SEEKR2: Versatile Multiscale Milestoning Utilizing the OpenMM Molecular Dynamics Engine.

We present SEEKR2 (simulation-enabled estimation of kinetic rates version 2)─the latest iteration in the family of SEEKR programs for using multiscale simulation methods to computationally estimate the kinetics and thermodynamics of molecular processes, in particular, ligand-receptor binding. SEEKR2 generates equivalent, or improved, results compared to the earlier versions of SEEKR but with significant increases in speed and capabilities. SEEKR2 has also been built with greater ease of usability and with extensible features to enable future expansions of the method. Now, in addition to supporting simulations using NAMD, calculations may be run with the fast and extensible OpenMM simulation engine. The Brownian dynamics portion of the calculation has also been upgraded to Browndye 2. Furthermore, this version of SEEKR supports hydrogen mass repartitioning, which significantly reduces computational cost, while showing little, if any, loss of accuracy in the predicted kinetics.

A Computational Assay that Explores the Hemagglutinin/Neuraminidase Functional Balance Reveals the Neuraminidase Secondary Site as a Novel Anti-Influenza Target.

Studies of pathogen-host specificity, virulence, and transmissibility are critical for basic research as well as for assessing the pandemic potential of emerging infectious diseases. This is especially true for viruses such as influenza, which continue to affect millions of people annually through both seasonal and occasional pandemic events. Although the influenza virus has been fairly well studied for decades, our understanding of host-cell binding and its relation to viral transmissibility and infection is still incomplete. Assessing the binding mechanisms of complex biological systems with atomic-scale detail is challenging given current experimental limitations. Much remains to be learned, for example, about how the terminal residue of influenza-binding host-cell receptors (sialic acid) interacts with the viral surface. Here, we present an integrative structural-modeling and physics-based computational assay that reveals the sialic acid association rate constants (k on) to three influenza sites: the hemagglutinin (HA), neuraminidase (NA) active, and NA secondary binding sites. We developed a series of highly detailed (atomic-resolution) structural models of fully intact influenza viral envelopes. Brownian dynamics simulations of these systems showed how structural properties, such as stalk height and secondary-site binding, affect sialic acid k on values. Comparing the k on values of the three sialic acid binding sites across different viral strains suggests a detailed model of encounter-complex formation and indicates that the secondary NA binding site may play a compensatory role in host-cell receptor binding. Our method elucidates the competition among these sites, all present on the same virion, and provides a new technology for directly studying the functional balance between HA and NA.

SEEKR: Simulation Enabled Estimation of Kinetic Rates, A Computational Tool to Estimate Molecular Kinetics and Its Application to Trypsin-Benzamidine Binding.

We present the Simulation Enabled Estimation of Kinetic Rates (SEEKR) package, a suite of open-source scripts and tools designed to enable researchers to perform multiscale computation of the kinetics of molecular binding, unbinding, and transport using a combination of molecular dynamics, Brownian dynamics, and milestoning theory. To demonstrate its utility, we compute the kon, koff, and ΔGbind for the protein trypsin with its noncovalent binder, benzamidine, and examine the kinetics and other results generated in the context of the new software, and compare our findings to previous studies performed on the same system. We compute a kon estimate of (2.1 ± 0.3) × 107 M-1 s-1, a koff estimate of 83 ± 14 s-1, and a ΔGbind of -7.4 ± 0.1 kcal·mol-1, all of which compare closely to the experimentally measured values of 2.9 × 107 M-1 s-1, 600 ± 300 s-1, and -6.71 ± 0.05 kcal·mol-1, respectively.

Two Relations to Estimate Membrane Permeability Using Milestoning.

Prediction of passive permeation rates of solutes across lipid bilayers is important to drug design, toxicology, and other biological processes such as signaling. The inhomogeneous solubility-diffusion (ISD) equation is traditionally used to relate the position-dependent potential of mean force and diffusivity to the permeability coefficient. The ISD equation is derived via the Smoluchowski equation and assumes overdamped system dynamics. It has been suggested that the complex membrane environment may exhibit more complicated damping conditions. Here we derive a variant of the inhomogeneous solubility diffusion equation as a function of the mean first passage time (MFPT) and show how milestoning, a method that can estimate kinetic quantities of interest, can be used to estimate the MFPT of membrane crossing and, by extension, the permeability coefficient. We further describe a second scheme, agnostic to the damping condition, to estimate the permeability coefficient from milestoning results or other methods that compute a probability of membrane crossing. The derived relationships are tested using a one-dimensional Langevin dynamics toy system confirming that the presented theoretical methods can be used to estimate permeabilities given simulation and milestoning results.

Bridging scales through multiscale modeling: a case study on protein kinase A.

The goal of multiscale modeling in biology is to use structurally based physico-chemical models to integrate across temporal and spatial scales of biology and thereby improve mechanistic understanding of, for example, how a single mutation can alter organism-scale phenotypes. This approach may also inform therapeutic strategies or identify candidate drug targets that might otherwise have been overlooked. However, in many cases, it remains unclear how best to synthesize information obtained from various scales and analysis approaches, such as atomistic molecular models, Markov state models (MSM), subcellular network models, and whole cell models. In this paper, we use protein kinase A (PKA) activation as a case study to explore how computational methods that model different physical scales can complement each other and integrate into an improved multiscale representation of the biological mechanisms. Using measured crystal structures, we show how molecular dynamics (MD) simulations coupled with atomic-scale MSMs can provide conformations for Brownian dynamics (BD) simulations to feed transitional states and kinetic parameters into protein-scale MSMs. We discuss how milestoning can give reaction probabilities and forward-rate constants of cAMP association events by seamlessly integrating MD and BD simulation scales. These rate constants coupled with MSMs provide a robust representation of the free energy landscape, enabling access to kinetic, and thermodynamic parameters unavailable from current experimental data. These approaches have helped to illuminate the cooperative nature of PKA activation in response to distinct cAMP binding events. Collectively, this approach exemplifies a general strategy for multiscale model development that is applicable to a wide range of biological problems.

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.