Introduction

Highly crystalline cellulose occurs in nature as Iα or Iβ allomorphs or their mixture (Atalla and VanderHart 1984). Higher plants produce cellulose with a less-defined structure (Fernandes et al. 2011). However, the basic molecular conformation and lateral arrangement of cellulose chains as well as hydrogen-bonding schemes can be considered to be common to all native celluloses as can be judged from the similarity of NMR and infrared spectra, and X-ray diffraction patterns (Nishiyama 2009).

The structures of cellulose Iα and Iβ have been determined by X-ray and neutron fiber diffraction at atomic resolution (Nishiyama et al. 2002, 2003). On the one hand, in both cases, the positions of carbon and oxygen atoms as well as the hydrogen atoms involved in the intramolecular hydrogen bonds (HBs) were clearly determined. On the other hand, the HBs implicating the primary hydroxyl group O6 were less clearly defined in the Fourier difference maps. The statistical analysis of the fit to the diffraction data supported the existence of a HB disorder, referred to as pattern B, in addition to the major HB pattern A (Fig. 1 and Supplementary Material Table S1).

Fig. 1
figure 1

Hydrogen bonding patterns in cellulose Iα and Iβ: a pattern A in Iα; b pattern B in Iα; c pattern A in the center chains of Iβ; d pattern B in the center chains of Iβ; e pattern B in the origin chains of Iβ. The HB pattern A in the origin chains of Iβ is similar to that in the center chain and was thus not presented. The hydrogen bonds are indicated with red dotted lines. The gray ellipses in e indicate the HO2 and HO6 hydrogen atoms that are separated by 0.094 nm when the origin chains of Iβ adopt HB pattern B

Full size image

It was unsure whether these two HB patterns could interconvert dynamically or if they statistically occurred in different regions of a crystalline microfibril. Quantum mechanics (QM) calculation and molecular dynamics (MD) simulation based on empirical force field methods (Nishiyama et al. 2008) suggest that pattern A is stable, energetically more favorable than pattern B, and probably occurs in the core regions with perfect crystalline order, while pattern B is energetically less favorable. Pattern B is either a spatial average of many different HB patterns (Mazeau 2005) or occurs in the defects of the crystalline regions (Nishiyama et al. 2008). Most of the MD simulation studies were performed on allomorph Iβ using HB pattern A. Only a few studies were carried out on the structure having pattern B (Mazeau 2005; Matthews et al. 2012), and MD studies on Iα with HB pattern B, although accounting for approximately half of the total HBs, have not been reported. In this study, we carried out MD simulations using HB pattern B to introduce a perturbation to the major structure in the starting model and analyzed its fate under thermal agitation compared to HB pattern A.

Materials and methods

Computational details

The models

Infinite models were used throughout the study (Mazeau and Heux 2003). This strategy seemed the most relevant since the crystals used in the experimental crystal structure determination are about 20 nm wide and several micrometers long, and the contribution of surfaces is negligible.

The initial coordinates for the construction of the models were those obtained from the X-ray and neutron diffraction experiments and contain explicit positions of the hydroxyl hydrogen atoms (Nishiyama et al. 2002, 2003). The models contain 64 chains (8 × 8) for Iα and 36 (6 × 6) chains for Iβ. Each chain contains eight glucose residues. The periodic boundaries in the Iα models are parallel to the (\(11\bar{4}\) ), (010) and (100) planes, while those in the Iβ models are parallel to the (110), (\(1\bar{1}0\) ) and (001) planes. Along the chain direction, the chains are covalently bonded to their own periodic images. Periodic boundary conditions were applied along the x, y and z directions, yielding models without boundaries that simulate infinite systems.

For both Iα and Iβ, three super cells were constructed: (1) all HBs in pattern A (referred to as model A), (2) all HBs in pattern B (referred to as model B) and (3) alternating patterns A and B (referred to as model AB). Since only one position for HO2 in the origin chain was refined experimentally, pattern A was attributed to the origin chains and pattern B to the center ones in models AB. In this work, we did not take into account irregular models in which patterns A and B were randomly located in the super cells; this issue might be addressed in a future work.

System setup

All simulations were performed with the GROMACS package (Hess et al. 2008). The Gr56Acarbo force field was used (Hansen and Hunenberger 2011) with a revised Lennard-Jones parameter for the CH1 atom type (Chen et al. in preparation).

Energy minimization was performed before any MD simulation, using the steepest descent method followed by conjugated gradient methods. The convergence criterion to stop the minimization process was a maximum force of 1 kJ mol−1 Å−1. MD simulations were performed in the NPT ensemble (constant number of particles, temperature and pressure). The integration time step was 1 × 10−15 s. The velocity-scaling algorithm was used to control the temperature (Bussi et al. 2007). Berendsen’s algorithm was used to control the pressure (Berendsen et al. 1984). All bonds were constrained by using the LINCS algorithm (Hess et al. 1997). The long-range electrostatic interaction was calculated by using the particles mesh Ewald (PME) method (Essmann et al. 1995). The long-range Lennard-Jones interaction was corrected for energy and pressure. The cutoff radius was 0.9 nm. The xx, yy, zz, xy, yz, zx components of the compressibility were set to 2.5 × 10−5, 2.2 × 10−5, 7.9 × 10−7, 1.2 × 10−5, 4.2 × 10−5, 4.4 × 10−5 bar−1 for the model of cellulose Iβ; 7.3 × 10−7, 6.1 × 10−5, 3.1 × 10−5, 5.4 × 10−5, 4.9 × 10−5, 1.2 × 10−5 for Iα.

To reach a target temperature, a stepwise strategy of heating or cooling was used: the temperature was increased or decreased by 10 K at a rate of 50 K/ns followed by an equilibration at this temperature. The duration of the equilibration varied from 100 ps to 12 ns.

Analysis

The unit cell parameters were calculated from the total box size of the system, using the last 5 ns of the MD simulation. The orientation of the hydroxymethyl groups is described by the torsion angle ω defined by the O5–C5–C6–O6 sequence of atoms. With this definition, the gg, gt and tg orientations correspond to ω = 240°–360°, 0°–120° and 120°–240°, respectively.

Hydrogen bonds were detected from geometric criteria using the g_hbond command of GROMACS: the distance between the donor and acceptor was smaller than 0.35 nm and the acceptor–donor-hydrogen angle smaller than 30°.

Results and discussion

We have studied the Iα and Iβ crystal structures of cellulose by considering three models for each allomorph differing by their initial HB network. The structures were heated, initially up to room temperature (RT), to produce the RT models, then to 600 K to produce the high-temperature (HT) models and then cooled down to room temperature to generate RTc models. Figures 2 and 3 show selected snapshots (last frame at each temperature) of the RT models having HB patterns A and B, respectively, in projections parallel and perpendicular to the chain axis. Snapshots of the HT and RTc models can be found in Figs. 6 and 7, respectively. The evolution of the conformation of the hydroxymethyl group with temperature can be followed in Fig. 4, and the populations of its different orientations for the RT, HT and RTc models are reported in Table 1. The time evolution of the different HBs in the models is given in Fig. 5, and their occurrences in the various models are given in Table 2.

Fig. 2
figure 2

Snapshot of the models of cellulose Iα and Iβ with hydrogen bonding pattern A (dotted lines) at room temperature (RT models)

Full size image
Fig. 3
figure 3

Snapshot of the models of cellulose Iα and Iβ with hydrogen bonding pattern B (dotted lines) at room temperature (RT models)

Full size image
Fig. 4
figure 4

Variation of the three-staggered conformation of the hydroxymethyl group in the three models of Iα (top) and those of Iβ (bottom) as a function of temperature. Red: hydrogen bonding pattern A, green: hydrogen bonding pattern B, blue: hydrogen bonding pattern AB

Full size image
Table 1 Populations (%) of the conformation of the hydroxymethyl groups in various models
Full size table
Fig. 5
figure 5

Variation of the number of hydrogen bonds as a function of temperature in the Iα (top) and Iβ (bottom) models

Full size image
Table 2 Number of hydrogen bonds per 100 residues in the different systems
Full size table

Room temperature

The Iα and Iβ structures with pattern A

The structures of both Iα and Iβ allomorphs with HB pattern A are stable at room temperature and remain close to the initial crystal structures (Nishiyama et al. 2002, 2003). The conformation of the individual chains in which the hydroxymethyl group is exclusively tg (Table 1) is in good agreement with solid-state 13C NMR data (Horii et al. 1983). The simulated unit cell parameters reproduce the experimental values (Supplementary Material Tables S1 and S2). The largest observed deviation reaches 2.3 % for parameter a in Iα and 3.0 % for the monoclinic angle γ in Iβ. Such close agreement between experiments and simulation has rarely been achieved using force field methods, where typical deviations on unit cell parameters are of the order 8–10 % (Chen et al. 2012). Similarly, HB pattern A, characterized by intra-chain O3H···O5 and O2H···O6 and inter-chain O6H···O3 HBs, remains stable (Table 2). Each residue participates in 2.8–2.9 HBs on average. HB pattern A in native cellulose is considered dominant. The stability of the models at room temperature, for which very precise experimental data are available, supports the validity of the force field and the modeling approach to study crystalline cellulose.

The structures with patterns B and AB

The structures constructed with patterns B and AB are expected to be of minor occurrence, as neutron diffraction data refinement converged to an occupancy of pattern B of 20–30 % for Iβ (Nishiyama et al. 2002) and 45 % for Iα (Nishiyama et al. 2003). During heating from 0 K to room temperature (300 K), part of the hydroxymethyl groups having HB patterns B and AB reorient, as can be visualized by the loss of the initial tg conformation (Fig. 4). A similar reorientation to gt conformation of half of the hydroxymethyl groups with pattern B is observed using DFT-D2 (Lee et al. 2013). For the Iα allomorph, a massive reorientation of hydroxymethyl groups occurs at 30–50 and 250–350 K. For the Iβ allomorph, the crystal structures containing pattern B in the origin chains are not stable because of the proximity of the HO6 and HO2 atoms in the starting structure (Fig. 1). Consequently, they locally reorganize at the very beginning of the minimization process, where the HO2 hydrogen atom rotates away by about 120°. Notably, the HB network did not change to the supposedly more stable pattern A. Then, during MD, hydroxymethyl groups start to reorient at 100 K in Iβ (Fig. 4) and at 30 K in Iα. The population of tg conformation gradually decreases when the temperature increases up to room temperature.

At room temperature, the unit cell dimensions of the different models (Supplementary Material Table S2) remain close to those of models with pattern A or to experimental values (Supplementary Material Table S2) despite various HB schemes and hydroxymethyl conformations (Nishiyama et al. 2002, 2003). This similarity between the modeled parameters indicates that the unit cell can accommodate a disorder of hydroxymethyl conformation. Cell angles differ from the expected experimental values: α and γ in Iα with pattern B deviate by −8 and +5 %, respectively, whereas the γ angle in Iβ deviates by −7.5 % (pattern AB). Such deviation indicates that the cellulose chains undergo some sliding with respect to their neighboring chains.

The Iα structures with patterns B and AB

At room temperature, half of the hydroxymethyl groups of the Iα structures with pattern B keep the initial tg orientation, whereas the other half move to gt in a regular way (Fig. 3): the tg and gt conformation alternate along the chains. On average, there are 2.77 and 2.81 HBs per residue for patterns B and AB, respectively (Table 2), compared to 2.89 in the case of pattern A. The number of intra-chain O3H···O5 HBs per residue decreases to 0.80 (0.75 and 0.85 for patterns B and AB, respectively). The inter-chain O2H···O6 HB in pattern B of the experimental structure is weak because of the very large oxygen-to-oxygen distance of 0.36 nm (Supplementary Material Table S1). In the MD trajectory, every other residue participates in this HB with the oxygen-to-oxygen distance of 0.27 nm, allowed by the change in torsion angle of O6 and the translation the molecules along the chain (Supplementary Material Figures S1b and S1c). The number of such HBs decreases by a factor of two, but they contribute better to the cohesion of the crystal. Besides, additional inter-chain O6H···O3 HBs can be formed when the hydroxymethyl group is in gt.

The Iβ structures with patterns B and AB

At room temperature, the conformation of the hydroxymethyl groups is complex. The three orientations are present, differently populated (Table 1) and randomly distributed (Fig. 3). As a consequence of this reorientation of the hydroxymethyl groups, the HB network is also complex (Table 2). On average, there are 2.78 and 2.89 HBs per glucose residue in the models with patterns B and AB, respectively.

Heating

All models were then heated to 600 K. The transition to the HT phases of the Iα and Iβ structures with HB pattern A is induced by the concerted rotation of the hydroxymethyl groups, as suggested by the drastic decrease of the population of the tg orientation shown in Fig. 4. In parallel, one can observe a significant modification of the HB systems in Fig. 5: rapid loss of 40 % of the intra-chain O2H···O6 HBs, 70 % of the inter-chain O6H···O3 HBs and 20 % of the intra-chain O3H···O5 HBs, whereas a significant amount of inter-chain O6H···O2 HBs appears at the transition. A sharp transition from the RT to the HT forms has already been observed on the Iβ allomorph with pattern A in MD simulations with other force fields (Bergenstråhle et al. 2007; Agarwal et al. 2011; Zhang et al. 2011; Chen et al. 2012; Matthews et al. 2012) and has also been reported experimentally for both allomorphs using X-ray diffraction (Wada 2002; Wada et al. 2003; Hori and Wada 2005; Hidaka et al. 2010) and IR spectroscopy (Watanabe et al. 2006, 2007).

Any transition in the 450–550 K temperature range is perceptible in the Iα structures with HB patterns B and AB. The loss of the tg orientation of the hydroxymethyl group (Fig. 4) and the changes in the HB scheme (Fig. 5) in these models are gradual. In contrast, the structures derived from Iβ having HB patterns B and AB undergo a first transition in the 400–500 K temperature range, in which hydroxymethyl groups return to the tg conformation (Fig. 4) and the HB scheme converts to pattern A (Fig. 5). Consequently, the second transition is similar to the allomorphic conversion observed for model A.

The three models of Iα, as well as those of Iβ, converge to a unique HT form, as suggested by the similarity of the cell parameters (Supplementary Material Table S2), the identical populations of the three hydroxymethyl group conformations (Table 1) and HB systems (Fig. 5; Table 2). Most of the HBs still occur within the cellulose layers, although some inter-layer HBs exist. As a consequence of the diversity of orientations adopted by the hydroxymethyl groups in these two HT forms, their HB system is complex (Fig. 6; Table 2). On average, each glucosyl unit participates in 2.2 HBs. Compared to the RT structures, the geometry of the hydrogen bonds in the HT structures is characterized by similar distances and larger angles (Supplementary Material Figures S1). This result is consistent with the fact that the infrared OH stretching at higher wave number increases on heating, which suggests that HT structures are stabilized by weak hydrogen bonds (Watanabe et al. 2006, 2007).

Fig. 6
figure 6

Snapshots of the high temperature models of cellulose Iα and Iβ. The dotted lines correspond to hydrogen bonds

Full size image

The HT form of Iα is triclinic. Compared to the RT model (Nishiyama et al. 2003), its expansion is isotropic and modest. Unit cell parameters a and b increase by only 3–4 %. The HT form of Iβ is monoclinic (Supplementary Material Table S2). Its expansion is anisotropic, and parameter a increases by 6 %, whereas the other parameters are similar to the values observed at 300 K (Nishiyama et al. 2002). The unit cell dimensions of the HT-Iβ model are similar to the experimental values (Wada et al. 2010). Parameters a and b are identical (0.82 nm). The monoclinic angle is 94° in our models, while the experimental one is 96.4°.

Cooling

The HT models were cooled down to room temperature. Since only two HT forms (Iα and Iβ) have been identified, the behavior during the cooling step and the cooled structures (RTc) are independent of the initial HB pattern but depend on the allomorph.

The Iα structures

When temperature was decreased from 600 to 300 K, the three models of Iα progressively evolved to the same structure that was different from any starting model, but similar to the simulated structure of model B at 300 K, in which the tg and gt conformations alternate along the chain (Fig. 7). Unfortunately, our models did not reproduce the experimental behavior. Indeed, the HT form of Iα should transform into RT-Iβ upon cooling (Wada et al. 2003). However, the experimental time scales are always much longer (minutes to hours) than the simulation time scales of nanoseconds.

Fig. 7
figure 7

Snapshots of the room temperature models of cellulose Iα and Iβ after cooling. The dotted lines correspond to hydrogen bonds

Full size image

Furthermore, the potential energy of the room temperature structure after cooling (RTc) was 0.66 ± 0.58 kJ mol−1 per glucose unit lower than that of the RT model with pattern A. The lower energy can be partly explained by the formation of new HB networks in the cooling structure, as shown in Fig. 7. On the one hand, in this HB network, each hydroxymethyl group that adopted a tg conformation participates in one intra-chain O6H···O2 HB and one inter-chain O2H···O6 HB. This pattern seems to be similar to pattern B in Iβ. On the other hand, the other hydroxymethyl groups that adopted the gt conformation also participate in two inter-chain hydrogen bonds. On average, each glucose residue has 2.74 HBs. The hydrogen-acceptor distances are shorter than experimental values (Supplementary Material Figure S1). The formation of this new HB network also requires a relative translation of the neighboring chain in the (110) planes of Iα by about 0.12 nm along the chain direction. If such a structure does not exist in reality, it might be due to some sort of penalty of the gt conformation or the relative translation that is not taken into account in the current force field parameters.

The Iβ structures

Upon cooling, at 500 K, the hydroxymethyl groups readily go back to tg orientation. The simulated phase transition of Iβ is reversible, with a hysteresis of 50 K, which is in good agreement with experiments (Chen et al. 2012). The orientation of the hydroxymethyl groups in cooled structures of Iβ is identical to that in the initial Iβ with pattern A at room temperature. However, the RTc structure is stabilized by approximately two intra-chain and one inter-chain HB, with an average of 2.92 HBs per glucose unit. The intra-chain O3H···O5 HB is restored at 0.94 HBs per glucose unit, and bifurcated inter-chain HBs can be observed involving O2H···O6 (0.99 HBs per glucose unit) and O6H···O3 (0.97 HBs per glucose unit) HBs (Fig. 6).

Conclusion

The hydrogen bonding disorder in the allomorphs of native crystalline cellulose was studied by MD simulation using infinite models and the revised Gr56Acarbo force field. The calculation suggests that HB pattern B is not stable in the core region of both Iβ and Iα and can only exist in a frozen state. The Iβ structure with pattern B converted into pattern A at high temperature (490 K), which is just below the phase transition temperature to the high temperature phase. In the case of Iα, pattern A was stable at room temperature but irreversibly transformed to a more stable structure common to any starting hydrogen bonding pattern. This structure had hydroxymethyl conformation of gt and tg regularly alternating along the chain, which is probably due to the deficiency of the force field parameters, but suggests the existence of relatively stable structures.