . 8 0 1 9 6 21 H -02 - 2 . 2 6 7 9 7 2 . 7 1 5 5 5 4 . 2 8 1 9 9 22 H -03 - 1 . 5 1 7 1 2 1 . 9 5 1 2 8 - . 1 9 8 5 7 23 С4 ' - . 3 9 9 3 1 . 8 9 3 1 0 6 . 3 8 6 6 9 2 4 C 5 ' - . 9 4 2 1 7 1 . 8 3 1 4 9 7 . 4 7 4 2 8 25 0 5 ' - . 9 8 5 3 8 1 . 1 1 9 7 9 8 . 7 0 7 7 9 26 C l ' . 3 1 1 9 9 . 7 5 2 5 2 9 . 1 7 5 7 6 27 C 2' . 9 1 2 8 3 - . 2 2 9 0 0 8 . 1 7 6 7 5 28 C3 ' . 9 9 3 3 6 . 3 9 8 2 3 6 . 7 8 7 3 2 29 C6' - 2 . 3 7 8 2 1 2 . 2 8 4 1 9 7 . 2 0 2 4 1 A unit o f the cellulose chain showing the num bering of the ring and glycosidic atoms and the torsion and bond angle variables of the PLMR program . В o o t В I 0 Ю Model U l, after MM3 minimization, showing the unit cell parameters a, b and y. The view is down the chain axes of the seven tetram ers. Intermoiecular hydrogen bonding occurs in the 110 planes of the crystal (the planes are defined in inset). Studies of Crystalline Native Celluloses Using Potential Energy Calculations. Running Title: Model Cellulose ia and \ß Alvo Aabloo' U n ive rs ity o f Tartu , Ins titu te o f Experimental Physics and Technology, Tähe 4 S tree t, EE2400 Tartu Estonia; Alfred D. French Southern Regional Research Center, U. S. Departm ent o f A gricu ltu re , 110 0 Robert E. Lee B lvd., P. 0 . Box 1Э 687, N ew Orleans, LA 7 0 1 7 9 , U. S. A ; Raik-Hiio Mikelsaar U niversity o f Tartu, Ins titu te of General and M olecular Pathology, Veski 35 S treet, EE2400 Tartu, Estonia; Aleksandr J. Pertain Ins titu te o f Element-Organic Com pounds, Vavilova 28 S tree t, GSP1, V -3 3 4 , 1 1 7 8 1 3 M oscow , Russia. Keywords: Cellulose I, molecular mechanics, crystal structure, phase change, modelling Abstract Energies for various trial packing arrangements of unit cells for the I a and \ß phases of native cellulose discovered by Sugiyama et al. were evaluated. Both a rigid-ring method, PLMR, and the full- optimization, molecular mechanics program, MM3(90) were used. For both phases, the models that had lowest PLMR energy also had the lowest MM3 energy. Both have the chains packed "up", 0-6 's in tg positions, and the same sheets of hydrogen bonded chains. The \ß structure is essentially identical to the structure proposed previously for ramie cellulose by Woodcock and Sarko. It is also the same as the best parallel model previously proposed that was based on the X-ray data of Mann, Gonzalez and Wellard, once the various unit cell conventions are considered. Also, the energies from both methods for all three celluloses, la, \ß and II are in the order that rationalizes their relative stabilities. Introduction The tw o main forms of cellulose are I, the major native type, and II, which occurs after mercerization or regeneration. A proposal for the solid-state conversion from I into cellulose II, including different intermediates, is described elsewhere (Nishimura et al., 1991, Nishimura and Sarko, 1991) Some years ago, it was discovered (VanderHart and Atalla, 1984, Atalla and VanderHart, 1984) that native cellulose occurs mostly as combinations of the tw o phases, la and \ß. Depending on the sample, these phases are in different ratios. For example, the ratio \al\ß was estimated to be 65% /35% for Valonia cellulose (VanderHart and Atalla, 1984). Initially, electron diffraction patterns from this mixture were indexed based on an 8-chain unit cell (Honjo and Watanabe, 1958). More recently, however, electron diffraction from small selected areas of the same microfibril showed tw o patterns that were interpreted (Sugiyama et al., 1991) to have, respectively, one-chain, triclinic and two-chain monoclinic unit cells. One of the most important conclusions from the finding of a 1-chain unit cell is that the chains must have a parallel orientation, i.e. the reducing ends of the cellulose molecules must all be at the same end in a given microfibril. Because both phases are found within the same microfibril in that work, the conclusion of parallel packing for \ß is almost inescapable. Several decades ago, Ränby (1952) showed that cellulose II is slightly more stable than cellulose I, by about 2 cal/gram or 0.3 kcal/mol of glucose residues. Because hydrothermal annealing converts mixtures of la and \ß into pure \ß (Horii et al., 1987), it is thought that \ß is more stable than la. As X-ray diffraction intensity data for the pure phases of native cellulose are yet not available, it is reasonable to propose structures based on energy calculations. This was especially so for I a, because of the limited number of variables that must be considered for a 1-chain model, and our preliminary results for I a were already published (Aabloo and French, in press). In the present work we have studied various possible model structures for the I a and \ß celluloses, based on the published unit cell dimensions and on calculated packing energy. These results are then compared w ith other work. Methods. All of our computer models consisted of parallel chains and were based on published unit cell dimensions (Sugiyama et al., 1991). For I a, a = 6.74 Ä, b = 5.93 Л, с = 10.36 Ä, a = 1 1 7 ° , /3=113° and к= 8 1 °, and for I/?, a = 8.01 Ä, b = 8 .17Ä, c= 10.36Ä, o = 90 °, 0 = 90° and к = 9 7 .3 ° . Space group P1 was used for the I a form, and the cellulose \ß chain models conformed to space group P2,. We used tw o different methods to calculate packing energies, PLMR and MM3. The PLMR (derived from a word polymer) program, described by Pertsin et al. (1984) and Pertsin and Kitaigorodsky (1987), uses a "rigid-ring" strategy. In PLMR models of the cellulose chains, most of the intraresidue parameters of the glucose rings are kept at average values reported by Arnott and Scott (1972). Only the exocyclic torsion angles r, (see Fig. 1) that locate the hydroxymethyl and three hydroxyl groups were varied. The chains were free to rotate about their axes in the unit cell. The angles , describe those rotations. They are defined as the angles formed by vectors A (see Fig. 2) and projection of the unit cell axes a' =a*cos(K-tf/2). For I a, the torsion angles and bond angles at the glycosidic linkages were allowed to vary. For I/?, the monomer residues were linked to form the chain w ith the variable virtual bond method (Zugenmaier and Sarko, 1980). Keeping 2, symmetry requires an additional parameter that characterizes the chain conformation (see Fig. 2). The angle 6 describes rotation of the monomer residue about the 0 4 -0 4 ' virtual bond. It is defined by three vectors A, fJ, and v. The vector A is perpendicular to the с-axis, и is along the 04-C4 bond, and v is along the 0 4 - 0 4 ’ virtual bond. The angle 6 is the dihedral angle between the plane f/v and the plane vA. In the variable virtual bond method, the conformational parameters at the junction of tw o successive residues are not independent variables, but are implicit functions of h (the rise per monomer along the c-axis), 6 and the residue conformation. For the two-chain unit cell, one more parameter, s, characterizes the vertical shift, or stagger, of the central chain. In all, there were 1 2 independent variables to be minimized for I a and 13 for I/?. One binary variable parameter defines the chain direction as "up" or "dow n". A chain is "up" if the z coordinate of 0-5 is greater than the z-coordinate of C-5. The PLMR potential energy U includes the intramonomer energy, junction energy, and intermolecular energy: U = Umon+ U,unc,+ Uinttr in which Umi)n includes the torsional and nonbonded contributions from dihedral angles and nonbonded contacts that are influenced by variation of the monomer parameters r . Briefly, U|unc, includes contributions from the bending of the glycosidic bond angle, from the torsional angles at the junction and from non-bonded contacts between two successive residues. U,nte, includes nonbonded interactions between the atoms belonging to different chains, consisting of hydrogen bonding and van der Waals terms. Previously published formulas and the values of parameters are used to calculate bond angle energies (Pertsin and Kitaigordsky, 1987). A Morse-like equation is used for hydrogen bond modelling and a 6th order exponential potential function is used for van der Waals calculations (Pertsin and Kitaigordsky, 1987). As PLMR uses continuous chains, no electrostatic interactions were considered Calculations were executed in internal coordinates. PLMR uses periodic boundary conditions to calculate the interchain energies. Model cellulose crystals for the MM3(90) (Allinger et al., 1989, Allinger et al., 1990) molecular mechanics calculations were built of seven cellotetraose molecules which represented the very long cellulose chain molecules. They were placed in a manner similar to hexagonal close packing, but conformed to the unit cell dimensions. Terminating 0-4 and 0 -1 ” ' hydrogens were moved manually to positions that gave low energy. The dielectric constant was 4.0, a value used for crystalline amides, polypeptides and proteins (Lii and Allinger, 1991). Starting structures in the MM3 calculations were taken from the best models from the PLMR process. The model crystals were optimized w ith MM3(90) w ith no restrictions such as unit cell dimensions or space group. All atoms were allowed to seek positions of minimum energy. The MM3 minimization process should be more valid than rigid-residue calculations because the molecule can relax and adapt to the local environment. Also, the energies calculated by MM3 are likely to be fairly accurate; the standard deviation in calculated heat of formation for 40 isolated alcohols and ethers was 0.38 kcal/mol, although energies for the minicrystals may be less accurate. On the other hand, MM3 takes considerable computer time to optimize a miniature crystal. PLMR rapidly scanned hundreds of trial structures and maintained the unit cell dimensions precisely. Using these two minimization processes we got most probable models for both crystalline phases of cellulose. To learn the differences between the structures determined by PLMR and by MM3, we computed mean atomic movement using a routine in CHEM-X, developed and distributed by Chemical Design, Ltd, Oxford, U. K. These atomic movements were calculated w ith the hydrogen atoms included and excluded. The mean atomic movement indicates the degree of stability of the PLMR models in the MM3 force field. Some lattice expansion in the miniature crystal models is expected, because they are small, and do not fully account for long-range forces present in the somewhat larger actual microfibrils. However, the movements for the best cellulose models are somewhat smaller than computed for fully optimized similar models of small carbohydrate molecules (about O .lk ) . This is because the averaged molecular geometries in the PLMR starting models are not changad as much by MM3 optimization as are structures determined individually by diffraction methods. Also, the crystals of the small molecules are much larger than cellulose microfibrils, and their long range forces result in slightly greater lattice compression. The starting models for PLMR were developed with Tartu space filling models (Mikelsaar, 1986) and computer graphics modeling. To avoid missing some reasonable energy minima we built several models in the regions of conformational space where we found structures having low energies. We also tried many models in other regions. The initial sets of starting models consisted of about five hundred models. "Up" and "down" starting models were constructed independently for both polymorphs la and I/?. Results and discussion Cellulose la The models having the six lowest PLMR energies for Iff are presented in Table 1. The best model, U„1, has an energy of -19.5 kcal/mol of cellobiose residues and is packed "up". The energy value can be compared w ith the value of -21.4 kcal/mol for a model of cellulose II calculated w ith same method (Pertsin et al., 1984). The best "dow n” model has an energy of -16.8 kcal/mol and is in second place. All six models have 0-6 in the tg conformation. The best gg model had an energy of -14.1 kcal/mol and the best gt mode! had an energy of -12.3 kcal/mol. The hydrogen bonds of these six models are listed in Table 3. The gg and gt models had very complicated hydrogen bonding systems. The structures having the lowest PLMR energies were then minimized using MM3. The best model, U01, kept its leading position, but some other models changed places (Table 3). Table 3 also presents mean atomic movements. The structure U„1 preserves its conformation after MM3 minimization. Its MM3 energy is 185 kcal/mol for the assembly of 28 glucose residues. The structures U„3 and Ua4 were not stable in the MM3 force field, but were trapped during PLMR minimization because of the use of rigid residues. These models optimized to structures similar to U01 in the MM3 calculations. The coordinates of atoms in the PLMR-minimized la structure are in Table 4. Cellulose Iß The models w ith the seven lowest PLMR energies for \ß are shown in Table 2. The best model, U ^ l, has an energy of -19.9 kcal/mol. It is packed "up", and has 0-6 in tg positions. The best gg and gt models had energies higher than -12 kcal/mol. Model \Jß2 has the same hydrogen bonding scheme (Table 3) and chain conformation as U#1, and differs only in the shift of the central chain. The results of minimizing these seven structures with MM3 are shown in Table 3. As with the la studies, the model best by PLMR calculations also gave the lowest MM3 energy for \ß, 182 kcal/mol. This was slightly lower than for the la model and slightly higher than for cellulose II. Also shown are the mean atomic movements. It seems that models U#2, Ц,3 and U#4 were trapped in local minima in the PLMR calculations. Structures U„2 and Ц 4 had high movements of oxygen atoms during MM3 minimizations. Thus, those PLMR structures were substantially disrupted by MM3 optimization. As in the PLMR work on la, the U3 structure did not have any intersheet hydrogen bonds. MM3 minimization did result in such hydrogen bonds for the U3 model, showing that these structures were caught in local minima in the PLMR studies and are not really stable. Structure U„6 also formed new, intersheet hydrogen bonds during MM3 minimization. Structure U„1 is essentially identical to the structure proposed by Woodcock and Sarko for ramie cellulose I on the basis of X-ray fiber diffraction data and the limited force field incorporated in the PS-79 software (Woodcock and Sarko, 1980). Our previously published (French et al., 1993) value of 201 kcal/mol for the MM3 energy of their structure is in error because our model was inadvertently an incorrect representative of their structure. In our incorrect model, the central chain was translated in the opposite direction, causing the high energy. The U#1 structure is also the same as the best parallel model proposed (Pertsin et al., 1986) based on the PLMR program and the fiber diffraction data of Mann et al., (1958), once adjustments are made for the differences in unit cell conventions (French and Howley, 1989). The coordinates of atoms in the PLMR model of \ß are in Table 5. Despite the difficulties w ith the application of M M 3to miniature crystals of cellulose that were documented in earlier (French et al., 1993), both minimization procedures agreed on the most probable structures for I a and \ß cellulose, models U„1 and U#1. PLMR energies for cellulose I a, \ß and II were -19.5, -19.9 and -21.4 (Pertsin et al.,1984) kcal/mol of cellobiose units. MM3(90) energies for the same series were 185, 182 and 181 kcal for the 7-chain minicrystals. (To obtain 181 kcal/mol for II, both model structures of cellulose II must be averaged, i.e., the model composed of four up gt chains and three down tg chains must be balanced by the model with four up tg chains and three down g t chains.) These trends of relative energies agree well with experiment. The energies of both phases of cellulose I are slightly higher than the energy of cellulose II, as expected from Ränby's experimental difference of 0.6 kcal/mol of cellobiose units. The energies of la and I/? are very close. This may explain why these celluloses coexist in a single microfibril. Both models have the same hydrogen bonding schemes. The conversion from la to \ß may take place by a vertical shifting of sheets. During a modeled shift of sheets, w ithout change in the lateral dimensions of the unit cell, PLMR calculations gave a barrier of 9 kcal/mol. Fully optimized structures with annealing conditions would probably give a barrier w ith lower energy. The finding of the same hydrogen bonds in both systems conflicts w ith the conclusions of Wiley and Atalla (1987), who found that the hydrogen bonds must change during conversion from la to I/?. However, O-H stretching frequencies are easily affected by very small structural differences, and the Wiley-Atalia results may not indicate important differences in the hydrogen bonding schemes.lt is remarkable that the structures of \ß cellulose obtained by three different methods agree so well. The unit cells varied by 0.23 Ä in the x-axis direction, as well as smaller differences in the other dimensions, and the energy functions differed substantially among the PS-79, PLMR and MM3 methods. Finally, the models in the earlier studies/ were affected by fiber diffraction intensity data, known to have low reliability (French et al., 1987), while the unit cell dimensions were the only experimental data in the present calculations. The packing energies of both phases of cellulose I and of cellulose II are all very close, and the errors in the minicrystal modeling calculations are unknown. Since fiber diffraction methods depend on modeling studies for discrimination between alternative models, conclusive results will be difficult to obtain, even when diffraction intensities are available. Conclusions Available experimental diffraction and calorimetric data for cellulose I and II have been rationalized by computer models. Because the predicted energies were in qualitative agreement with experimental values, and because the structure predicted for cellulose \ß matched tw o based on fiber diffraction data, the method herein appears to be worth further development. According to these calculations, cellulose la and \ß are each at local minima and thus metastable. References A. Aabloo and A. D. French, Preliminary potential energy calculations of cellulose I a crystal structure, Macromolek. Chem., Theory and Simulations, in press. N. L. Allinger, Y. H. Yuh and J.-H. Lii, Molecular Mechanics. The MM3 Force Field fo r Hydrocarbons. J. Amer. Chem. Soc. 111, 8551-8566 (1989) N. L. Allinger, M. Rahman and J.-H. Lii, A molecular mechanics force field (MM3) for alcohols and ethers. J. Amer.Chem. Soc. 112, 8293-8307 (1990) S. Arnott and W. E. Scott, Accurate X-ray diffraction analysis of fibrous polysaccharides containing pyranose rings. Part I. The linked-atom approach, J. Chem Soc Perkin II, 324 (1972) R. H. Atalla and D. L. VanderHart, Native cellulose: a composite of tw o distinct crystalline forms, Science 223, 283 (1984) A. D. French and P. S. Howley, Comparisons of structures proposed for cellulose. Cellulose and Wood - Chemistry and Technology, C. Schuerch, ed., John Wiley & Sons, New York, p. 159-167, 1989 A. D. French, D. P. Miller and A. Aabloo, Miniature crystal models of cellulose polymorphs and other carbohydrates, Int. J. Biol. MacromoLAb, 1993, 30-36. A. D. French, W. A. Roughead and D. P. Miller, X-ray diffraction studies of ramie cellulose I. ACS Symposium Series 340, 15-37 (1987) G. Honjo and M. Watanabe, Examination of cellulose fibers by the low-temperature specimen method of electron diffraction and electron microscopy. Nature 181, 326-328 (1958) F. Horii, H. Yamamoto, R. Kitamura, M. Tanahashi and T. Higuchi, Transformation of native cellulose crystals induced by saturated steam at high temperatures. Macromolecules 20, 2946-2949 (1987) J. H. Lii and N. L. Allinger, The MM3 force field for amides, polypeptides and proteins, J. Comput. Chem. 12, 186-199 (1991) J. Mann, L. Roldan-Gonzalez and H. J. Wellard, Crystalline modifications of cellulose. Part IV. Determination of X-ray intensity data. J. Polym. Sei., 47, 165-171 (1960) R. - H. Mikelsaar, New space-filling atomic-molecular models, Trends in Biotechnology 4, 162-163 (1986) H. Nishimura, T. Okano and A. Sarko, Mercerization of cellulose. 5. Crystal and molecular structure of Na-cellulose I. Macromolecules 24, 759-770 (1991) H. Nishimura and A. Sarko, Mercerization of cellulose. 6. Crystal and molecular structure of Na- cellulose IV. Macromolecules 24, 771-778 (1991) A. J. Pertsin. A. I. Kitaigorodsky, " The Atom-Atom Potential Method Applications to Organic Molecular Solids”, Springer Ser. Chem Phys., V43, Springer Verlag, Berlin, 1987 A. J. Pertsin, A. I. Kitaigorodsky and G. N. Marchenko, Crystal structure of cellulose polymorphs by potential energy calculations: 2. Regenerated and native celluloses. Polymer 27, 597-601 (1986) A. J. Pertsin, O. K. Nugmanov, G. N. Marchenko, A. I. Kitaigorodsky, Crystal structure of cellulose polymorphs by potential energy calculations: 1. Most probable models for mercerized cellulose. Polymer 25, 107-114 (1984) B. G. Ränby, The mercerization of cellulose. I. A thermodynamic discussion. Acta Chem. Scand. 6, 101-115 (1952) J. Sugiyama, R. Vuong and H. Chanzy, Electron diffraction study on the two crystalline phases occurring in native cellulose from an algal cell wall. Macromolecules 24, 4168-4175 (1991) D. L. VanderHart and R. H. Atalla, Studies of microstructure in native celluloses using solid state l3C NMR. Macromolecules 17, 1465-1472 (1984) J. H. Wiley and R. H. Atalla, Raman spectra of celluloses, /4CS Symposium Series 340, 151-168 (1987) C. Woodcock and A. Sarko, Packing analysis of carbohydrates and polysaccharides. 11. Molecular and crystal structure of native ramie cellulose. Macromolecules 13, 1183 (1980) P. Zugenmaier and A. Sarko, The variable virtual bond, ACS Symposium Series 141, 226-237 (1980). Table 1. Most probable PLMR models of cellulose la U - "up" models; D - "down" models; r, = C4-C5-C6-06; r 2 = C5-C6-06-H ;r3 = C1-C2-02-H; r 4 = C2-C3-03-H; r 5 = C4 '-C 5 '-C 6'-06 '; re = C 5 '-C 6 '-06 '-H '; r 7 = C 1 '-C 2 '-02 '-H '; r 8 = C2 '-C 3'-03 '-H '; 0, = C1-04'-C4'; 02 = 05-C1-01-C 4'; 0 3 = C1-01-C4'-C5'; ( - angle describing chain rotation. Energy г, r2 T3 r„ . f , r b T, г, г. ( kcal/mol U.1 -1 9 .5 -71 116 52 -175 118 -93 -1 4 6 73 -1 6 6 52 -175 77 D.1 -1 в .8 -59 166 53 -168 117 -87 -143 7 4 -1 6 3 53 -1 7 0 1 1в.З -вэ 61 164 -168 119 -92 -148 -72 63 170 -171 72 и.э • 1в.2 -68 102 56 -161 115 -94 -147 69 102 56 -161 78 и.* -1 5 .7 6 4 -во 79 -177 116 -95 -1 4 6 -66 -57 79 -1 7 7 79 U .6 -1 5 .0 69 34 54 -72 116 -94 -1 4 6 -71 -35 5 4 -72 78 Table 2. Most probable PLMR models of cellulose \ß Variables: r 11( r 12 = C4-C5-C6-06 for a corner and a central chain;r21, r 22 = C5- C6-06-H for a corner and a central chain;r31, r 32 = C1-C2-02-H for a corner and a central chain; r41, r 42 = C2-C3-03-H for a corner and a central chain; w 0 2 = angles describing the chain rotation; S2 = angles describing a virtual bond rotation; s = a verical shift of a central chain (unit = 1 / 1 Oc). Е г„ г „ г„ тп гзг U i V, * 7 S kcal/mol U,1 19 .9 -71 -1 6 6 52 -175 -71 -166 52 -1 7 5 42 42 -127 -1 2 6 -2 .7 U ,2 -1 9 .0 67 160 61 162 68 160 60 161 4 4 4 4 -1 2 2 -1 2 6 2 .6 U ,3 -1 8 .7 -68 -67 62 -178 -70 63 60 -1 7 6 44 44 -1 1 6 -1 3 5 3.4 11,4 -1 7 .8 67 64 61 163 69 62 60 163 43 43 -1 1 6 136 3.3 U ,5 16 .6 -63 56 61 59 68 61 60 -61 46 43 -1 2 0 -1 3 0 3.1 и ,в -1 6 .4 72 60 -160 180 -72 67 -149 -1 7 6 41 42 -1 2 5 -1 2 4 2.6 U,7 -16.1 -72 58 -1 7 2 61 -72 60 -167 -65 40 42 -1 2 5 -1 2 4 2.7 Table 3. Most probable models of cellulose I a and \ß. U__- “ up" models; D___- "down" models; e - models of phase la; ß - models of phase \ß. Energy kcal/mol Mean atom movement H-bonds in chain H-bonds in H-bonds Model sheet found by PLMR M M 3 with without ММЗ H's H's •я -19.5 186 .175 .106 05..H 03 06 H02 оз.. нов D,1 'а 16.8 206 .158 .108 0 5 ..H 0 3 0 6 ..H 0 2 0 3 . нов U.2 19 16.3 222 .178 .148 0 5 ..H 0 3 0 2 ;0 2 ..H 0 6 и.з 'д 16 .2 218 .177 .092 0 5 ..H 0 3 0 6 ..H 0 2 0 3 ..Н 0 6 U.4 'а 15.7 215 .193 .098 0 5 ..H 0 3 0 6 ..H 0 2 0 3 ..Н 0 6 U.5 >а 15 .0 234 .056 .035 0 6 ..H 0 2 0 6 . .НОЗ 4-1 V -19.9 182 .187 .167 06 .H03 06..H 02 оз.нов U,2 'в -1 9 .0 185 .186 .153 0 5 ..H 0 3 0 6 ..H 0 2 0 3 . .нов и , 3 'а 18.7 200 .176 .140 0 5 ..H 0 3 0 6 ..H 0 2 'в 17.8 196 .185 .143 0 5 ..H 0 3 0 6 ..H 0 2 U ,5 ta 16.6 212 .201 .177 0 6 ..H 0 2 0 6 . .НОЗ и,в ta 16 .4 200 .267 .234 0 5 ..H 0 3 0 2 ;0 4 ..H 0 6 0 6 ..Н 0 2 VP ta 16.1 207 .254 .199 0 2 ;0 4 ..H 0 6 0 6 . НОЗ Table 4. Cartesian coordinates (Ä) of the best model (U01) of the cellulose la crystal. Name X Y Z Name X Y Z 1 02 . 183 , 809 . 000 22 0 2 ' - 1 . . 708 1.. 162 , 281 2 03 , 3 0 0 . 072 1 . 171 23 0 3 ' . 288 , 065 6 .. 338 3 04 . 86 0 . 976 2 ., 2 61 24 0 4 ' . 88 8 , 949 7 ., 424 4 05 . 928 . 267 3 ., 508 25 0 5 ' 945 . 2 3 5 8 .. 668 5 06 . 3 6 4 . 141 3 .. 965 26 0 6 ' . 354 . 133 9 .. 137 6 C l . 968 1.. 114 2 .. 961 27 C l ' 1.. 000 - 1 , . 083 8 .. 138 7 С2 - 1 , . 049 . 475 1,. 581 28 С2 ' 1.. 074 . 43 9 6 .. 7 60 8 СЗ 2 . 2 6 1 - -1 ., 462 1,. 955 29 C3 ' - 2 .. 3 0 0 1.. 390 7 .. 104 9 C4 . 183 . 809 5.. 169 30 C4 ' 2 ., 301 - 1 . . 44 1 8 .. 600 10 C5 - 2 . 2 6 2 1.. 512 3 .. 41 1 31 C5 ' 1.. 595 - 1 . 3 7 6 5 .. 820 11 C6 - 1 ,. 530 1 ., 43 1 . 639 32 C6 ' . 933 . 784 6 .. 167 12 HI . 973 . 757 1.. 010 33 H I ' . 281 1 ., 8 3 5 7 ,, 544 13 H2 . 2 2 4 - 1 , . 842 n . 373 34 H2 ' . 96 4 , 7 5 2 9 .. 239 14 H3 - 1 . 003 . 724 4 . 059 35 H3 ' . 421 - 1 . , 993 8 .. 080 15 H4 . 3 6 0 2 .. 005 2 . 91 1 36 H 4 ' 1,. 7 1 8 ,427 6 ., 801 16 H5 - 1 . 7 2 1 . 3 7 0 1 .. 613 37 H 5 ' - 2 . 3 2 6 2 .. 3 7 9 6 ., 077 17 H61 2 ,. 2 7 2 - 2 ., 40 8 . 888 38 H 6 1 ' - 2 .. 884 . 535 6 .. 7 9 6 18 H62 2 .. 8 86 . 620 1 ,. 696 39 H62 ' - 2 .. 765 1 ., 7 8 4 7. , 996 19 H02 2 . 688 - -1 ., 91 1 2 . 83 9 40 H02 ' - 3 . 137 2 .. 898 5. . 921 20 H03 3 ,. 065 - 2 ., 952 . 726 41 H03 ' 2 .. 4 1 9 - 1 .. 7 86 9 ,, 504 21 H06 - 2 ,. 378 1 ., 860 4 . 31 5 42 H06 ' 1 , 770 - 1 ., 100 4 .. 902 Figur« 1. Th« vanabte angle;» of ce'lMo.«* unit PLMR Table 5. Carthesian coordinates (Ä)of the best model (U^D of cellulose \ß crystal. Name x у z Name x у z C o r n e r C h a i n C e n t r a l c h a i n 1 02 .339 2. . 694 3. 434 1 02 3. 573 6. , 262 685 2 03 . 084 2. , 107 658 2 03 4. 009 5. . 684 - 2 . 091 3 04 .487 , 651 000 3 04 3. 500 2. . 915 - 2 . 750 4 05 . 403 . 882 3. , 508 4 05 4. , 396 2 .. 703 759 5 06 . 326 - 3 . , 280 , 867 5 06 3. 718 . 289 - 1 . 882 6 Cl . 134 . 358 3. , 972 6 Cl 3. 831 3. . 931 1 . 223 7 C2 . 208 1.. 459 2 .. 977 7 C2 4. ,147 5.. 039 . 227 8 C3 . 325 1.. 111 1., 593 8 C3 3. 622 4. . 679 - 1 . 156 9 C4 . 145 , 264 1.. 175 9 C4 4. 123 3.. 3 15 - 1 . 574 10 C5 . 174 - 1 . . 287 2. , 257 10 C5 3. , 827 2. . 286 492 11 C6 . 3 7 6 - 2 . , 662 1.. 943 11 C6 4 ., 408 . 923 807 12 HI - 1 . . 207 , 274 4. . 063 12 HI 2. , 760 3.. 823 1.. 314 13 H2 1.. 2 7 9 1,. 582 2. . 930 13 H2 5.. 216 5.. 187 , 180 14 H3 - 1 , . 404 1., 066 1., 623 14 H3 2. ,545 4. . 61 0 - 1 . . 126 15 H4 1.. 213 , 230 1.. 016 15 H4 5 .. 190 3.. 374 - 1 . , 734 16 H5 - 1 , . 245 - 1 . . 374 2. . 366 16 H5 2 .. 758 2. . 175 . 383 17 H61 1,. 4 2 3 - 2 . . 582 1.. 691 17 H61 5.. 453 1.. 027 - 1 . , 060 18 H62 . 3 1 0 - 3 . . 286 2, . 822 18 H62 4. . 358 . 29 8 . 072 19 H02 . 152 3.. 005 4. . 339 19 H02 3. . 753 6.. 576 1.. 590 20 НОЗ . 233 2.. 071 . 263 20 НОЗ 3.. 693 5.. 641 - 3 .. 012 21 H06 . 2 1 9 - 4 . . 234 . 699 21 H06 3,. 847 . 663 - 2 .. 0 50 22 02 ' . 3 3 9 - 2 . . 694 8. . 614 22 02 ' 4 ., 372 . 891 5.. 865 23 03 • . 0 8 4 - 2 , . 107 5 .. 838 23 03 ' 3. . 936 1,. 468 3 .. 089 24 0 4 ' . 487 . 651 5.. 180 24 04 ' 4.. 445 4. . 2 37 2 .. 4 30 25 05 ' . 4 0 3 . 882 8. . 688 25 05 ' 3.. 549 4, . 44 9 5,. 939 26 0 6 ' . 3 2 6 3.. 28 0 6.. 047 26 06 ' 4. . 227 6,. 863 3.. 298 27 Cl ’ . 134 . 358 9,. 152 27 C l ' 4. . 114 3.. 2 21 6.. 403 28 C2 ' . 2 0 8 - 1 . . 459 8. . 157 28 C2 ' 3., 798 2. . 11 3 5.. 407 29 C3 ' . 3 2 5 - 1 . . 111 6.. 773 29 C3 ' 4. , 323 2,. 4 73 4. . 0 24 30 C 4 ' . 145 . 264 6.. 355 30 C 4 ' 3.. 822 3.. 837 3.. 6 06 31 C5 ' . 174 1,. 287 7 ,. 437 31 C5 ' 4.. 1 1 8 4.. 867 4. . 688 32 C6 ' . 3 7 6 2 . 662 7.. 123 32 C6 ' 3. . 537 6,. 22 9 4, . 373 33 HI ' 1.. 2 0 7 . 274 9.. 243 33 H I ' 5,. 185 3,. 329 6,. 494 34 H2 ' - 1 . .2 7 9 - 1 , . 582 8.. 110 34 H2 ' 2 .. 729 1,. 9 6 6 5 ,. 360 35 H3 ' 1,. 4 0 4 - 1 . . 066 6.. 803 35 H3 ' 5., 400 2 ,. 542 4 ,. 054 36 H4 ' - 1 , . 2 1 3 . 230 6.. 196 36 H4 ' 2 ,. 755 3.. 7 7 8 3 ,. 4 46 37 H5 ' 1,. 245 1,. 374 7,. 546 37 H5 ' 5.. 187 4,. 97 8 4. . 797 38 H 6 1 ' - 1 ,. 4 2 3 2.. 582 6.. 871 38 H 6 1 ' 2.. 492 6,. 125 4 , 120 39 H62 ' . 3 1 0 3,. 286 8,. 002 39 H62 ' 3.. 587 6.. 8 54 5,. 252 40 H02 ' . 152 - 3 , . 005 9,. 519 40 H02 ' 4.. 192 . 57 6 6,. 77 0 41 НОЗ' . 2 3 3 - 2 , . 071 4.. 917 41 НОЗ' 4. . 252 1.. 511 2 , 168 42 H06 ' . 2 1 9 4.. 234 5.. 879 42 H06 ' 4.. 098 7.. 8 15 3. . 130 PARALLEL AND ANTIPARALLEL MODELS FOR CRYSTALLINE PHASES OF NATIVE CELLULOSE Parallel and antiparallel models of cellulose Raik-Hiio Mikelsaar' Institute of General and Molecular Pathology, Tartu University, Veski Street 34, Tartu EE2400, Estonia; Alvo Aabloo Institute of Experimental Physics and Technology, Tartu University, Tähe Street 4, Tartu EE2400, Estonia. ABSTRACT Tartu plastic space-filling atomic-molecular models were used to investigate the structure of cellulose do and \ß) phases. It was elucidated that both parallel and antiparallel structures can be accommodated with unit cell geometries described by Sugiyama et al. (1991). Packing energy calculations revealed that parallel models of I a and \ß phases have very close energy. In contrast, in case of antiparallel structure models, lyJis energetically much more favourable in comparison w ith I a phase. Our data indicate that antiparallel structure proposed for cellulose la phase is metastable and should be easily converted to \ß phase. So the antiparallel models are more suitable for explanation of cellulose lo-H£-HI interconversion. Keywords, cellulose molecular and crystalline structure, molecular modelling by plastic atomic models, packing energy calculations. INTRODUCTION Native cellulose I is a wide-spread biopolymer which, through either mercerization or regeneration, can be converted irreversibly into another form - cellulose II. It is generally accepted that both mercerized and regenerated cellulose II have nearly identical crystal structures w ith two-chain unit cells (Stipanovic and Sarko, 1976; Kolpak and Blackwell, 1976; Kolpak era/., 1978; Pertsin et al., 1984; Nishimura era/., 1991; Nishimura and Sarko, 1991). In contrast, IR-spectroscopy, X-ray, electron diffraction and NMR methods revealed that cellulose I occurs in tw o forms; type IA (algal-bacterial) cellulose and type IB (ramie-cotton) cellulose (Marrinan and Mann, 1956; Honjo and Watanabe, 1958; Fisher and Mann, 1960; Hebert, 1985; Horii era/., 1987a). On 1984 by NMR investigations it was elucidated that both forms are a mixture of tw o crystalline phases (a and ß) which proportion depends on the source of cellulose (Atalla and VanderHart. 1984; VanderHart and Atalla, 1984). Also w ith NMR spectroscopy Horii et al. (1987b) showed that the lo phase of cellulose is metastable and, through a hydrothermal annealing treatment, can be converted readily into the thermodynamically stable \ß phase. Recently Sugiyama et al. (1991) studied cellulose from a green alga Microdictyon by electron diffraction. It was found that the major lo phase has a one- chain, triclinic (P1) structure and the minor \0 phase is characterized by two-chain unit cell and a munoclinic (P2,) structure. This study disclosed the unit cell parameters but did not present a detailed molecular structure of these native cellulose crystalline phases. The aim of the current paper was using molecular modelling method and packing energy calculations to elucidate the most favourable stereochemical structures corresponding to unit cell parameters found by Sugiyama et al. (1991) in cellulose la and I/S crystalline phases. MATERIAL AND METHODS Molecular modelling was carried out by Tartu plastic space filling models having improved parameters and design (Mikelsaar et al.. 1985; Mikelsaar 1986). Packing energy calculations were carried out by the PLMR program, a rigid-ring method (Pertsin et al., 1984). To present graphically the stereochemical models investigated, we drew unit cell projections on the plane crossing the с-axis at 90°. Cross-sections of up cellulose chains were given by white and down chains by grey ovals. The number of c/4 shifts of molecules in the direction of the с-axis is noted by numbers inside of the ovals. To make a short digital designation of the cellulose models: 1) symbols "P" and "A " were used to represent correspondingly "parallel" and "antiparallel", 2) numbers indicating c/4 shifts were applied for characterizing of each chain in the unit cell, 3) underlining was used to differentiate down chains from up chains. RESULTS 1. Molecular models fitting with cettulose la unit cell parameters 1.1. Model PI Fig. 1 The investigation of green alga Microdictyon by Sugiyama et at. (1991) is the first work where unit cell parameters are given for pure cellulose la microcrystals: a = 0 .674 nm, b = 0.593 nm, с = 1.036 nm, а = 117°, ß = 113° and у = 81 °. One-chain unit cells result in parallel packing of molecular chains. In Figure 1 there are our graphic presentations of above­ described one-chain unit cell and sterically corresponding two- and eight-chain cells on the plane crossing the с-axis at 90°. Molecular modelling by Tartu devices showed that if there are the usual intramolecular bonds 03 -H ...05 and 02 -H ...06 the hydroxymethyl groups should be in tg conformation and all parallel chains are bound by intrasheet bonds 06 -H ...03 (Fig. 2 and Fig.3). Fig. 2 Fig. 3 2 Packing energy calculations of the above-described cellulose structure imitation revealed that model P1 has potential energy -19.5 kcal/mol. 1.2. Models A 1a and A 1b Fig. 4 Fig. 5 Two antiparallel models A1a and A1b characterized by eight-chain unit cell may be geometrically derived from the one-chain unit cell described by Sugiyama et at. (1991) (Fig. 4 and 5). The geometry of these two models is very similar. The only difference is that in A1a parallel chains follow each other from down right to up left dividing major angles of unit cell and in A1b from down left to up right dividing minor angles of unit cell. So A1a may be called "le ft" and A1b "right" type of structures. Fig. 6 Fig. 7 According to molecular modelling data, chains having usual intramolecular H-bonds and tg conformation of hydroxymethyl groups should be in models A1a and A1b bound by intrasheet bonds 06 -H ...02 (Fig. 6 and 7). The potential energy values of above-described structures are rather similar: model A1a has - 16.4 kcal/mol and A1b - 15.5 kcal/mol. 2. Molecular models fitting with cellulose Iß unit cell parameters 2.1. Model P2 Sugiyama et al. (1991) have established that \ß phase of Microdictyon cellulose has a two-chain monoclinic structure with unit cell parameters of a = 0.801 nm, b = 0.817 nm, с = 1.036 nm and у = 97 .3°. The authors suppose that this structure consists of parallel molecules and the center and corner chains are staggered by c/4. Figure 8 shows our graphic presentation of above-mentioned structure. Fig. 8 Molecular modelling revealed that intra- and intermolecular H-bonds in model P2 are identical to those in model P1 (Fig. 2 and 3). The energy value of model P2 is close to the model P1 one: -19.9 kcal/mol. 2.2. Model A 2 A graphic presentation of the structure corresponding to model A2 is demonstrated in Figure 9. 3 Fig. 9 Molecular modelling showed that chain conformation and intrasheet H-bonding network in model A2 are identical to the model P2 one's.The only difference is that sheets are parallel in model P2 and antiparallel in model A2. Potential energy of model A2 is relatively high: - 15.8 kcal/mol. 2.3. Models A 3a and A3b Fig. 10 Fig. 11 Two antiparallel models A3a and A3b characterized by eight-chain unit cell may be geometrically derived from the two-chain unit cell described by Sugiyama et al. (1991) (Fig. 10 and 11). These structures are similar to the "left" and "right" models A1a and A1b differing mainly by the presence of intrasheet stagger of cellulose chains. Fig. 12 Fig. 13 The investigation by plastic models indicated that in case of the preservation of standard intramolecular H-bonds and tg conformation of hydroxymethyl groups the antiparallel molecular chains are bound by bonds 06 -H ...03 (Fig. 12 and 13). There is a considerable difference between energies of above-described tw o structures: the "le ft” type model A3a has -21.0 kcal/mol and "right" model A3b -15.1 kcal/mol. Table 1 A generalized characterization of above-described cellulose models is presented in Table 1. DISCUSSION Our investigation revealed that both parallel and antiparallel structure models can be proposed, based on cellulose la and \ß crystalline phase unit cell parameters published by Sugiyama era/. (1991). Although all they have usual chain conformation and intramolecular H- bonding network, the potential energy values between seemingly close structures in certain cases are very different. Sugiyama ef al. (1991) interpret their experimental data in the light of all-parallel- structure view. Following this view, the la phase structure should correspond to our model P1 and \ß phase to model P2. However, the conception of Sugiyama et al. (1991) meets many difficulties when one try to explain the molecular mechanisms of cellulose la-»l/?-»ll interconversion. First, if the structures of la and \ß phases correspond to the models P1 and P2, the only change after the process of \a-*\ß conversion will be a c/2 shift of each third and fourth molecular sheet. The intra- and intersheet distances between molecular chains should remain 4 unchanged. However the comparison of \ß phase two-chain unit cell parameters in the work of Sugiyama et al. (1991) w ith corresponding data derived by us from lo one-chain unit cell indicates that there are rather considerable differences: 1) unit cell of \ß phase: a = 0.801 nm, b = 0.817 nm, у = 97 .3°, and 2) corresponding unit cell derived from lo phase: a = 0.814 nm, b = 0.825 nm, у - 99 .2°. Second, if the only rearrangement in the lo-H/3 conversion was a c/2 shift of chains, the H-bonding network in the cellulose structure must remain unchanged. However, Raman spectroscopic data reveal that H-bonds in lo phase cellulose are different from those of \ß (Atalla, 1989). Third, if there only c/2 shift of chains occurs and sheets are bound only by weak VanderWaals' interactions, the energy barrier between molecular structures of lo and \ß phases should be very small. It would be expected that cellulose I crystallites contain equai amounts of both phases. However, lo dominates in IA and \ß in IB celluloses. Fourth, because annealing of cellulose lo converts it irreversibly to \ß, the energy of stable \ß should be considerably lower than the metastable lo energy. However, the packing energy difference between P1 and P2 models is very small. Fifth, cellulose II is generally considered to have antiparallel molecular structure. Sarko eta l. (1987) and Nishimura et al. (1991) established that already Na-cellulose I, formed during the initial step of a controlled mercerization of ramie cellulose, has antiparallel-chain structure. Because the change of chain direction in this phase is not possible, it would be very difficult to imagine how an antiparallel structure could arise from the parallel one. It is true that antiparallel structure of cellulose II can arise through a process of "interdigitation” (see French, 1985) and energy minimization procedure reveal a possibility of parallel chain packing in cellulose II (Sakthivel et al. , 1988), but these arguments seem to be not very convincing. In our opinion the molecular mechanisms of cellulose lo-»l/?-»ll interconversion can be easier explained in the light of antiparallel structure models. Comparing cellulose parallel model P1 with antiparallel models A1a and A1b one can see that these models are sterically very similar. If the H-bonding network and chain polarity are not clearly established, the structure characterized by eight-chain unit ceil can be considered as structure of one-chain unit cell. We think that antiparallel model A la having lower energy (-1 6.4 kcal/mol) in comparison with the model A1 b (-15.5 kcal/mol) is a possible pretender for a "masked" eight-chain unit cell in the cellulose lo crystal structure described by Sugiyama et al. (1991). It may be that the experimental procedure of electron diffraction in above-mentioned investigation allowed to record only the parameters of subunits of eight-chain unit celis. The antiparallel structure is not excluded also for cellulose \ß crystalline phase because these authors marked that the exact position of the cellulose chains in the monoclinic unit cell was even more difficult to ascertain as long as the structure refinemant was not achieved. No doubt, A3a is the best antiparallel model for fitting to the unit cell structure of \ß 5 crystalline phase because it has an excellent packing energy: -21.0 kcal/mol. For both A1 and A3 models, the "left type” structures A1a and A3a have lower energy than the "right type" A1b and A3b models. If the "left type" antiparallel models A1a and A3a are thought to be the candidates for structures of cellulose lo and \ß crystalline phases, correspondingly, it would be easy to explain the experimental data on the interconversion of these phases. Model A1a, having relatively high energy -16.4 kcal/mol, is metastable and can during annealing process easily to be converted irreversibly into the model A3a, having very low energy -21.0 kcal/mol. Because the models A la and A3a have different H-bonding network, our conception on antiparallel cellulose structure is in accordance also with Raman-spectroscopic data of Atalla (1989). The high energy barrier between lo and \ß crystalline phases, bound w ith rearrangement of hydrogen bonds, may be the reason why the proportion of these phases in different samples of native cellulose is relatively constant. The notable structural differences between models A1a and A3a allow one also to understand the differences between corresponding unit cell parameters of I a and I/? cellulose crystalline phases. The order of chain rearrangements in the transformation of models A1a-*A3a, probably corresponding to the cellulose Ia-Aß phase conversion, seems to be simple. A fter the interruption in model A1a of intrasheet bonds 02 -H ...06 the alternate sheets of parallel chains must move one step diagonally in the plane of these sheets and new intrasheet bonds ОЗ- H ...0 6 characteristic of model A3a should be formed. The process of cellulose U?~»ll conversion can be also easily interpreted by all-antiparallel conception. Because already Na-cellulose I, formed in the initial step of mercerization, has antiparallel structure (Sarko et al., 1987; Nishimura et al., 1991), no change of chain direction is needed. The conversion from the structure corresponding to model A3a to Na-cellulose I may contain following steps: 1) interruption of intrasheet H-bonds, 2) including of Na+ and OH ions and water molecules, 3) forming of a large four-chain unit cell. The intersheet hydrogen bonding found in cellulose II is one of the most significant differences between this structure and the native cellulose and may be the reason of irreversibility of cellulose l-HI conversion (Kolpak et a/.. 1978) In some electron-microscopical studies it was shown that the reducing ends of cellulose exposed at the tip of a fragmented microfibril of Valonia and Acetobacter can be asymmetrically labeled w ith silver indicating a unidirectional alignment of glucan chains (Hieta et al., 1984; Kuga and Brown, 1988). The same feature was visualized also by Chanzy and Henrissat (1985), who showed that the digestion of Valonia cellulose by cellobiohydrolase proceeds in one direction in a single microfibril. These data have been used in favour of conception on parallel cellulose structure. In our opinion these results may equally well be explained from the position of antiparallel conception. 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Science 1984, v. 223, p. 283. 3. VanderHart, D. L.; Atalla, R. H. Macromolecules 1984, v. 17, p. 1465. 4. Horii, F.; Yamamoto, H.; Kitamaru, R.; Takahashi, M.; Higuchi, T. Macromolecules 1987, v. 20, p. 2946. 5. Mikelsaar, R. Trends Biotechnol. 1986, v. 6, p. 162. 6. Pertsin, A. J.; Nugmanov, 0 . K.; Marchenko, G. N.; Kitaigorodsky, A. I. Polymer 1984, v. 25, p. 107. 7. Mikelsaar, R.-H.; Aabloo, A. In: Cellulosics: Chemical, Biochemical and Material Aspects. Eds. J. F. Kennedy, G. 0 . Phillips, P. A. Williams. Ellis Horwood, Chichester, 1993, p. 57. 8. Atalla, R. H. In: Cellulose Structural and Functional Aspects. Eds. J. F. Kennedy, G. 0. Phillips, P. A. Williams. Ellis Horwood, Chichester, 1989, p .61. 9. Sarko, A.; Nishimura, H.; Okano, T. In: Structure of Cellulose; ACS Symposium Series 340; Amercan Chemical Society: Washington, DC, 1987 p. 169. 10. Nishimura, H.; Okano, Т.; Sarko, A. Macromolecules 1991, v. 24, p. 759. Parallel and antiparallel stereochemical models for cellulose I a and I/? crystalline phases. Phase Model Unit cell Intramolecular H-bonds Intrasheet H- -CH20H Packing designation bonds group energy confor­ kcal/mol mation lo P1 1 03 -H ...05 02 -H ...06 06 -H ...03 t9 -19.5 W P2 01 03 -H ...05 02-H ...06 0 6 -H ...03 tg -19.9 1 a A1 a 0Q112233 C3-H ...05 02 -H ...06 0 6 -H ...02 tg -16.4 lo A1b 00112232 03 -H ...05 02 -H ...06 06 H ...02 tg -15.5 \ß A2 01 03 -H ...05 02 -H ...06 06 -H ...03 tg -15.8 \ß A3a 01123243 03 -H ...05 02 -H ...06 0 6 -H ...03 tg -21.0 \ß A3b 01213234 03 -H ...05 02 -H ...06 06 -H ...03 tg -15.1 Ос ф fõb CÕ} CÕ} 0 1 ■•*€ о О О CD О О CD iм <* ?о> О© C D0 О 0 ОG )̂<2?0 C Dо С I.- D © О о с 5/4с 0 0 0 j 0 j \ Ž j j 0 О 6/ 4С ̂ 0 0 7/4С О О 0 ©0 00- 0.0 © Cl о 2с 5 CD О 0 © СЕ 9 1C 0 © 0 0 0<->0«© 10,4с > < *кГ) С ю Ъ 114с 2D CD CD CDм CD ̂ CD •■'CD ,1c f5 ) 0 —сУэ—0 CÕ4 <*у*з— i/'fc CD О © - © - © - 0 - 0 2 4c t > 0 О CD О CD CD С 3/4c Ic 5/4c 6 /4c 5 7/4c 0 © ic > C D © 9/4c < T ) ю/4с v c ^ _~C&— »-»CB* n /4 c 2 D C D C D C D - C D - C D - O — Fig 4 Model A1a. Eight-chain unif cell: 00112233 Symbols: grey ovals - cross sections of down chains: 6-2 - intrasheet bonds 06-H 02 : other symbols see Fig 1 Fig. 3 M o d e /P f Plastic space-filling molecular model - Cf. Fig.2 Fig. 6 Models A a end A lb Stereochemical formula with H-bonding network. Oc © Ф с l/4c I— © — Oc 2 > - < õ > < o > r C £ > « < D - ’ C l/4c © ^ - © ‘■ 'O '- 'O Oc © © © © © I4< > © CD © © © 1 1'. I о оТс^э © Or ^ »-><"? M< © © © ^ © t ^ © "• °> О © и® н© н<» Fig. 13 Models A3a and АЗЬ Plastic space-fillina molecular model Cf Fig 12 Packing Energy Calculations on the Crystalline Structure of Cellulose I Alvo Aabloo', Alfred D. French2, Raik-Hiio Mikelsaar3 - 1 Tartu University, Institute of Experimental Physics and Technology, Tähe 4 Street, EE2400 Tartu, Estonia;2 Southern Regional Research Center, USDA, 1100 Robert E. Lee Blvd, P.O. Box 19687, New Orleans, LA 70179, USA; 3 Tartu University, Institute of General and Molecular Pathology, Veski 34 Street, EE2400 Tartu, Estonia. Abstract The crystalline structure of native cellulose were investigated with packing energy calculations of crystals. Unit cell measures based on dimensions proposed by Sugiyama et al . The packing energy calculations of phases lo and \ß of native cellulose (I) were evaluated using tw o different algorithms. As a first step we used rigid ring method. The best structures found by this method were further minimized with a full optimization molecular mechanics program MM3(90). Different minimization methods gave analogous structures for best models of both phases. The best mode! for phase lo one-chain unit cell is in tg position and is packed "up". The chains of the best model for phase \ß two-chain unit cell are also in tg positions and are packed "up” . The structure found for the phase \ß of native cellulose is completely similar w ith a structure proposed several years ago by Woodcock and Sarko for ramie cellulose Introduction Several years ago, VanderHart and Atalla found that all crystalline native cellulose I is composed from two phases1. Different samples consists these phases in different relation. Later Sugiyama et al2, described those phases as lo w ith a triclinic one-chain unit cell and as \ß with a monoclinic two chain unit cell. They investigated Microdlctyon tenius with electron diffraction techniques. The one-chain triclinic unit cell for the phase lo has parameters of a = 0,674 nm, b = 0.593 nm, с = 1.036 nm, а = 117°, ß = 113° and у = 81 °. The two-chain unit monoclinic unit cell has parameters of a = 0.801 nm, b = 0.817 nm, с = 1.036 nm and V = 97 .3° as published by Sugiyama et al2. Early these two phases together were indexed as eight-chain unit cell3. Material and methods We used tw o different strategies to find the most probable models using the crystal packing energy calculations. A t the first step we using molecular modelling4 and rigid ring calculations6 6 to find the most probable models of both phases of native cellulose. The parallel packing of chains were presupposed. During these calculations we used P1 symmetry for the phase lo and P2, symmetry for the \ß phase. The rigid-ring method means that during the minimization process the glucose ring was kept fixed. The Arnott-Scott7 glucose ring was used. The torsion angles of the hydroxymethyl and hydroxyl groups and the torsion angles and the bond angles at the glycosidic linkages were allowed to vary (see Figure 1.). In the case of space group P2, the monomer residues were linked into the chain with virtual bond method8. The best models of these calculations were further minimized with a full molecular mechanics program■ММЗ(ЭО)9 ,0. During these minimizations ttie dielectric constant was chosen of 4. th is value was also used for crystalline amides, polypeptides and proteins” . In this method, a model of the crystal of cellulose was built of seven ceilotetraose molecules placed to hexagonal close packing. All chains were arranged according to the unit cell measures. The best model of both phases of cellulose I obtained by rigid-ring method preserved their leader position after MM3 minimization. While the conformation of these models have not changed significally. The best model of both phases w ith needed results of calculations are presented in table 1. As we can see in the case of the phase lo the hydroxymethyl groups are in tg position. The orientation of chain is "up". In the case of the phase \ß the hydroxymethyl groups of both chains are also in tg position and they are also packed "up". The central chain is shifted down approximately 1/4 с (see Figure 2.). Hydrogen bonds are completely same in the case of both phases. The conversion from lo phase to \ß phase is possible by simple vertical shifting of sheets of chains. The direct shifting of sheets needs to cross the barrier of 9 kcal/mol. Results and discussion The best model of the phase lo has an energy of -19.5 kcal/mol by rigid-ring method and 185 kcal/mol by MM3. The best model of the phase \ß has an energies of -19.9 kcal/mol and 182 kcal/mol, respectively. We can compare it w ith energies of -21.4 kcal/mol6 and 176 kcal/mol” calculated for cellulose II. Although the energies Molecular Modelling of Parallel and Antiparallel Structure of Native Cellulose M k-H Io ШМаааг and Alvo Aabioo' ■ T*rtu Urivaraity, In rttu ti al Qcneral and Molecular Pathology, 34 Veski Street, EE2400 Tutu Estonia “Tartu Unvanty, Institute d Experimental Physica and Technology. 4 Tiha Street, EE2400 Tartu, Eatonia Abstract Tartu plastic space-filling atomic-molecular models were used to investigate die structure of cellulose crystalline (la and Iß) phases. It was elucidated that both parallel and antipanllel structures can be accommodated with unit cell geometries described by Sugiyama et al.1. Packing energy calculations revealed that parallel models of la and Iß phases have similar energy. In contrast, in case of antiparallel structure models, Iß is energetically much more favourable in comparison with la phase. Our data indicate that antiparallel structure proposed for cellulose la phase is metastable and should be easily converted to Iß phase. So the antiparallel models are more suitable for explanations of cellulose Ia-»Iß-»II interconversion. Introduction Recently it was elucidated that native cellulose is a mixture of two crystalline phases (a and ß ) the proportion of which depends on the source of cellulose15. Horii et al.* showed that the la phase of cellulose is metastable and, through a hydrothermal annealing treatment, can be converted readily into the thermodynamically stable Iß phase. Sugiyama et al.1 studied cellulose from a green alga Microdictyon by electron diffraction and found that the major la phase has a one-chain, triclinic structure and the minor Iß phase is characterized by two-chain unit cell and a monoclinic structure. This study disdoeed the detail molecular structure of native cellulose crystalline phases. The aim of current paper was to use the molecular modelling method and packing energy calculations to elucidate die most favourable stereochemical structures corresponding to unit cell parameters found by Sugiyama et al.1 in cellulose l a and Iß crystalline pluses. Material and methods Molecular modelling was carried out by Tartu plastic space-filling models having improved parameters and design3. Packing energy calculations were carried out by rigid-ring method6. To present graphically the stereochemical models investigated, we drew unit cell projections on the plane crossing the с-axis at 90“. Cross-sections of up cellulose chains were given by white and down chains by grey ovals. The number of c/4 shifts of molecules in the direction of с-axis is noted by numbers inside of ovals1. To make a short digital designation of the cellulose models: 1) symbols "P" and "A* were used to represent correspondingly "parallel" and "antipanller, 2) numbers indicating c/4 shifts were applied for characterizing each chain is the unit cell, 3) underlining was used to differ up and down chains. of both phases of native cellulose are very close, these energies are in a good agreement w ith experimental data about lo-*l/?-»ll conversion. It is remarkable that the most probable model for \ß phase is completely analogous w ith a structure proposed by Woodcock and Sarko'2 for ramie cellulose. Also it is close to structure proposed by Pertsin et at for ramie cellulose using similar minimization technique'3. It means that the diffraction patterns of ramie cellulose mostly belong to the phase \ß. We got same result for phase \ß without any diffraction data. Table 1. The best model for the phase lo and for the phase \ß of native cellulose. Model Energy kcal/mol H-bonds in chain H-bonds -CH2OH Rigid-ring MM3 in sheet position Uo -19.5 185 05 ..H 03 06 ..H 02 03 ..H 06 tg u/? -19.9 182 05 ..H 03 06 ..H 02 03 ..H 06 19 References 1. VanderHart D. L.; Atalla R. H., Macromolecules 1984, v. 17, p. 1465. 2. Sugiyama,J; Vuong, R; Chanzy, H. Macromolecules 1991, v. 24, p. 4168. 3. Honjo G.;Watanabe M. Nature 1958, v. 181, p. 326. 4. Mikelsaar, R. Trends Biotechnol. 1986, v. 6, p. 162. 5. Pertsin, A. J.; Nugmanov, 0. K.; Marchenko, G. N.; Kitaigorodsky, A. I. Polymer 1984, v. 25, p. 107. 6. Mikelsaar, R. H.; Aabloo, A. In: Cellulosics: Chemical, Biochemical and Material Aspects. Eds. J. F. Kennedy, G. 0 . Phillips, P. A. Williams. Ellis Horwood, Chichester, 1993, p. 61. 7. Arnott S.; Scott W. E. J. Chem. Soc. Perkin II 1972, p. 324. 8. Zugenmayer P.; Sarko A. ,4CS series 1980, v. 141, p. 226. 9. Allinger N. L.; Yuh Y. H.; Lii J.-H. J. Amer. chem. Soc. 1989, v. 111, p. 8551. 10. Allinger N. L.; Rahman, M.; Lii J.-H. J. Amer. chem. Soc. 1990, v. 112, p. 8293. 11. Stipanovic A. J.; Sarko A. Macromolecules 1976. v. 9, p. 851. 12. Woodcock C.; Sarko A. Macromolecules 1980, v. 13, p. 1183. 13. Pertsin A. J.; Nugmanov O. K.; Marchenko G. N. Polymer 1986, v. 27, p. 597. Results The characteristics of the cellulose structure models investigated is presented in Table 1. 1. Molecular models fitting with cellulose lor unit cell parameters 1J . Models PI The investigation of green alga Microdktyon by Sugiyama et a l1 is the first work where unit ceil parameters are given for pure cellulose la phase microcrystals: a = 0.674 nm, b - 0.593 nm, с = 1.036 nm, a = 117°, ß = 113° and у = 81°. This one-chain unit cell requires parallel packing of molecular chains. Molecular modelling by Tartu devices showed that if there are the usual intramolecular bonds 03-H...05 and 02-H...06 the hydroxymethyl groups should be in tg conformation and all parallel chains are bound by intrasheet bonds 06-H...03. Packing energy calculations of the above-described cellulose structure imitation revealed that model PI has potential energy -193 kcal/mol. 13. Models A la and A lb Two antiparallel models A la and Alb characterized by eight-chain unit cell maybe geometrically derived from the one-chain unit cell described by Sugiyama et alЛ The geometry of these two models is very similar. The only difference is that in Ala parallel chains follow each other from down right to up left dividing major angles of unit cell and in A lb from down left to up right dividing minor angles of unit cell. So Ala may be called ’left" and A lb 'right* type of structures. According to molecular modelling data chains having usual intramolecular H-bonds and tg conformation of hydroxymethyl groups should be in models Ala and A lb bound by intrasheet bonds 06-H...02. The potential energy values of above-described structures are rather similar: model A la has -16.4 kcal/mol and A lb -15-5 kcal/mol. 1. Molecular models fitting with cellulose Iß unit cell parameters 2J . Model P2 Sugiyama et al.1 have established that Iß phase of Microdictyon cellulose has two-chain monoclinic structure with unit cell parameters of a = 0.801 nm, b = 0.817 nm, с = 1.036 nm and у = 97.3°. The authors suppose that this structure consists of parallel molecules and die center and comer chain are staggered by c/4. Molecular modelling revealed that intra- and intermoiecular H-bonds in model P2 are identical to those in model PI. The energy value of model P2 is close to model PI: -19.9 kcal/mol. 23. Model A2 Molecular modelling showed that a chain conformation and an intrasheet H-bonding network in model A2 are identical to model P2. The only difference is that sheets are parallel in model P2 and antiparallel in model A2. The potential energy of model A2 is relatively high: -15.8 kcal/mol. 23. Models A3a and A3b Two antiparallel models A3a and A3b characterized by eight-chain unit cell may be geometrically derived from the two-chain unit cell described by Sugiyama et al.1. These structures are similar to the "left'' and ’right" models Ala and Alb differing mainly by pretence of intrashect stagger of celluloee chains. The investigation by plastic models indicated that in the case where standard intramolecular H-bonds and tg conformation of hydroxymethyl group« are preserved the antiparallel molecular chains are bound by bonds 06-H...03. There is considerable difference between energies of above-described two structures: the "left* type model A3a has -21.0 kcal/mol and "right" mode] A3b -15.1 kcal/mol. Discus§ion Our investigation revealed (hat both parallel and antiparallel structure models can be proposed based on cellulose la snd Iß crystalline phases unit cell parameters published by Sugiyama et al.1. Although they all have usual chain conformation and intramolecular H-bonding network, the potential energy values between seemingly close structure* in certain cases are very different Sugiyama et al.' interpret their experimental data in the light of all-parallel structure view. Following this view, the l a phase structure should correspond to our model PI and Iß phase to model PZ Comparing cellulose psrallel model PI with antiparallel models Ala and A lb one can see that these models are sterically very similar. If the H-bonding network and chain polarity are not clearly established the structure characterized by eight-chain unit cell can be considered as the one-chain unit cell. We think that antiparallel model Ala having lower energy (-16.4 kcal/mol) in comparisoa with the model A lb (-15.5 kcal/mol) is a possible pretender for a "masked* eight-chain unit cell in the cellulose la crystal structure described by Sugiyama et al.'. The antiparallel structure is not excluded also for cellulose Iß crystalline phase because these authors marked that the exact position of the celluloee chains in the monoclinic unit cell was even more difficult to ascertain as long as the structure refinement was not achieved. No doubt, A3a is the best antiparallel model for fitting to the unit cell structure of Iß crystalline phase because it has sn excellent pscking energy: -21.0 kcal/mol. Table 1. Parallel and antipanllel stereochemical models for celluloee l a and Iß crystalline phases. Model Unit cell Intramolecular H-bonda Intrasheet -CHjOH Packing designation H-bonds group con­ energy formation kcal/mol .a PI 1 ОЗ-H...05 02-H ...06 Об-H .03 •* -19-5 Iß P2 01 03-H ...05 02-H ...06 06-H...03 -19.9 la Ala 00112233 03-H ...05 02-H ...06 06-H...02 -16.4 la A lb 00112233 03-H ...05 02-H ...06 06-H...02 tg -15.5 ip A2 01 03-H...05 02-H ...06 06-H...03 4 -158 ip A3a 01123243 03-H ...05 02-H ...06 06-H...03 •« -21.0 ip A3b 01213234 03-H ...05 02-H ...06 Об-H .03 4 -15.1 If the "left" type antiparallel models Ala and A3i are thought to be the candidates for structures of cellu lose la and Iß crystalline phases, correspondingly, it would be easy to explain the experimental data on the interconversion o f these phases. Model Ala, having relatively high energy -16.4 kcal/mol. is metasUble and can during annealing process easily be converted irreversibility into the model A3a, having very low energy -21.0 kcal/mol. Because the models Ala and A3a have different H-bonding netw orks, our conception on antiparallel cellulose structure is in accordance also with Raman- spectroscopic data*. The high energy barrier between la and Iß crystalline phases, bound with rearrangement of hydrogen bonds, may be the reason why the proportion of these phases in different samples of native cellulose is relatively constant The notable structural differences between models Ala and A3a allow one also to understand the differences between corresponding unit cell parameters of la and Iß cellulose crystalline phases. The process of cellulose I-»II conversion can be also easily interpreted by all-antiparallel conception, because already Na-celluloee I, formed in the initial step of mercerization, has antiparallel structure9'10. References 1. Sugiyama,J; Vuong, R; Chanzy, H. Macromolecules 1991,v. 24, p. 4168. 2. Atalla, R. H.; VanderHart, D. L. Science 1984, v. 223, p. 283. 3. VanderHart, D. L.; Atalla, R H. Macromolecules 1984, v. 17, p. 1465. 4. Horii, F.; Yamamoto, H.; Kitamaru, R ; Takahashi, M.; Higuchi, T. Macromolecules 1987, v. 20, p. 2946. 5. Mikelsaar, R Trends BiotechnoL 1986, v. 6, p. 162. 6. Pertsin, A J.; Nugmanov, O. K.; Marchenko, G. N.; Kitaigorodsky, A I. Polymer 1984, v. 25, p. 107. 7. Mikelsaar, R-H.; Aabloo, A In: Cellulosics: Chemical, Biochemical and Material Aspects. Eds. J. F. Kennedy, G. O. Phillips, P. A Williams. Ellis Horwood, Chichester, 1993, p. 57. 8. Atalla, R H. In: Cellulose Structural and Functional Aspects. Eds. J. F. Kennedy, G. O. Phillips, P. A Williams. Ellis Horwood, Chichester, 1989, p.61. 9. Sarko, A ; Nishimura, H.; Oka oo, T. In: Structure of Cellulose; ACS Symposium Series 340; Amercan Chemical Society: Washington, DC, 1987 p. 169. 10. Nishimura, H.; Oka no, Т.; Sarko, A Macromolecules 1991, v. 24, p. 759. TÜ 94. Т. 124. 150. 6,0.