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

Co-localization and confinement of ecto-nucleotidases modulate extracellular adenosine nucleotide distributions

Nucleotides comprise small molecules that perform critical signaling roles in biological systems. Adenosine-based nucleotides, including adenosine tri-, di-, and mono-phosphate, are controlled through their rapid degradation by diphosphohydrolases and ecto-nucleotidases (NDAs). The interplay between nucleotide signaling and degradation is especially important in synapses formed between cells, which create signaling 'nanodomains'. Within these 'nanodomains', charged nucleotides interact with densely-packed membranes and biomolecules. While the contributions of electrostatic and steric interactions within such nanodomains are known to shape diffusion-limited reaction rates, less is understood about how these factors control the kinetics of nucleotidase activity. To quantify these factors, we utilized reaction-diffusion numerical simulations of 1) adenosine triphosphate (ATP) hydrolysis into adenosine monophosphate (AMP) and 2) AMP into adenosine (Ado) via two representative nucleotidases, CD39 and CD73. We evaluate these sequentially-coupled reactions in nanodomain geometries representative of extracellular synapses, within which we localize the nucleotidases. With this model, we find that 1) nucleotidase confinement reduces reaction rates relative to an open (bulk) system, 2) the rates of AMP and ADO formation are accelerated by restricting the diffusion of substrates away from the enzymes, and 3) nucleotidase co-localization and the presence of complementary (positive) charges to ATP enhance reaction rates, though the impact of these contributions on nucleotide pools depends on the degree to which the membrane competes for substrates. As a result, these contributions integratively control the relative concentrations and distributions of ATP and its metabolites within the junctional space. Altogether, our studies suggest that CD39 and CD73 nucleotidase activity within junctional spaces can exploit their confinement and favorable electrostatic interactions to finely control nucleotide signaling.

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.

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.

Solvent fluctuations in hydrophobic cavity-ligand binding kinetics

Water plays a crucial part in virtually all protein-ligand binding processes in and out of equilibrium. Here, we investigate the role of water in the binding kinetics of a ligand to a prototypical hydrophobic pocket by explicit-water molecular dynamics (MD) simulations and implicit diffusional approaches. The concave pocket in the unbound state exhibits wet/dry hydration oscillations whose magnitude and time scale are significantly amplified by the approaching ligand. In turn, the ligand's stochastic motion intimately couples to the slow hydration fluctuations, leading to a sixfold-enhanced friction in the vicinity of the pocket entrance. The increased friction considerably decelerates association in the otherwise barrierless system, indicating the importance of molecular-scale hydrodynamic effects in cavity-ligand binding arising due to capillary fluctuations. We derive and analyze the diffusivity profile and show that the mean first passage time distribution from the MD simulation can be accurately reproduced by a standard Brownian dynamics simulation if the appropriate position-dependent friction profile is included. However, long-time decays in the water-ligand (random) force autocorrelation demonstrate violation of the Markovian assumption, challenging standard diffusive approaches for rate prediction. Remarkably, the static friction profile derived from the force correlations strongly resembles the profile derived on the Markovian assumption apart from a simple shift in space, which can be rationalized by a time-space retardation in the ligand's downhill dynamics toward the pocket. The observed spatiotemporal hydrodynamic coupling may be of biological importance providing the time needed for conformational receptor-ligand adjustments, typical of the induced-fit paradigm.

Finite Element Estimation of Protein-Ligand Association Rates with Post-Encounter Effects: Applications to Calcium binding in Troponin C and SERCA

We introduce a computational pipeline and suite of software tools for the approximation of diffusion-limited binding based on a recently developed theoretical framework. Our approach handles molecular geometries generated from high-resolution structural data and can account for active sites buried within the protein or behind gating mechanisms. Using tools from the FEniCS library and the APBS solver, we implement a numerical code for our method and study two Ca(2+)-binding proteins: Troponin C and the Sarcoplasmic Reticulum Ca(2+) ATPase (SERCA). We find that a combination of diffusional encounter and internal 'buried channel' descriptions provide superior descriptions of association rates, improving estimates by orders of magnitude.

Intrinsic disorder: signaling via highly specific but short-lived association

Association between signaling proteins and their cellular targets is generally thought to be highly specific (implicating a high association constant, K(a)) and, at the same time, transient or short-lived (corresponding to a high dissociation rate constant, k(d)). However, a combination of high K(a) and high k(d) would lead to a high association rate constant (k(a) = K(a)k(d)), which poses a problem because there is a limit to which k(a) can be increased, set by the diffusional approach to form the complex. In this Opinion article, I propose that having the signaling protein disordered before binding to the target provides a way out of this quandary. The intrinsic disorder of the signaling protein would decrease K(a) without sacrificing the specificity of the complex, and thus would allow k(d) to be increased to a range appropriate for signaling.