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

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.

Structural and dynamic basis of substrate permissiveness in hydroxycinnamoyltransferase (HCT)

Substrate permissiveness has long been regarded as the raw materials for the evolution of new enzymatic functions. In land plants, hydroxycinnamoyltransferase (HCT) is an essential enzyme of the phenylpropanoid metabolism. Although essential enzymes are normally associated with high substrate specificity, HCT can utilize a variety of non-native substrates. To examine the structural and dynamic basis of substrate permissiveness in this enzyme, we report the crystal structure of HCT from Selaginella moellendorffii and molecular dynamics (MD) simulations performed on five orthologous HCTs from several major lineages of land plants. Through altogether 17-μs MD simulations, we demonstrate the prevalent swing motion of an arginine handle on a submicrosecond timescale across all five HCTs, which plays a key role in native substrate recognition by these intrinsically promiscuous enzymes. Our simulations further reveal how a non-native substrate of HCT engages a binding site different from that of the native substrate and diffuses to reach the catalytic center and its co-substrate. By numerically solving the Smoluchowski equation, we show that the presence of such an alternative binding site, even when it is distant from the catalytic center, always increases the reaction rate of a given substrate. However, this increase is only significant for enzyme-substrate reactions heavily influenced by diffusion. In these cases, binding non-native substrates ‘off-center’ provides an effective rationale to develop substrate permissiveness while maintaining the native functions of promiscuous enzymes.

Examples abound of enzymes that can process substrates other than their native ones. However, the structural and dynamic basis of this promiscuity remains to be fully understood. In this work, we examine HCT, an intrinsically promiscuous acyltransferase with conserved function in all land plants. We uncover the sub-microsecond swing motion of a key arginine residue facilitating the recognition of both native and non-native substrates of HCT. We also quantify the impact of an off-center binding site on the non-native reaction rate. Although our calculations were inspired by HCT, the results apply in general, i.e., for enzymes heavily influenced by diffusion, binding non-native substrates ‘off-center’, even with rather weak affinity, can accelerate non-native reactions to appreciable levels.

Synthesis meets theory: Past, present and future of rational chemistry

Chemical synthesis has its roots in the empirical approach of alchemy. Nonetheless, the birth of the scientific method, the technical and technological advances (exploiting revolutionary discoveries in physics) and the improved management and sharing of growing databases greatly contributed to the evolution of chemistry from an esoteric ground into a mature scientific discipline during these last 400 years. Furthermore, thanks to the evolution of computational resources, platforms and media in the last 40 years, theoretical chemistry has added to the puzzle the final missing tile in the process of “rationalizing” chemistry. The use of mathematical models of chemical properties, behaviors and reactivities is nowadays ubiquitous in literature. Theoretical chemistry has been successful in the difficult task of complementing and explaining synthetic results and providing rigorous insights when these are otherwise unattainable by experiment. The first part of this review walks the reader through a concise historical overview on the evolution of the “model” in chemistry. Salient milestones have been highlighted and briefly discussed. The second part focuses more on the general description of recent state-of-the-art computational techniques currently used worldwide by chemists to produce synergistic models between theory and experiment. Each section is complemented by key-examples taken from the literature that illustrate the application of the technique discussed therein.

Kinetics for Drug Discovery: an industry-driven effort to target drug residence time

A considerable number of approved drugs show non-equilibrium binding characteristics, emphasizing the potential role of drug residence times for in vivo efficacy. Therefore, a detailed understanding of the kinetics of association and dissociation of a target-ligand complex might provide crucial insight into the molecular mechanism-of-action of a compound. This deeper understanding will help to improve decision making in drug discovery, thus leading to a better selection of interesting compounds to be profiled further. In this review, we highlight the contributions of the Kinetics for Drug Discovery (K4DD) Consortium, which targets major open questions related to binding kinetics in an industry-driven public-private partnership.

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.

Modeling of enhanced catalysis in multienzyme nanostructures: effect of molecular scaffolds, spatial organization, and concentration

Colocalized multistep enzymatic reaction pathways within biological catabolic and metabolic processes occur with high yield and specificity. Spatial organization on membranes or surfaces may be associated with increased efficiency of intermediate substrate transfer. Using a new Brownian dynamics package, GeomBD, we explored the geometric features of a surface-anchored enzyme system by parallel coarse-grained Brownian dynamics simulations of substrate diffusion over microsecond (μs) to millisecond (ms) time scales. We focused on a recently developed glucose oxidase (GOx), horseradish peroxidase (HRP), and DNA origami-scaffold enzyme system, where the H2O2 substrate of HRP is produced by GOx. The results revealed and explained a significant advantage in catalytic enhancement by optimizing interenzyme distance and orientation in the presence of the scaffold model. The planar scaffold colocalized the enzymes and provided a diffusive barrier that enhanced substrate transfer probability, becoming more relevant with increasing interenzyme distance. The results highlight the importance of protein geometry in the proper assessment of distance and orientation dependence on the probability of substrate transfer. They shed light on strategies for engineering multienzyme complexes and further investigation of enhanced catalytic efficiency for substrate diffusion between membrane-anchoring proteins.

Contribution of Electrostatics to the Kinetics of Electron Transfer from NADH-Cytochrome b5 Reductase to Fe(III)-Cytochrome b5

Brownian dynamics (BD) simulations provide here a theoretical atomic-level treatment of the reduction of human ferric cytochrome b5 (cyt b5) by NADH-cytochrome b5 reductaste (cyt b5r) and several of its mutants. BD is used to calculate the second-order rate constant of electron transfer (ET) between the proteins for direct correlation with experiments. Interestingly, the inclusion of electrostatic forces dramatically increases the reaction rate of the native proteins despite the overall negative charge of both proteins. The role played by electrostatic charge distribution in stabilizing the ET complexes and the role of mutations of several amino acid residues in stabilizing or destabilizing the complexes are analyzed. The complex with the shortest ET reaction distance (d = 6.58 Å) from rigid body BD is further subjected to 1 ns of molecular dynamics (MD) in a periodic box of TIP3P water to produce a more stable complex allowed by flexibility and with a shorter average reaction distance d = 6.02 Å. We predict a docking model in which the following ion-ion interactions are dominant (cyt b5r/cyt b5): Lys162-Heme O1D/Lys163-Asp64/Arg91-Heme O1A/Lys125-Asp70.

Advanced molecular dynamics simulation methods for kinase drug discovery

Interest in the application of molecular dynamics (MD) simulations has increased in the field of protein kinase (PK) drug discovery. PKs belong to an important drug target class because they are directly involved in a number of diseases, including cancer. MD methods simulate dynamic biological and chemical events at an atomic level. This information can be combined with other in silico and experimental methods to efficiently target selected receptors. In this review, we present common and advanced methods of MD simulations and we focus on the recent applications of MD-based methodologies that provided significant insights into the elucidation of biological mechanisms involving PKs and into the discovery of novel kinase inhibitors.

Multiscale Estimation of Binding Kinetics Using Brownian Dynamics, Molecular Dynamics and Milestoning

The kinetic rate constants of binding were estimated for four biochemically relevant molecular systems by a method that uses milestoning theory to combine Brownian dynamics simulations with more detailed molecular dynamics simulations. The rate constants found using this method agreed well with experimentally and theoretically obtained values. We predicted the association rate of a small charged molecule toward both a charged and an uncharged spherical receptor and verified the estimated value with Smoluchowski theory. We also calculated the kon rate constant for superoxide dismutase with its natural substrate, O2-, in a validation of a previous experiment using similar methods but with a number of important improvements. We also calculated the kon for a new system: the N-terminal domain of Troponin C with its natural substrate Ca2+. The kon calculated for the latter two systems closely resemble experimentally obtained values. This novel multiscale approach is computationally cheaper and more parallelizable when compared to other methods of similar accuracy. We anticipate that this methodology will be useful for predicting kinetic rate constants and for understanding the process of binding between a small molecule and a protein receptor.

Substrate tunnels in enzymes: structure-function relationships and computational methodology

In enzymes, the active site is the location where incoming substrates are chemically converted to products. In some enzymes, this site is deeply buried within the core of the protein, and, in order to access the active site, substrates must pass through the body of the protein via a tunnel. In many systems, these tunnels act as filters and have been found to influence both substrate specificity and catalytic mechanism. Identifying and understanding how these tunnels exert such control has been of growing interest over the past several years because of implications in fields such as protein engineering and drug design. This growing interest has spurred the development of several computational methods to identify and analyze tunnels and how ligands migrate through these tunnels. The goal of this review is to outline how tunnels influence substrate specificity and catalytic efficiency in enzymes with buried active sites and to provide a brief summary of the computational tools used to identify and evaluate these tunnels.

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.