MM Study of the Molecular

Article pubs.acs.org/JPCB

How Cellulose ElongatesA QM/MM Study of the Molecular Mechanism of Cellulose Polymerization in Bacterial CESA Hui Yang,† Jochen Zimmer,‡ Yaroslava G. Yingling,§ and James D. Kubicki*,†,∥ †

Department of Geosciences, The Pennsylvania State University, University Park, Pennsylvania 16802, United States Center for Membrane Biology and Department of Molecular Physiology and Biological Physics, University of Virginia School of Medicine, Charlottesville, Virginia 22908, United States § Department of Materials Science and Engineering, North Carolina State University, Raleigh, North Carolina 27695, United States ∥ The Earth & Environmental Systems Institute, The Pennsylvania State University, University Park, Pennsylvania 16802, United States ‡

S Supporting Information *

ABSTRACT: The catalytic mechanism of bacterial cellulose synthase was investigated by using a hybrid quantum mechanics and molecular mechanics (QM/MM) approach. The Michaelis complex model was built based on the X-ray crystal structure of the cellulose synthase subunits BcsA and BcsB containing a uridine diphosphate molecule and a translocating glucan. Our study identified an SN2-type transition structure corresponding to the nucleophilic attack of the nonreducing end O4 on the anomeric carbon C1, the breaking of the glycosidic bond C1−O1, and the transfer of proton from the nonreducing end O4 to the general base D343. The activation barrier found for this SN2-type transition state is 68 kJ/mol. The rate constant of polymerization is estimated to be ∼8.0 s−1 via transition state theory. A similar SN2-type transition structure was also identified for a second glucose molecule added to the growing polysaccharide chain, which aligned with the polymer 180° rotated compared to the initially added unit. This study provides detailed insights into how cellulose is extended by one glucose molecule at a time and how the individual glucose units align into cellobiose repeating units.

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membrane.7 The recently published cellulose synthase crystal structure (PDB entry: 4HG6) contains the BcsA and BcsB subunits from Rhodobacter sphaeroides together with a translocating glucan and a uridine diphosphate (UDP) molecule.8 This work provided the architecture of the catalytic pocket, as well as the functions of the highly conserved amino acid motifs, DDG, DXD, TED, and Q(Q/R)XRW (also known as the “D, D, D, Q(Q/R)XRW” motif) which characterizes processive βglycosyltransferases.4,8 The first 2 D’s (D179, D246) coordinate UDP and a divalent cation required for catalysis, respectively. Glycosyl transfer requires a general base that deprotonates the acceptor hydroxyl group during sugar transfer. Accordingly, the third D (D343) is part of an invariant “TED” sequence and resides at the N terminus of a short α-helix, in close proximity to the nonreducing end of the translocating glucan (the acceptor), thus presumably representing the general base for catalysis. The W (W383) in “Q(Q/R)XRW” forms van der Waals interactions with the glucose molecule at the acceptor site and is located at the entrance of the cellulose trans-

INTRODUCTION Cellulose is a linear polymer of glucose molecules and represents the most abundant renewable hydrocarbon source in the world. Cellulose synthesis in plants is mediated by cellulose synthase (CESA), a membrane-bound glycosyltransferase family 2 enzyme,1 polymerizing glucose molecules via glycosidic bonds between the C1 and C4 carbons. CESA utilizes activated glucose, UDP-α-D-glucose (UDP-α-D-Glc, the donor), as substrate and inverts the configuration of the newly added glucosyl residue from α to β during catalysis.2 However, due to difficulties in expressing and manipulating catalytically active CESA enzymes, the molecular mechanism of plant cellulose biosynthesis is still elusive.3 Cellulose is also produced by some bacteria, especially Gramnegative species, where its biosynthesis is often concomitant with the formation of biofilms. Bacterial biofilms are of particular concern to human health due to their increased tolerance to antibiotics and disinfectant chemicals.4−6 Bacteria produce cellulose via a protein complex consisting of at least three subunits, BcsA, BcsB, and BcsC (bacterial cellulose synthesis).4 BcsA is the catalytically active subunit and homologous to plant CESAs responsible for the formation of bacterial cellulose and its translocation across the inner © XXXX American Chemical Society

Received: February 11, 2015 Revised: April 29, 2015

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DOI: 10.1021/acs.jpcb.5b01433 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B

Figure 1. (A) Schematic diagram of cellullose synthesis catalyzed by CESA in the presence of Mg2+. (B) QM/MM model of cellulose synthesis based on the X-ray crystal structure of BcsA from Rhodobacter sphaeroides (PDB entry: 4HG6).8 The QM layer contains UDP-α-D-Glc donor, the cellotriose acceptor, Mg2+, one H2O molecule coordinating with Mg2+, and the side chains of seven residues involved in the catalytic reaction, or binding with the substrates. It is treated at the M05-2X/6-31G(d) level of theory. The MM layer is treated by the AMBER force field.

further investigation. Furthermore, a molecular model describing details of how the addition of a second glucosyl residue to the cellulose occurs is needed. In this paper, to bridge the gap, we studied the catalytic mechanism of the bacterial CESA homologue BcsA using a QM/MM approach, as depicted in Figure 1. QM/MM calculations were used to model the sequential addition of two glucoses to the end of a cellulose polymer (modeled as cellotriose) within BcsA. The activation energy barrier of the formation of the glycosidic bond estimated via QM/MM calculations is used to estimate a rate constant of polymerization via transition state theory and compared to observed polymerization rates.

membrane channel formed by BcsA’s transmembrane region. This structural information enables a detailed computational analysis of the many reactions underlying cellulose biosynthesis. Theoretical studies of enzyme-catalyzed reactions have been the subject of great interest because they provided detailed information on the microscopic level.9,10 The hybrid quantum mechanics and molecular mechanics (QM/MM) approach first outlined by Warshel and Levitt in 197611 has been a major approach to study enzymatic reactions, because the high-level quantum mechanical calculations can provide a deeper understanding of enzymatic reactions, while force-field-based MM methods can simulate large systems very efficiently. Previous QM/MM studies of nonprocessive glycosyltransferases, such as N-acetylglucosaminyltransferase-I12 and β-1,4galactosyltransferase-I,13 have provided useful information such that inverting glycosyltransferases use an SN2-type mechanism with one amino acid functioning as the general base, showing a nearly simultaneous nucleophilic addition of an O atom from the acceptor to the anomeric C1 of the sugar donor, as well as the dissociation of the glycosidic bond C1−O1 of UDP-(sugar donor). However, the specific mechanism of processively adding glucosyl residues to an existing cellulose polymer is still unknown. Cellulose is a polysaccharide consisting of β-(1 → 4)-linked D-glucose molecules, with each succeeding glucose unit being flipped 180° with respect to its proceeding one to form a 2-fold screw-axis conformation.14 Whether the individual glucose units spontaneously “relax” into the plane of the polymer in opposite orientations directly after glycosyl transfer or align by a different mechanism is currently unknown. Several hypothetical models have been proposed. The double addition model suggested adding two glucosyl residues with opposite orientations simultaneously to the growing glucan chain.15,16 Another model proposed that one glucose unit is added to the growing glucan chain each time, and each glucose unit added can rotate freely so as to adopt the inverted orientation with respect to its neighbors.8,17 In addition, whether the D (D343) of an invariant TED sequence indeed functions as the general base, as proposed,8,17 is worth

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METHODS

Enzyme−Substrate Initial Structure. The formation of β-(1 → 4)-linked cellulose is catalyzed by the cytosolic domain of BcsA using a UDP-α-D-Glc donor in the presence of a divalent cation, as shown in Figure 1A, in which the divalent cation, usually Mg2+ or Mn2+, is coordinated with UDP and a DXD motif similar to other inverting glycosyltransferases.18,19 On the basis of our previous simulation results in a plant CesA20 which showed insignificant differences between Mg2+UDP and Mn2+-UDP and the indistinguishable catalytic activity of Rhodobacter BcsA in the presence of either cation,21 we decided to use Mg2+ for our studies to lower computational costs. Modeling the Mg2+-UDP-α-D-Glc donor at the active site of BcsA was guided by structural information from donorbound nonprocessive glycosyltransferases, such as α-1,3galactosyltransferase in complex with the donor substrate UDP-galactose (PDB entry: 2VS5)22 and β-1,4-galactosyltransferase 7 in complex with UDP-galactose and the acceptor substrate xylobiose (PDB entry: 4M4K).23 In this case, as shown in Figure 1, O3 and O5 of the glucose donor form hydrogen bonding interactions with E342 and W383, respectively, and the pyrophosphate of UDP forms a salt bridge interaction with K226. The uracil moiety of UDP is stabilized by π−π interactions with Y149. The hexa-coordinated Mg2+ binds to UDP as well as D246 and D248 of the conserved B


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31G(d) basis set.33,34 Hydrogen link atoms were added to the MM-bounded QM atoms to fulfill the valence of the QM system. All atoms in both layers were free to move in the geometry optimization calculations. Transition State. Our primary goal of this paper is to study the catalytic mechanism and to determine the structure of the transition state, the Gibbs free energy of activation, ΔGa, and rate constant, k, for cellulose polymerization in BcsA. As shown in Figure 1, the enzymatic reaction catalyzed by BcsA results in breakage of an α-glycosidic bond between the incoming glucose and the UDP (C1−O1), and formation of a new β-glycosidic bond between O4 of the cellotriose acceptor and the anomeric carbon C1. The reaction mechanism is monitored by the reaction coordinate rO4−C1, which is defined as the distance between O4 of the cellotriose acceptor and the anomeric carbon C1 of the incoming glucose, representing the nucleophilic attack of O4 on the anomeric carbon C1. The energy profile of the reaction path is determined by the potential energy surface scan. The reaction coordinate was changed by −0.2 Å increments between 3.6 and 2.8 Å and by −0.1 Å increments between 2.8 and 1.8 Å. In the reverse scan, the reaction coordinate was varied by 0.05 Å increments, between 1.6 and 2.2 Å. All atoms in both layers were free to move in the geometry optimization calculations. Defining the C1 and O4 distance as the reaction coordinate could lead to overestimation of the calculated ΔGa compared to the true reaction path,35 so this transition state and ΔGa should be further refined. The results presented here represent a reasonable first-order approximation of the reaction mechanism. On the basis of the obtained energy profile, the structure with the maximum energy was used to start the transition state search using Gaussian 09. The transition state was characterized by the vibrational frequency calculation on the whole QM/MM system. All the figures are generated using Maestro36 and PyMOL.37 Cellobiose Synthesis in Aqueous Solution. In order to clarify the catalytic power of the enzyme with the activated glucose donor and explore the nature of glucose inversion as polymerization occurs, the reaction barrier obtained in the protein environment has been compared to the barrier obtained in the aqueous solution. The cellobiose aqueous solution model consists of one cellobiose molecule and 26 explicit H2O molecules within the first solvation shell sufficient to fully hydrate the glycosidic bond. This model was used to obtain the abiotic reaction barrier of cellobiose synthesis in aqueous solution, as shown in Figure S1 (Supporting Information). A similar model (cellobiose +25 H2O) was also adopted by Pincu and co-workers to investigate solvation and dynamics of βcellobiose by means of ab initio dynamics.38 In our calculations, the reaction mechanism is monitored by the reaction coordinate rO4−C1. The energy profile of the reaction path is determined by the potential energy surface scan against the reaction coordinate rO4−C1, representing the nucleophilic attack of O4 on the anomeric carbon C1. In the forward scan, the reaction coordinate was varied by 0.05 Å increments, between 1.48 and 3.08 Å. In the reverse scan, the reaction coordinate was varied by −0.05 Å increments, between 2.58 and 1.48 Å. The geometries of the total molecular system were optimized using M05-2X/6-31G(d). On the basis of the obtained energy profile, the structure with the maximum energy was used to start the transition state search in Gaussian 09. The transition state was characterized by the vibrational frequency calculation using Gaussian 09.

DXD motif together with the O atom of a H2O molecule, adopting a regular octahedral geometry as in other Mg2+nucleotide-binding enzymes.24,25 A cellotriose molecule was chosen to represent the growing glucan chain, the glycosyl acceptor, considering the computation cost. When modeling the cellotriose acceptor based on PDB entry 4HG6 and the UDP-α-D-Glc donor within the active site, we found that the binding pocket cannot accommodate both the UDP-α-D-Glc donor and the nonreducing end of the cellulose polymer at the same time. Similarly, as revealed by the structure of the catalytic domain of bovine α-1,3-galactosyltransferase in complex with UDPgalactose and a galactose molecule as the acceptor, 1G93,26 the acceptor was stabilized by van der Waals interactions with a tryptophan residue (W314). In the initial BcsA crystal structure (PDB entry: 4HG6), W383 of the conserved “Q(Q/R)XRW” forms van der Waals interactions with the penultimate glucose molecule at the acceptor site, likely representing a state after glycosyl transfer but prior to polymer translocation.8,17 Therefore, the position of the cellotriose molecule was modeled by superimposing its nonreducing end glucosyl residue with the penultimate glucosyl residue of the translocating polysaccharide in the crystal structure 4HG6. The recently published crystal structure of the cyclic-di-GMP-activated BcsA−BcsB complex (PDB entry: 4P00)27 indeed demonstrates that the acceptor binding site is formed by W383, consistent with our modeling and simulation results, as demonstrated in Figure S4 (Supporting Information). Residue D343 of the conserved “TED” motif was proposed as the general base.8 However, in our initial model, D343 was ∼5 Å away from the nonreducing end of cellotriose, which is considered too long for a direct H+-transfer. In order to ascertain if D343 could perhaps move closer to cellotriose, the “TED”-containing α-helix (E342−R353) was optimized with density functional theory at the M05-2X/6-31G(d) level. After the relaxation, the distance between D343 and the nonreducing end of the cellulose is 2.6 Å, nearly a low-barrier hydrogen bond.28 This position is indeed observed in the new crystal structure of the cyclic-di-GMP activated BcsA−B complex (PDB entry: 4P00)27 containing one UDP molecule, a translocating glucan, and one Mg2+. In the new BcsA−B structure, D343 is about 3.0 Å away from the acceptor’s nonreducing end (4′OH), supporting its putative function as a general base.27 QM/MM Model. The multilayered (Our own N-layered Integrated molecular Orbital and molecular Mechanics) ONIOM scheme29 in Gaussian 0930 was implemented to carry out the hybrid QM/MM simulation. The entire molecular system was partitioned into two layers, a QM system treated by a high-level method and a MM system consisting of the entire molecular system treated by a low-level method. In this study, the MM system, described by the AMBER force field,31 consists of the UDP-α-D-Glc donor, the cellotriose acceptor, Mg2+, one H2O molecule (to fulfill the hexa-coordination of Mg2+), and residues 13−759 of the cytosolic domain in the crystallographic structure (PDB entry: 4HG6). The QM system, as shown in Figure 1B, containing 227 atoms, is composed of the UDP-αD-Glc donor, the cellotriose acceptor, Mg2+, one H2O molecule coordinating with Mg2+, and the side chains of seven residues involved in the catalytic reaction, or binding with the substrates, Y149, K226, D246, D248, E342, D343, and W383. The density functional M05-2X32 was used to treat the model system. The geometries of the model system were optimized with the 6C


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The Journal of Physical Chemistry B Cellotriose Rotation Barrier. To assess whether the observed glucose inversion could form after the glucose addition step or whether it must occur during addition, we modeled glucose rotation energies in a cellotriose molecule. The rotation barrier for the end glucose unit of the cellotriose has been assessed by carrying out a relaxed potential energy surface (PES) scan in ΦH/ΨH space on a 20° × 20° grid. As shown in Figure S2 (Supporting Information), the Φ/Ψ dihedral angles are defined using heavy atoms, O5′−C1′−O4− C4 and C1′−O4−C4−C5, respectively. By adding 120°, they can be converted to the widely used ΦH/ΨH dihedral angles, that is, H1′−C1′−O4−C4 and C1′−O4−C4−H4, respectively. The geometries were optimized using M05-2X/6-31+G(d) in Gaussian 09. The optimized structures were then subjected to single point calculations using the same method and including the default polarizable continuum model (PCM)39 implemented in Gaussian 09, IEF-PCM, to account for solvation effects.

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RESULTS AND DISCUSSION The QM/MM PES scan results suggested that BcsA catalyzes cellulose synthesis via a direct displacement SN2-type reaction with D343 being the general base. The optimized structures of the model system in the enzyme−product, enzyme−substrate, and transition state complexes are shown in Figure S3 (Supporting Information) and Figure 2, and key structural parameters are listed in Table 1. Reactant, Transition State, and Product Structures. The initial structure of reactant was generated by docking the UDP-α-D-Glc motif and Mg2+ into the crystal structure 4HG6 after translocating the nascent cellulose chain into the pore by one glucose unit, as detailed in the Methods section. The structure of the enzyme−substrate complex model was obtained from a QM/MM geometry optimization of this initial structure. In the optimized structure of the enzyme−substrate complex model, as shown in Figure S3A (Supporting Information) and Figure 2A, the Mg2+ ion is coordinated by two O atoms from D246, D248, of the conserved DXD motif, two O atoms from the diphosphate of UDP, and the O atom in a H2O molecule with distances of 2.02, 2.16, 2.17, 2.02, 2.01, 2.13, and 2.11 Å, respectively, approximately equal to the mean Mg−O bond length of ∼2.1 Å40 for hexa-coordinate Mg2+. As shown in Figure S3A (Supporting Information) and Figure 2A, the nonreducing end of the cellotriose acceptor O4 is 3.35 Å away from the anomeric carbon C1 of the glucose donor, UDP-Glc. The distance between O4 and H4 is 1.01 Å, and the distance between H4 and OD343, D343 of the highly conserved “TED” motif, is 1.60 Å, forming a hydrogen bond. This suggests that D343 will function as the general base as proposed in ref 8, facilitating the nucleophilic attack of the nonreducing end O4 on the anomeric carbon C1. The energy profile obtained by QM/MM PES scan calculations is shown in Figure 2D. A transition state is at the saddle point of the potential energy surface, which has exactly one imaginary frequency (negative frequency). However, the frequency calculation on the structure with the maximum energy obtained no imaginary frequency corresponding to either the nucleophilic attack of the nonreducing end O4 on the anomeric carbon C1 or the breaking of the glycosidic bond C1− O1, indicating a possible “overshooting”. Conducting a reverse QM/MM PES scan with the reaction coordinate being 0.05 Å increments from 1.55 to 2.15 Å, a structure of transition state was found, the point TS in Figure 2D. As shown in Figure S3B

Figure 2. (A) Enzyme−substrate, (B) transition state (arrows represent the normal mode of the calculated imaginary frequency), and (C) enzyme−product complex models obtained by QM/MM calculation. (D) Energy profile obtained by QM/MM PES scan calculations. (E) A proton was found transferred from the protonated general base D343 to UDP via O2 of the incoming glucose unit. (Left: the proton transfer channel found after a QM/MM optimization on the enzyme−product complex. Middle: the transition state model obtained via QM/MM PES calculation. Right: after the proton was fully transferred to UDP, the protonated UDP started to leave the active site.) Protons are shown as gray spheres.

(Supporting Information) and Figure 2B, in the structure of the SN2-type transition state, the distance of the forming glycosidic bond between the nonreducing end O4 and the anomeric D


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Table 1. Relevant Geometric Parameters for Enzyme−Substrate, Enzyme−Product, and Transition State Complex Models Obtained by QM/MM Calculations enzyme−substrate addinga 1st bond length (Å)

bond angle (deg)

torsion angle (deg)

a

OD343−H4 O4−H4 O1−C1 O4−C1 H1−C1−C2 C2−C1−O5 O5−C1−H1 Φ ΦH Ψ ΨH

enzyme−TS

addingb 2nd

enzyme−product

addinga 1st

addingb 2nd

addinga 1st

addingb 2nd

0.98 1.93 2.93 1.55 113.1 112.1 112.2 −104.0 16.9 160.4 −82.4

0.99 1.73 2.97 1.45 109.9 113.2 109.3 −18.2 101.6 −92.8 31.2

1.60 1.01 1.44 3.35 109.5 112.1 115.2 −61.3

1.69 0.99 1.44 3.01 110.4 111.2 105.9 25.4

1.48 1.04 1.65 2.10 122.1 115.7 115.5 −92.4

1.11 1.32 2.49 2.00 117.8 121.5 115.9 −13.2

100.6

−147.1

141.9

−80.8

The QM/MM model of adding the first glucose. bThe QM/MM model of adding the second glucose.

BcsA is found as ∼68 kJ/mol. Assuming the transmission coefficient is unity, the rate constant of polymerization is estimated to be ∼8.0 s−1 via transition state theory. The transmission coefficient for enzymatic reactions in water ranges from 0.3 to 1.0.43,44 Therefore, the rate constant of polymerization catalyzed by BcsA (8.0 s−1) estimated herein can be considered as the lower limit. It can range from ∼8.0 to ∼26.7 s−1. The experimental turnover number for BcsA has been estimated to be about ∼90 s−1.21 According to the above Eyring equation, assuming the transmission coefficient is unity, it corresponds to the activation Gibbs free energy of ∼62 kJ/mol. This is in reasonably good agreement with what we obtained through QM/MM simulations and suggests that overall cellulose biosynthesis is slow compared to many other enzymatic reactions. In the enzyme−product complex, the glucose is completely transferred from the UDP-α-D-Glc donor to the cellotriose acceptor. The distance of the new glycosidic bond between O4 and the anomeric carbon C1 is 1.55 Å, and the distance between C1 and O1 is 2.93 Å, indicating a complete breaking of the old linkage. The general base D343 is protonated, with the H+ being 0.98 Å away; at the same time, the distance between O4 and H4 is increased to 1.93 Å, indicating a full H+-transfer. In agreement with our data, the new crystal structure of the cyclic-di-GMP-activated Rhodobacter BcsA−B complex (PDB entry: 4P00) indeed shows D343 about 3.0 Å away from the nonreducing end (4′OH) of the cellulose (Figure S4A, Supporting Information).27 The position of the terminal glucose unit of the translocating glucan chain in the new structure is at about where the penultimate glucosyl residue of the translocating polysaccharide is located in the 4HG6 crystal structure (i.e., adjacent to W383 of the Q(Q/R)XRW motif), Figure S4 (Supporting Information). Hence, the initial 4HG6 structure was considered as representing a state after glycosyl transfer but before cellulose translocation, whereas the crystal structure 4P00 likely represents a state after cellulose translocation.27 This is also consistent with the position of the cellotriose acceptor in the enzyme−substrate complex in our QM/MM modeling and simulation (Figure S4, Supporting Information). Protonated UDP. After a QM/MM optimization on the enzyme−product complex, as shown in Figure 2E (left), the protonated general base D343 was found around 2.40 Å away from O2 of the incoming glucose unit, forming a characteristic

carbon C1 is 2.10 Å. The distance of the breaking glycosidic bond C1−O1 is increased from 1.44 to 1.65 Å. The distance between O4 and H4 is increased from 1.01 to1.04 Å; meanwhile, the distance between H4 and the carboxylate O of D343 decreases from 1.60 to 1.48 Å, forming a characteristic low-barrier hydrogen bond.28 The structure of the SN2-type transition state has revealed a concerted catalytic mechanism, where the nucleophilic attack of the nonreducing end O4 on the anomeric carbon C1, the breaking of the glycosidic bond C1− O1, and the transfer of proton H4 from the nonreducing end O4 to the general base D343 occur simultaneously. Concomitantly, the sum of the angles around C1 increases from 336.8 to 353.3°, showing that the anomeric carbon becomes planar (i.e., sp2 hybridized). The transition state, as shown in Figure 2B, has been confirmed by the vibrational frequency calculation on the whole QM/MM system. The only imaginary frequency, −333 cm−1, is the vibration corresponding to forming the new glycosidic bond between O4 and the anomeric carbon C1, the breaking of the glycosidic bond C1−O1, and the transfer of H4 from the nonreducing end O4 to the general base D343, as shown in Figure 2B. The calculated activation electronic energy (ΔEa) for this SN2-type transition state is ∼110 kJ/mol. In consideration of the thermal correction to the Gibbs free energies obtained via vibrational frequency calculations on the whole QM/MM system of the transition state and enzyme− substrate complex, the calculated activation Gibbs free energy (ΔGa) for this SN2-type transition state is ∼68 kJ/mol. This activation energy is consistent with estimates for Nacetylglucosaminyltransferase-I12 and β-1,4-galactosyltransferase-I.13 According to transition state theory (TST), the rate of reaction is related to the activation free energy via the Eyring equation41 as

⎛k T ⎞ k = ⎜ B ⎟e−ΔGa / RT ⎝ h2 ⎠ where k is the rate constant, kB is the Boltzmann constant, T is the absolute temperature, h is the Planck’s constant, ΔGa is the activation Gibbs free energy, and 2 is the transmission coefficient. Transition state theory is considered to estimate reliable reaction rate constants when activation energy barriers are 42 kJ/mol and above.42 The barrier height for the SN2-type transition state of adding the first glucose unit to cellulose in E


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Adding the Second GlucoseFormation of Alternating Glucose Unit in Cellulose. In order to investigate the mechanism of the formation of alternating glucose units with each succeeding glucose unit being flipped 180° relative to its neighbors, another QM/MM model adding a second glucose was constructed. The structure of the enzyme−substrate complex model was adapted from the previous enzyme− substrate complex model, as shown in Figure 2A but with the cellotriose acceptor being flipped as demonstrated in Figure 3A. The hexa-coordinated Mg2+ ion is also coordinated by two O atoms from D246, D248, of the conserved DXD motif, two O atoms from the diphosphate of UDP, and the O atom of a H2O

low-barrier hydrogen bond as the proton donor. Meanwhile, O1 of UDP diphosphate was around 2.7 Å away from O2 of the incoming glucose unit, forming a strong hydrogen bond as the H+ acceptor. This may suggest a H+-transfer channel, from the protonated general base D343 to UDP via the newly added glucose, facilitating UDP leaving the active site. The QM/MM PES scan simulation, as shown in Figure 2E, supported this hypothesis. The transition state has been confirmed by the vibrational frequency calculation on the model system. The frequency, −483 cm−1, is the vibration corresponding to transferring the proton from D343 to O2 and transferring another proton from O2 to UDP. The activation energy obtained from this QM/MM PES scan simulation for the H+transfer was ∼10 kJ/mol. Generally, a conserved water molecule in the active site may also assist the proton transfer to UDP. However, since structural studies on the Mg2+-UDPbound BcsA−B structure27 have not identified the conserved water molecules due to resolution limits, no water molecule was modeled here to serve this function. Addition of H2O within the active site could serve to lower the activation energy barrier, so we take our model value as an upper limit. Cellobiose Synthesis in the Aqueous Solution. The energy profile of cellobiose synthesis in the aqueous solution, as shown in Figure S5D (Supporting Information), was obtained by combining the forward and reverse PES scans against the reaction coordinate rO4−C1, as described in the Methods section. The local maximum at around 1.7 Å refers to the reorganization of the water shell surrounding cellobiose, as the hydrogen-bond network disturbed by the elongation of the O4−C1 bond. The calculated ΔEa for cellobiose synthesis in the aqueous solution is ∼150 kJ/mol. For cellobiose hydrolysis in the aqueous solution, the calculated ΔEa is ∼148 kJ/mol. In consideration of the thermal correction to the Gibbs free energies obtained via vibrational frequency calculations on the transition state, product complex (β-cellobiose + 26 H2O), and reactant complex (2 β-glucose + 25 H2O), the calculated ΔGa for cellobiose synthesis in the aqueous solution is ∼141 kJ/mol, and for cellobiose hydrolysis in the aqueous solution, the calculated ΔGa is ∼144 kJ/mol. Experimental activation energies for cellobiose hydrolysis reaction catalyzed by acids, such as sulfuric acid45 and 7.5% propylsulfonic acid,46 range from 110 to 133 kJ/mol.45,46 The energy barrier result obtained by PES scans is close the upper bound of experimental values, off by ∼10 kJ/mol, which suggests that a PES scanning against one reaction coordinate rO4−C1 is suitable for simulating cellobiose hydrolysis/synthesis reactions in the aqueous solution. Both the forward and the reverse PES scans against the reaction coordinate rO4−C1 identified a SN2-type transition state structure, as shown in Figure S5B (Supporting Information). When breaking the glycosidic bond, the anomeric configuration changed from β to α, whereas, when forming the glycosidic bond, the anomeric configuration changed from α to β, which suggests that in the aqueous solution both forming and breaking a glycosidic bond are via a mechanism resulting in the inversion of the anomeric configuration. Compared to the calculated Gibbs free energy reaction barrier for cellobiose synthesis in the aqueous solution, ∼141 kJ/mol, the Gibbs free energy barrier obtained in the enzymatic system with the activated glucose donor using QM/MM PES scan calculations is much lower, ∼68 kJ/mol. It is within the range of experimental activation barriers for glycosyltransferases (63−80 kJ/mol).47

Figure 3. (A) Enzyme−substrate, (B) transition state, and (C) enzyme−product complex models for adding the second glucose obtained by QM/MM calculation. (D) Energy profile obtained by QM/MM PES scan along the reaction coordinate rO4−C1. F


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for the surprisingly large difference between ΔEa and the corresponding ΔGa for the transfer of the first and second glucose. Therefore, together with the structural analysis in the previous paragraph, we believe that the transition state in the second model probably represents a “overshooting”, which usually results in an overestimated energy barrier. In both models, the UDP-Glc donors are at the same place and orientation. However, the distances between OD343 of the general base D343 and H4 of the cellotriose acceptor are different in the two enzyme−substrate complex models. In the enzyme−substrate complex model for adding the first glucose (referred to as the first model), the general base D343 forms a strong hydrogen bonding with O4 of glucose at the nonreducing end of the cellotriose receptor, and the OD343−H4 distance is 1.60 Å. However, the OD343−H4 distance is 1.69 Å in the enzyme−substrate complex model for adding the second glucose, and the general base D343 forms a bidentate hydrogen bonding not only with O4 but also with O3 of glucose at the nonreducing end of the cellotriose receptor. The longer distance between OD343 and H4, therefore the weaker hydrogen bonding, might contribute to the higher energy barrier. Another reason may be that QM/MM geometry optimizations are not sufficient to represent protein structure changes induced by the conformational change of the cellotriose (being flipped), which may help the enzyme to stabilize of the transition state so as to decrease the entropy. Molecular dynamics (MD) simulations on the second QM/MM model could serve to test this possibility. Long-time-scale MD simulations sampling together with QM/MM may lower the calculated activation Gibbs free energy for adding the second glucose to the flipped cellotriose. Relaxing the Newly Added End Glucose Unit. As shown in Figures 2C and 3C, in the enzyme−product complex model obtained via QM/MM optimization, the newly added glucose was not yet in the plane of the cellotriose. In order to enter the cellulose transmembrane channel, the newly added glucose unit needs to be in the plane of the cellulose polymer, as indicated in the crystal structure 4HG6 (colored in gray in Figure 4). In order to investigate whether the newly added glucose unit can rotate into the plane of the polymer, the newly formed cellotetraose was further relaxed via a QM simulation in which all atoms but the newly added glucose unit were fixed. As demonstrated in Figure 4 and Table 2, after the relaxation via QM calculations, the end glucose units of the first and second QM/MM models can both rotate into the plane of the polymer. However, the rotation directions are opposite, as indicated in Figure 4C and D. The ΦH and ΨH angles of the end glucoses are closer to a syn-ΦH/syn-ΨH configuration, representing a conformation similar to the last four glucose units of the cellulose polymer in the crystal structure 4HG6,8 supporting the notion that the crystal structure represents a reaction state directly after glycosyl transfer. Intrachain hydrogen bonding interactions, such as O3H3···O5 and O2H2···O6, are the essential interactions that stabilize β-1,4 glucans.48 To investigate if the O3H3···O5 H-bond formation could be the driving force for the rotation of the newly added glucose unit, we replaced the O3H3 group of the penultimate glucose unit with an H atom. Interestingly, as shown in Figure 4C and D and Table 2, we found that in this case the newly added end glucose unit still rotates closely into the plane of the cellotriose, with ΦH and ΨH angles of the end glucose being at a more syn-ΦH/syn-ΨH configuration, relative to the configuration right after QM/MM optimization. However, as shown

molecule with all the distances being ∼2.1 Å, as shown in Figure 3A top and Table 1. The nonreducing end of the cellotriose acceptor O4 is 3.01 Å away from the anomeric C1 of the glucose donor, UDP-Glc. The distance between H4 and OD343, D343 of the highly conserved “TED” motif, is 1.69 Å, also forming a strong hydrogen bond to facilitate the nucleophilic attack of the nonreducing end O4 on the anomeric C1. However, the distance between H4 and OD343 is 1.60 Å in the previous QM/MM model. The energy profile obtained by QM/MM PES scan calculations is shown in Figure 3D. Conducting a forward QM/MM PES scan with the reaction coordinate being −0.10 Å increments from 3.01 to 1.51 Å and a reverse QM/MM PES scan with the reaction coordinate being 0.05 Å increments from 1.45 to 2.70 Å, a transition state structure (the point TS in Figure 3D) was found. The structure of the SN2-type transition state reveals a similar concerted catalytic mechanism as revealed by the previous QM/MM model. As shown in Figure 3B and Table 1, in the structure of the SN2-type transition state, the sum of the angles around C1 increases from 327.5 to 355.2°, showing that the anomeric carbon becomes planar as well. The distance of the forming glycosidic bond between the nonreducing end O4 and the anomeric carbon C1 is 2.00 Å, similar to the one in the previous QM/MM model. However, the distance of the breaking glycosidic bond C1−O1 is 2.49 Å instead of 1.65 Å in the previous QM/MM model. Moreover, the distance between O4 and H4 is increased from 0.99 to 1.32 Å instead of 1.04 Å in the previous QM/MM model; meanwhile, the distance between H4 and OD343 is decreased from 1.69 to 1.11 Å instead of 1.48 Å in the previous QM/MM model. These geometric differences indicate that the transition state structure obtained in the second QM/MM model is closer to the reaction product compared to the first. The transition state, as shown in Figure 3B, has been confirmed by the vibrational frequency calculation on the whole QM/MM system. The single imaginary frequency, −278 cm−1, corresponds to the formation of the new glycosidic bond between O4 and the anomeric C1, breaking the glycosidic bond C1−O1, and the transfer of H4 from the nonreducing end O4 to the general base D343, as shown in Figure 3B. The calculated ΔEa for this SN2type transition state is ∼159 kJ/mol. In consideration of the thermodynamic correction to the Gibbs free energies obtained via vibrational frequency calculations on the whole QM/MM system of the transition state and enzyme−substrate complex, the calculated activation Gibbs free energy (ΔGa) for this SN2type transition state is ∼161 kJ/mol. In this case, the ΔGa is not significantly lower than the ΔEa, as was found for adding the first glucose unit. Compared to what we obtained for adding the first glucose, ∼68 kJ/mol, the Gibbs free energy barrier of adding the second glucose, ∼161 kJ/mol, is significantly higher. After analyzing the energetics of both QM/MM models, as shown in Table S1 (Supporting Information), we found that in the previous model the entropy of the transition state is lower than that of the ground state by ∼34 kJ/mol, as shown in Table S1 (Supporting Information), which indicated that the BcsA enzyme catalyzed the glycosyl transfer reaction through typical “entropy reduction”. However, in the second model when transferring the second glucose, the entropy of the transition state is increased from that of the ground state by ∼18 kJ/mol, as shown in Table S1 (Supporting Information). The opposite entropy changes in these two models are also the main reason G


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the intramolecular hydrogen bonding O3H3···O5 (O5 of the newly added glucose at site −1) is not the primary driving force for relaxation. However, it facilitates the closer rotation of the end glucose units into the plane of the polymer. The second intramolecular hydrogen bonding O2H2···O6 was not formed during the polymerization or relaxation, as depicted in Figure 4C and D. This bond is likely formed during cellulose translocation into the pore after the polymerization. Rotating the End Glucose Unit after the Polymerization Step. In nature, cellulose has a 2-fold screw-axis conformation.14,49 In order to investigate whether the newly added end glucose unit can rotate freely to adopt the inverted orientation with respect to its neighbors,8 we determined the energy barrier for rotating the end glucose unit around the glycosidic bond. Our hypothesis is that, if the rotational energy barrier is high, then the rotation must occur during polymerization rather than rotating after polymerization. To address this question, we conducted a relaxed PES scanning through the dihedral angles ΦH and ΨH of the end glucose unit of a cellotriose molecule. We found that the energy barrier for rotating the end glucose unit of cellotriose is about 129 kJ/mol in the gas phase and about 124 kJ/mol in water, as shown in Tables S2 and S3 (Supporting Information). This indicates that the formation of alternating glucose units in cellulose, i.e., the 2-fold screw-axis conformation, is likely to occur during polymerization before the newly added glucose unit relaxes into the plane of the cellulose polymer, and not after. Previous computational results on cellobiose conformation demonstrated that anti-ΦH/syn-ΨH is the preferred gas phase conformation, whereas syn-ΦH/syn-ΨH is the preferred aqueous phase conformation.50−52 Our conformation analysis of cellotriose showed that syn-ΦH/syn-ΨH is the preferred conformation in both gas and aqueous phases for the end glucose unit of cellotriose, consistent with the 2-fold screw axis of cellulose. As shown in Figure 5, the most preferable structure is at the syn-ΦH/syn-ΨH conformation with the relative energy value of zero in both gas and aqueous phases. Also, most of the low energy conformations adopted the syn-Φ H /syn-Ψ H conformation, whereas only a few adopted anti-ΦH/syn-ΨH or syn-ΦH/anti-ΨH conformations. In order to find out the constraint of the active site to the rotation of the end glucose unit, we rotated the end glucose unit within the catalytic pocket of PDB entry 4HG6. We found that, due to the steric hindrance of residues lying in the catalytic pocket, such as K226, D246, H249, C318, G319, S320, T341, D343, Q379, R382, and W383, the end glucose unit cannot freely rotate within the catalytic pocket. The rotation of the end glucose unit is limited to certain syn-ΦH/syn-ΨH and syn-ΦH/ anti-ΨH areas, shown as the black contour line in Figure 5A. It covers almost all of the low-energy syn-ΦH/syn-ΨH, and very few low-energy syn-ΦH/anti-ΨH conformations. However, no anti-ΦH/syn-ΨH conformation is allowed within the catalytic pocket, which is the low-energy gas-phase structure predicted by QM calculations.50−52

Figure 4. Relaxing the newly formed cellotetraose in the enzyme− product complex model (adding the first glucose model, colored in cyan; adding the second glucose model, colored in green) obtained via QM/MM optimization. (A) In the enzyme−product complex model obtained via QM/MM optimization, the newly added end glucose unit was not yet in the plane of the cellotriose, compared with that of the cellulose in crystal structure 4HG6 (colored in gray). (B) After the newly formed cellotetraose is further relaxed via structural optimizations at the M05-2X/6-31G(d) level, the newly added end glucose unit rotated into the plane of the cellotriose. (C) The newly added end glucose units in both models can rotate into the plane of the polymer. The intrachain hydrogen bonds (O3H3···O5 and O2H2··· O6) are designated using dashed lines. The newly added glucose unit is at site −1. (D) When the O3 in the proceeding glucose with respect to the newly added end glucose is replaced by a H atom, the newly added end glucose unit can still rotate very closely into the plane of the cellotriose.

Table 2. Torsion Angles of the Newly Transferred End Glucose Unit

adding the first glucose

adding the second glucose

ΦH (deg)

ΨH (deg)

cellotetraose via QM/MM

16.9

−82.4

cellotetraose after relaxation cellotetraose (O3 → H) after relaxation cellotetraose via QM/MM

29.9 41.5

−42.0 −35.8

101.6

31.2

30.7 36.4

2.7 21.4

cellotetraose after relaxation cellotetraose (O3 → H) after relaxation

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CONCLUSIONS Overall, cellulose is an abundant and exceedingly versatile polymer. Its glucose units are arranged in a pseudo-2-fold screw symmetry, which confers distinct hydrophobic and hydrophilic polymer properties. Our QM/MM analyses provide the first theoretical model of the mechanism by which BcsA, a member of processive glycosyltransferases,4,8,16 elongates a cellulose polymer one glucosyl moiety at a time. Following glycosyl

in Figure 4C, the ΦH and ΨH angles of the cellotetraose containing a H3O3 were at a slightly more syn-ΦH/syn-ΨH configuration with respect to the ΦH and ΨH angles of the cellotetraose lacking the 3′ hydroxyl group. This indicates that H


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Furthermore, a cellulose biosynthesis rate of approximately 8 s−1 compares well with other polymer translocation systems, such as bacterial post-translational protein translocation occurring at an estimated rate of about 4−5 amino acids per second.54 Bacterial and plant cellulose synthases share many sequence motifs implicated in substrate binding, glycosyl transfer, and cellulose translocation. It is thus likely that the mechanism of cellulose biosynthesis is evolutionarily conserved. Cellulose microfibril formation, primarily observed in plants, may arise from the close association of multiple CesA’s in the plant plasma membrane (referred to as rosettes), which allows individual glucan chains to interact and align as they emerge from the CesA TM channel.

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ASSOCIATED CONTENT

S Supporting Information *

Cellobiose surrounded by 26 H2O molecules (Figure S1), definition of Φ/Ψ dihedral angles using heavy atom (Figure S2), schematic representation of QM/MM models (Figure S3), comparison of the relative position of cellotriose/cellulose acceptor (Figure S4), QM/MM models and the energy profile of cellobiose synthesis (Figure S5), energetics of QM/MM models (Table S1), and relative energies of cellotriose when rotating ΦH and ΨH of the end glucose unit in the gas phase (Table S2) and in water (Table S3). The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.5b01433.

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Figure 5. Contour maps of relative energies of cellotriose when rotating ΦH and ΨH of the end glucose unit in gas (A) and water (B). Contour lines are drawn from 5 to 125 kJ/mol with an interval of 10 kJ/mol. The energy barrier for rotating the end glucose unit of cellotriose is about 129 kJ/mol in the gas phase and about 124 kJ/mol in water. The black contour line in part A represents the allowed ΦH and ΨH of the end glucose unit due to the constraints when rotating inside the catalytic pocket of BcsA PDB entry 4HG6. The point X represents the polymerization product obtained from the first QM/ MM model.

AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS We thank Dr. Ming Tien (The Pennsylvania State University) for his help and useful discussions. This work was supported as part of The Center for LignoCellulose Structure and Formation, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, under Award No. DE-SC0001090. Computational support was provided by the Research Computation and Cyberinfrastructure (RCC) group at The Pennsylvania State University. This work also used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant No. OCI1053575. Specifically, it used the Blacklight system at the Pittsburgh Supercomputing Center (PSC).

transfer via a direct SN2-type displacement reaction, the newly added glucosyl residue rotates into the plane of the cellulose polymer, where it is stabilized by intramolecular hydrogen bonds with the penultimate glucose unit. The rotation direction is dictated by the acceptor orientation and alternates between neighboring glucose units, consistent with a 2-fold screw symmetry. This symmetry is maintained, even when the newly added glucose unit cannot form hydrogen bonds with the penultimate glucosyl moiety, suggesting that the alternating orientation is primarily a consequence of intrachain steric interactions. On the basis of transition state theory and the calculated activation free energy obtained from our analyses, BcsA catalyzes cellulose polymerization at a rate of approximately 8 glucose units per second. In agreement with other experimental data, this suggests that cellulose biosynthesis is rather slow; however, modulation of the catalytic rate by enzyme oligomerization or interaction with other components cannot be excluded. Cellulose biosynthesis requires not only glycosyl transfer but also the translocation of the polysaccharide by one glucose unit after each elongation step. Our calculated reaction rate is comparable with rates obtained for nonprocessive glycosyltransferases, suggesting that the additional translocation step performed by the processive enzymes is not rate limiting.53

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K


MM Study of the Molecular

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