Gated Diffusion-controlled Reactions

Multiscale Approach for Computing Gated Ligand Binding from Molecular Dynamics and Brownian Dynamics Simulations

We develop an approach to characterize the effects of gating by a multiconformation protein consisting of macrostate conformations that are either accessible or inaccessible to ligand binding. We first construct a Markov state model of the apo-protein from atomistic molecular dynamics simulations from which we identify macrostates and their conformations, compute their relative macrostate populations and interchange kinetics, and structurally characterize them in terms of ligand accessibility. We insert the calculated first-order rate constants for conformational transitions into a multistate gating theory from which we derive a gating factor γ that quantifies the degree of conformational gating. Applied to HIV-1 protease, our approach yields a kinetic network of three accessible (semi-open, open, and wide-open) and two inaccessible (closed and a newly identified, "parted") macrostate conformations. The parted conformation sterically partitions the active site, suggesting a possible role in product release. We find that the binding kinetics of drugs and drug-like inhibitors to HIV-1 protease falls in the slow gating regime. However, because γ = 0.75, conformational gating only modestly slows ligand binding. Brownian dynamics simulations of the diffusional association of eight inhibitors to the protease─having a wide range of experimental association constants (∼10⁴-10¹⁰ M^-1 s^-1)─yields gated rate constants in the range of ∼0.5-5.7 × 10⁸ M^-1 s^-1. This indicates that, whereas the association rate of some inhibitors could be described by the model, for many inhibitors either subsequent conformational transitions or alternate binding mechanisms may be rate-limiting. For systems known to be modulated by conformational gating, the approach could be scaled computationally efficiently to screen association kinetics for a large number of ligands.

Molecular Mechanics Study of Flow and Surface Influence in Ligand-Protein Association

Ligand–protein association is the first and critical step for many biological and chemical processes. This study investigated the molecular association processes under different environments. In biology, cells have different compartments where ligand–protein binding may occur on a membrane. In experiments involving ligand–protein binding, such as the surface plasmon resonance and continuous flow biosynthesis, a substrate flow and surface are required in experimental settings. As compared with a simple binding condition, which includes only the ligand, protein, and solvent, the association rate and processes may be affected by additional ligand transporting forces and other intermolecular interactions between the ligand and environmental objects. We evaluated these environmental factors by using a ligand xk263 binding to HIV protease (HIVp) with atomistic details. Using Brownian dynamics simulations, we modeled xk263 and HIVp association time and probability when a system has xk263 diffusion flux and a non-polar self-assembled monolayer surface. We also examined different protein orientations and accessible surfaces for xk263. To allow xk263 to access to the dimer interface of immobilized HIVp, we simulated the system by placing the protein 20Å above the surface because immobilizing HIVp on a surface prevented xk263 from contacting with the interface. The non-specific interactions increased the binding probability while the association time remained unchanged. When the xk263 diffusion flux increased, the effective xk263 concentration around HIVp, xk263–HIVp association time and binding probability decreased non-linearly regardless of interacting with the self-assembled monolayer surface or not. The work sheds light on the effects of the solvent flow and surface environment on ligand–protein associations and provides a perspective on experimental design.

Effect of surface curvature on diffusion-limited reactions on a curved surface

To investigate how the curvature of a reactive surface can affect reaction kinetics, we use a simple model in which a diffusion-limited bimolecular reaction occurs on a curved surface that is hollowed inward, flat, or extended outward while keeping the reactive area on the surface constant. By numerically solving the diffusion equation for this model using the finite element method, we find that the rate constant is a non-linear function of the surface curvature and that there is an optimal curvature providing the maximum value of the rate constant, which indicates that a spherical reactant whose entire surface is reactive (a uniformly reactive sphere) is not the most reactive species for a given reactive surface area. We discuss how this result arises from the interplay between two opposing effects: the exposedness of the reactive area to its partner reactants, which causes the rate constant to increase as the curvature increases, and the competition occurring on the reactive surface, which decreases the rate constant. This study helps us to understand the role of curvature in surface reactions and allows us to rationally design reactants that provide a high reaction rate.

Effect of stochastic gating on channel-facilitated transport of non-interacting and strongly repelling solutes

Ligand- or voltage-driven stochastic gating-the structural rearrangements by which the channel switches between its open and closed states-is a fundamental property of biological membrane channels. Gating underlies the channel's ability to respond to different stimuli and, therefore, to be functionally regulated by the changing environment. The accepted understanding of the gating effect on the solute flux through the channel is that the mean flux is the product of the flux through the open channel and the probability of finding the channel in the open state. Here, using a diffusion model of channel-facilitated transport, we show that this is true only when the gating is much slower than the dynamics of solute translocation through the channel. If this condition breaks, the mean flux could differ from this simple estimate by orders of magnitude.

DNA Internal Motion Likely Accelerates Protein Target Search in a Packed Nucleoid

Transcription factors must diffuse through densely packed and coiled DNA to find their binding sites. Using a coarse-grained model of DNA and lac repressor (LacI) in the Escherichia coli nucleoid, simulations were performed to examine how LacI diffuses in such a space. Despite the canonical picture of LacI diffusing rather freely, in reality the DNA is densely packed, is not rigid but highly mobile, and the dynamics of DNA dictates to a great extent the LacI motion. A possibly better picture of unbound LacI motion is that of gated diffusion, where DNA confines LacI in a cage, but LacI can move between cages when hindering DNA strands move out of the way. Three-dimensional diffusion constants for unbound LacI computed from simulations closely match those for unbound LacI in vivo reported in the literature. The internal motions of DNA appear to be governed by strong internal forces arising from being crowded into the small space of the nucleoid. A consequence of the DNA internal motion is that protein target search may be accelerated.

Understanding ligand-receptor non-covalent binding kinetics using molecular modeling

Kinetic properties may serve as critical differentiators and predictors of drug efficacy and safety, in addition to the traditionally focused binding affinity. However the quantitative structure-kinetics relationship (QSKR) for modeling and ligand design is still poorly understood. This review provides an introduction to the kinetics of drug binding from a fundamental chemistry perspective. We focus on recent developments of computational tools and their applications to non-covalent binding kinetics.

Enzyme Tunnels and Gates As Relevant Targets in Drug Design

Many enzymes contain tunnels and gates that are essential to their function. Gates reversibly switch between open and closed conformations and thereby control the traffic of small molecules-substrates, products, ions, and solvent molecules-into and out of the enzyme's structure via molecular tunnels. Many transient tunnels and gates undoubtedly remain to be identified, and their functional roles and utility as potential drug targets have received comparatively little attention. Here, we describe a set of general concepts relating to the structural properties, function, and classification of these interesting structural features. In addition, we highlight the potential of enzyme tunnels and gates as targets for the binding of small molecules. The different types of binding that are possible and the potential pharmacological benefits of such targeting are discussed. Twelve examples of ligands bound to the tunnels and/or gates of clinically relevant enzymes are used to illustrate the different binding modes and to explain some new strategies for drug design. Such strategies could potentially help to overcome some of the problems facing medicinal chemists and lead to the discovery of more effective drugs.

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.

Exploration of gated ligand binding recognizes an allosteric site for blocking FABP4-protein interaction

Fatty acid binding protein 4 (FABP4), reversibly binding to fatty acids and other lipids with high affinities, is a potential target for treatment of cancers. The binding site of FABP4 is buried in an interior cavity and thereby ligand binding/unbinding is coupled with opening/closing of FABP4. It is a difficult task both experimentally and computationally to illuminate the entry or exit pathway, especially with the conformational gating. In this report we combine extensive computer simulations, clustering analysis, and the Markov state model to investigate the binding mechanism of FABP4 and troglitazone. Our simulations capture spontaneous binding and unbinding events as well as the conformational transition of FABP4 between the open and closed states. An allosteric binding site on the protein surface is recognized for the development of novel FABP4 inhibitors. The binding affinity is calculated and compared with the experimental value. The kinetic analysis suggests that ligand residence on the protein surface may delay the binding process. Overall, our results provide a comprehensive picture of ligand diffusion on the protein surface, ligand migration into the buried cavity, and the conformational change of FABP4 at an atomic level.

Investigation of Structural Dynamics of Enzymes and Protonation States of Substrates Using Computational Tools

This review discusses the use of molecular modeling tools, together with existing experimental findings, to provide a complete atomic-level description of enzyme dynamics and function. We focus on functionally relevant conformational dynamics of enzymes and the protonation states of substrates. The conformational fluctuations of enzymes usually play a crucial role in substrate recognition and catalysis. Protein dynamics can be altered by a tiny change in a molecular system such as different protonation states of various intermediates or by a significant perturbation such as a ligand association. Here we review recent advances in applying atomistic molecular dynamics (MD) simulations to investigate allosteric and network regulation of tryptophan synthase (TRPS) and protonation states of its intermediates and catalysis. In addition, we review studies using quantum mechanics/molecular mechanics (QM/MM) methods to investigate the protonation states of catalytic residues of β-Ketoacyl ACP synthase I (KasA). We also discuss modeling of large-scale protein motions for HIV-1 protease with coarse-grained Brownian dynamics (BD) simulations.

Diffusive flux in a model of stochastically gated oxygen transport in insect respiration

Oxygen delivery to insect tissues is controlled by transport through a branched tubular network that is connected to the atmosphere by valve-like gates, known as spiracles. In certain physiological regimes, the spiracles appear to be randomly switching between open and closed states. Quantitative analysis of this regime leads a reaction-diffusion problem with stochastically switching boundary condition. We derive an expression for the diffusive flux at long times in this problem. Our approach starts with the derivation of the passage probability for a single particle that diffuses between a stochastically gated boundary, which models the opening and closing spiracle, and the perfectly absorbing boundary, which models oxygen absorption by the tissue. This passage probability is then used to derive an expression giving the diffusive flux as a function of the geometric parameters of the tube and characteristic time scales of diffusion and gate dynamics.

A wrench in the works of human acetylcholinesterase: soman induced conformational changes revealed by molecular dynamics simulations

Irreversible inactivation of human acetylcholinesterase (hAChE) by organophosphorous pesticides (OPs) and chemical weapon agents (CWA) has severe morbidity and mortality consequences. We present data from quantum mechanics/molecular mechanics (QM/MM) and 80 classical molecular dynamics (MD) simulations of the apo and soman-adducted forms of hAChE to investigate the effects on the dynamics and protein structure when the catalytic Serine 203 is phosphonylated. We find that the soman phosphonylation of the active site Ser203 follows a water assisted addition-elimination mechanism with the elimination of the fluoride ion being the highest energy barrier at 6.5 kcal/mole. We observe soman-dependent changes in backbone and sidechain motions compared to the apo form of the protein. These alterations restrict the soman-adducted hAChE to a structural state that is primed for the soman adduct to be cleaved and removed from the active site. The altered motions and resulting structures provide alternative pathways into and out of the hAChE active site. In the soman-adducted protein both side and back door pathways are viable for soman adduct access. Correlation analysis of the apo and soman adducted MD trajectories shows that the correlation of gorge entrance and back door motion is disrupted when hAChE is adducted. This supports the hypothesis that substrate and product can use two different pathways as entry and exit sites in the apo form of the protein. These alternative pathways have important implications for the rational design of medical countermeasures.

Catch-and-hold activation of muscle acetylcholine receptors having transmitter binding site mutations

Agonists turn on receptors because their target sites have a higher affinity in the active versus resting conformation of the protein. We used single-channel electrophysiology to measure the lower-affinity (LA) and higher-affinity (HA) equilibrium dissociation constants for acetylcholine in adult-type muscle mouse nicotinic receptors (AChRs) having mutations of agonist binding site amino acids. For a series of agonists and for all mutations of αY93, αG147, αW149, αY190, αY198, εW55, and δW57, the change in LA binding energy was approximately half that in HA binding energy. The results were analyzed as a linear free energy relationship between LA and HA agonist binding, the slope of which (κ) gives the fraction of the overall binding chemical potential where the LA complex is established. The linear correlation between LA and HA binding energies suggests that the overall binding process is by an integrated mechanism (catch-and-hold). For the agonist and the above mutations, κ ∼ 0.5, but side-chain substitutions of two residues had a slope that was significantly higher (0.90; αG153) or lower (0.25; εP121). The results suggest that backbone rearrangements in loop B, loop C, and the non-α surface participate in both LA binding and the LA ↔ HA affinity switch. It appears that all of the intermediate steps in AChR activation comprise a single, energetically coupled process.

Crystal structures of Acetobacter aceti succinyl-coenzyme A (CoA):acetate CoA-transferase reveal specificity determinants and illustrate the mechanism used by class I CoA-transferases

Coenzyme A (CoA)-transferases catalyze transthioesterification reactions involving acyl-CoA substrates, using an active-site carboxylate to form covalent acyl anhydride and CoA thioester adducts. Mechanistic studies of class I CoA-transferases suggested that acyl-CoA binding energy is used to accelerate rate-limiting acyl transfers by compressing the substrate thioester tightly against the catalytic glutamate [White, H., and Jencks, W. P. (1976) J. Biol. Chem. 251, 1688-1699]. The class I CoA-transferase succinyl-CoA:acetate CoA-transferase is an acetic acid resistance factor (AarC) with a role in a variant citric acid cycle in Acetobacter aceti. In an effort to identify residues involved in substrate recognition, X-ray crystal structures of a C-terminally His(6)-tagged form (AarCH6) were determined for several wild-type and mutant complexes, including freeze-trapped acetylglutamyl anhydride and glutamyl-CoA thioester adducts. The latter shows the acetate product bound to an auxiliary site that is required for efficient carboxylate substrate recognition. A mutant in which the catalytic glutamate was changed to an alanine crystallized in a closed complex containing dethiaacetyl-CoA, which adopts an unusual curled conformation. A model of the acetyl-CoA Michaelis complex demonstrates the compression anticipated four decades ago by Jencks and reveals that the nucleophilic glutamate is held at a near-ideal angle for attack as the thioester oxygen is forced into an oxyanion hole composed of Gly388 NH and CoA N2″. CoA is nearly immobile along its entire length during all stages of the enzyme reaction. Spatial and sequence conservation of key residues indicates that this mechanism is general among class I CoA-transferases.

Rational prediction with molecular dynamics for hit identification

Although the motions of proteins are fundamental for their function, for pragmatic reasons, the consideration of protein elasticity has traditionally been neglected in drug discovery and design. This review details protein motion, its relevance to biomolecular interactions and how it can be sampled using molecular dynamics simulations. Within this context, two major areas of research in structure-based prediction that can benefit from considering protein flexibility, binding site detection and molecular docking, are discussed. Basic classification metrics and statistical analysis techniques, which can facilitate performance analysis, are also reviewed. With hardware and software advances, molecular dynamics in combination with traditional structure-based prediction methods can potentially reduce the time and costs involved in the hit identification pipeline.

Biochemical, structural and molecular dynamics analyses of the potential virulence factor RipA from Yersinia pestis

Human diseases are attributed in part to the ability of pathogens to evade the eukaryotic immune systems. A subset of these pathogens has developed mechanisms to survive in human macrophages. Yersinia pestis, the causative agent of the bubonic plague, is a predominately extracellular pathogen with the ability to survive and replicate intracellularly. A previous study has shown that a novel rip (required for intracellular proliferation) operon (ripA, ripB and ripC) is essential for replication and survival of Y. pestis in postactivated macrophages, by playing a role in lowering macrophage-produced nitric oxide (NO) levels. A bioinformatics analysis indicates that the rip operon is conserved among a distally related subset of macrophage-residing pathogens, including Burkholderia and Salmonella species, and suggests that this previously uncharacterized pathway is also required for intracellular survival of these pathogens. The focus of this study is ripA, which encodes for a protein highly homologous to 4-hydroxybutyrate-CoA transferase; however, biochemical analysis suggests that RipA functions as a butyryl-CoA transferase. The 1.9 Å X-ray crystal structure reveals that RipA belongs to the class of Family I CoA transferases and exhibits a unique tetrameric state. Molecular dynamics simulations are consistent with RipA tetramer formation and suggest a possible gating mechanism for CoA binding mediated by Val227. Together, our structural characterization and molecular dynamic simulations offer insights into acyl-CoA specificity within the active site binding pocket, and support biochemical results that RipA is a butyryl-CoA transferase. We hypothesize that the end product of the rip operon is butyrate, a known anti-inflammatory, which has been shown to lower NO levels in macrophages. Thus, the results of this molecular study of Y. pestis RipA provide a structural platform for rational inhibitor design, which may lead to a greater understanding of the role of RipA in this unique virulence pathway.