Markov state models from hierarchical density-based assignment.

Markov state models (MSMs) have become one of the preferred methods for the analysis and interpretation of molecular dynamics (MD) simulations of conformational transitions in biopolymers. While there is great variation in terms of implementation, a well-defined workflow involving multiple steps is often adopted. Typically, molecular coordinates are first subjected to dimensionality reduction and then clustered into small "microstates," which are subsequently lumped into "macrostates" using the information from the slowest eigenmodes. However, the microstate dynamics is often non-Markovian, and long lag times are required to converge the relevant slow dynamics in the MSM. Here, we propose a variation on this typical workflow, taking advantage of hierarchical density-based clustering. When applied to simulation data, this type of clustering separates high population regions of conformational space from others that are rarely visited. In this way, density-based clustering naturally implements assignment of the data based on transitions between metastable states, resulting in a core-set MSM. As a result, the state definition becomes more consistent with the assumption of Markovianity, and the timescales of the slow dynamics of the system are recovered more effectively. We present results of this simplified workflow for a model potential and MD simulations of the alanine dipeptide and the FiP35 WW domain.

The synergistic mechanisms of apo-ferritin structural transitions and Au(iii) ion transportation: molecular dynamics simulations with the Markov state model.

Due to its unique structure, recent years have witnessed the use of apo-ferritin to accumulate various non-natural metal ions as a scaffold for nanomaterial synthesis. However, the transport mechanism of metal ions into the cavity of apo-ferritin is still unclear, limiting the rational design and controllable preparation of nanomaterials. Here, we conducted all-atom classical molecular dynamics (MD) simulations combined with Markov state models (MSMs) to explore the transportation behavior of Au(iii) ions. We exhibited the complete transportation paths of Au(iii) from solution into the apo-ferritin cage at the atomic level. We also revealed that the transportation of Au(iii) ions is accompanied by coupled protein structural changes. It is shown that the 3-fold axis channel serves as the only entrance with the longest residence time of Au(iii) ions. Besides, there are eight binding clusters and five 3-fold structural metastable states, which are important during Au(iii) transportation. The conformational changes of His118, Asp127, and Glu130, acting as doors, were observed to highly correlate with the Au(iii) ion's position. The MSM analysis and Potential Mean Force (PMF) calculation suggest a remarkable energy barrier near Glu130, making it the rate-limiting step of the whole process. The dominant transportation pathway is from cluster 3 in the 3-fold channel to the inner cavity to cluster 5 on the inner surface, and then to cluster 6. These findings provide inspiration and theoretical guidance for the further rational design and preparation of new nanomaterials using apo-ferritin.

Validation of DBFOLD: An efficient algorithm for computing folding pathways of complex proteins.

Atomistic simulations can provide valuable, experimentally-verifiable insights into protein folding mechanisms, but existing ab initio simulation methods are restricted to only the smallest proteins due to severe computational speed limits. The folding of larger proteins has been studied using native-centric potential functions, but such models omit the potentially crucial role of non-native interactions. Here, we present an algorithm, entitled DBFOLD, which can predict folding pathways for a wide range of proteins while accounting for the effects of non-native contacts. In addition, DBFOLD can predict the relative rates of different transitions within a protein's folding pathway. To accomplish this, rather than directly simulating folding, our method combines equilibrium Monte-Carlo simulations, which deploy enhanced sampling, with unfolding simulations at high temperatures. We show that under certain conditions, trajectories from these two types of simulations can be jointly analyzed to compute unknown folding rates from detailed balance. This requires inferring free energies from the equilibrium simulations, and extrapolating transition rates from the unfolding simulations to lower, physiologically-reasonable temperatures at which the native state is marginally stable. As a proof of principle, we show that our method can accurately predict folding pathways and Monte-Carlo rates for the well-characterized Streptococcal protein G. We then show that our method significantly reduces the amount of computation time required to compute the folding pathways of large, misfolding-prone proteins that lie beyond the reach of existing direct simulation. Our algorithm, which is available online, can generate detailed atomistic models of protein folding mechanisms while shedding light on the role of non-native intermediates which may crucially affect organismal fitness and are frequently implicated in disease.

A multi-modal coarse grained model of DNA flexibility mappable to the atomistic level.

We present a new coarse grained method for the simulation of duplex DNA. The algorithm uses a generalized multi-harmonic model that can represent any multi-normal distribution of helical parameters, thus avoiding caveats of current mesoscopic models for DNA simulation and representing a breakthrough in the field. The method has been parameterized from accurate parmbsc1 atomistic molecular dynamics simulations of all unique tetranucleotide sequences of DNA embedded in long duplexes and takes advantage of the correlation between helical states and backbone configurations to derive atomistic representations of DNA. The algorithm, which is implemented in a simple web interface and in a standalone package reproduces with high computational efficiency the structural landscape of long segments of DNA untreatable by atomistic molecular dynamics simulations.

Principles and Overview of Sampling Methods for Modeling Macromolecular Structure and Dynamics.

Investigation of macromolecular structure and dynamics is fundamental to understanding how macromolecules carry out their functions in the cell. Significant advances have been made toward this end in silico, with a growing number of computational methods proposed yearly to study and simulate various aspects of macromolecular structure and dynamics. This review aims to provide an overview of recent advances, focusing primarily on methods proposed for exploring the structure space of macromolecules in isolation and in assemblies for the purpose of characterizing equilibrium structure and dynamics. In addition to surveying recent applications that showcase current capabilities of computational methods, this review highlights state-of-the-art algorithmic techniques proposed to overcome challenges posed in silico by the disparate spatial and time scales accessed by dynamic macromolecules. This review is not meant to be exhaustive, as such an endeavor is impossible, but rather aims to balance breadth and depth of strategies for modeling macromolecular structure and dynamics for a broad audience of novices and experts.

GeauxDock: A novel approach for mixed-resolution ligand docking using a descriptor-based force field.

Molecular docking is an important component of computer-aided drug discovery. In this communication, we describe GeauxDock, a new docking approach that builds on the ideas of ligand homology modeling. GeauxDock features a descriptor-based scoring function integrating evolutionary constraints with physics-based energy terms, a mixed-resolution molecular representation of protein-ligand complexes, and an efficient Monte Carlo sampling protocol. To drive docking simulations toward experimental conformations, the scoring function was carefully optimized to produce a correlation between the total pseudoenergy and the native-likeness of binding poses. Indeed, benchmarking calculations demonstrate that GeauxDock has a strong capacity to identify near-native conformations across docking trajectories with the area under receiver operating characteristics of 0.85. By excluding closely related templates, we show that GeauxDock maintains its accuracy at lower levels of homology through the increased contribution from physics-based energy terms compensating for weak evolutionary constraints. GeauxDock is available at http://www.institute.loni.org/lasigma/package/dock/.

Exact goodness-of-fit tests for Markov chains.

Goodness-of-fit tests are useful in assessing whether a statistical model is consistent with available data. However, the usual χ² asymptotics often fail, either because of the paucity of the data or because a nonstandard test statistic is of interest. In this article, we describe exact goodness-of-fit tests for first- and higher order Markov chains, with particular attention given to time-reversible ones. The tests are obtained by conditioning on the sufficient statistics for the transition probabilities and are implemented by simple Monte Carlo sampling or by Markov chain Monte Carlo. They apply both to single and to multiple sequences and allow a free choice of test statistic. Three examples are given. The first concerns multiple sequences of dry and wet January days for the years 1948-1983 at Snoqualmie Falls, Washington State, and suggests that standard analysis may be misleading. The second one is for a four-state DNA sequence and lends support to the original conclusion that a second-order Markov chain provides an adequate fit to the data. The last one is six-state atomistic data arising in molecular conformational dynamics simulation of solvated alanine dipeptide and points to strong evidence against a first-order reversible Markov chain at 6 picosecond time steps.

Using molecular simulations to probe pharmaceutical materials.

Evolved through the past 60 years, molecular simulations have become one of the most important analytical tools in many theoretical and applied scientific disciplines. This paper provides a brief introduction to molecular simulations as a means of addressing important scientific questions of interest to pharmaceutical scientists. The focus is on fundamental questions such as: (1) Why do simulations work? (2) How to simulate? (3) How to make the results of simulations "real?" (4) Where can simulations be applied? To demonstrate the fundamental rationale of molecular simulations, three perspectives, thermodynamics, statistical mechanics, and general statistics, are compared. The concept of stochasticity is introduced, followed by a brief account of the two major methods used in simulations, molecular dynamics and Monte Carlo simulations. A brief discussion is then given on force fields to indicate their central importance. To facilitate the discussion about possible applications to pharmaceutical systems, the characteristics of molecular simulations are first compared with those of laboratory experiments. Case studies are then introduced to demonstrate the strengths of simulations. Some frequently encountered questions also are presented and discussed.