Connecting Conformational Motions to Rapid Dynamics in Human Purine Nucleoside Phosphorylase

Abstract

The influence of protein motions on enzyme catalysis remains a topic of active discussion. Protein motions occur across a variety of time scales, from vibrational fluctuations in femtoseconds, to collective motions in milliseconds. There have been numerous studies that show conformational motions may assist in catalysis, protein folding, and substrate specificity. It is also known through transition path sampling studies that rapid promoting vibrations contribute to enzyme catalysis. Human purine nucleoside phosphorylase (PNP) is one enzyme that contains both an important conformational motion and a rapid promoting vibration. The slower motion in this enzyme is associated with a loop motion, that when open allows substrate entry and product release but closes over the active site during catalysis. We examine the differences between an unconstrained PNP structure and a PNP structure with constraints on the loop motion. To investigate possible coupling between the slow and fast protein dynamics, we employed transition path sampling, reaction coordinate identification, electric field calculations, and free energy calculations reported here.

Graphical Abstract

INTRODUCTION

Protein motions occur on time scales that span many orders of magnitude: from femtoseconds to milliseconds. Understanding how these motions may contribute to enzyme catalysis remains a central challenge. Connections between protein conformational dynamics and catalysis have been demonstrated for microsecond–millisecond motions.¹ Rapid dynamics occurring at the active site in femtoseconds is also connected to enzyme catalysis.^2-4 While recent studies have focused on finding connections between catalytically relevant motions in enzymes that span a wide variety of time scales,⁵ more detailed mechanistic work on other systems will be illuminating. Fifteen years ago, Kern and Karplus suggested that a hierarchy of motions that are interrelated must be involved in catalysis.^1,6 In this work we focus on identifying the coupling between the rapid dynamics that plays a role in catalysis and slower, conformational motions in human purine nucleoside phosphorylase (PNP). PNP is a well-studied enzyme that contains the presence of promoting vibrations, rapid motions coupled to catalysis on the femtosecond time scale,^7-9 as well as conformational loop motions on a far slower time scale.¹⁰ The concept of a promoting vibration is simply a motion in the protein of the enzyme on the same general time scale as individual events of barrier passage (i.e., femtoseconds to picoseconds) that is identified as an essential part of the reaction coordinate through methods we will employ below. These methods allow us to identify the individual protein residues involved in creating the promoting vibration. In addition, we have shown through use of coherent dynamical structure factors that these motions have sharp spectra and so are not simply single stochastic motions.^11,12

Human purine nucleoside phosphorylase is a homotrimeric enzyme essential for purine metabolism, as it is the only enzyme that catalyzes the reversible phosphorolysis of 6-oxopurine nucleosides to form α-d-ribose-1-phosphate. PNP is a key target for drug discovery, as well as developing inhibitors for antitumor and antiviral activities.^13,14 The chemical reaction catalyzed by this enzyme is shown below in Figure 1. This dissociative substitution mechanism involves breaking the glycosidic bond of N9 and C1′ and then formation of a bond with C1′ and O3 of the phosphate.^13,15 We have shown that the promoting vibration is created by a relative motion by the residue histidine 257, which pushes the O5′–O4′–O3 oxygens into a stacked formation that contributes to polarization of the purine ring and facilitates transition state formation.^15,16

Figure 1.

Transition state formation of PNP for guanosine phosphorolysis. The reaction mechanism leads to α-d-ribose-1-phosphate and guanine products.

Histidine 257 is found at the hinge of the 241–256 loop above the active site. This loop motion is essential for substrate accessibility to the active site and thus the reaction mechanism.¹⁰ The challenge to understanding any connection between the loop motion and promoting vibration lies in the difference in time scales between the two motions. Our approach reported here will be to study the chemical reaction with the loop closed, and compare with it just slightly held open, to mimic the effects of chemistry in the presence of a conformational motion. In our molecular dynamics simulations we constrained the α carbon of the centroid residue Glu250 of the loop motion to a slightly open conformation, shown below in Figure 2. We then use further calculations to find a connection between this constrained structure and an unconstrained structure of PNP. We employ transition path sampling to determine whether or not the constrained loop affects the presence and effectiveness of the promoting vibration. We will also calculate the electric fields in both active sites, as there is a correlation between the strength of the electric field in an active site and an enzyme’s catalytic rate enhancement.¹⁷

Figure 2.

PNP chain A (red) with the constrained loop open (green) and substrate (cyan). The loop is held open by constraining the α carbon of Glu250 to the α carbon of Pro122. The unconstrained loop is shown in blue. The difference in loop positions is less than 2 Å.

Boxer et al. have shown the importance and relevance of how substrate configuration and rigidity affects electric fields in enzyme catalysis.¹⁸ These electric field effects can be studied with enzymes whose substrate configurations can be approximated as electric dipoles. Electrostatic interactions in enzymes are crucial for catalysis, specifically in terms of electrostatic preorganization that allows the enzyme to find an optimal configuration for the chemical step.^17-20 We have in fact shown that the promoting vibration is central to creation of the electric field milieu at the active site.^20,21 In PNP, the dipole of the carbonyl group on the purine ring plays a role in forming the appropriate electric field at the active site coinciding with the compression of the stacking oxygens.²⁰ As this compression relies on the promoting vibration from the histidine 257 residue, we will examine the difference in activities of the electric field dependent on the 241–256 loop position.

One final method to identify the connection between the loop motion and the promoting vibration is to calculate the difference in the free energy barriers for the two PNP structures with the transition path sampling method.²² Free energy calculations based on transition path ensembles are possible without any bias forces and are comparable to experimental measurements. For two structures of the same enzyme with one minor conformational difference, a difference in free energies could be attributed to the effectiveness of that conformational change in terms of the catalytic rate.²³

The purpose of this work is to study any possible connection between the rapid promoting vibration and conformational motion without making major structural changes to the enzyme. We will perform molecular dynamics simulations on two PNP structures: one with no constraints and one with the 241–256 loop held slightly open. The connection between the loop motion and the promoting vibration within the active site will be illustrated through reaction coordinate identification, electric field calculations, and free energy calculations.

METHODS

System Preparation.

We prepared two structures of PNP with guanosine as the substrate. The starting crystal structure was taken from the Protein Data Bank (PDB) with the PDB ID: 1RR6. This PNP structure contained the transition state inhibitor immucillin-H, as well as a phosphate cofactor. The first step was to use the Schrödinger software to modify immucillin-H by exchanging the N4 and C9 atoms with O4′ and N9, respectively, to produce the guanosine substrate. The crystallized structures were solvated in a sphere of waters with the TIP3P water model with the water atoms placed 15 Å away in all directions from the protein’s surface.^24,25 Potassium ions were used to neutralize the total charge of the system.

Molecular dynamics simulations were performed using CHARMM42.²⁶ The system was partitioned according to the QM/MM method, where the active site was defined as the quantum mechanics (QM) region and contained 40 atoms, consisting of the guanosine and phosphate. The QM region was treated with the PM3 semiempirical method.²⁷ The molecular mechanics (MM) region included the rest of the system and had no bonds to the QM region. The MM region was treated with the CHARMM36 Force Field.²⁶

QM was on for minimization, heating, and equilibration. The energies of both structures were minimized with 50 steps of steepest descent (SD), followed by 2000 steps using the adopted basis Newton–Raphson method (ABNR).^25,28 The systems were then slowly heated to 300 K, beginning with 5 ps of small harmonic constraints on non-hydrogen atoms except waters, followed by 15 ps with harmonic constraints on QM atoms that were gradually reduced, followed by 50 ps with all constraints removed. The SHAKE algorithm was used for hydrogen atoms. For the constrained loop structure of PNP, the α carbon of Glu250 was constrained to the α carbon of Pro122 during simulation to keep the loop slightly open. The distance between Glu250 and Pro122 was determined by the unconstrained equilibrated structure coordinates and set to a value of 18.6 Å with a force constant of 22 kcal/mol/Ų. The unconstrained structure had no additional constraints. The difference in the loop positions between the two structures was less than 2 Å. The equilibrated structures were then used for transition path sampling.

Transition Path Sampling.

We used transition path sampling (TPS) to generate transition state ensembles for both the unconstrained and constrained PNP structures. This computational method enables us to study transition pathways for rare events in complex systems.²⁹ We built a transition path ensemble from reactive trajectories that connect the reactant and product states in PNP. We defined the reactant state, which contains the intact glycosidic bond C1′–N9, with an order parameter that has the bond-breaking length C1′–N9 < 1.65 Å and the bond-forming length C1′–O3 > 1.65 Å. The product state, which has α-d-ribose-1-phosphate and guanine, was defined by an order parameter for the C1′–O3 product-forming bond between the sugar and phosphate as C1′–O3 < 1.65 Å. We created an initial biased reactive trajectory, by introducing constraints that drive the reaction from reactants to products: we used harmonic forces between C1′–O3 and O4′–O5′ with a force constant of 65 kcal/mol/Ų followed by propagation for 250 fs. Once this initial reactive trajectory was generated, we used the TPS shooting algorithm (randomly perturbing the momenta of each time slice drawing from a Boltzmann distribution²⁷) to iteratively generate reactive trajectories by using a generated reactive trajectory as a seed for the generation of the next reactive trajectory.

We generated over 150 reactive trajectories to build our transition path ensemble. The first 70 trajectories were omitted to ensure decorrelation from the initial biased trajectory. Committor distribution analysis was then performed to generate the transition state ensemble.^28-30 For this, we chose a random time slice from one of our reactive trajectories, assigned momenta randomly, and ran dynamics for 500 fs, 250 fs forward and 250 fs backward propagation. We calculated the probability of a time slice committing to the reactant or product state, as determined by the order parameters. This procedure was repeated at least 50 times for each time slice. The time slice where the commitment probabilities for the reactant state and product state are equal is the equicommittor point, or transition state. The collection of transition states as determined by this process defines the stochastic separatrix, or transition state ensemble.³⁰ The reaction coordinate consists of the degrees of freedom that define a subspace that describes the system motion toward the transition state and are orthogonal to the stochastic separatrix.³¹

Next we identified the reaction coordinate. In the TPS framework this is performed by guessing a set of residues that are part of a candidate reaction coordinate and performing a committor analysis on “constrained-walk” trajectories. For that, one starts from a transition state that has been identified, and initiates trajectories from that structure by assigning random momenta from a Boltzmann distribution. We then propagate while keeping constrained the motion of the reaction coordinate candidate residues. After that, one performs committor tests at slices along this constrained-walk trajectory. If the choice of reaction coordinate degrees of freedom was correct, the system has walked along the transition state ensemble surface and the commitment probability histograms for the committor test would be peaked at 0.5. If not, one makes a new choice and repeats. As an initial guess for the constrained residues, we used those that in our earlier studies had been a part of the reaction coordinate.⁹ The reaction coordinate was determined for both unconstrained and constrained PNP structures.

Electric Field Calculations.

To determine how the constrained loop affects the active site electrostatic interactions of PNP, we calculated the electric field that acts on the carbonyl dipole of the purine ring. This technique works with PNP because the structure is not affected by any rotational rearrangement and the dipole maintains its structure throughout the reaction.^17-20 The superposition of the electrostatic contributions from all the charges of the atoms in a protein make up the electric field inside the active site. While rate enhancements depend on positioning of the substrate and active site residues, they can be separated from electric field effects.¹⁸ Our earlier work showed that the oxygen compression of O5′–O4′–O3 pushes the electrons toward the purine ring for transition state stabilization.⁷

Multiple trajectories generated from TPS were used to calculate the dipole on the C6–O6 carbonyl within the active site, for both the constrained and unconstrained PNP structures. For that, we calculated the Mulliken charges at various frames of the reactive trajectories.²⁰ The forces projected along the C6–O6 axis come from the other QM atoms in the active site:

$$\overrightarrow{E_j}=\sum _i{\text{charge}}_i\times \frac{\overrightarrow{R_i}-\overrightarrow{R_j}}{\mid \overrightarrow{R_i}-\overrightarrow{R_j}{\mid }^3}$$ (1)

The field on point j is a sum over contributions from all neighboring charges i. We calculated two projections along the C═O axis, one for the field on C6 and the other on O6. The electric field on the dipole is 1/2 of this sum. We calculated the electric field at various times before, during, and after the maximum compression of the O5′–O4′ oxygens for both structures. This electric field depends on the configuration of atoms in the active site.^18,32

Free Energy Calculations.

Free energy calculations were performed within the transition path sampling (TPS) method²² for the reaction catalyzed by the human PNP enzyme. The order parameter $\overline{\xi }$ for both the constrained and unconstrained PNP systems was chosen to be d_NC-d_OC where NC is the reactant N9–C1′ bond and OC the product O3–C1′ bond. A reactive trajectory from the TPS ensemble was selected for both the constrained and unconstrained PNP systems as the starting point for the equilibrium sampling of configurations corresponding to order parameter values within the range of [−3.0,3.0] Å. This order parameter range was divided into 30 overlapping windows with an overlap of 0.08 Å between neighboring windows. Within each window i (defined by the set of order parameter values $([{\xi }_i^{\text{min}},{\xi }_i^{\max }])$ configurations are sampled starting from a time frame in the TPS reactive trajectory with an order parameter $\overline{\xi }$ that satisfies ${\xi }_i^{\text{min}}\le \overline{\xi }\le {\xi }_i^{\max }$. Using the shooting algorithm^29,33 the momenta of all the atoms of the enzymatic system are perturbed and the system is propagated to obtain a short 20 fs trajectory (10 fs forward and backward from the shooting point) with a time step of 1 fs. After sampling 3000 trajectories within each window, the converged probability distribution of the order parameter (w_i) is obtained as normalized histograms. The free energy is calculated by Boltzmann inversion F_i = −k_BT log(w_i) within each window and combined to obtain a continuous free energy profile.

RESULTS AND DISCUSSION

Committor distribution analysis was used to identify the reaction coordinates for both structures from the transition state ensembles that we generated using TPS. Both the unconstrained and constrained PNP structures’ reaction coordinates included the QM region, Asn243, Ser33, Tyr88, and His86. The unconstrained structure alone found His257 to be part of the reaction coordinate. Results are shown in Figure 3.

Figure 3.

Committor probability distributions for unconstrained and constrained PNP. Both constrained the QM region, Asn243, Tyr88, His86, and Ser33. The unconstrained PNP also included His257.

Histidine 257 is found on the hinge of the loop motion and was expected to be affected by constraining the loop motion. The difference in positioning of His257 between unconstrained and constrained structures is shown in Figure 4. Even with a slight change in this conformational motion, Histidine 257 is not found in the reaction coordinate of the constrained structure. The remainder of the reaction coordinate residues found in the unconstrained PNP are present in the constrained structure as well, as the loop constraint did not affect the structural placement of the nearby residues. The results confirm that there exists a coupling between the conformational loop motion and the rapid promoting vibrations in PNP. With the loop motion fixed in place, the critical residue for rapid dynamics is not a part of the reaction coordinate.

Figure 4.

Aligned active sites for both structures shown with the difference in location of His257. Blue shows the His257 in the unconstrained PNP closer to the substrate. Red is the His257 belonging to PNP with the open loop.

While the loop constraint affected the His257 positioning, the rest of the protein including the other reaction coordinate residues remained largely unaffected by the open loop, as shown in Figure 5. The lack of structural changes signifies that this connection between the promoting vibration and the loop motion is dynamic.

Figure 5.

PNP active site with residues Asn243, Tyr88, His86, and Ser33. Constrained is red while unconstrained is blue. Superimposed active site and chain A during the transition state for both structures.

Figure 6 shows how the O5′–O4′ oxygen compression assisted by His257 in the normal protein is uncoupled in the constrained PNP. With the loop in native PNP, the maximum compression of the O5′–O4′ oxygens is at 2.8 Å following the decrease in distance between His257 and O5′. When the loop is held open, the O5′–O4′ compression occurs later and is larger than 3 Å. The decrease in the His257–O5′ distance does not occur simultaneously with the O5′–O4′ oxygen compression, as shown by the constrained example in Figure 6. While this does not confirm that there is no promoting vibration from the histidine 257, clearly it has less of an effect on the compression of the oxygens which facilitate transition state formation.

Figure 6.

Distances between O5′–O4′, His257–O5′, and the bond breaking and formation throughout an entire reactive trajectory for the unconstrained PNP (left) and constrained PNP (right). The black lines show the breaking of N9–C1′ and formation of C1′–O3.

The electric field calculations shown in Figure 7 also illustrate the difference in effectiveness of the oxygen compression for the two PNP structures. The electric field calculations along the C6–O6 dipole are plotted before, during, and after the compression of O5′–O4′ until the transition state formation. For the unconstrained structure, the electric field rises significantly at the O5′–O4′ minimum distance (maximum compression), peaking at 240 MV/cm. In the constrained system, the electric field peaks at 220 MV/cm slightly before maximum compression of O5′–O4′ and decreases to 216 MV/cm at the O5′–O4′ minimum.

Figure 7.

Electric field calculations for constrained and unconstrained PNP. The Mulliken charges were calculated before, during, and after the maximum compression of the O5′–O4′ oxygens. The time range for the unconstrained oxygen compression is longer than that of the constrained structure’s time range. The black lines show the breaking of N9–C1′ and formation of C1′–O3.

The oxygen compression still occurs naturally in the constrained structure but without the significant effect from His257. The electric field is calculated starting from the beginning of the maximum compression until the transition state and has a shorter time range for the constrained structure than the unconstrained.

This compression of oxygens is a necessary component of the reaction, and the unconstrained structure shows another result of the role of His257 vibrations in PNP.²⁰ With the loop constrained open, the oxygen distance decreases but is less compressed than the unconstrained PNP and the electric field is also 20 MV/cm lower. The promoting vibration pushes the O5′–O4′–O3 oxygens together and as a result also increases the electric field values. This compression facilitates the electrostatic preorganization required for the chemical step. The decreased oxygen compression and electric field values at the C6–O6 carbonyl show that there is a connection between the loop motion and the promoting vibration.

Finally, the free energy barriers shown in Figure 8 show that constraining the loop motion results to a higher free energy barrier. The difference between the free energy barrier for the constrained and unconstrained structures is 4 kcal/mol.

Figure 8.

Free energy profile for the unconstrained (left) and constrained (right) PNP systems calculated using the TPS-based method. Standard deviations are calculated using the bootstrapping method and denoted as blue error bars while the continuous black curve represents the polynomial fitting function.

The free energy barriers for the unconstrained and constrained PNP systems are calculated to be 23 kcal mol⁻¹ and 27 kcal mol⁻¹, respectively. It can be noted that at the location of the free energy maximum, the values of the order parameter are 0.77 and 0.45 Å for the unconstrained and constrained PNP systems, respectively, in agreement with the structures of the transition states obtained from TPS committor analysis. By holding the loop motion slightly open above the active site (by less than 2 Å), the free energy barrier increases by 4 kcal/mol. One point to make regards the relatively high endergonic nature of the curves. This is likely due to not extending the reaction profile out to product release where solvation will significantly energetically stabilize the products, but we note the important result is the difference in barrier heights between the two curves. Both the constrained and unconstrained systems were treated in exactly the same fashion, and so the difference truly measures changes in barrier height because any error due to lack of water solvation after product release is clearly the same for both, and the barrier occurs at or near the transition state.

CONCLUSION

Connections between protein motions and catalysis have been shown for microsecond–millisecond motions and also for femtosecond–nanosecond motions. Earlier work has shown the atomic details of the PNP reaction mechanism, particularly focusing on the promoting vibration that compresses the oxygens. Using this previous knowledge, we were able to further our understanding of protein motions in PNP by finding a connection between this motion and the slower loop motion. Transition path sampling computations, electric field calculations, and free energy barrier calculations were all able to illustrate the effect of the 241–256 loop motion in PNP.

The rapid promoting vibration in the active site is clearly shown to be less effective when the 241–256 loop is held slightly open in PNP, due to a connection between these promoting vibrational motions and slower, conformational motions. The electric field effect that corresponds to the oxygen compression from the promoting vibration is more than 20 EV/cm higher for the native PNP as well. Without imposing any wholescale structural change, constraining the loop motion slightly toward the open position resulted in a free energy barrier 4 kcal/mol higher than that of native PNP. There is clearly a coupling between slow loop motions and rapid femtosecond promoting vibrations.