Molecular dynamics simulation of the last step of a catalytic cycle: Product release from the active site of the enzyme chorismate mutase from Mycobacterium tuberculosis

Authors


Abstract

The protein chorismate mutase MtCM from Mycobacterium tuberculosis catalyzes one of the few pericyclic reactions known in biology: the transformation of chorismate to prephenate. Chorismate mutases have been widely studied experimentally and computationally to elucidate the transition state of the enzyme catalyzed reaction and the origin of the high catalytic rate. However, studies about substrate entry and product exit to and from the highly occluded active site of the enzyme have to our knowledge not been performed on this enzyme. Crystallographic data suggest a possible substrate entry gate, that involves a slight opening of the enzyme for the substrate to access the active site. Using multiple molecular dynamics simulations, we investigate the natural dynamic process of the product exiting from the binding pocket of MtCM. We identify a dominant exit pathway, which is in agreement with the gate proposed from the available crystallographic data. Helices H2 and H4 move apart from each other which enables the product to exit from the active site. Interestingly, in almost all exit trajectories, two residues arginine 72 and arginine 134, which participate in the burying of the active site, are accompanying the product on its exit journey from the catalytic site.

Introduction

Chorismate mutase (CM) catalyzes the Claisen rearrangement of chorismate to prephenate (Fig. 1), which is the first step in the biosynthesis of tyrosine and phenylalanine in bacteria, fungi, and plants.1 The shikimate pathway, responsible for the biosynthesis of aromatic compounds, is absent from mammals which thus do not possess CM activity. Additionally, the presence of exported CMs has been shown to correlate with the pathogenicity of certain organisms, like Mycobacterium tuberculosis. CM represents therefore a promising target for the development of antibiotics, fungicides, and herbicides. The transformation of chorismate to prephenate (Fig. 1), formally a [3,3]-pericyclic rearrangement, also known as a Claisen rearrangement, proceeds in the absence of enzymatic catalysis as a concerted but asynchronous process.2 The mechanism of the uncatalyzed CM reaction is known to involve a transition state with a chair-like conformation.3 The endoxabicyclic dicarboxylic acid 1,4 is a good geometric mimic of this transition state (Fig. 1 on the right).

Figure 1.

Schematic diagram illustrating the transformation of chorismate to prephenate, a reaction catalyzed by chorismate mutase. On the right the TSA for the reaction.

Natural CMs accelerate the rearrangement of chorismate more than a million-fold.4 CMs have been widely studied experimentally5–8 and computationally,9–11 mainly to elucidate the transition state of the enzyme catalyzed reaction and the origin of the very high catalytic rate enhancement over the solution phase reaction. As these matters have been so extensively studied, we turned our interest to another critical aspect of catalysis, though less determining for catalytic rate, which is substrate entry into the active site and product release from it.

Interestingly, two unrelated protein scaffolds carry out the CM reaction: CMs are found to exhibit one of two folds: the homotrimeric α–β fold of the relatively rare AroH class12 and the homodimeric all-α-helical fold of the more abundant AroQ class.5, 7, 13 In the present investigation, we have chosen the secreted CM from Mycobacterium tuberculosis (MtCM, Fig. 2) as a model system for the AroQ subclass. Its crystal structure was determined at high resolution, both in its unliganded form and in complex with the transition state analog (TSA). In the TSA bound enzyme structure, the TSA is completely buried in the active site pocket of MtCM. As the active site is shielded from bulk solvent and leaves no gate for substrate entry, it is puzzling how the ligand can enter the cavity. Examination of the crystal structure indicated one region where substrate entry and/or product exit could possibly occur. In the structure of the apo enzyme, helices H2 and H4 (see Fig. 2) are further apart from each other than in the TSA complexed enzyme, which has led to the hypothesis that the substrate entry gate is located between those helices.7 Yet it remains of interest to confirm this hypothesis and to investigate the pathway the substrate would take to enter or the product to exit from the still relatively shielded active site.

Figure 2.

Monomeric MtCM and the three ligands, the substrate chorismate, the TSA, and the product prephenate after the energy minimization for the mMtCM-CHR (left), mMtCM-TSA (middle) and mMtCM-PRE-1(right) systems. For the mMtCM-PRE-1 system, protein residues Arg49, Lys60, Arg72, Thr105, and Arg134 are shown. Black lines are drawn between the Cα atoms of those residues and carbon C10 of prephenate. For the three ligands, carbon atoms are depicted in cyan, oxygen atoms in red and hydrogen atoms in white. MtCM is represented as a ribbon diagram.

Previously molecular dynamics (MD) and other computer simulations have been used to investigate substrate entry and product exit from protein binding pockets.14–16 Using standard MD simulations, however, it is rather unlikely to observe substrate, TSA or product entry into the binding pocket, and as the chorismate and TSA are strongly bound to the protein and therefore, not likely to exit during the simulation time, we only assessed the question most accessible using MD simulations: which pathway does the product take when exiting the catalytic pocket buried inside the enzyme.

Using MD, we simulated the last step of the catalytic cycle, the product exit from the active site. We performed simulations of the apo enzyme, and of the enzyme bound to its three ligands chorismate, TSA, and prephenate. Additionally, we performed multiple simulations of the prephenate bound to the enzyme to statistically investigate product exit from the active site. We analyzed the physical pathways for product egress and the key residues involved in the gating mechanism.

Results

Table I gives an overview of the 19 simulations performed. The 326-residue protein M. tuberculosis CM (Fig. 2) was simulated in its naturally occurring dimeric form, free or with one of its three ligands chorismate, TSA, and prephenate and in an artificial monomeric form, free (starting from two different X ray structures I and II, see Methods section) or with one of its three ligands (MtCM complexed with prephenate was simulated eleven times). The monomeric MtCM is shown in Figure 2 bound to its three ligands, chorismate on the left, TSA in the middle and prephenate on the right. CM catalyses the reaction depicted in Figure 1: the transformation of chorismate to prephenate, passing through a transition state which is geometrically similar to the TSA depicted in the same Figure.

Table I. Overview of the MD Simulations. I: PDB Entry 2FPI, II: PDB Entry 2FP2
Simulation nameX-ray starting structureFormLigandNumber of water molecules
dMtCM-IIDimer36619
dMtCM-CHRIIDimerChorismate36585
dMtCM-TSAIIDimerTransition state analog36587
dMtCM-PREIIDimerPrephenate36591
mMtCM-IIMonomer21539
mMtCM-IIIIMonomer24040
mMtCM-CHRIIMonomerChorismate21351
mMtCM-TSAIIMonomerTransition state analog20993
mMtCM-PRE-1IIMonomerPrephenate21309
mMtCM-PRE-2IIMonomerPrephenate21309
mMtCM-PRE-3IIMonomerPrephenate21309
mMtCM-PRE-4IIMonomerPrephenate21309
mMtCM-PRE-5IIMonomerPrephenate21309
mMtCM-PRE-6IIMonomerPrephenate21309
mMtCM-PRE-7IIMonomerPrephenate21309
mMtCM-PRE-8IIMonomerPrephenate21309
mMtCM-PRE-9IIMonomerPrephenate21309
mMtCM-PRE-10IIMonomerPrephenate21309
mMtCM-PRE-11IIMonomerPrephenate21309

In this section, the results of the analysis of structural and dynamic properties of the protein and the substrates are presented. Atom-positional root-mean-square deviations (RMSD) of the simulated proteins relative to the initial structure and the occurrence of regular secondary structure are presented as a function of time. Five protein-prephenate atomic distances (drawn in Fig. 2 in the right panel) Arg49-Cα − PRE-C10, Lys60-Cα − PRE-C10, Arg72-Cα − PRE-C10, Thr105-Cα − PRE-C10, and Arg134-Cα − PRE-C10 are calculated from the simulation trajectories to monitor product exit from the active site.

The atom-positional RMSD of different sets of atoms of the protein from the energy-minimized X-ray structures are shown as a function of simulation time in Figure 3 for five monomer MtCM MD simulations. These simulations are: two free enzyme simulations started from different X-ray structures, structure I crystallized without ligand and structure II crystallized with TSA, from which the TSA was removed before simulating, and three simulations in which the enzyme is bound to its ligands chorismate, TSA or prephenate. All simulations display an RMSD below 0.4 nm for the Cα atoms that are part of an α-helix. Simulations mMtCM-I and mMtCM-TSA show an all atom RMSD value below 0.4 nm as well. Those two simulations have starting structures which correspond exactly to the simulated system, the X-ray structure I crystallized without ligand for mMtCM-I and X-ray structure II crystallized with TSA for mMtCM-TSA. It is thus not surprising that those two simulations display the lowest RMSD values. The three other simulations have an all atom RMSD below 0.6 nm, simulation mMtCM-PRE-1 deviates most from the initial X-ray structure.

Figure 3.

Time evolution of atom-positional RMSD with respect to the energy-minimized X-ray starting structures for five monomer MtCM MD simulations. From top to bottom for the mMtCM-I, mMtCM-II, mMtCM-CHR, mMtCM-TSA, and mMtCM-PRE-1 simulations. RMSD of all Cα atoms in black, Cα atoms that are part of an α-helix in red, Cα atoms that are part of a loop in blue and all atoms in green.

The atom-positional RMSD of different sets of atoms of the protein from the energy-minimized X-ray structures are shown as a function of simulation time in Figure 4 for four dimer MtCM MD simulations. These simulations are: free enzyme started from the energy-minimized X-ray structure I and three simulations in which the enzyme is bound to its ligands chorismate, TSA or prephenate. All RMSD values are shown for the second subunit of the dimer only (the one where the ligand is bound), to allow comparison with the mMtCM simulations. All simulations display an RMSD below 0.3 nm for the Cα atoms that are part of an α-helix. Simulations dMtCM and dMtCM-TSA show an all atom RMSD value below 0.4 nm. Those two simulations have starting structures which correspond exactly to the simulated system, the X-ray structure I crystallized without ligand for dMtCM and the X-ray structure II crystallized with TSA for dMtCM-TSA. It is thus not surprising that those two simulations display the lowest RMSD values. The two other simulations have an all atom RMSD deviation below 0.5 nm, simulation dMtCM-PRE deviates most from the original X-ray structure, mainly due to changes in the structure of the loops.

Figure 4.

Time evolution of atom-positional RMSD with respect to the energy-minimized X-ray starting structures for the four dimer MtCM MD simulations. From top to bottom for the dMtCM-I, dMtCM-CHR, dMtCM-TSA, and dMtCM-PRE simulations. RMSD of all the Cα atoms in black, Cα atoms that are part of an α-helix in red, Cα atoms that are part of a loop in blue and all atoms in green.

The occurrence of regular α-helical secondary structure as a function of time for five mMtCM simulations is presented in Figure 5. The presence of a (i + 4)NH-(i) CO hydrogen bond indicates the presence of α-helical structure. Each protein monomer consists of six α-helices (see Fig. 2). Those six helices are mostly conserved during the course of the MD simulations. The secondary structure is thus stable in all five simulations, which is consistent with the relatively small RMS deviation of the backbone atoms from the initial X-ray structures. The occurrence of regular α-helical secondary structure is not shown for the dimer simulations as it is very similar to that in the monomer simulations.

Figure 5.

Time evolution of the six alpha helices in the monomeric MtCM in five mMtCM MD simulations. The presence of a (i + 4) NH − (i)CO hydrogen bond is indicated with a black dot. From top to bottom for the mMtCM-I, mMtCM-II, mMtCM-CHR, mMtCM-TSA, and mMtCM-PRE simulations.

Substrate protein hydrogen bonds which occur during more than 5% of the simulation time for all dimer simulations dMtCM-TSA, dMtCM-PRE and all monomer simulations mMtCM-CHR, mMtCM-TSA, mMtCM-PRE-1 to mMtCM-PRE-11 are shown in Table II. The number and extent of occurrence of the hydrogens bonds are higher for the simulations where the protein is complexed with chorismate or the TSA than for the simulations where the protein is complexed with prephenate. Hydrogen bonds which occur longest are between the substrate chorismate and the protein (up to 82% of the simulation time). The greatest number of different hydrogen bonds appear in the simulations where the protein is complexed with the TSA (up to 20 different hydrogen bonds). In the simulations where the protein is complexed with the product, different hydrogen-bond patterns are observed. Most hydrogen bonds occur in the simulation mMtCM-11, where prephenate is not leaving the binding pocket.

Table II. Protein Ligand Hydrogen Bonds for All Simulations
DonorAcceptorCHRTSAPRE
dmdmdm1m2m3m4m5m6m7m8m9m10m11
  1. Only occurrences of hydrogen bonds larger than 5% in any of the simulations are listed.

Arg49 NηO10472019195
Lys60 NζO4518754222
Lys60 NζO1054
Lys60 NζO111539516
Ile67 NO1114
Glu68 NO1115
Asp69 NO4132228108369
Asp69 NO1110
Ser70 OγO47
Ser70 OγO10917156
Ser70 OγO119
Gly71 NO106
Gly71 NO1124
Arg72 NO481313
Arg72 NO10931
Arg72 NO111837
Arg72 NϵO410885
Arg72 NϵO10217740
Arg72 NϵO111199118
Arg72 NηO466
Arg72 NηO10936
Arg72 NηO116
Val73 NO11936
Glu74 NO113911
Gln75 NO1141
Gln75 NϵO103628
Gln76 NO1134
Gln76 NϵO431
Gln76 NϵO103524911611612712135881328335
Gln76 NϵO1122581852
Thr105 OγO4773
Thr195 OγO10100499671834
Ser133 OγO1118
Arg134 NϵO467
Arg134 NϵO10611
Arg134 NϵO1121513636176965
Arg134 NηO48
Arg134 NηO1014
Arg134 NηO111619271911639126
Arg143 NϵO45
Gln147 NϵO1116

The monomer and dimer MtCM simulations are comparable in the RMSD deviations from the starting structure and in their secondary structures observed during 25 ns of simulations. Therefore, we decided to simulate the product exit from the exit site multiple times for the monomeric MtCM system, as this reduced the required simulation time considerably.

Product exit analysis

The time evolution of five protein-product atomic distances (drawn in Fig. 2 in the right panel) Arg49-Cα − PRE-C10, Lys60-Cα − PRE-C10, Arg72-Cα − PRE-C10, Thr105-Cα − PRE-C10, and Arg134-Cα − PRE-C10 was calculated from the simulation trajectories to monitor prephenate exiting from the active site. Those five residues were chosen as they are part of the active site, see Figure 2. The arginine 49 is situated on helix H1, the two arginines 72 and 134 are situated on the two helices (H2 and H4) which are thought to open for substrate entry or product exit to occur.7 Threonine 105 is buried deep in the catalytic pocket and lysine 60 is situated higher on helix H4. Mutation experiments have identified arginines 49, 72, and 134 and lysine 60 as important for catalysis17, 18

Those five distances were calculated as well for the mMtCM-CHR, mMtCM-TSA, dMtCM-CHR, and dMtCM-TSA simulations and are displayed in the lower panels of Figure 6. The distances did not change during the course of the simulations and were similar for the four systems, with average values of the five distances over the whole simulation trajectories of 0.9 nm, 0.9 nm, 0.8 nm, 1.1 nm, and 0.9 nm for the four aforementioned simulations, respectively. Thus, chorismate and TSA do not leave the binding pocket in the monomer or dimer simulations.

Figure 6.

Time evolution of five ligand-protein atom-atom distances for all 12 MtCM prephenate simulations, 2 MtCM chorismate and 2 MtCM TSA simulations. On the left from top to bottom for mMtCM-PRE-1, 3, 5, 7, 9, 11, mMtCM-CHR, mMtCM-TSA and on the right from top to bottom for mMtCM-PRE-2, 4, 6, 8, 10 and dMtCM-PRE, dMtCM-CHR, dMtCM-TSA. The protein-prephenate distances Arg49-Cα − PRE-C10, Lys60-Cα − PRE-C10, Arg72-Cα − PRE-C10, Thr105-Cα − PRE-C10, and Arg134-Cα − PRE-C10 are shown in yellow, black, red, green and blue, respectively.

For the 12 simulations of prephenate bound to MtCM, the time evolution of the five distances is displayed in the upper panels of Figure 6. Product exit occurs when all five distances reach a value of at least 1.3 nm. In eight out of the 12 simulations, product exit from the binding pocket occurs: simulations mMtCM-PRE-1, 2, 3, 5, 7, 9, 10, and dMtCM-PRE. Prephenate exit occurs between 12 and 25 ns simulation time in those eight trajectories. When bound to the protein, prephenate shows more variation in and larger values of the five distances than the bound chorismate or TSA.

A visual analysis of the simulation trajectories was performed for the eight cases where the product exits the active site, leading to the conclusion that the product exit always occurs in a similar fashion. The product exit mechanism is illustrated in Figures 7 and 8 for the dimer protein-prephenate and one of the monomer-prephenate simulations. Configurations were taken at the beginning (violet) of the simulations, at the end (red) of the simulations and at a time point where prephenate is about to exit the binding pocket, 22 ns for dMtCM-PRE, and 17 ns for mMtCM-PRE-2. As proposed from an analysis of two X-ray structures,7 product exit occurs with helix H2 and helix H4 coming further apart. This can be seen at time steps 17 ns (dMtCM) and 22 ns (mMtCM) and at the end of the simulations, where the orange and red ribbon structures have the two helices further apart from each other than in the violet ribbon structure (0 ns). Arginines 72 (on helix H2) and 134 (on helix H4) form a barrier for prephenate (or chorismate or TSA) to enter or to exit the active site at the beginning of the simulation (and in the X-ray structures). However during the course of the simulations those arginines move further apart so prephenate can exit. Furthermore, those two arginines actually accompany prephenate during the exit process, that is, those arginines move outwards together with prephenate.

Figure 7.

Configurations taken at three time points during the course of the MD simulation dMtCM-PRE. On the left the protein and the products are superimposed at time 0 ns and at time 22 ns, on the right they are superimposed at time 0 ns and 25 ns. Residues Arg72 and Arg134 and the product prephenate are shown in a van der Waals filling fashion. MtCM is represented as a violet (0 ns), orange (22 ns), and red (25 ns) ribbon diagram. Prephenate is shown in yellow (0 ns), green (22 ns) or is not present (25 ns).

Figure 8.

Configurations taken at three time points during the course of the MD simulation mMtCM-PRE-2. On the left the protein and the product are superimposed at time 0 ns and at time 17 ns, on the right they are superimposed at time 0 ns and 25 ns. Residues Arg72 and Arg134 and the product prephenate are shown in a van der Waals filling fashion. MtCM is represented as a violet (0 ns), orange (17 ns), and red (25 ns) ribbon diagram. Prephenate is shown in yellow (0 ns), green (17 ns) or is not present (25 ns).

Discussion

We have performed MD simulations for a set of enzyme-ligand complexes. The CM from Mycobacterium tuberculosis was simulated with its ligands chorismate, TSA or prephenate in a naturally occurring dimeric form and in an artificial monomeric form. The structures determined by X-ray crystallography were stable during simulation and atom-positional RMS deviations from the X-ray starting structure were minimal in both the monomer and dimer simulations. Yet, the product bound protein displayed a larger deviation from the apo- or TSA- bound protein crystal structure and also displayed larger average values and fluctuations of the five distances between ligand and protein atoms. In an effort to learn more about the mechanism of product exit from the active site, we have consequently performed multiple simulations of prephenate bound to MtCM in a monomeric form as this was computationally less time consuming. We have monitored five protein-product atom–atom distances and performed a visual analysis of the product exit conformations to learn more about the mechanism of product exit from the binding pocket. We note, however, that product exit is a stochastic event that may occur early or late or not at all in a simulation of limited length. Therefore, product residence times in the active site could not be meaningfully evaluated from the 11 protein-product simulations. We can conclude though that a specific path is taken by prephenate to exit the protein active site. This path does not involve large structural rearrangements, but we do see the largest changes in secondary structure and RMSD deviations in the simulations where MtCM is complexed with prephenate; the two helices H2 and H4 move apart from each other, leaving the binding pocket less occluded from the surrounding media. Arginines 72 and 134 are thought to make hydrogen bonds to a water molecule in the active site and to the carboxyl group at C10 of prephenate, respectively7 and are crucial for enzymatic catalysis. We find that those residues are involved in prephenate release and might guide it out of the binding pocket. Those residues might as well be involved in guiding the substrate chorismate into the binding pocket, in a mechanism similar to product release. Residues 72 and 134 might fetch the substrate from the solvent and guide its entrance into the binding pocket where catalysis then occurs.

As the mentioned residues are as well involved in catalysis and are conserved throughout all available CM proteins,19 it is not possible to investigate their role in substrate binding or product release by experimental means. Mutations of those residues would lead to loss of catalytic activity and probably a loss of ligand binding as well. Thus, it is not possible to distinguish experimentally between the role of those residues in chorismate and TSA positioning inside the enzymatic pocket versus their role in substrate binding and product release. In contrast, alchemical MD simulations could provide further insights into this issue. One could, for example mutate those residues when the substrate or TSA or product are bound in the enzymatic pocket to see the effect of those mutations on the protein–ligands interactions. Mutation of those residues to lysine (as well positively charged), to a noncharged arginine or to a leucine would be of interest. Detailed investigation of the effect of certain changes to the charge, shape, and structure of those two arginines promises to extend our understanding of how those residues influence the accessibility of the catalytic pocket of this enzyme.

Methods

Molecular model

Table I gives an overview of the simulations performed, which were carried out using the GROMOS20 simulations software and the GROMOS 45A4 force field.21 A total of 19 MD simulations of the enzyme MtCM were performed, summing to a total simulation time of 450 ns. Four simulations of the dimeric MtCM and 15 simulations of the monomeric MtCM were performed (see Table I). The enzyme was simulated in its free form, or bound to one of its ligands: substrate chorismate, TSA or product prephenate. The two enzymes are graphically depicted in Figure 2, the ligands and the reactions catalyzed by the enzyme are shown in Figure 1.

The X-ray structures I (PDB entry 2FP1)7 and II (PDB entry 2FP2)7 were taken as the protein model starting structures. The simulated protein consisted of 326 residues. The ionizeable groups were set to their protonated or deprotonated state according to the standard pKa values of amino acids and a pH of 6.8. Thus, the histidine residues were protonated at Nδ for histidine 151 and at Nε for histidines 88 and 176, the lysine and arginine side chains and the N-terminus were protonated, while the aspartic and glutamic acid side chains and the C-terminus were deprotonated, resulting in a net charge of −10e for the MtCM dimer and of −5e for the MtCM monomer. All residue numbers are given in terms of residue number in the sequence of MtCM plus 36, to simplify comparison to the more studied CM from E. coli. The ligands were parametrized according to the 45A4 force field21 (Supporting Information, Tables 3, 4, and 5), their net charge was −2e. Therefore, 5 Na+, 10 Na+, 7 Na+, and 12 Na+, were added to neutralize the system charge for the free monomer MtCM, free dimer MtCM, monomer MtCM with ligand, and dimer MtCM with ligand simulations, respectively. Water molecules were modeled as rigid three point molecules using the SPC water model.22

Simulation setup

The MtCM structure had been determined when crystalized with (II: PDB entry 2FP2) and without (I: PDB entry 2FP1) its TSA. The X-ray structure II was taken as the protein model starting structure for all but the mMtCM-I and dMtCM simulations. The X-ray structure I was taken as starting structure for the mMtCM-I and dMtCM simulations. For the monomeric MtCM complexed with ligand simulations as well as for mMtCM-II, the second subunit from structure II was used, as that subunit was crystallized together with the TSA. For the mMtCM-II simulation, the TSA was removed and the protein was simulated alone. For the mMtCM simulations, where the protein is bound to one of its ligands, chorismate, TSA, or prephenate, atom positions were mapped onto the atom positions of the TSA and the structures were then energy minimized while keeping the protein atoms positionally restrained in the following manner. A total of three energy minimizations were performed for the chorismate or prephenate bound systems and one for the TSA bound systems. In a first energy minimization, SHAKE23 was turned off, the bond forces were calculated and the torsional-angle forces were set to zero. In a second energy minimization, SHAKE was turned on, the torsional-angle forces were accounted for while the protein atoms were positionally restrained. The resulting protein–ligand (chorismate, TSA, or prephenate) systems were energy minimized once more to improve ligand–protein contacts with all atom position restraints removed. Position restraints were performed with a force constant of 2.5 104 kJ mol−1nm−2.

The systems were then solvated in a rectangular periodic box using a pre-equilibrated box of SPC water resulting in a system size of over 113,000 atoms for the dimer and over 65,000 atoms for the monomer simulations (Table I). In a further energy minimization, water molecules were relaxed with the atoms of the ligand and the protein positionally restrained. Thereafter, water molecules were replaced by sodium ions to neutralize the charge of the protein and ligand.

The equilibration process was started by taking initial velocities from a Maxwellian distribution at 60 K, the atoms of the enzyme and ligands were positionally restrained using a harmonic restraining force with a force constant of 2.5 104 kJ mol−1nm−2. During 300 ps, the force constant of the restraining force was step-wise reduced to zero while the temperature was increased to 300 K. The 11 mMtCM-PRE simulations differ in their initial velocities, which were taken from a Maxwellian distributions at 60 K, leading to different MD trajectories.

All simulations were carried out for 25 ns at a constant temperature of 300 K and a constant pressure of 1 atm using the weak coupling algorithm.24 Protein and solvent were separately coupled to the heat bath. The temperature coupling time was set to 0.1 ps and the pressure coupling time to 0.5 ps, an isothermal compressibility of 4.575 × 10−4 (kJ mol−1 nm−3)−1 was used.25

All bond lengths were kept rigid at ideal bond lengths using the SHAKE algorithm,23 allowing a time step of 2 fs in the leap-frog algorithm to integrate the equations of motion. Nonbonded interactions were calculated using a triple-range cutoff scheme with cutoff radii of 0.8/1.4 nm. Interactions within 0.8 nm were evaluated every time step. The intermediate range interactions were updated every fifth time step, and the long-range electrostatic interactions beyond 1.4 nm were approximated by a reaction field force26 representing a dielectric continuum with a dielectric permittivity of 61 for the water model.27

Analysis

The analyses were performed on the ensemble of system configurations extracted at 0.5 ps time intervals from the simulations.

Atom-positional RMSD were calculated after translational superposition of the solute centers of mass and least-squares rotational fitting of atomic positions, using all Cα atoms, or Cα atoms that are part of an α-helix, or Cα atoms that are part of a loop, or all atoms, are shown in Figures 3 and 4.

The hydrogen bonds in Figure 5 were calculated using a geometric criterion. A hydrogen bond is defined by a minimum donor-hydrogen-acceptor angle of 135° and a maximum hydrogen-acceptor distance of 0.25 nm. Hydrogen bonds between (i + 4)NH and (i) CO were calculated to account for the presence or absence of α-helical structure. When such a hydrogen bond is present, a black dot is drawn at residue i.

Five ligand–protein atom–atom distances were chosen to monitor the product exiting from the active site: the distances Arg49-Cα − PRE-C10, Lys60-Cα − PRE-C10, Arg72-Cα − PRE-C10, Thr105-Cα − PRE-C10, and Arg134-Cα − PRE-C10.

Acknowledgements

The authors would like to thank Peter Kast for his project idea and Daniel R. Perez for many discussions and his help in setting up the project. This work was financially supported by the National Center of Competence in Research (NCCR) in Structural Biology and by grant number 228076 of the European Research Council, which is gratefully acknowledged.

Ancillary

Advertisement