Enhanced configurational sampling with hybrid non-equilibrium molecular dynamics–Monte Carlo propagator

Advanced computational approaches to understand protein aggregation

Protein aggregation is a widespread phenomenon implicated in debilitating diseases like Alzheimer's, Parkinson's, and cataracts, presenting complex hurdles for the field of molecular biology. In this review, we explore the evolving realm of computational methods and bioinformatics tools that have revolutionized our comprehension of protein aggregation. Beginning with a discussion of the multifaceted challenges associated with understanding this process and emphasizing the critical need for precise predictive tools, we highlight how computational techniques have become indispensable for understanding protein aggregation. We focus on molecular simulations, notably molecular dynamics (MD) simulations, spanning from atomistic to coarse-grained levels, which have emerged as pivotal tools in unraveling the complex dynamics governing protein aggregation in diseases such as cataracts, Alzheimer's, and Parkinson's. MD simulations provide microscopic insights into protein interactions and the subtleties of aggregation pathways, with advanced techniques like replica exchange molecular dynamics, Metadynamics (MetaD), and umbrella sampling enhancing our understanding by probing intricate energy landscapes and transition states. We delve into specific applications of MD simulations, elucidating the chaperone mechanism underlying cataract formation using Markov state modeling and the intricate pathways and interactions driving the toxic aggregate formation in Alzheimer's and Parkinson's disease. Transitioning we highlight how computational techniques, including bioinformatics, sequence analysis, structural data, machine learning algorithms, and artificial intelligence have become indispensable for predicting protein aggregation propensity and locating aggregation-prone regions within protein sequences. Throughout our exploration, we underscore the symbiotic relationship between computational approaches and empirical data, which has paved the way for potential therapeutic strategies against protein aggregation-related diseases. In conclusion, this review offers a comprehensive overview of advanced computational methodologies and bioinformatics tools that have catalyzed breakthroughs in unraveling the molecular basis of protein aggregation, with significant implications for clinical interventions, standing at the intersection of computational biology and experimental research.

Studying the Collective Functional Response of a Receptor in Alchemical Ligand Binding Free Energy Simulations with Accelerated Solvation Layer Dynamics

Ligand binding free energy simulations (LB-FES) that involve sampling of protein functional conformations have been longstanding challenges in research on molecular recognition. Particularly, modeling of the conformational transition pathway and design of the heuristic biasing mechanism are severe bottlenecks for the existing enhanced configurational sampling (ECS) methods. Inspired by the key role of hydration in regulating conformational dynamics of macromolecules, this report proposes a novel ECS approach that facilitates binding-associated structural dynamics by accelerated hydration transitions in combination with the λ-exchange of free energy perturbation (FEP). Two challenging protein-ligand binding processes involving large configurational transitions of the receptor are studied, with hydration transitions at binding sites accelerated by Hamiltonian-simulated annealing of the hydration layer. Without the need for pathway analysis or ad hoc barrier flattening potential, LB-FES were performed with FEP/λ-exchange molecular dynamics simulation at a minor overhead for annealing of the hydration layer. The LB-FES studies showed that the accelerated rehydration significantly enhances the collective conformational transitions of the receptor, and convergence of binding affinity calculations is obtained at a sweet-spot simulation time scale. Alchemical LB-FES with the proposed ECS strategy is free from the effort of trial and error for the setup and realizes efficient on-the-fly sampling for the collective functional response of the receptor and bound water and therefore presents a practical approach to high-throughput screening in drug discovery.

Configurational Sampling of All-Atom Solvated Membranes Using Hybrid Nonequilibrium Molecular Dynamics Monte Carlo Simulations

All-atom simulations are a powerful approach to study the structure and dynamics of biological membranes. However, sampling the atomic configurations of inhomogeneous membranes can be challenging due to the slow lateral diffusion of the various constituents. To address this issue, a hybrid nonequilibrium molecular dynamics Monte Carlo (neMD/MC) simulation method is proposed in which randomly chosen lipid molecules are swapped to generate configurations that are subsequently accepted or rejected according to a Metropolis criterion based on the alchemical work for the attempted swap calculated via a short trajectory. A dual-topology framework constraining the common atoms of the exchanging molecules yields a good acceptance probability using switching trajectories as short as 10 ps. The performance of the hybrid neMD/MC algorithm and its ability to sample the distribution of lipids near a transmembrane helix carrying a net charge are illustrated for a binary mixture of charged and zwitterionic lipids.

Next-Generation Vitrimers Design through Theoretical Understanding and Computational Simulations

Vitrimers are an innovative class of polymers that boast a remarkable fusion of mechanical and dynamic features, complemented by the added benefit of end-of-life recyclability. This extraordinary blend of properties makes them highly attractive for a variety of applications, such as the automotive sector, soft robotics, and the aerospace industry. At their core, vitrimer materials consist of crosslinked covalent networks that have the ability to dynamically reorganize in response to external factors, including temperature changes, pressure variations, or shifts in pH levels. In this review, the aim is to delve into the latest advancements in the theoretical understanding and computational design of vitrimers. The review begins by offering an overview of the fundamental principles that underlie the behavior of these materials, encompassing their structures, dynamic behavior, and reaction mechanisms. Subsequently, recent progress in the computational design of vitrimers is explored, with a focus on the employment of molecular dynamics (MD)/Monte Carlo (MC) simulations and density functional theory (DFT) calculations. Last, the existing challenges and prospective directions for this field are critically analyzed, emphasizing the necessity for additional theoretical and computational advancements, coupled with experimental validation.

Modern Alchemical Free Energy Methods for Drug Discovery Explained

This Perspective provides a contextual explanation of the current state-of-the-art alchemical free energy methods and their role in drug discovery as well as highlights select emerging technologies. The narrative attempts to answer basic questions about what goes on "under the hood" in free energy simulations and provide general guidelines for how to run simulations and analyze the results. It is the hope that this work will provide a valuable introduction to students and scientists in the field.

Grand-canonical molecular dynamics simulations powered by a hybrid 4D nonequilibrium MD/MC method: Implementation in LAMMPS and applications to electrolyte solutions

Molecular simulations in an open environment, involving ion exchange, are necessary to study various systems, from biosystems to confined electrolytes. However, grand-canonical simulations are often computationally demanding in condensed phases. A promising method [L. Belloni, J. Chem. Phys. 151, 021101 (2019)], one of the hybrid nonequilibrium molecular dynamics/Monte Carlo algorithms, was recently developed, which enables efficient computation of fluctuating number or charge density in dense fluids or ionic solutions. This method facilitates the exchange through an auxiliary dimension, orthogonal to all physical dimensions, by reducing initial steric and electrostatic clashes in three-dimensional systems. Here, we report the implementation of the method in LAMMPS with a Python interface, allowing facile access to grand-canonical molecular dynamics simulations with massively parallelized computation. We validate our implementation with two electrolytes, including a model Lennard-Jones electrolyte similar to a restricted primitive model and aqueous solutions. We find that electrostatic interactions play a crucial role in the overall efficiency due to their long-range nature, particularly for water or ion-pair exchange in aqueous solutions. With properly screened electrostatic interactions and bias-based methods, our approach enhances the efficiency of salt-pair exchange in Lennard-Jones electrolytes by approximately four orders of magnitude, compared to conventional grand-canonical Monte Carlo. Furthermore, the acceptance rate of NaCl-pair exchange in aqueous solutions at moderate concentrations reaches about 3% at the maximum efficiency.

Structural Optimization Design of Microfluidic Chips Based on Fast Sequence Pair Algorithm

The market for microfluidic chips is experiencing significant growth; however, their development is hindered by a complex design process and low efficiency. Enhancing microfluidic chips' design quality and efficiency has emerged as an integral approach to foster their advancement. Currently, the existing structural design schemes lack careful consideration regarding the impact of chip area, microchannel length, and the number of intersections on chip design. This inadequacy leads to redundant chip structures resulting from the separation of layout and wiring design. This study proposes a structural optimization method for microfluidic chips to address these issues utilizing a simulated annealing algorithm. The simulated annealing algorithm generates an initial solution in advance using the fast sequence pair algorithm. Subsequently, an improved simulated annealing algorithm is employed to obtain the optimal solution for the device layout. During the wiring stage, an advanced wiring method is used to designate the high wiring area, thereby increasing the success rate of microfluidic chip wiring. Furthermore, the connection between layout and routing is reinforced through an improved layout adjustment method, which reduces the length of microchannels and the number of intersections. Finally, the effectiveness of the structural optimization approach is validated through six sets of test cases, successfully achieving the objective of enhancing the design quality of microfluidic chips.

Glycosidic α-linked mannopyranose disaccharides: an NMR spectroscopy and molecular dynamics simulation study employing additive and Drude polarizable force fields

D-Mannose is a structural component in N-linked glycoproteins from viruses and mammals as well as in polysaccharides from fungi and bacteria. Structural components often consist of D-Manp residues joined via α-(1→2)-, α-(1→3)-, α-(1→4)- or α-(1→6)-linkages. As models for these oligo- and polysaccharides, a series of mannose-containing disaccharides have been investigated with respect to conformation and dynamics. Translational diffusion NMR experiments were performed to deduce rotational correlation times for the molecules, 1D ¹H,¹H-NOESY and 1D ¹H,¹H-T-ROESY NMR experiments were carried out to obtain inter-residue proton-proton distances and one-dimensional long-range and 2D J-HMBC experiments were acquired to gain information about conformationally dependent heteronuclear coupling constants across glycosidic linkages. To attain further spectroscopic data, the doubly ¹³C-isotope labeled α-D-[1,2-¹³C₂]Manp-(1→4)-α-D-Manp-OMe was synthesized thereby facilitating conformational analysis based on ¹³C,¹³C coupling constants as interpreted by Karplus-type relationships. Molecular dynamics simulations were carried out for the disaccharides with explicit water as solvent using the additive CHARMM36 and Drude polarizable force fields for carbohydrates, where the latter showed broader population distributions. Both simulations sampled conformational space in such a way that inter-glycosidic proton-proton distances were very well described whereas in some cases deviations were observed between calculated conformationally dependent NMR scalar coupling constants and those determined from experiment, with closely similar root-mean-square differences for the two force fields. However, analyses of dipole moments and radial distribution functions with water of the hydroxyl groups indicate differences in the underlying physical forces dictating the wider conformational sampling with the Drude polarizable versus additive C36 force field and indicate the improved utility of the Drude polarizable model in investigating complex carbohydrates.

ACES: Optimized Alchemically Enhanced Sampling

We present an alchemical enhanced sampling (ACES) method implemented in the GPU-accelerated AMBER free energy MD engine. The methods hinges on the creation of an "enhanced sampling state" by reducing or eliminating selected potential energy terms and interactions that lead to kinetic traps and conformational barriers while maintaining those terms that curtail the need to otherwise sample large volumes of phase space. For example, the enhanced sampling state might involve transforming regions of a ligand and/or protein side chain into a noninteracting "dummy state" with internal electrostatics and torsion angle terms turned off. The enhanced sampling state is connected to a real-state end point through a Hamiltonian replica exchange (HREMD) framework that is facilitated by newly developed alchemical transformation pathways and smoothstep softcore potentials. This creates a counterdiffusion of real and enhanced-sampling states along the HREMD network. The effect of a differential response of the environment to the real and enhanced-sampling states is minimized by leveraging the dual topology framework in AMBER to construct a counterbalancing HREMD network in the opposite alchemical direction with the same (or similar) real and enhanced sampling states at inverted end points. The method has been demonstrated in a series of test cases of increasing complexity where traditional MD, and in several cases alternative REST2-like enhanced sampling methods, are shown to fail. The hydration free energy for acetic acid was shown to be independent of the starting conformation, and the values for four additional edge case molecules from the FreeSolv database were shown to have a significantly closer agreement with experiment using ACES. The method was further able to handle different rotamer states in a Cdk2 ligand identified as fractionally occupied in crystal structures. Finally, ACES was applied to T4-lysozyme and demonstrated that the side chain distribution of V111χ1 could be reliably reproduced for the apo state, bound to p-xylene, and in p-xylene→ benzene transformations. In these cases, the ACES method is shown to be highly robust and superior to a REST2-like enhanced sampling implementation alone.

Conformational Fluctuations in GTP-Bound K-Ras: A Metadynamics Perspective with Harmonic Linear Discriminant Analysis

Biomacromolecules often undergo significant conformational rearrangements during function. In proteins, these motions typically consist in nontrivial, concerted rearrangement of multiple flexible regions. Mechanistic, thermodynamics, and kinetic predictions can be obtained via molecular dynamics simulations, provided that the simulation time is at least comparable to the relevant time scale of the process of interest. Because of the substantial computational cost, however, plain MD simulations often have difficulty in obtaining sufficient statistics for converged estimates, requiring the use of more-advanced techniques. Central in many enhanced sampling methods is the definition of a small set of relevant degrees of freedom (collective variables) that are able to describe the transitions between different metastable states of the system. The harmonic linear discriminant analysis (HLDA) has been shown to be useful for constructing low-dimensional collective variables in various complex systems. Here, we apply HLDA to study the free-energy landscape of a monomeric protein around its native state. More precisely, we study the K-Ras protein bound to GTP, focusing on two flexible loops and on the region associated with oncogenic mutations. We perform microsecond-long biased simulations on the wild type and on G12C, G12D, G12 V mutants, describe the resulting free-energy landscapes, and compare our predictions with previous experimental and computational studies. The fast interconversion between open and closed macroscopic states and their similar thermodynamic stabilities are observed. The mutation-induced effects include the alternations of the relative stabilities of different conformational states and the introduction of many microscopic metastable states. Together, our results demonstrate the applicability of the HLDA-based protocol for the conformational sampling of multiple flexible regions in folded proteins.

CORE-MD II: A fast, adaptive, and accurate enhanced sampling method

In this paper, we present a fast and adaptive correlation guided enhanced sampling method (CORE-MD II). The CORE-MD II technique relies, in part, on partitioning of the entire pathway into short trajectories that we refer to as instances. The sampling within each instance is accelerated by adaptive path-dependent metadynamics simulations. The second part of this approach involves kinetic Monte Carlo (kMC) sampling between the different states that have been accessed during each instance. Through the combination of the partition of the total simulation into short non-equilibrium simulations and the kMC sampling, the CORE-MD II method is capable of sampling protein folding without any a priori definitions of reaction pathways and additional parameters. In the validation simulations, we applied the CORE-MD II on the dialanine peptide and the folding of two peptides: TrpCage and TrpZip2. In a comparison with long time equilibrium Molecular Dynamics (MD), 1 µs replica exchange MD (REMD), and CORE-MD I simulations, we find that the level of convergence of the CORE-MD II method is improved by a factor of 8.8, while the CORE-MD II method reaches acceleration factors of ∼120. In the CORE-MD II simulation of TrpZip2, we observe the formation of the native state in contrast to the REMD and the CORE-MD I simulations. The method is broadly applicable for MD simulations and is not restricted to simulations of protein folding or even biomolecules but also applicable to simulations of protein aggregation, protein signaling, or even materials science simulations.

Overcoming Free-Energy Barriers with a Seamless Combination of a Biasing Force and a Collective Variable-Independent Boost Potential

Amid collective-variable (CV)-based importance-sampling algorithms, a hybrid of the extended adaptive biasing force and the well-tempered metadynamics algorithms (WTM-eABF) has proven particularly cost-effective for exploring the rugged free-energy landscapes that underlie biological processes. However, as an inherently CV-based algorithm, this hybrid scheme does not explicitly accelerate sampling in the space orthogonal to the chosen CVs, thereby limiting its efficiency and accuracy, most notably in those cases where the slow degrees of freedom of the process at hand are not accounted for in the model transition coordinate. Here, inspired by Gaussian-accelerated molecular dynamics (GaMD), we introduce the same CV-independent harmonic boost potential into WTM-eABF, yielding a hybrid algorithm coined GaWTM-eABF. This algorithm leans on WTM-eABF to explore the transition coordinate with a GaMD-mollified potential and recovers the unbiased free-energy landscape through thermodynamic integration followed by proper reweighting. As illustrated in our numerical tests, GaWTM-eABF effectively overcomes the free-energy barriers in orthogonal space and correctly recovers the unbiased potential of mean force (PMF). Furthermore, applying both GaWTM-eABF and WTM-eABF to two biologically relevant processes, namely, the reversible folding of (i) deca-alanine and (ii) chignolin, our results indicate that GaWTM-eABF reduces the uncertainty in the PMF calculation and converges appreciably faster than WTM-eABF. Obviating the need of multiple-copy strategies, GaWTM-eABF is a robust, computationally efficient algorithm to surmount the free-energy barriers in orthogonal space and maps with utmost fidelity the free-energy landscape along selections of CVs. Moreover, our strategy that combines WTM-eABF with GaMD can be easily extended to other biasing-force algorithms.

Reaction Pathway Sampling and Free-Energy Analyses for Multimeric Protein Complex Disassembly by Employing Hybrid Configuration Bias Monte Carlo/Molecular Dynamics Simulation

Physicochemical characterization of multimeric biomacromolecule assembly and disassembly processes is a milestone to understand the mechanisms for biological phenomena at the molecular level. Mass spectroscopy (MS) and structural bioinformatics (SB) approaches have become feasible to identify subcomplexes involved in assembly and disassembly, while they cannot provide atomic information sufficient for free-energy calculation to characterize transition mechanism between two different sets of subcomplexes. To combine observations derived from MS and SB approaches with conventional free-energy calculation protocols, we here designed a new reaction pathway sampling method by employing hybrid configuration bias Monte Carlo/molecular dynamics (hcbMC/MD) scheme and applied it to simulate the disassembly process of serum amyloid P component (SAP) pentamer. The results we obtained are consistent with those of the earlier MS and SB studies with respect to SAP subcomplex species and the initial stage of SAP disassembly processes. Furthermore, we observed a novel dissociation event, ring-opening reaction of SAP pentamer. Employing free-energy calculation combined with the hcbMC/MD reaction pathway trajectories, we moreover obtained experimentally testable observations on (1) reaction time of the ring-opening reaction and (2) importance of Asp42 and Lys117 for stable formation of SAP oligomer.

Improved Alchemical Free Energy Calculations with Optimized Smoothstep Softcore Potentials

Progress in the development of GPU-accelerated free energy simulation software has enabled practical applications on complex biological systems and fueled efforts to develop more accurate and robust predictive methods. In particular, this work re-examines concerted (a.k.a., one-step or unified) alchemical transformations commonly used in the prediction of hydration and relative binding free energies (RBFEs). We first classify several known challenges in these calculations into three categories: endpoint catastrophes, particle collapse, and large gradient-jumps. While endpoint catastrophes have long been addressed using softcore potentials, the remaining two problems occur much more sporadically and can result in either numerical instability (i.e., complete failure of a simulation) or inconsistent estimation (i.e., stochastic convergence to an incorrect result). The particle collapse problem stems from an imbalance in short-range electrostatic and repulsive interactions and can, in principle, be solved by appropriately balancing the respective softcore parameters. However, the large gradient-jump problem itself arises from the sensitivity of the free energy to large values of the softcore parameters, as might be used in trying to solve the particle collapse issue. Often, no satisfactory compromise exists with the existing softcore potential form. As a framework for solving these problems, we developed a new family of smoothstep softcore (SSC) potentials motivated by an analysis of the derivatives along the alchemical path. The smoothstep polynomials generalize the monomial functions that are used in most implementations and provide an additional path-dependent smoothing parameter. The effectiveness of this approach is demonstrated on simple yet pathological cases that illustrate the three problems outlined. With appropriate parameter selection, we find that a second-order SSC(2) potential does at least as well as the conventional approach and provides vast improvement in terms of consistency across all cases. Last, we compare the concerted SSC(2) approach against the gold-standard stepwise (a.k.a., decoupled or multistep) scheme over a large set of RBFE calculations as might be encountered in drug discovery.

Scalable molecular dynamics on CPU and GPU architectures with NAMD

NAMDis a molecular dynamics program designed for high-performance simulations of very large biological objects on CPU- and GPU-based architectures. NAMD offers scalable performance on petascale parallel supercomputers consisting of hundreds of thousands of cores, as well as on inexpensive commodity clusters commonly found in academic environments. It is written in C++ and leans on Charm++ parallel objects for optimal performance on low-latency architectures. NAMD is a versatile, multipurpose code that gathers state-of-the-art algorithms to carry out simulations in apt thermodynamic ensembles, using the widely popular CHARMM, AMBER, OPLS, and GROMOS biomolecular force fields. Here, we review the main features of NAMD that allow both equilibrium and enhanced-sampling molecular dynamics simulations with numerical efficiency. We describe the underlying concepts utilized by NAMD and their implementation, most notably for handling long-range electrostatics; controlling the temperature, pressure, and pH; applying external potentials on tailored grids; leveraging massively parallel resources in multiple-copy simulations; and hybrid quantum-mechanical/molecular-mechanical descriptions. We detail the variety of options offered by NAMD for enhanced-sampling simulations aimed at determining free-energy differences of either alchemical or geometrical transformations and outline their applicability to specific problems. Last, we discuss the roadmap for the development of NAMD and our current efforts toward achieving optimal performance on GPU-based architectures, for pushing back the limitations that have prevented biologically realistic billion-atom objects to be fruitfully simulated, and for making large-scale simulations less expensive and easier to set up, run, and analyze. NAMD is distributed free of charge with its source code at www.ks.uiuc.edu.

The Mechanism of Cholesterol Modification of Hedgehog Ligand

Hedgehog (Hh) proteins are important components of signal transduction pathways involved in animal development, and their defects are implicated in carcinogenesis. Their N-terminal domain (HhN) acts as a signaling ligand, and their C-terminal domain (HhC) performs an autocatalytic function of cleaving itself away, while adding a cholesterol moiety to HhN. HhC has two sub-domains: a hedgehog/intein (hint) domain that primarily performs the autocatalytic activity, and a sterol-recognition region (SRR) that binds to cholesterol and properly positions it with respect to HhN. The three-dimensional details of this autocatalytic mechanism remain unknown, as does the structure of the precursor Hh protein. In this study, a complete cholesterol-bound precursor form of the drosophila Hh precursor is modeled using known crystal structures of HhN and the hint domain, and a hypothesized similarity of SRR to an unrelated but similar-sized cholesterol binding protein. The restrained geometries and topology switching (RGATS) strategy is then used to predict atomic-detail pathways for the full autocatalytic reaction starting from the precursor and ending in a cholesterol-linked HhN domain and a cleaved HhC domain. The RGATS explicit solvent simulations indicate the roles of individual HhC residues in facilitating the reaction, which can be confirmed through mutational experiments. These simulations also provide plausible structural models for the N/S acyl transfer intermediate and the product states of this reaction. This study thus provides a good framework for future computational and experimental studies to develop a full structural and dynamic understanding of Hh autoprocessing. © 2019 Wiley Periodicals, Inc.

Taming Rugged Free Energy Landscapes Using an Average Force

The observation of complex structural transitions in biological and abiological molecular objects within time scales amenable to molecular dynamics (MD) simulations is often hampered by significant free energy barriers associated with entangled movements. Importance-sampling algorithms, a powerful class of numerical schemes for the investigation of rare events, have been widely used to extend simulations beyond the time scale common to MD. However, probing processes spanning milliseconds through microsecond molecular simulations still constitutes in practice a daunting challenge because of the difficulty of taming the ruggedness of multidimensional free energy surfaces by means of naive transition coordinates. To address this limitation, in recent years we have elaborated importance-sampling methods relying on an adaptive biasing force (ABF). In this Account, we review recent developments of algorithms aimed at mapping rugged free energy landscapes that correspond to complex processes of physical, chemical, and biological relevance. Through these developments, we have broadened the spectrum of applications of the popular ABF algorithm while improving its computational efficiency, notably for multidimensional free energy calculations. One major algorithmic advance, coined meta-eABF, merges the key features of metadynamics and an extended Lagrangian variant of ABF (eABF) by simultaneously shaving the barriers and flooding the valleys of the free energy landscape, and it possesses a convergence rate up to 5-fold greater than those of other importance-sampling algorithms. Through faster convergence and enhanced ergodic properties, meta-eABF represents a significant step forward in the simulation of millisecond-time-scale events. Here we introduce extensions of the algorithm, notably its well-tempered and replica-exchange variants, which further boost the sampling efficiency while gaining in numerical stability, thus allowing quantum-mechanical/molecular-mechanical free energy calculations to be performed at a lower cost. As a paradigm to bridge microsecond simulations to millisecond events by means of free energy calculations, we have applied the ABF family of algorithms to decompose complex movements in molecular objects of biological and abiological nature. We show here how water lubricates the shuttling of an amide-based rotaxane by altering the mechanism that underlies the concerted translation and isomerization of the macrocycle. Introducing novel collective variables in a computational workflow for the rigorous determination of standard binding free energies, we predict with utmost accuracy the thermodynamics of protein-ligand reversible association. Because of their simplicity, versatility, and robust mathematical foundations, the algorithms of the ABF family represent an appealing option for the theoretical investigation of a broad range of problems relevant to physics, chemistry, and biology.

Layered nested Markov chain Monte Carlo

A configurational sampling algorithm based on nested layerings of Markov chains (Layered Nested Markov Chain Monte Carlo or L-NMCMC) is presented for simulations of systems characterized by rugged free energy landscapes. The layerings are generated using a set of auxiliary potential energy surfaces. The implementation of the method is demonstrated in the context of a rugged, two-dimensional potential energy surface. The versatility of the algorithm is next demonstrated on a simple, many-body system, namely, a canonical Lennard-Jones fluid in the liquid state. In that example, different layering schemes and auxiliary potentials are used, including variable cutoff distances and excluded-volume tempering. In addition to calculating a variety of properties of the system, it is also shown that L-NMCMC, when combined with a free-energy perturbation formalism, provides a straightforward means to construct approximate free-energy surfaces at no additional computational cost using the sampling distributions of each auxiliary Markov chain. The proposed L-NMCMC scheme is general in that it could be complementary to any number of methods that rely on sampling from a target distribution or methods that exploit a hierarchy of time scales and/or length scales through decomposition of the potential energy.

A mixed alchemical and equilibrium dynamics to simulate heterogeneous dense fluids: Illustrations for Lennard-Jones mixtures and phospholipid membranes

An algorithm to efficiently simulate multi-component fluids is proposed and illustrated. The focus is on biological membranes that are heterogeneous and challenging to investigate quantitatively. To achieve rapid equilibration of spatially inhomogeneous fluids, we mix conventional molecular dynamics simulations with alchemical trajectories. The alchemical trajectory switches the positions of randomly selected pairs of molecules and plays the role of an efficient Monte Carlo move. It assists in accomplishing rapid spatial de-correlations. Examples of phase separation and mixing are given in two-dimensional binary Lennard-Jones fluid and a DOPC-POPC membrane. The performance of the algorithm is analyzed, and tools to maximize its efficiency are provided. It is concluded that the algorithm is vastly superior to conventional molecular dynamics for the equilibrium study of biological membranes.

Zooming across the Free-Energy Landscape: Shaving Barriers, and Flooding Valleys

A robust importance-sampling algorithm for mapping free-energy surfaces over geometrical variables, coined meta-eABF, is introduced. This algorithm shaves the free-energy barriers and floods valleys by incorporating a history-dependent potential term in the extended adaptive biasing force (eABF) framework. Numerical applications on both toy models and nontrivial examples indicate that meta-eABF explores the free-energy surface significantly faster than either eABF or metadynamics (MtD) alone, without the need to stratify the reaction pathway. In some favorable cases, meta-eABF can be as much as five times faster than other importance-sampling algorithms. Many of the shortcomings inherent to eABF and MtD, like kinetic trapping in regions of configurational space already adequately sampled, the requirement of prior knowledge of the free-energy landscape to set up the simulation, are readily eliminated in meta-eABF. Meta-eABF, therefore, represents an appealing solution for a broad range of applications, especially when both eABF and MtD fail to achieve the desired result.