PyRETIS: A well-done, medium-sized python library for rare events

PyRETIS 3: Conquering rare and slow events without boundaries

We present and discuss the advancements made in PyRETIS 3, the third instalment of our Python library for an efficient and user-friendly rare event simulation, focused to execute molecular simulations with replica exchange transition interface sampling (RETIS) and its variations. Apart from a general rewiring of the internal code towards a more modular structure, several recently developed sampling strategies have been implemented. These include recently developed Monte Carlo moves to increase path decorrelation and convergence rate, and new ensemble definitions to handle the challenges of long-lived metastable states and transitions with unbounded reactant and product states. Additionally, the post-analysis software PyVisa is now embedded in the main code, allowing fast use of machine-learning algorithms for clustering and visualising collective variables in the simulation data.

Path sampling with memory reduction and replica exchange to reach long permeation timescales

Assessing kinetics in biological processes with molecular dynamics simulations remains a computational and conceptual challenge, given the large time and length scales involved. For kinetic transport of biochemical compounds or drug molecules, the permeability through the phospholipid membranes is a key kinetic property, but long timescales are hindering the accurate computation. Technological advances in high-performance computing therefore need to be accompanied by theoretical and methodological developments. In this contribution, the replica exchange transition interface sampling (RETIS) methodology is shown to give perspective toward observing longer permeation pathways. It is first reviewed how RETIS, a path-sampling methodology that gives in principle exact kinetics, can be used to compute membrane permeability. Next, recent and current developments in three RETIS aspects are discussed: several new Monte Carlo moves in the path-sampling algorithm, memory reduction by reducing pathlengths, and exploitation of parallel computing with CPU-imbalanced replicas. Finally, the memory reduction presenting a new replica exchange implementation, coined REPPTIS, is showcased with a permeant needing to pass a membrane with two permeation channels, either representing an entropic or energetic barrier. The REPPTIS results showed clearly that inclusion of some memory and enhancing ergodic sampling via replica exchange moves are both necessary to obtain correct permeability estimates. In an additional example, ibuprofen permeation through a dipalmitoylphosphatidylcholine membrane was modeled. REPPTIS succeeded in estimating the permeability of this amphiphilic drug molecule with metastable states along the permeation pathway. In conclusion, the presented methodological advances allow for deeper insight into membrane biophysics even if the pathways are slow, as RETIS and REPPTIS push the permeability calculations to longer timescales.

Enhanced path sampling using subtrajectory Monte Carlo moves

Path sampling allows the study of rare events, such as chemical reactions, nucleation, and protein folding, via a Monte Carlo (MC) exploration in path space. Instead of configuration points, this method samples short molecular dynamics (MD) trajectories with specific start- and end-conditions. As in configuration MC, its efficiency highly depends on the types of MC moves. Since the last two decades, the central MC move for path sampling has been the so-called shooting move in which a perturbed phase point of the old path is propagated backward and forward in time to generate a new path. Recently, we proposed the subtrajectory moves, stone-skipping (SS) and web-throwing, that are demonstrably more efficient. However, the one-step crossing requirement makes them somewhat more difficult to implement in combination with external MD programs or when the order parameter determination is expensive. In this article, we present strategies to address the issue. The most generic solution is a new member of subtrajectory moves, wire fencing (WF), that is less thrifty than the SS but more versatile. This makes it easier to link path sampling codes with external MD packages and provides a practical solution for cases where the calculation of the order parameter is expensive or not a simple function of geometry. We demonstrate the WF move in a double-well Langevin model, a thin film breaking transition based on classical force fields, and a smaller ruthenium redox reaction at the ab initio level in which the order parameter explicitly depends on the electron density.

ATESA: An Automated Aimless Shooting Workflow

Transition path sampling methods are powerful tools for studying the dynamics of rare events in molecular simulations. However, these methods are generally restricted to experts with the knowledge and resources to properly set up and analyze the often hundreds of thousands of simulations that constitute a complete study. Aimless Transition Ensemble Sampling and Analysis (ATESA) is a new open-source software program written in Python that automates a full transition path sampling workflow based on the aimless shooting algorithm, streamlining the process and reducing the barrier to use for researchers new to this approach. This introduction to ATESA includes a demonstration of a complete transition path sampling process flow for an example reaction, including finding an initial transition state, sampling with aimless shooting, building a reaction coordinate with inertial likelihood maximization, verifying that coordinate with committor analysis, and measuring the reaction energy profile with umbrella sampling. We also describe our implementation of a termination criterion for aimless shooting based on the Godambe information calculated during model building with likelihood maximization as well as a novel approach to constraining simulations to the desired rare event pathway during umbrella sampling.

Practical guide to replica exchange transition interface sampling and forward flux sampling

Path sampling approaches have become invaluable tools to explore the mechanisms and dynamics of the so-called rare events that are characterized by transitions between metastable states separated by sizable free energy barriers. Their practical application, in particular to ever more complex molecular systems, is, however, not entirely trivial. Focusing on replica exchange transition interface sampling (RETIS) and forward flux sampling (FFS), we discuss a range of analysis tools that can be used to assess the quality and convergence of such simulations, which is crucial to obtain reliable results. The basic ideas of a step-wise evaluation are exemplified for the study of nucleation in several systems with different complexities, providing a general guide for the critical assessment of RETIS and FFS simulations.

The role of pressure and defects in the wurtzite to rock salt transition in cadmium selenide

Using molecular dynamics and path sampling techniques we investigated the effect of pressure and defects in the wurtzite to rock salt transition in cadmium selenide (CdSe). In the pressure range 2-10 GPa, rate constants of transition are in the order of 10^-23 to 10⁵ s^-1 for the transformation of a relatively small wurtzite crystal consisting of 1024 atoms with periodic boundary conditions. The transition paths predominantly evolve through an intermediate 5-coordinated structure, as reported before, though its typical lifetime within the transition paths is particularly long in the intermediate pressure range (4-6 GPa). The defects were created by removing Cd-Se pairs from an otherwise perfect crystal. The removals were either selected fully randomized or grouped in clusters (cavity creation). We find that the rate of transition due to the defects increases by several orders of magnitude even for a single pair removal. This is caused by a change in the transition mechanism that no longer proceeds via the intermediate 5-coordinated structure, when defects are present. Further, the cavity creation yields a lower rate than the fully randomized removal.

Chemistrees: Data-Driven Identification of Reaction Pathways via Machine Learning

We propose to analyze molecular dynamics (MD) output via a supervised machine learning (ML) algorithm, the decision tree. The approach aims to identify the predominant geometric features which correlate with trajectories that transition between two arbitrarily defined states. The data-driven algorithm aims to identify these features without the bias of human “chemical intuition”. We demonstrate the method by analyzing the proton exchange reactions in formic acid solvated in small water clusters. The simulations were performed with ab initio MD combined with a method to efficiently sample the rare event, path sampling. Our ML analysis identified relevant geometric variables involved in the proton transfer reaction and how they may change as the number of solvating water molecules changes.

Sampling efficiency of the counting method for permeability calculations estimated with the inhomogeneous solubility-diffusion model

Permeability is a key property in various fields such as membrane technology for chemical separation and transport of substances through cell membranes. At the molecular scale, the counting method uses the number of membrane crossings in a conventional unbiased molecular dynamics simulation to predict the permeability. This contribution investigates under which conditions the counting method has insufficient statistics. An equation is derived for a compartmental model based on the inhomogeneous solubility-diffusion (Smoluchowski) model, giving insight into how the flux correlates with the solubility of permeants. This equation shows that a membrane crossing is a rare event not only when the membrane forms a large free energy barrier but also when the membrane forms a deep free energy well that traps permeants. Such a permeant trap has a high permeability; yet, the counting method suffers from poor statistics. To illustrate this, coarse-grained MD was run for 16 systems of dipalmitoylphosphatidylcholine bilayer membranes with different permeant types. The composition rule for permeability is shown to also hold for fluxes, and it is highlighted that the considered thickness of the membrane causes uncertainty in the permeability calculation of highly permeable membranes. In conclusion, a high permeability in itself is not an effective indicator of the sampling efficiency of the counting method, and caution should be taken for permeants whose solubility varies greatly over the simulation box. A practical consequence relevant in, e.g., drug design is that a drug with high membrane permeability might get trapped by membranes thus reducing its efficacy.

Defining the Energetic Basis for a Conformational Switch Mediating Ligand-Independent Activation of Mutant Estrogen Receptors in Breast Cancer

Although most primary estrogen receptor (ER)-positive breast cancers respond well to endocrine therapies, many relapse later as metastatic disease due to endocrine therapy resistance. Over one third of these are associated with mutations in the ligand-binding domain (LBD) that activate the receptor independent of ligand. We have used an array of advanced computational techniques rooted in molecular dynamics simulations, in concert with and validated by experiments, to characterize the molecular mechanisms by which specific acquired somatic point mutations give rise to ER constitutive activation. By comparing structural and energetic features of constitutively active mutants and ligand-bound forms of ER-LBD with unliganded wild-type (WT) ER, we characterize a spring force originating from strain in the Helix 11-12 loop of WT-ER, opposing folding of Helix 12 into the active conformation and keeping WT-ER off and disordered, with the ligand-binding pocket open for rapid ligand binding. We quantify ways in which this spring force is abrogated by activating mutations that latch (Y537S) or relax (D538G) the folded form of the loop, enabling formation of the active conformation without ligand binding. We also identify a new ligand-mediated hydrogen-bonding network that stabilizes the active, ligand-bound conformation of WT-ER LBD, and similarly stabilizes the active conformation of the ER mutants in the hormone-free state. IMPLICATIONS: Our investigations provide deep insight into the energetic basis for the structural mechanisms of receptor activation through mutation, exemplified here with ER in endocrine-resistant metastatic breast cancers, with potential application to other dysregulated receptor signaling due to driver mutations.

Exploring the effects of approach velocity on depletion force and coalescence in oil-in-water emulsions

An emulsion is a thermodynamically unstable system consisting of at least two immiscible liquid phases, one of which is dispersed in the other in the form of droplets of varying size. Most studies on emulsions have focused on the behaviour of emulsion droplets with diameter from ∼50 μm and upwards. However, the properties of smaller droplets may be highly relevant in order to understand the behaviour of emulsions, including their performance in numerous applications within the fields of food, industry, and medical science. The relatively long life-time and small size of these droplets compared to other emulsion droplets, make them suited for optical trapping and micromanipulation technologies. Optical tweezers have previously shown potential in the study of stabilized emulsions. Here we employ optical tweezers to examine unstable oil-in-water emulsions to determine the effects of system parameters on depletion force and coalescence times.

Path sampling for atmospheric reactions: formic acid catalysed conversion of SO3 + H2O to H2SO4

Atmospheric reactions, hitherto studied computationally mainly with static computations in conjunction with transition state theories, can be further described via path sampling calculations. Here we report on an exploratory study of the formic acid catalysed hydrolysis of SO3 to produce H2SO4. We demonstrate that precise measurements of rate coefficients can be obtained in principle for such reactions with an acceptable expenditure of computational resources, and that new insights into the reaction can be obtained by the analysis of the path space explored via path sampling techniques.

Ab Initio Molecular Dynamics Simulations of the Influence of Lithium Bromide Salt on the Deprotonation of Formic Acid in Aqueous Solution

The deprotonation of formic acid is investigated using metadynamics in tandem with Born-Oppenheimer molecular dynamics simulations. We compare our findings for formic acid in pure water with previous studies before examining formic acid in aqueous solutions of lithium bromide. We carefully consider different definitions for the collective variable(s) used to drive the metadynamics, emphasizing that the variables used must include all of the possible reactive atoms in the system, in this case carboxylate oxygens and water hydrogens. This ensures that all the various possible proton exchange events can be accommodated and the collective variable(s) can distinguish the protonated and deprotonated states, even over rather long ab initio simulation runs (ca. 200-300 ps). Our findings show that the formic acid deprotonation barrier and the free energy of the deprotonated state are higher in concentrated lithium bromide, in agreement with the available experimental data for acids in salt solution. We show that the presence of Br^- in proximity to the formic acid hydroxyl group effectively inhibits deprotonation. Our study extends previous work on acid deprotonation in pure water and at air-water interfaces to more complex multicomponent systems of importance in atmospheric and marine chemistry.

Predicting the mechanism and rate of H-NS binding to AT-rich DNA

Bacteria contain several nucleoid-associated proteins that organize their genomic DNA into the nucleoid by bending, wrapping or bridging DNA. The Histone-like Nucleoid Structuring protein H-NS found in many Gram-negative bacteria is a DNA bridging protein and can structure DNA by binding to two separate DNA duplexes or to adjacent sites on the same duplex, depending on external conditions. Several nucleotide sequences have been identified to which H-NS binds with high affinity, indicating H-NS prefers AT-rich DNA. To date, highly detailed structural information of the H-NS DNA complex remains elusive. Molecular simulation can complement experiments by modelling structures and their time evolution in atomistic detail. In this paper we report an exploration of the different binding modes of H-NS to a high affinity nucleotide sequence and an estimate of the associated rate constant. By means of molecular dynamics simulations, we identified three types of binding for H-NS to AT-rich DNA. To further sample the transitions between these binding modes, we performed Replica Exchange Transition Interface Sampling, providing predictions of the mechanism and rate constant of H-NS binding to DNA. H-NS interacts with the DNA through a conserved QGR motif, aided by a conserved arginine at position 93. The QGR motif interacts first with phosphate groups, followed by the formation of hydrogen bonds between acceptors in the DNA minor groove and the sidechains of either Q112 or R114. After R114 inserts into the minor groove, the rest of the QGR motif follows. Full insertion of the QGR motif in the minor groove is stable over several tens of nanoseconds, and involves hydrogen bonds between the bases and both backbone and sidechains of the QGR motif. The rate constant for the process of H-NS binding to AT-rich DNA resulting in full insertion of the QGR motif is in the order of 10⁶ M⁻¹s⁻¹, which is rate limiting compared to the non-specific association of H-NS to the DNA backbone at a rate of 10⁸ M⁻¹s⁻¹.

The Histone-like Nucleoid Structuring protein (H-NS) occurs in enterobacteria, such as Salmonella typhimurium and Escherichia coli, and structures DNA by forming filaments along DNA duplexes. Several nucleotide sequences have been identified to which H-NS binds with high affinity. Yet, obtaining highly detailed structural information of the H-NS DNA complex has proven to be a major challenge, which has not been yet resolved. By employing molecular dynamics simulations we were able to provide high resolution insights into the mechanism of DNA binding by H-NS. We identified various ways in which H-NS can bind to DNA. In all binding events, a conserved region in the protein initiates the association of H-NS to DNA. Our results show that H-NS binds in the minor groove of AT-rich DNA via a series of intermediate steps. Using advanced molecular simulation methods we predicted that the process of H-NS binding to the DNA backbone to full insertion into the minor groove occurs in the order of a million times per second, which is slower than the non-specific association of H-NS to the DNA backbone.

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.