The opposing effects of isotropic and anisotropic attraction on association kinetics of proteins and colloids

The association and dissociation of particles via specific anisotropic interactions is a fundamental process, both in biology (proteins) and in soft matter (colloidal patchy particles). The presence of alternative binding sites can lead to multiple productive states and also to non-productive “decoy” or intermediate states. Besides anisotropic interactions, particles can experience non-specific isotropic interactions. We employ single replica transition interface sampling to investigate how adding a non-productive binding site or a nonspecific isotropic interaction alters the dimerization kinetics of a generic patchy particle model. The addition of a decoy binding site reduces the association rate constant, independent of the site’s position, while adding an isotropic interaction increases it due to an increased rebinding probability. Surprisingly, the association kinetics becomes non-monotonic for a tetramer complex formed by multivalent patchy particles. While seemingly identical to twoparticle binding with a decoy state, the cooperativity of binding multiple particles leads to a kinetic optimum. Our results are relevant for the understanding and modeling of biochemical networks and self-assembly processes. Published by AIP Publishing. https://doi.org/10.1063/1.500648

Path Sampling Simulations Reveal How the Q61L Mutation Alters the Dynamics of KRas

[Image: see text] Flexibility is essential for many proteins to function, but can be difficult to characterize. Experiments lack resolution in space and time, while the time scales involved are prohibitively long for straightforward molecular dynamics simulations. In this work, we present a multiple state transition path sampling simulation study of a protein that has been notoriously difficult to characterize in its active state. The GTPase enzyme KRas is a signal transduction protein in pathways for cell differentiation, growth, and division. When active, KRas tightly binds guanosine triphosphate (GTP) in a rigid state. The protein–GTP complex can also visit more flexible states, in which it is not active. KRas mutations can affect the conversion between these rigid and flexible states, thus prolonging the activation of signal transduction pathways, which may result in tumor formation. In this work, we apply path sampling simulations to investigate the dynamic behavior of KRas-4B (wild type, WT) and the oncogenic mutant Q61L (Q61L). Our results show that KRas visits several conformational states, which are the same for WT and Q61L. The multiple state transition path sampling (MSTPS) method samples transitions between the different states in a single calculation. Tracking which transitions occur shows large differences between WT and Q61L. The MSTPS results further reveal that for Q61L, a route to a more flexible state is inaccessible, thus shifting the equilibrium to more rigid states. The methodology presented here enables a detailed characterization of protein flexibility on time scales not accessible with brute-force molecular dynamics simulations

A replica exchange transition interface sampling method with multiple interface sets for investigating networks of rare events

The multiple state transition interface sampling (TIS) framework in principle allows the simulation of a large network of complex rare event transitions, but in practice suffers from convergence problems. To improve convergence, we combine multiple state TIS [J. Rogal and P. G. Bolhuis, J. Chem. Phys. 129, 224107 (2008)] with replica exchange TIS [T. S. van Erp, Phys. Rev. Lett. 98, 268301 (2007)]. In addition, we introduce multiple interface sets, which allow more than one order parameter to be defined for each state. We illustrate the methodology on a model system of multiple independent dimers, each with two states. For reaction networks with up to 64 microstates, we determine the kinetics in the microcanonical ensemble, and discuss the convergence properties of the sampling scheme. For this model, we find that the kinetics depend on the instantaneous composition of the system. We explain this dependence in terms of the system's potential and kinetic energy

Atomistic insight into the kinetic pathways for Watson-Crick to Hoogsteen transitions in DNA

DNA predominantly contains Watson-Crick (WC) base pairs, but a non-negligible fraction of base pairs are in the Hoogsteen (HG) hydrogen bonding motif at any time. In HG, the purine is rotated similar to 180 degrees relative to the WC motif. The transitions between WC and HG may play a role in recognition and replication, but are difficult to investigate experimentally because they occur quickly, but only rarely. To gain insight into the mechanisms for this process, we performed transition path sampling simulations on a model nucleotide sequence in which an AT pair changes from WC to HG. This transition can occur in two ways, both starting with loss of hydrogen bonds in the base pair, followed by rotation around the glycosidic bond. In one route the adenine base converts from WC to HG geometry while remaining entirely within the double helix. The other route involves the adenine leaving the confines of the double helix and interacting with water. Our results indicate that this outside route is more probable. We used transition interface sampling to compute rate constants and relative free energies for the transitions between WC and HG. Our results agree with experiments, and provide highly detailed insights into the mechanisms of this important process

OpenPathSampling: A Python Framework for Path Sampling Simulations. 1. Basics

Transition path sampling techniques allow molecular dynamics simulations of complex systems to focus on rare dynamical events, providing insight into mechanisms and the ability to calculate rates inaccessible by ordinary dynamics simulations. While path sampling algorithms are conceptually as simple as importance sampling Monte Carlo, the technical complexity of their implementation has kept these techniques out of reach of the broad community. Here, we introduce an easy-to-use Python framework called OpenPathSampling (OPS) that facilitates path sampling for (bio)molecular systems with minimal effort and yet is still extensible. Interfaces to OpenMM and an internal dynamics engine for simple models are provided in the initial release, but new molecular simulation packages can easily be added. Multiple ready-to-use transition path sampling methodologies are implemented, including standard transition path sampling (TPS) between reactant and product states and transition interface sampling (TIS) and its replica exchange variant (RETIS), as well as recent multistate and multiset extensions of transition interface sampling (MSTIS, MISTIS). In addition, tools are provided to facilitate the implementation of new path sampling schemes built on basic path sampling components. In this paper, we give an overview of the design of this framework and illustrate the simplicity of applying the available path sampling algorithms to a variety of benchmark problems