Advances in Enhanced Sampling Molecular Dynamics Simulations for Biomolecules

Molecular dynamics simulation has emerged as a powerful computational tool for studying biomolecules as it can provide atomic insights into the conformational transitions involved in biological functions.However,when applied to complex biological macromolecules,the conformational sampling ability of conventional molecular dynamics is limited by the rugged free energy landscapes,leading to inherent timescale gaps between molecular dynamics simulations and real biological processes.To address this issue,several advanced enhanced sampling methods have been proposed to improve the sampling efficiency in molecular dynamics.In this review,the theoretical basis,practical applications,and recent improvements of both constraint and unconstrained enhanced sampling methods are summarized.Furthermore,the combined utilizations of different enhanced sampling methods that take advantage of both approaches are also briefly discussed.

Enhanced Sampling Simulations on Transition-Metal-Catalyzed Organic Reactions:Zirconocene-Catalyzed Propylene Polymerization and Sharpless Epoxidation

The bond breaking and forming in chemical reactions is a typical rare event,which is one of the difficult problems in molecular dynamics simulations.Numerous enhanced sampling methods have been developed to extend the time scale covered by molecular simulations.However,the difficulties of obtaining appropriate collective variables from complicated reaction pathways and a controlled sampling over the desired phase space remain as challenges.Herein,we use MetaITS,which combines metadynamics and integrated tempered sampling,to increase the sampling efficiency for chemical reactions.Metadynamics with collective variables obtained by harmonic linear discriminant analysis can efficiently decrease the main energy barrier of chemical reaction.Meanwhile,integrated tempered sampling can enhance the exploration of other degrees of freedom.In this study,we applied the MetaITS method to two transition-metal-catalyzed organic reactions with complicated reaction coordinates.We simulated here a zirconocene-catalyzed propylene polymerization to investigate the regioselectivity and temperature effects.We also studied a Sharpless epoxidation reaction,for which both chiral products are observed through simulation.

Enhanced sampling in molecular dynamics simulations and their latest applications--A review

Molecular dynamics(MD)simulations are capable of reproducing dynamic evolution at the molecular scale,but are limited by temporal scales.Enhanced sampling has emerged as a powerful tool to improve sampling efficiency,thereby extending the simulation timescales of a range of simulation studies in materials,chemistry,biology,nanoscience,and related fields.Here,we provide a systematic overview of established enhanced sampling methods and clarify the principles and interconnections between these methods.Furthermore,we categorically elaborate on the state-of-the-art applications of enhanced sampling in the last five years.Through these exemplified applications,we discuss the unique advantages of this technique,showing the prospects and challenges for its future development.This review could help researchers in different fields gain a comprehensive understanding of the enhanced sampling technique,and jointly facilitate its application and advancement.

Recent advances in protein conformation sampling by combining machine learning with molecular simulation

The rapid advancement and broad application of machine learning(ML)have driven a groundbreaking revolution in computational biology.One of the most cutting-edge and important applications of ML is its integration with molecular simulations to improve the sampling efficiency of the vast conformational space of large biomolecules.This review focuses on recent studies that utilize ML-based techniques in the exploration of protein conformational landscape.We first highlight the recent development of ML-aided enhanced sampling methods,including heuristic algorithms and neural networks that are designed to refine the selection of reaction coordinates for the construction of bias potential,or facilitate the exploration of the unsampled region of the energy landscape.Further,we review the development of autoencoder based methods that combine molecular simulations and deep learning to expand the search for protein conformations.Lastly,we discuss the cutting-edge methodologies for the one-shot generation of protein conformations with precise Boltzmann weights.Collectively,this review demonstrates the promising potential of machine learning in revolutionizing our insight into the complex conformational ensembles of proteins.

SPONGE:A GPU-Accelerated Molecular Dynamics Package with Enhanced Sampling and AI-Driven Algorithms

SPONGE(Simulation Package tOward Next GEneration molecular modeling)is a software package for molecular dynamics(MD)simulation of solution and surface molecular systems.In this version of SPONGE,the all-atom potential energy functions used in AMBER MD packages are used by default and other all-atom/coarse-grained potential energy functions are also supported.SPONGE is designed to extend the timescale being approached in MD simulations by utilizing the latest CUDA-enabled graphical processing units(GPU)and adopting highly efficient enhanced sampling algorithms,such as integrated tempering,selective integrated tempering and enhanced sampling of reactive trajectories.It is highly modular and new algorithms and functions can be incorporated con veniently.Particularly,a specialized Python plugin can be easily used to perform the machine learning MD simulation with MindSpore,TensorFlow,PyTorch or other popular machine learning frameworks.Furthermore,a plugin of Finite-Element Method(FEM)is also available to handle metallic surface systems.All these advanced features increase the power of SPONGE for modeling and simulation of complex chemical and biological systems.

Machine learning potential for Ab Initio phase transitions of zirconia

Zirconia has been extensively used in aerospace,military,biomedical and industrial fields due to its unusual combination of high mechanical,electrical and thermal properties.However,the fundamental and critical phase transition process of zirconia has not been well studied because of its difficult first-order phase transition with formidable energy barrier.Here,we generated a machine learning interatomic potential with ab initio accuracy to discover the mechanism behind all kinds of phase transition of zirconia at ambient pressure.The machine learning potential precisely characterized atomic interactions among all zirconia allotropes and liquid zirconia in a wide temperature range.We realized the challenging reversible first-order monoclinic-tetragonal and cubicliquid phase transition processes with enhanced sampling techniques.From the thermodynamic information,we gave a better understanding of the thermal hysteresis phenomenon in martensitic monoclinic-tetragonal transition.The phase diagram of zirconia from our machine learning potential based molecular dynamics simulations corresponded well with experimental results.

Reweighted ensemble dynamics simulations:Theory,improvement,and application

Based on multiple parallel short molecular dynamics simulation trajectories, we designed the reweighted ensem- ble dynamics （RED） method to more efficiently sample complex （biopolymer） systems, and to explore their hierarchical metastable states. Here we further present an improvement to depress statistical errors of the RED and we discuss a few keys in practical application of the RED, provide schemes on selection of basis functions, and determination of the free parameter in the RED. We illustrate the application of the improvements in two toy models and in the solvated alanine dipeptide. The results show the RED enables us to capture the topology of multiple-state transition networks, to detect the diffusion-like dynamical behavior in an entropy-dominated system, and to identify solvent effects in the solvated peptides. The illustrations serve as general applications of the RED in more complex biopolymer systems.

Fast and accurate determination of phase transition temperature via individual generalized canonical ensemble simulation

It is very important to determine the phase transition temperature,such as the water/ice coexistence temperature in various water models,via molecular simulations.We show that a single individual direct simulation is sufficient to get the temperature with high accuracy and small computational cost based on the generalized canonical ensemble(GCE).Lennard–Jones fluids,the atomic water models,such as TIP4P/2005,TIP4P/ICE,and the mW water models are applied to illustrate the method.We start from the coexistent system of the two phases with a plane interface,then equilibrate the system under the GCE,which can stabilize the coexistence of the phases,to directly derive the phase transition temperature without sensitive dependence on the applied parameters of the GCE and the size of the simulation systems.The obtained result is in excellent agreement with that in literatures.These features make the GCE approach in determining the phase transition temperature of systems be robust,easy to use,and particularly good at working on computationally expensive systems.

Ligand Binding and Release Investigated by Contact-Guided Iterative Multiple Independent Molecular Dynamics Simulations

Binding and releasing ligands are critical for the biological functions of many proteins,so it is important to determine these highly dynamic processes.Although there are experimental techniques to determine the structure of a protein-ligand complex,it only provides a static picture of the system.With the rapid increase of computing power and improved algorithms,molecular dynamics(MD)simulations have diverse of superiority in probing the binding and release process.However,it remains a great challenge to overcome the time and length scales when the system becomes large.This work presents an enhanced sampling tool for ligand binding and release,which is based on iterative multiple independent MD simulations guided by contacts formed between the ligand and the protein.From the simulation results on adenylate kinase,we observe the process of ligand binding and release while the conventional MD simulations at the same time scale cannot.

Fast adaptive flat-histogram ensemble to enhance the sampling in large systems

An efficient novel algorithm was developed to estimate the Density of States(DOS) for large systems by calculating the ensemble means of an extensive physical variable, such as the potential energy, U, in generalized canonical ensembles to interpolate the interior reverse temperature curve β_s(U)=SU/U, where S(U) is the logarithm of the DOS. This curve is computed with different accuracies in different energy regions to capture the dependence of the reverse temperature on U without setting prior grid in the U space. By combining with a U-compression transformation, we decrease the computational complexity from O(N3/2) in the normal Wang Landau type method to O(N1/2) in the current algorithm, as the degrees of freedom of system N. The efficiency of the algorithm is demonstrated by applying to Lennard Jones fluids with various N, along with its ability to find different macroscopic states, including metastable states.

Microanalysis of silver jewellery by laser-ablation laser-induced breakdown spectroscopy with enhanced sensitivity and minimal sample ablation

Laser-ablation laser-induced breakdown spectroscopy （LA-LIBS） based on single Nd：YAG laser is used to analyze copper impurity in silver jewellery with enhanced sensitivity and minimal sample ablation. 6-30 folds signal enhancement can be achieved under the re-excitation of the breakdown laser and the spatial resolution is only determined by the ablation laser. 50 ppm limit of detection of copper is achieved when the crater diameter is 17.2 μm under current experimental condition. This technique gives higher analysis sensitivity under the same sample ablation in comparison with single pulse （SP） LIBS. It is useful for high sensitive element mieroanalvsis of precious samples.

Parallel Tempering Simulation on Generalized Canonical Ensemble

Parallel tempering simulation is widely used in enhanced sampling of systems with complex energy surfaces.We hereby introduce generalized canonical ensemble(GCE)instead of the usual canonical ensemble into the parallel tempering to further improve abilities of the simulation technique.GCE utilizes an adapted weight function to obtain a unimodal energy distribution even in phase-coexisting region and then the parallel tempering on GCE yields the steady swap acceptance rates(SARs)instead of the fluctuated SARs in that on canonical ensemble.With the steady SARs,we can facilitate assign the parameters of the parallel tempering simulation to more efficiently reach equilibrium among different phases.We illustrate the parallel tempering simulation on GCE in the phase-coexisting region of 2-dimensional Potts model,a benchmark system for new simulation method developing.The result indicates that the new parallel tempering method is more efficient to estimate statistical quantities(i.e.,to sample the conformational space)than the normal parallel tempering,specially in phase-coexisting regions of larger systems.