Simulation of enzyme-substrate encounter with gated active sites

Use of Molecular Dynamics Simulations in Structure-Based Drug Discovery

BACKGROUND

Traditional drug discovery is a lengthy process which involves a huge amount of resources. Modern-day drug discovers various multidisciplinary approaches amongst which, computational ligand and structure-based drug designing methods contribute significantly. Structure-based drug designing techniques require the knowledge of structural information of drug target and drug-target complexes. Proper understanding of drug-target binding requires the flexibility of both ligand and receptor to be incorporated. Molecular docking refers to the static picture of the drug-target complex(es). Molecular dynamics, on the other hand, introduces flexibility to understand the drug binding process.

OBJECTIVE

The aim of the present study is to provide a systematic review on the usage of molecular dynamics simulations to aid the process of structure-based drug design.

METHOD

This review discussed findings from various research articles and review papers on the use of molecular dynamics in drug discovery. All efforts highlight the practical grounds for which molecular dynamics simulations are used in drug designing program. In summary, various aspects of the use of molecular dynamics simulations that underline the basis of studying drug-target complexes were thoroughly explained.

RESULTS

This review is the result of reviewing more than a hundred papers. It summarizes various problems that use molecular dynamics simulations.

CONCLUSION

The findings of this review highlight how molecular dynamics simulations have been successfully implemented to study the structure-function details of specific drug-target complexes. It also identifies the key areas such as stability of drug-target complexes, ligand binding kinetics and identification of allosteric sites which have been elucidated using molecular dynamics simulations.

Uncovering the Role of Key Active-Site Side Chains in Catalysis: An Extended Brønsted Relationship for Substrate Deprotonation Catalyzed by Wild-Type and Variants of Triosephosphate Isomerase

We report results of detailed empirical valence bond simulations that model the effect of several amino acid substitutions on the thermodynamic (ΔG°) and kinetic activation (ΔG^⧧) barriers to deprotonation of dihydroxyacetone phosphate (DHAP) and d-glyceraldehyde 3-phosphate (GAP) bound to wild-type triosephosphate isomerase (TIM), as well as to the K12G, E97A, E97D, E97Q, K12G/E97A, I170A, L230A, I170A/L230A, and P166A variants of this enzyme. The EVB simulations model the observed effect of the P166A mutation on protein structure. The E97A, E97Q, and E97D mutations of the conserved E97 side chain result in ≤1.0 kcal mol^-1 decreases in the activation barrier for substrate deprotonation. The agreement between experimental and computed activation barriers is within ±1 kcal mol^-1, with a strong linear correlation between ΔG^⧧ and ΔG° for all 11 variants, with slopes β = 0.73 (R² = 0.994) and β = 0.74 (R² = 0.995) for the deprotonation of DHAP and GAP, respectively. These Brønsted-type correlations show that the amino acid side chains examined in this study function to reduce the standard-state Gibbs free energy of reaction for deprotonation of the weak α-carbonyl carbon acid substrate to form the enediolate phosphate reaction intermediate. TIM utilizes the cationic side chain of K12 to provide direct electrostatic stabilization of the enolate oxyanion, and the nonpolar side chains of P166, I170, and L230 are utilized for the construction of an active-site cavity that provides optimal stabilization of the enediolate phosphate intermediate relative to the carbon acid substrate.

Brownian Dynamics Simulations of Biological Molecules

Brownian dynamics (BD) is a technique for carrying out computer simulations of physical systems that are driven by thermal fluctuations. Biological systems at the macromolecular and cellular level, while falling in the gap between well-established atomic-level models and continuum models, are especially suitable for such simulations. We present a brief history, examples of important biological processes that are driven by thermal motion, and those that have been profitably studied by BD. We also present some of the challenges facing developers of algorithms and software, especially in the attempt to simulate larger systems more accurately and for longer times.

Multiscale Simulation of Receptor-Drug Association Kinetics: Application to Neuraminidase Inhibitors

A detailed understanding of the drug-receptor association process is of fundamental importance for drug design. Due to the long time scales of typical binding kinetics, the atomistic simulation of the ligand traveling from bulk solution into the binding site is still computationally challenging. In this work, we apply a multiscale approach of combined Molecular Dynamics (MD) and Brownian Dynamics (BD) simulations to investigate association pathway ensembles for the two prominent H1N1 neuraminidase inhibitors oseltamivir and zanamivir. Including knowledge of the approximate binding site location allows for the selective confinement of detailed but expensive MD simulations and application of less demanding BD simulations for the diffusion controlled part of the association pathway. We evaluate a binding criterion based on the residence time of the inhibitor in the binding pocket and compare it to geometric criteria that require prior knowledge about the binding mechanism. The method ranks the association rates of both inhibitors in qualitative agreement with experiment and yields reasonable absolute values depending, however, on the reaction criteria. The simulated association pathway ensembles reveal that, first, ligands are oriented in the electrostatic field of the receptor. Subsequently, a salt bridge is formed between the inhibitor's carboxyl group and neuraminidase residue Arg368, followed by adopting the native binding mode. Unexpectedly, despite oseltamivir's higher overall association rate, the rate into the intermediate salt-bridge state was found to be higher for zanamivir. The present methodology is intrinsically parallelizable and, although computationally demanding, allows systematic binding rate calculation on selected sets of potential drug molecules.

Rate Constants and Mechanisms of Protein-Ligand Binding

Whereas protein-ligand binding affinities have long-established prominence, binding rate constants and binding mechanisms have gained increasing attention in recent years. Both new computational methods and new experimental techniques have been developed to characterize the latter properties. It is now realized that binding mechanisms, like binding rate constants, can and should be quantitatively determined. In this review, we summarize studies and synthesize ideas on several topics in the hope of providing a coherent picture of and physical insight into binding kinetics. The topics include microscopic formulation of the kinetic problem and its reduction to simple rate equations; computation of binding rate constants; quantitative determination of binding mechanisms; and elucidation of physical factors that control binding rate constants and mechanisms.

A Network of Conformational Transitions Revealed by Molecular Dynamics Simulations of the Binary Complex of Escherichia coli 6-Hydroxymethyl-7,8-dihydropterin Pyrophosphokinase with MgATP

6-Hydroxymethyl-7,8-dihydropterin pyrophosphokinase (HPPK) catalyzes the first reaction in the folate biosynthetic pathway. Comparison of its X-ray and nuclear magnetic resonance structures suggests that the enzyme undergoes significant conformational change upon binding to its substrates, especially in three catalytic loops. Experimental research has shown that, in its binary form, even bound by analogues of MgATP, loops 2 and 3 remain rather flexible; this raises questions about the putative large-scale induced-fit conformational change of the HPPK-MgATP binary complex. In this work, long-time all-atomic molecular dynamics simulations were conducted to investigate the loop dynamics in this complex. Our simulations show that, with loop 3 closed, multiple conformations of loop 2, including the open, semiopen, and closed forms, are all accessible to the binary complex. These results provide valuable structural insights into the details of conformational changes upon 6-hydroxymethyl-7,8-dihydropterin (HP) binding and biological activities of HPPK. Conformational network analysis and principal component analysis related to the loops are also discussed.

Electrostatic Steering Accelerates C3d:CR2 Association

Electrostatic effects are ubiquitous in protein interactions and are found to be pervasive in the complement system as well. The interaction between complement fragment C3d and complement receptor 2 (CR2) has evolved to become a link between innate and adaptive immunity. Electrostatic interactions have been suggested to be the driving factor for the association of the C3d:CR2 complex. In this study, we investigate the effects of ionic strength and mutagenesis on the association of C3d:CR2 through Brownian dynamics simulations. We demonstrate that the formation of the C3d:CR2 complex is ionic strength-dependent, suggesting the presence of long-range electrostatic steering that accelerates the complex formation. Electrostatic steering occurs through the interaction of an acidic surface patch in C3d and the positively charged CR2 and is supported by the effects of mutations within the acidic patch of C3d that slow or diminish association. Our data are in agreement with previous experimental mutagenesis and binding studies and computational studies. Although the C3d acidic patch may be locally destabilizing because of unfavorable Coulombic interactions of like charges, it contributes to the acceleration of association. Therefore, acceleration of function through electrostatic steering takes precedence to stability. The site of interaction between C3d and CR2 has been the target for delivery of CR2-bound nanoparticle, antibody, and small molecule biomarkers, as well as potential therapeutics. A detailed knowledge of the physicochemical basis of C3d:CR2 association may be necessary to accelerate biomarker and drug discovery efforts.

Can structural features of kinase receptors provide clues on selectivity and inhibition? A molecular modeling study

Cancer is a complex disease resulting from the uncontrolled proliferation of cell signaling events. Protein kinases have been identified as central molecules that participate overwhelmingly in oncogenic events, thus becoming key targets for anticancer drugs. A majority of studies converged on the idea that ligand-binding pockets of kinases retain clues to the inhibiting abilities and cross-reacting tendencies of inhibitor drugs. Even though these ideas are critical for drug discovery, validating them using experiments is not only difficult, but also in some cases infeasible. To overcome these limitations and to test these ideas at the molecular level, we present here the results of receptor-focused in-silico docking of nine marketed drugs to 19 different wild-type and mutated kinases chosen from a wide range of families. This investigation highlights the need for using relevant models to explain the correct inhibition trends and the results are used to make predictions that might be able to influence future experiments. Our simulation studies are able to correctly predict the primary targets for each drug studied in majority of cases and our results agree with the existing findings. Our study shows that the conformations a given receptor acquires during kinase activation, and their micro-environment, defines the ligand partners. Type II drugs display high compatibility and selectivity for DFG-out kinase conformations. On the other hand Type I drugs are less selective and show binding preferences for both the open and closed forms of selected kinases. Using this receptor-focused approach, it is possible to capture the observed fold change in binding affinities between the wild-type and disease-centric mutations in ABL kinase for Imatinib and the second-generation ABL drugs. The effects of mutation are also investigated for two other systems, EGFR and B-Raf. Finally, by including pathway information in the design it is possible to model kinase inhibitors with potentially fewer side-effects.

A Multi-Scale Method for Dynamics Simulation in Continuum Solvent Models I: Finite-Difference Algorithm for Navier-Stokes Equation

A multi-scale framework is proposed for more realistic molecular dynamics simulations in continuum solvent models by coupling a molecular mechanics treatment of solute with a fluid mechanics treatment of solvent. This article reports our initial efforts to formulate the physical concepts necessary for coupling the two mechanics and develop a 3D numerical algorithm to simulate the solvent fluid via the Navier-Stokes equation. The numerical algorithm was validated with multiple test cases. The validation shows that the algorithm is effective and stable, with observed accuracy consistent with our design.

Theoretical frameworks for multiscale modeling and simulation

Biomolecular systems have been modeled at a variety of scales, ranging from explicit treatment of electrons and nuclei to continuum description of bulk deformation or velocity. Many challenges of interfacing between scales have been overcome. Multiple models at different scales have been used to study the same system or calculate the same property (e.g., channel conductance). Accurate modeling of biochemical processes under in vivo conditions and the bridging of molecular and subcellular scales will likely soon become reality.

Modeling protein association mechanisms and kinetics

Substantial advances have been made in modeling protein association mechanisms and in calculating association rate constants (ka). We now have a clear understanding of the physical factors underlying the wide range of experimental ka values. Half of the association problem, where ka is limited by diffusion, is perhaps solved, and for the other half, where conformational changes become rate-limiting, a number of promising methods are being developed for ka calculations. Notably, the binding kinetics of disordered proteins are receiving growing attention, with 'dock-and-coalesce' emerging as a general mechanism. Progress too has been made in the modeling of protein association kinetics under conditions mimicking the heterogeneous, crowded environments of cells, an endeavor that should ultimately lead to a better understanding of cellular functions.

Quantum mechanical modeling: a tool for the understanding of enzyme reactions

Most enzyme reactions involve formation and cleavage of covalent bonds, while electrostatic effects, as well as dynamics of the active site and surrounding protein regions, may also be crucial. Accordingly, special computational methods are needed to provide an adequate description, which combine quantum mechanics for the reactive region with molecular mechanics and molecular dynamics describing the environment and dynamic effects, respectively. In this review we intend to give an overview to non-specialists on various enzyme models as well as established computational methods and describe applications to some specific cases. For the treatment of various enzyme mechanisms, special approaches are often needed to obtain results, which adequately refer to experimental data. As a result of the spectacular progress in the last two decades, most enzyme reactions can be quite precisely treated by various computational methods.

Hydrodynamic effects on the relative rotational velocity of associating proteins

Hydrodynamic steering effects on the barnase-barstar association were studied through the analysis of the relative rotational velocity of the proteins. We considered the two proteins approaching each other in response to their electrostatic attraction and employed a method that accounts for the long-range and many-body character of the hydrodynamic interactions, as well as the complicated shapes of the proteins. Hydrodynamic steering effects were clearly seen when attractive forces were applied to the geometric centers of the proteins (resulting in zero torques) and the attraction acted along the line that connects centers of geometry of proteins in their crystallographic complex. When we rotated barstar relative to barnase around this line by an angle in the range from -90° to 60°, the rotational velocity arising solely from hydrodynamic interactions restored the orientation of the proteins in the crystal structure. However, because, in reality, both electrostatic forces and torques act on the proteins and these forces and torques depend on the protein-protein distance and the relative orientation of the binding partners, we also investigated more realistic situations employing continuum electrostatics calculations based on atomistic protein models. Overall, we conclude that hydrodynamic interactions aid barnase and barstar in assuming a proper relative orientation upon complex formation.

BDflex: a method for efficient treatment of molecular flexibility in calculating protein-ligand binding rate constants from brownian dynamics simulations

A method developed by Northrup et al. [J. Chem. Phys. 80, 1517 (1984)] for calculating protein-ligand binding rate constants (k(a)) from brownian dynamics (BD) simulations has been widely used for rigid molecules. Application to flexible molecules is limited by the formidable computational cost to treat conformational fluctuations during the long BD simulations necessary for k(a) calculation. Here, we propose a new method called BDflex for k(a) calculation that circumvents this problem. The basic idea is to separate the whole space into an outer region and an inner region, and formulate k(a) as the product of k(E) and η(d), which are obtained by separately solving exterior and interior problems. k(E) is the diffusion-controlled rate constant for the ligand in the outer region to reach the dividing surface between the outer and inner regions; in this exterior problem conformational fluctuations can be neglected. η(d) is the probability that the ligand, starting from the dividing surface, will react at the binding site rather than escape to infinity. The crucial step in reducing the determination of η(d) to a problem confined to the inner region is a radiation boundary condition imposed on the dividing surface; the reactivity on this boundary is proportional to k(E). By confining the ligand to the inner region and imposing the radiation boundary condition, we avoid multiple-crossing of the dividing surface before reaction at the binding site and hence dramatically cut down the total simulation time, making the treatment of conformational fluctuations affordable. BDflex is expected to have wide applications in problems where conformational fluctuations of the molecules are crucial for productive ligand binding, such as in cases where transient widening of a bottleneck allows the ligand to access the binding pocket, or the binding site is properly formed only after ligand entrance induces the closure of a lid.

Spatial simulations in systems biology: from molecules to cells

Cells are highly organized objects containing millions of molecules. Each biomolecule has a specific shape in order to interact with others in the complex machinery. Spatial dynamics emerge in this system on length and time scales which can not yet be modeled with full atomic detail. This review gives an overview of methods which can be used to simulate the complete cell at least with molecular detail, especially Brownian dynamics simulations. Such simulations require correct implementation of the diffusion-controlled reaction scheme occurring on this level. Implementations and applications of spatial simulations are presented, and finally it is discussed how the atomic level can be included for instance in multi-scale simulation methods.

Theory and simulation of diffusion-influenced, stochastically gated ligand binding to buried sites

We consider the diffusion-influenced rate coefficient of ligand binding to a site located in a deep pocket on a protein; the binding pocket is flexible and can reorganize in response to ligand entrance. We extend to this flexible protein-ligand system a formalism developed previously [A. M. Berezhkovskii, A, Szabo, and H.-X. Zhou, J. Chem. Phys. 135, 075103 (2011)] for breaking the ligand-binding problem into an exterior problem and an interior problem. Conformational fluctuations of a bottleneck or a lid and the binding site are modeled as stochastic gating. We present analytical and Brownian dynamics simulation results for the case of a cylindrical pocket containing a binding site at the bottom. Induced switch, whereby the conformation of the protein adapts to the incoming ligand, leads to considerable rate enhancement.

Theory and simulation on the kinetics of protein-ligand binding coupled to conformational change

Conformational change during protein-ligand binding may significantly affect both the binding mechanism and the rate constant. Most earlier theories and simulations treated conformational change as stochastic gating with transition rates between reactive and nonreactive conformations uncoupled to ligand binding. Recently, we introduced a dual-transition-rates model in which the transition rates between reactive and nonreactive conformations depend on the protein-ligand distance [H.-X. Zhou, Biophys. J. 98, L15 (2010)]. Analytical results of that model showed that the apparent binding mechanism switches from conformational selection to induced fit, when the rates of conformational transitions increase from being much slower than the diffusional approach of the protein-ligand pair to being much faster. The conformational-selection limit (k(CS)) and the induced-fit limit (k(IF)) provide lower and upper bounds, respectively, for the binding rate constant. Here we introduce a general model in which the energy surface of the protein in conformational space is coupled to ligand binding, and present a method for calculating the binding rate constant from Brownian dynamics simulations. Analytical and simulation results show that, for an energy surface that switches from favoring the nonreactive conformation while the ligand is away to favoring the reactive conformation while the ligand is near, k(CS) and k(IF) become close and, thus, provide tight bounds to the binding rate constant. This finding has significant mechanistic implications and presents routes for obtaining good estimates of the rate constant at low cost.

Gated Diffusion-controlled Reactions

The binding and active sites of proteins are often dynamically occluded by motion of the nearby polypeptide. A variety of theoretical and computational methods have been developed to predict rates of ligand binding and reactivity in such cases. Two general approaches exist, "protein centric" approaches that explicitly treat only the protein target, and more detailed dynamical simulation approaches in which target and ligand are both treated explicitly. This mini-review describes recent work in this area and some of the biological implications.

Browndye: A Software Package for Brownian Dynamics

A new software package, Browndye, is presented for simulating the diffusional encounter of two large biological molecules. It can be used to estimate second-order rate constants and encounter probabilities, and to explore reaction trajectories. Browndye builds upon previous knowledge and algorithms from software packages such as UHBD, SDA, and Macrodox, while implementing algorithms that scale to larger systems.

Molecular dynamics studies on the interactions of PTP1B with inhibitors: from the first phosphate-binding site to the second one

Protein tyrosine phosphatases 1B (PTP1B) is a major negative regulator of both insulin and leptin signaling pathways. In view of this, it becomes an important target for drug development against cancers, diabetes and obesity. The aim of the current study is to use the long time-scale molecular dynamics (MD) simulations to investigate the structural and dynamic factors that cause its inhibition by INTA and INTB, the two most potent and highly selective PTP1B inhibitors known so far. In order to investigate the mode of collective motions that is vitally important to the biological function, the covariance matrix of C(alpha) atoms was introduced for performing the dynamic analysis of the inhibition systems. It has been observed that the conformational and dynamic features of WPD-Loop, R-Loop and S-Loop play a key role in providing a smooth entrance for the inhibitors moving into the binding pocket as well as a favorable microenvironment to stabilize them. Furthermore, the hydrogen bonding networks formed around the active site with INTA and INTB may be the main reason of why the inhibition of PTP1B by the two ligands is so potent and selective. All these findings might provide useful insights for developing novel and effective drugs to treat cancer, diabetes and obesity.

Gated binding of ligands to HIV-1 protease: Brownian dynamics simulations in a coarse-grained model

The internal motions of proteins may serve as a "gate" in some systems, which controls ligand-protein association. This study applies Brownian dynamics simulations in a coarse-grained model to study the gated association rate constants of HIV-1 proteases and drugs. The computed gated association rate constants of three protease mutants, G48V/V82A/I84V/L90M, G48V, and L90M with three drugs, amprenavir, indinavir, and saquinavir, yield good agreements with experiments. The work shows that the flap dynamics leads to "slow gating". The simulations suggest that the flap flexibility and the opening frequency of the wild-type, the G48V and L90M mutants are similar, but the flaps of the variant G48V/V82A/I84V/L90M open less frequently, resulting in a lower gated rate constant. The developed methodology is fast and provides an efficient way to predict the gated association rate constants for various protease mutants and ligands.

NMR dynamic studies suggest that allosteric activation regulates ligand binding in chicken liver bile acid-binding protein

Apo chicken liver bile acid-binding protein has been structurally characterized by NMR. The dynamic behavior of the protein in its apo- and holo-forms, complexed with chenodeoxycholate, has been determined via (15)N relaxation and steady state heteronuclear (15)N((1)H) nuclear Overhauser effect measurements. The dynamic parameters were obtained at two pH values (5.6 and 7.0) for the apoprotein and at pH 7.0 for the holoprotein, using the model free approach. Relaxation studies, performed at three different magnetic fields, revealed a substantial conformational flexibility on the microsecond to millisecond time scales, mainly localized in the C-terminal face of the beta-barrel. The observed dynamics are primarily caused by the protonation/deprotonation of a buried histidine residue, His(98), located on this flexible face. A network of polar buried side chains, defining a spine going from the E to J strand, is likely to provide the long range connectivity needed to communicate motion from His(98) to the EF loop region. NMR data are accompanied by molecular dynamics simulations, suggesting that His(98) protonation equilibrium is the triggering event for the modulation of a functionally important motion, i.e. the opening/closing at the protein open end, whereas ligand binding stabilizes one of the preexisting conformations (the open form). The results presented here, complemented with an analysis of proteins belonging to the intracellular lipid-binding protein family, are consistent with a model of allosteric activation governing the binding mechanism. The functional role of this mechanism is thoroughly discussed within the framework of the mechanism for the enterohepatic circulation of bile acids.

Molecular dynamics simulations of interaction between protein-tyrosine phosphatase 1B and a bidentate inhibitor

AIM

To investigate the dynamic properties of protein-tyrosine phosphatase (PTP) 1B and reveal the structural factors responsible for the high inhibitory potency and selectivity of the inhibitor SNA for PTP1B.

METHODS

We performed molecular dynamics (MD) simulations using a long time-scale for both PTP1B and PTP1B complexed with the inhibitor SNA, the most potent and selective PTP1B inhibitor reported to date. The trajectories were analyzed by using principal component analysis.

RESULTS

Trajectory analyses showed that upon binding the ligand, the flexibility of the entire PTP1B molecule decreases. The most notable change is the movement of the WPD-loop. Our simulation results also indicated that electrostatic interactions contribute more to PTP1B-SNA complex conformation than the van der Waals interactions, and that Lys41, Arg47, and Asp48 play important roles in determining the conformation of the inhibitor SNA and in the potency and selectivity of the inhibitor. Of these, Arg47 contributed most. These results were in agreement with previous experimental results.

CONCLUSION

The information presented here suggests that potent and selective PTP1B inhibitors can be designed by targeting the surface residues, for example the region containing Lys41, Arg47, and Asp48, instead of the second phosphate binding site (besides the active phosphate binding site).

Finite element solution of the steady-state Smoluchowski equation for rate constant calculations

This article describes the development and implementation of algorithms to study diffusion in biomolecular systems using continuum mechanics equations. Specifically, finite element methods have been developed to solve the steady-state Smoluchowski equation to calculate ligand binding rate constants for large biomolecules. The resulting software has been validated and applied to mouse acetylcholinesterase. Rates for inhibitor binding to mAChE were calculated at various ionic strengths with several different reaction criteria. The calculated rates were compared with experimental data and show very good agreement when the correct reaction criterion is used. Additionally, these finite element methods require significantly less computational resources than existing particle-based Brownian dynamics methods.

Robust biased Brownian dynamics for rate constant calculation

A reaction probability is required to calculate the rate constant of a diffusion-dominated reaction. Due to the complicated geometry and potentially high dimension of the reaction probability problem, it is usually solved by a Brownian dynamics simulation, also known as a random walk or path integral method, instead of solving the equivalent partial differential equation by a discretization method. Building on earlier work, this article completes the development of a robust importance sampling algorithm for Brownian dynamics-i.e., biased Brownian dynamics with weight control-to overcome the high energy and entropy barriers in biomolecular association reactions. The biased Brownian dynamics steers sampling by a bias force, and the weight control algorithm controls sampling by a target weight. This algorithm is optimal if the bias force and the target weight are constructed from the solution of the reaction probability problem. In reality, an approximate reaction probability has to be used to construct the bias force and the target weight. Thus, the performance of the algorithm depends on the quality of the approximation. Given here is a method to calculate a good approximation, which is based on the selection of a reaction coordinate and the variational formulation of the reaction probability problem. The numerically approximated reaction probability is shown by computer experiments to give a factor-of-two speedup over the use of a purely heuristic approximation. Also, the fully developed method is compared to unbiased Brownian dynamics. The tests for human superoxide dismutase, Escherichia coli superoxide dismutase, and antisweetener antibody NC6.8, show speedups of 17, 35, and 39, respectively. The test for reactions between two model proteins with orientations shows speedups of 2578 for one set of configurations and 3341 for another set of configurations.

Structure of Plasmodium falciparum triose-phosphate isomerase-2-phosphoglycerate complex at 1.1-A resolution

Triose-phosphate isomerase, a key enzyme of the glycolytic pathway, catalyzes the isomerization of dihydroxy acetone phosphate and glyceraldehyde 3-phosphate. In this communication we report the crystal structure of Plasmodium falciparum triose-phosphate isomerase complexed to the inhibitor 2-phosphoglycerate at 1.1-A resolution. The crystallographic asymmetric unit contains a dimeric molecule. The inhibitor bound to one of the subunits in which the flexible catalytic loop 6 is in the open conformation has been cleaved into two fragments presumably due to radiation damage. The cleavage products have been tentatively identified as 2-oxoglycerate and meta-phosphate. The intact 2-phosphoglycerate bound to the active site of the other subunit has been observed in two different orientations. The active site loop in this subunit is in both open and "closed" conformations, although the open form is predominant. Concomitant with the loop closure, Phe-96, Leu-167, and residues 208-211 (YGGS) are also observed in dual conformations in the B-subunit. Detailed comparison of the active-site geometry in the present case to the Saccharomyces cerevisiae triose-phosphate isomerase-dihydroxy acetone phosphate and Leishmania mexicana triose-phosphate isomerase-phosphoglycolate complexes, which have also been determined at atomic resolution, shows that certain interactions are common to the three structures, although 2-phosphoglycerate is neither a substrate nor a transition state analogue.

Modeling of ionic relaxation around a biomembrane disk

A simplified Brownian dynamics model and the corresponding software implementation have been developed for the simulation of electrolyte dynamics on the mesoscopic scale. In addition to direct control simulations, the model system has been verified by a quantitative comparison with the Debye-Hückel theory. As a first application, the model was used to simulate ionic relaxation processes following abrupt intramembrane charge rearrangements in the case of a disk shaped membrane. In addition to its general implications, the obtained properties of the relaxation kinetics confirm the assumptions of the theory of the so-called suspension method, a technique capable of tracing molecular charge motions of membrane proteins in three dimensions.

How FMN binds to anabaena apoflavodoxin: a hydrophobic encounter at an open binding site

Molecular recognition begins when two molecules approach and establish interactions of certain strength. The mechanisms of molecular recognition reactions between biological molecules are not well known, and few systems have been analyzed in detail. We investigate here the reaction between an apoprotein and its physiological cofactor (apoflavodoxin and flavin mononucleotide) that binds reversibly to form a non-covalent complex (flavodoxin) involved in electron transfer reactions. We have analyzed the fast binding reactions between the FMN cofactor (and shorter analogs) and wild type (and nine mutant apoflavodoxins where residues interacting with FMN in the final complex have been replaced). The x-ray structures of two such mutants are reported that show the mutations are well tolerated by the protein. From the calculated microscopic binding rate constants we have performed a Phi analysis of the transition state of complex formation that indicates that the binding starts by interaction of the isoalloxazine-fused rings in FMN with residues of its hydrophobic binding site. In contrast, the phosphate in FMN, known to contribute most to the affinity of the final holoflavodoxin complex, is not bound in the transition state complex. Both the effects of ionic strength and of phosphate concentration on the wild type complex rate constant agree with this scenario. As suggested previously by nmr data, it seems that the isoalloxazine-binding site may be substantially open in solution. Interestingly, although FMN is a charged molecule, electrostatic interactions seem not to play a role in directing the binding, unlike what has been reported for other biological complexes. The binding can thus be best described as a hydrophobic encounter at an open binding site.

The Poisson-Boltzmann equation for biomolecular electrostatics: a tool for structural biology

Electrostatics plays a fundamental role in virtually all processes involving biomolecules in solution. The Poisson-Boltzmann equation constitutes one of the most fundamental approaches to treat electrostatic effects in solution. The theoretical basis of the Poisson-Boltzmann equation is reviewed and a wide range of applications is presented, including the computation of the electrostatic potential at the solvent-accessible molecular surface, the computation of encounter rates between molecules in solution, the computation of the free energy of association and its salt dependence, the study of pKa shifts and the combination with classical molecular mechanics and dynamics. Theoretical results may be used for rationalizing or predicting experimental results, or for suggesting working hypotheses. An ever-increasing body of successful applications proves that the Poisson-Boltzmann equation is a useful tool for structural biology and complementary to other established experimental and theoretical methodologies.

Protein-protein association: investigation of factors influencing association rates by brownian dynamics simulations

The rate of protein-protein association limits the response time due to protein-protein interactions. The bimolecular association rate may be diffusion-controlled or influenced, and in such cases, Brownian dynamics simulations of protein-protein diffusional association may be used to compute association rates. Here, we report Brownian dynamics simulations of the diffusional association of five different protein-protein pairs: barnase and barstar, acetylcholinesterase and fasciculin-2, cytochrome c peroxidase and cytochrome c, the HyHEL-5 antibody and hen egg lysozyme (HEL), and the HyHEL-10 antibody and HEL. The same protocol was used to compute the diffusional association rates for all the protein pairs in order to assess, by comparison to experimentally measured rates, whether the association of these proteins can be explained solely on the basis of diffusional encounter. The simulation protocol is similar to those previously derived for simulation of the association of barnase and barstar, and of acetylcholinesterase and fasciculin-2; these produced results in excellent agreement with experimental data for these protein pairs, with changes in association rate due to mutations reproduced within the limits of expected computational and modeling errors. Here, we find that for all protein pairs, the effects of mutations can be well reproduced by the simulations, even though the degree of the electrostatic translational and orientational steering varies widely between the cases. However, the absolute values of association rates for the acetylcholinesterase: fasciculin-2 and HyHEL-10 antibody: HEL pairs are overestimated. Comparison of bound and unbound protein structures shows that this may be due to gating resulting from protein flexibility in some of the proteins. This may lower the association rates compared to their bimolecular diffusional encounter rates.

Binding free energies and free energy components from molecular dynamics and Poisson-Boltzmann calculations. Application to amino acid recognition by aspartyl-tRNA synthetase

Specific amino acid binding by aminoacyl-tRNA synthetases (aaRS) is necessary for correct translation of the genetic code. Engineering a modified specificity into aminoacyl-tRNA synthetases has been proposed as a means to incorporate artificial amino acid residues into proteins in vivo. In a previous paper, the binding to aspartyl-tRNA synthetase of the substrate Asp and the analogue Asn were compared by molecular dynamics free energy simulations. Molecular dynamics combined with Poisson-Boltzmann free energy calculations represent a less expensive approach, suitable for examining multiple active site mutations in an engineering effort. Here, Poisson-Boltzmann free energy calculations for aspartyl-tRNA synthetase are first validated by their ability to reproduce selected molecular dynamics binding free energy differences, then used to examine the possibility of Asn binding to native and mutant aspartyl-tRNA synthetase. A component analysis of the Poisson-Boltzmann free energies is employed to identify specific interactions that determine the binding affinities. The combined use of molecular dynamics free energy simulations to study one binding process thoroughly, followed by molecular dynamics and Poisson-Boltzmann free energy calculations to study a series of related ligands or mutations is proposed as a paradigm for protein or ligand design. The binding of Asn in an alternate, "head-to-tail" orientation observed in the homologous asparagine synthetase is analyzed, and found to be more stable than the "Asp-like" orientation studied earlier. The new orientation is probably unsuitable for catalysis. A conserved active site lysine (Lys198 in Escherichia coli) that recognizes the Asp side-chain is changed to a leucine residue, found at the corresponding position in asparaginyl-tRNA synthetase. It is interesting that the binding of Asp is calculated to increase slightly (rather than to decrease), while that of Asn is calculated, as expected, to increase strongly, to the same level as Asp binding. Insight into the origin of these changes is provided by the component analyses. The double mutation (K198L,D233E) has a similar effect, while the triple mutation (K198L,Q199E,D233E) reduces Asp binding strongly. No binding measurements are available, but the three mutants are known to have no ability to adenylate Asn, despite the "Asp-like" binding affinities calculated here. In molecular dynamics simulations of all three mutants, the Asn ligand backbone shifts by 1-2 A compared to the experimental Asp:AspRS complex, and significant side-chain rearrangements occur around the pocket. These could reduce the ATP binding constant and/or the adenylation reaction rate, explaining the lack of catalytic activity in these complexes. Finally, Asn binding to AspRS with neutral K198 or charged H449 is considered, and shown to be less favorable than with the charged K198 and neutral H449 used in the analysis.

A Grand Canonical Monte Carlo-Brownian dynamics algorithm for simulating ion channels

A computational algorithm based on Grand Canonical Monte Carlo (GCMC) and Brownian Dynamics (BD) is described to simulate the movement of ions in membrane channels. The proposed algorithm, GCMC/BD, allows the simulation of ion channels with a realistic implementation of boundary conditions of concentration and transmembrane potential. The method is consistent with a statistical mechanical formulation of the equilibrium properties of ion channels (; Biophys. J. 77:139-153). The GCMC/BD algorithm is illustrated with simulations of simple test systems and of the OmpF porin of Escherichia coli. The approach provides a framework for simulating ion permeation in the context of detailed microscopic models.

Bimolecular reaction simulation using Weighted Ensemble Brownian dynamics and the University of Houston Brownian Dynamics program

We discuss here the implementation of the Weighted Ensemble Brownian (WEB) dynamics algorithm of Huber and Kim in the University of Houston Brownian Dynamics (UHBD) suite of programs and its application to bimolecular association problems. WEB dynamics is a biased Brownian dynamics (BD) algorithm that is more efficient than the standard Northrup-Allison-McCammon (NAM) method in cases where reaction events are infrequent because of intervening free energy barriers. Test cases reported here include the Smoluchowski rate for association of spheres, the association of the enzyme copper-zinc superoxide dismutase with superoxide anion, and the binding of the superpotent sweetener N-(p-cyanophenyl)-N'-(diphenylmethyl)-guanidinium acetic acid to a monoclonal antibody fragment, NC6.8. Our results show that the WEB dynamics algorithm is a superior simulation method for enzyme-substrate reaction encounters with large free energy barriers.

Computer simulation of protein-protein association kinetics: acetylcholinesterase-fasciculin

Computer simulations were performed to investigate the role of electrostatic interactions in promoting fast association of acetylcholinesterase with its peptidic inhibitor, the neurotoxin fasciculin. The encounter of the two macromolecules was simulated with the technique of Brownian dynamics (BD), using atomically detailed structures, and association rate constants were calculated for the wild-type and a number of mutant proteins. In a first set of simulations, the ordering of the experimental rate constants for the mutant proteins was correctly reproduced, although the absolute values of the rate constants were overestimated by a factor of around 30. Rigorous calculations of the full electrostatic interaction energy between the two proteins indicate that this overestimation of association rates results at least in part from approximations made in the description of interaction energetics in the BD simulations. In particular, the initial BD simulations neglect the unfavourable electrostatic desolvation effects that result from the exclusion of high dielectric solvent that accompanies the approach of the two low dielectric proteins. This electrostatic desolvation component is so large that the overall contribution of electrostatics to the binding energy of the complex is unlikely to be strongly favourable. Nevertheless, electrostatic interactions are still responsible for increased association rates, because even if they are unfavourable in the fully formed complex, they are still favourable at intermediate protein-protein separation distances. It therefore appears possible for electrostatic interactions to promote the kinetics of binding even if they do not make a strongly favourable contribution to the thermodynamics of binding. When an approximate description of these electrostatic desolvation effects is included in a second set of BD simulations, the relative ordering of the mutant proteins is again correctly reproduced, but now association rate constants that are much closer in magnitude to the experimental values are obtained. Inclusion of electrostatic desolvation effects also improves reproduction of the experimental ionic strength dependence of the wild-type association rate.

Conformational change in the activation of lipase: an analysis in terms of low-frequency normal modes

The interfacial activation of Rhizomucor miehei lipase (RmL) involves the motion of an alpha-helical region (residues 82-96) which acts as a "lid" over the active site of the enzyme, undergoing a displacement from a "closed" to an "open" conformation upon binding of substrate. Normal mode analyses performed in both low and high dielectric media reveal that low-frequency vibrational modes contribute significantly to the conformational transition between the closed and open conformations. In these modes, the lid displacement is coupled to local motions of active site loops as well as global breathing motions. Atomic fluctuations of the first hinge of the lid (residues 83-84) are substantially larger in the low dielectric medium than in the high dielectric medium. Our results also suggest that electrostatic interactions of Arg86 play an important role in terms of both the intrinsic stability of the lid and its displacement, through enhancement of hinge mobility in a high dielectric medium. Additional calculations demonstrate that the observed patterns of atomic fluctuations are an intrinsic feature of the protein structure and not dependent on the nature of specific energy minima.

The loop opening/closing motion of the enzyme triosephosphate isomerase

To explore the origin of the large-scale motion of triosephosphate isomerase's flexible loop (residues 166 to 176) at the active site, several simulation protocols are employed both for the free enzyme in vacuo and for the free enzyme with some solvent modeling: high-temperature Langevin dynamics simulations, sampling by a "dynamics driver" approach, and potential-energy surface calculations. Our focus is on obtaining the energy barrier to the enzyme's motion and establishing the nature of the loop movement. Previous calculations did not determine this energy barrier and the effect of solvent on the barrier. High-temperature molecular dynamics simulations and crystallographic studies have suggested a rigid-body motion with two hinges located at both ends of the loop; Brownian dynamics simulations at room temperature pointed to a very flexible behavior. The present simulations and analyses reveal that although solute/solvent hydrogen bonds play a crucial role in lowering the energy along the pathway, there still remains a high activation barrier. This finding clearly indicates that, if the loop opens and closes in the absence of a substrate at standard conditions (e.g., room temperature, appropriate concentration of isomerase), the time scale for transition is not in the nanosecond but rather the microsecond range. Our results also indicate that in the context of spontaneous opening in the free enzyme, the motion is of rigid-body type and that the specific interaction between residues Ala176 and Tyr208 plays a crucial role in the loop opening/closing mechanism.

Simulation of the diffusional association of barnase and barstar

The rate of protein association places an upper limit on the response time due to protein interactions, which, under certain circumstances, can be diffusion-controlled. Simulations of model proteins show that diffusion-limited association rates are approximately 10(6)-10(7) M-1 s-1 in the absence of long-range forces (Northrup, S. H., and H. P. Erickson. 1992. Kinetics of protein-protein association explained by Brownian dynamics computer simulations. Proc. Natl. Acad. Sci. U.S.A. 89:3338-3342). The measured association rates of barnase and barstar are 10(8)-10(9) M-1 s-1 at 50 mM ionic strength, and depend on ionic strength (Schreiber, G., and A. R. Fersht. 1996. Rapid, electrostatically assisted association of proteins. Nat. Struct. Biol. 3:427-431), implying that their association is electrostatically facilitated. We report Brownian dynamics simulations of the diffusional association of barnase and barstar to compute association rates and their dependence on ionic strength and protein mutation. Crucial to the ability to reproduce experimental rates is the definition of encounter complex formation at the endpoint of diffusional motion. Simple definitions, such as a required root mean square (RMS) distance to the fully bound position, fail to explain the large influence of some mutations on association rates. Good agreement with experiments could be obtained if satisfaction of two intermolecular residue contacts was required for encounter complex formation. In the encounter complexes, barstar tends to be shifted from its position in the bound complex toward the guanine-binding loop on barnase.

A new method for modeling large-scale rearrangements of protein domains

A method for modeling large-scale rearrangements of protein domains connected by a single- or a double-stranded linker is proposed. Multidomain proteins may undergo substantial domain displacements, while their intradomain structure remains essentially unchanged. The method allows automatic identification of an interdomain linker and builds an all-atom model of a protein structure in internal coordinates. Torsion angles belonging to the interdomain linkers and side chains potentially able to form domain interfaces are set free while remaining torsions, bond lengths, and bond angles are fixed. Large-scale sampling of the reduced torsions conformational subspace is effected with the "biased probability Monte Carlo-minimization" method [Abagyan, R.A., Totrov, M.M. (1994): J. Mol. Biol. 235, 983-1002]. Solvation and side-chain entropic contributions are added to the energy function. A special procedure has been developed to generate concerted deformations of a double-stranded interdomain linker in such a way that the polypeptide chain continuity is preserved. The method was tested on Bence-Jones protein with a single-stranded linker and lysine/arginine/ornithine-binding (LAO) protein with a double-stranded linker. For each protein, structurally diverse low-energy conformations with ideal covalent geometry were generated, and an overlap between two sets of conformations generated starting from the crystallographically determined "closed" and "open" forms was found. One of the low-energy conformations generated in a run starting from the LAO "closed" form was only 2.2 A away from the structure of the "open" form. The method can be useful in predicting the scope of possible domain rearrangements of a multidomain protein.

Effects of protein stabilizing agents on thermal backbone motions: a disulfide trapping study

Chemical stabilizers are widely used to enhance protein stability, both in nature and in the laboratory. Here, the molecular mechanism of chemical stabilizers is studied using a disulfide trapping assay to measure the effects of stabilizers on thermal backbone dynamics in the Escherichia coli galactose/ glucose binding protein. Two types of backbone fluctuations are examined: (a) relative movements of adjacent surface alpha-helices within the same domain and (b) interdomain twisting motions. Both types of fluctuations are significantly reduced by all six stabilizers tested (glycerol, sucrose, trehalose, L-glucose, D-glucose, and D-galactose), and in each case larger amplitude motions are inhibited more than smaller ones. Motional inhibition does not require a high-affinity stabilizer binding site, indicating that the effects of stabilizers are nonspecific. Overall, the results support the theory that effective stabilizing agents act by favoring the most compact structure of a protein, thereby reducing local backbone fluctuations away from the fully folded state. Such inhibition of protein backbone dynamics may be a general mechanism of protein stabilization in extreme thermal or chemical environments.