Integrated Tempering Sampling Research Articles

A brief review of integrated tempering sampling molecular simulation

With the fast development of computation techniques, molecular dynamics (MD) simulations are becoming increasingly important in molecular studies. Numerous enhanced sampling methods were proposed to further increase the applicability of MD simulation to complex systems of slow dynamics. In this review, we briefly review some of these methods concerned with integrated enhanced sampling (ITS), which introduces an effective potential energy expressed as an integral of Boltzmann distributions over a range of temperatures. We, in particular, focus on ITS and its derived methods, such as selected ITS and the combination of ITS with other enhanced sampling methods, especially metadynamics (MetaITS). These methods show great sampling efficiency, and the hybrid methods represent a future direction of enhanced sampling. Applications of these methods, including but not limited to protein folding, phase transition, and chemical reactions, will be summarized. At the end of this review, we briefly introduce a number of other methods related to ITS, including partitioned ITS, integrated Hamiltonian sampling, integrated accelerated molecule dynamics, and infinite switch simulated tempering.

Enhanced Sampling Simulation Reveals How Solvent Influences Chirogenesis of the Intra-Molecular Diels-Alder Reaction.

The timescale involved in chemical reactions is quite often beyond that of normal molecular dynamics simulations. Here, we combine metadynamics with selective integrated tempering sampling to simulate an intra-molecular Diels-Alder reaction in explicit solvents. Based on a one-dimensional collective variable obtained from harmonic linear discriminant analysis, four chiral isomers of products were observed in the simulation. Analyses of reactive trajectories showed that this reaction follows a concerted mechanism in all four solvents. In addition, the hydrogen bond between the reactant and water solvent plays an important role in the water-accelerated reaction mechanism. The dynamics of chirality formation varies significantly with solvents. The chirality of products forms significantly before the transition state, especially in ionic liquid.

Enhanced QM/MM sampling for free energy calculation of chemical reactions: A case study of double proton transfer

Free energy calculations for chemical reactions with a steep energy barrier require well defined reaction coordinates (RCs). However, when multiple parallel channels exist along selected RC, the application of conventional enhanced samplings is difficult to generate correct sampling within limited simulation time and thus cannot give correct prediction about the favorable pathways, the relative stability of multiple products or intermediates. Here, we implement the selective integrated tempering sampling (SITS) method with quantum mechanical and molecular mechanical (QM/MM) potential to investigate the chemical reactions in solution. The combined SITS-QM/MM scheme is used to identify possible reaction paths, intermediate and product states, and the free energy profiles for the different reaction paths. Two double proton transfer reactions were studied to validate the implemented method and simulation protocol, from which the independent and correlated proton transfer processes are identified in two representative systems, respectively. This protocol can be generalized to various kinds of chemical reactions for both academic studies and industry applications, such as in exploration and optimization of potential reactions in DNA encoded compound library and halogen or deuterium substitution of the hit discovery and lead optimization stages of drug design via providing a better understanding of the reaction mechanism along the designed chemical reaction pathways.

Combining Metadynamics and Integrated Tempering Sampling.

The simulation of rare events is one of the key problems in atomistic simulations. Toward its solution, a plethora of methods have been proposed. Here we combine two such methods: metadynamics and integrated tempering sampling. In metadynamics, the fluctuations of a carefully chosen collective variable are amplified, while in integrated tempering sampling the system is pushed to visit an approximately uniform interval of energies and allows exploring a range of temperatures in a single run. We describe our approach and apply it to the two prototypical systems a SN2 chemical reaction and to the freezing of silica. The combination of metadynamics and integrated tempering sampling leads to a powerful method. In particular in the case of silica we have measured more than 1 order of magnitude acceleration.

Combined Molecular Dynamics and Coordinate Driving Method for Automatic Reaction Pathway Search of Reactions in Solution.

The combined molecular dynamics and coordinate driving (MD/CD) method is further refined in this work to automatically search reaction pathways for chemical reactions in solution. In this refined MD/CD method, the selective integrated tempering sampling based MD (SITS-MD) simulations are performed to efficiently sample conformers of the reactants in a realistic solution environment. Then, dozens of the reactant/solvent clusters from SITS-MD simulations were used in the subsequent CD step with the quantum mechanics/molecular mechanics (QM/MM) method to generate the reaction pathways. The present MD/CD method is able to search reaction pathways, in which solvent molecules may directly participate. This approach is applied to investigate two reactions without any prior knowledge of the reaction mechanism: Cope elimination of amine oxide in aqueous and dimethyl sulfoxide solutions, and dehydration of methanediol in aqueous solution. For both reactions, our calculations can locate a large number of low-energy reaction pathways. For the dehydration reaction in aqueous solution, free energy barriers for several reaction modes located by the MD/CD method have been obtained from the potential of mean force calculations. Our results show that the most likely reaction mode is the dehydration of methanediol catalyzed by two water molecules. These two illustrative applications demonstrate that the refined MD/CD method is a promising tool in predicting low-energy reaction pathways for reactions in solution.

Integrating Multiple Accelerated Molecular Dynamics To Improve Accuracy of Free Energy Calculations.

Accelerated Molecular Dynamics (aMD) is a promising enhanced sampling method to explore the conformational space of biomolecules. However, the large statistical noise in reweighting limits its accuracy to recover the original free energy profile. In this work, we propose an Integrated accelerated Molecule Dynamics (IaMD) method by integrating a series of aMD subterms with different acceleration parameters to improve the sampling efficiency and maintain the reweighting accuracy simultaneously. We use Alanine Dipeptide and three fast-folded proteins (Chignolin, Trp-cage, and Villin Headpiece) as the test objects to compare our IaMD method with aMD systematically. These case studies indicate that the statistical noise of IaMD in reweighting for free energy profiles is much smaller than that of aMD at the same level of acceleration and simulation time. To achieve the same accuracy as IaMD, aMD requires 1-3 orders of magnitude longer simulation time, depending on the complexity of the simulated system and the level of acceleration. Our method also outperforms aMD in controlling systematic error caused by the disappearance of the low-energy conformations when high acceleration parameters are used in aMD simulations for fast-folded proteins. Furthermore, the performance comparison between IaMD and the Integrated Tempering Sampling (ITS) in the case of Alanine Dipeptide demonstrates that IaMD possesses a better ability to control the potential energy region of sampling.

Simulation of the T-jump triggered unfolding and thermal unfolding vibrational spectroscopy related to polypeptides conformation fluctuation

We review in this article our recent simulation works on modeling peptide T-jump and thermal unfolding Fourier transform infrared spectroscopy (FTIR) and two-dimensional infrared (2DIR) spectra. The theoretical and computational techniques used, including Markov state model (MSM), integrated tempering sampling (ITS) and nonlinear exciton propagation (NEP), are first briefly introduced. The protocols for simulating the thermal unfolding as well as T-jump unfolding are then summarized in details. The simulated spectral features, such as the intensity and ellipticity, are demonstrated to agree well with the experimental observations.

Thermodynamic properties of solvated peptides from selective integrated tempering sampling with a new weighting factor estimation algorithm

ABSTRACTConformational sampling under rugged energy landscape is always a challenge in computer simulations. The recently developed integrated tempering sampling, together with its selective variant (SITS), emerges to be a powerful tool in exploring the free energy landscape or functional motions of various systems. The estimation of weighting factors constitutes a critical step in these methods and requires accurate calculation of partition function ratio between different thermodynamic states. In this work, we propose a new adaptive update algorithm to compute the weighting factors based on the weighted histogram analysis method (WHAM). The adaptive-WHAM algorithm with SITS is then applied to study the thermodynamic properties of several representative peptide systems solvated in an explicit water box. The performance of the new algorithm is validated in simulations of these solvated peptide systems. We anticipate more applications of this coupled optimisation and production algorithm to other complicated systems such as the biochemical reactions in solution.

Determining Protein Folding Pathway and Associated Energetics through Partitioned Integrated-Tempering-Sampling Simulation.

Replica exchange molecular dynamics (REMD) and integrated-tempering-sampling (ITS) are two representative enhanced sampling methods which utilize parallel and integrated tempering approaches, respectively. In this work, a partitioned integrated-tempering-sampling (P-ITS) method is proposed which takes advantage of the benefits of both parallel and integrated tempering approaches. Using P-ITS, the folding pathways of a series of proteins with diverse native structures are explored on multidimensional free-energy landscapes, and the associated thermodynamics are evaluated. In comparison to the original form of ITS, P-ITS improves the sampling efficiency and measures the folding/unfolding thermodynamic quantities more consistently with experimental data. In comparison to REMD, P-ITS significantly reduces the requirement of computational resources and meanwhile achieves similar simulation results. The observed structural characterizations of transition and intermediate states of the proteins under study are in good agreement with previous experimental and simulation studies on the same proteins and homologues. Therefore, the P-ITS method has great potential in simulating the structural dynamics of complex biomolecular systems.

Efficient free energy calculations by combining two complementary tempering sampling methods.

Although energy barriers can be efficiently crossed in the reaction coordinate (RC) guided sampling, this type of method suffers from identification of the correct RCs or requirements of high dimensionality of the defined RCs for a given system. If only the approximate RCs with significant barriers are used in the simulations, hidden energy barriers with small to medium height would exist in other degrees of freedom (DOFs) relevant to the target process and consequently cause the problem of insufficient sampling. To address the sampling in this so-called hidden barrier situation, here we propose an effective approach to combine temperature accelerated molecular dynamics (TAMD), an efficient RC-guided sampling method, with the integrated tempering sampling (ITS), a generalized ensemble sampling method. In this combined ITS-TAMD method, the sampling along the major RCs with high energy barriers is guided by TAMD and the sampling of the rest of the DOFs with lower but not negligible barriers is enhanced by ITS. The performance of ITS-TAMD to three systems in the processes with hidden barriers has been examined. In comparison to the standalone TAMD or ITS approach, the present hybrid method shows three main improvements. (1) Sampling efficiency can be improved at least five times even if in the presence of hidden energy barriers. (2) The canonical distribution can be more accurately recovered, from which the thermodynamic properties along other collective variables can be computed correctly. (3) The robustness of the selection of major RCs suggests that the dimensionality of necessary RCs can be reduced. Our work shows more potential applications of the ITS-TAMD method as the efficient and powerful tool for the investigation of a broad range of interesting cases.

Enhanced molecular dynamics simulation of the transformation between α-helix and β-hairpin structures for peptide

ABSTRACTHere, we investigated the secondary structure transformation for a design peptide, which has both the α-helix (PDB ID code 2DX3) and β-hairpin (PDB ID code 2DX4) structures in aqueous solution. We show that the transformation between α-helix and β-hairpin structures can be sampled efficiently using the enhanced sampling method based on integrated tempering without the definition of reaction coordinates. The reliable and smooth two-dimensional potential of mean force surfaces of the conformation space can be obtained efficiently, which has been used to propose the probable pathways for the transformation of the α-helix and β-hairpin structures. Our simulation results revealed the efficiency, and further suggested the general applicability of integrated tempering sampling method into complex biomolecule processes without prior structure knowledge.

Efficient sampling over rough energy landscapes with high barriers: A combination of metadynamics with integrated tempering sampling.

In order to efficiently overcome high free energy barriers embedded in a complex energy landscape and calculate overall thermodynamics properties using molecular dynamics simulations, we developed and implemented a sampling strategy by combining the metadynamics with (selective) integrated tempering sampling (ITS/SITS) method. The dominant local minima on the potential energy surface (PES) are partially exalted by accumulating history-dependent potentials as in metadynamics, and the sampling over the entire PES is further enhanced by ITS/SITS. With this hybrid method, the simulated system can be rapidly driven across the dominant barrier along selected collective coordinates. Then, ITS/SITS ensures a fast convergence of the sampling over the entire PES and an efficient calculation of the overall thermodynamic properties of the simulation system. To test the accuracy and efficiency of this method, we first benchmarked this method in the calculation of ϕ - ψ distribution of alanine dipeptide in explicit solvent. We further applied it to examine the design of template molecules for aromatic meta-C-H activation in solutions and investigate solution conformations of the nonapeptide Bradykinin involving slow cis-trans isomerizations of three proline residues.

Ab initio molecular dynamics with enhanced sampling for surface reaction kinetics at finite temperatures: CH2⇌ CH + H on Ni(111) as a case study.

A comprehensive understanding of surface thermodynamics and kinetics based on first-principles approaches is crucial for rational design of novel heterogeneous catalysts, and requires combining accurate electronic structure theory and statistical mechanics modeling. In this work, ab initio molecular dynamics (AIMD) combined with the integrated tempering sampling (ITS) method has been explored to study thermodynamic and kinetic properties of elementary processes on surfaces, using a simple reaction CH2⇌CH+H on the Ni(111) surface as an example. By a careful comparison between the results from ITS-AIMD simulation and those evaluated in terms of the harmonic oscillator (HO) approximation, it is found that the reaction free energy and entropy from the HO approximation are qualitatively consistent with the results from ITS-AIMD simulation, but there are also quantitatively significant discrepancies. In particular, the HO model misses the entropy effects related to the existence of multiple adsorption configurations arising from the frustrated translation and rotation motion of adsorbed species, which are different in the reactant and product states. The rate constants are evaluated from two ITS-enhanced approaches, one using the transition state theory (TST) formulated in terms of the potential of mean force (PMF) and the other one combining ITS with the transition path sampling (TPS) technique, and are further compared to those based on harmonic TST. It is found that the rate constants from the PMF-based TST are significantly smaller than those from the harmonic TST, and that the results from PMF-TST and ITS-TPS are in a surprisingly good agreement. These findings indicate that the basic assumptions of transition state theory are valid in such elementary surface reactions, but the consideration of statistical averaging of all important adsorption configurations and reaction pathways, which are missing in the harmonic TST, are critical for accurate description of thermodynamic and kinetic properties of surface processes. This work clearly demonstrates the importance of considering temperature effects beyond the HO model, for which the AIMD simulation in combination with enhanced sampling techniques like ITS provides a feasible and general approach.

Coil to globule transition of homo- and block-copolymer with different topological constraint and chain stiffness

In this paper, we present the coil-to-globule (CG) transitions of homopolymers and multiblock copolymers with different topology and stiffness by using molecular dynamics with integrated tempering sampling method. The sampling method was a novel enhanced method that efficiently sampled the energy space with low computational costs. The method proved to be efficient and precise to study the structural transitions of polymer chains with complex topological constraint, which may not be easily done by using conventional Monte Carlo method. The topological constraint affects the globule shape of the polymer chain, thus further influencing the CG transition. We found that increasing the topological constraint generally decreased CG transition temperature for homopolymers. For semiflexible chains, an additional first-order like symmetry-broken transition emerged. For block copolymers, the topological constraint did not obviously change the transition temperature, but greatly reduced the energy signal of the CG transition.

From thermodynamics to kinetics: enhanced sampling of rare events.

Despite great advances in molecular dynamics simulations, there remain large gaps between the simulations and experimental observations in terms of the time and length scales that can be approached. Developing fast and accurate algorithms and methods is of ultimate importance to bridge these gaps. In this Account, we briefly summarize recent efforts in such directions. In particular, we focus on integrated tempering sampling. The efficiency of this sampling method has been demonstrated by applications to a range of chemical and biological problems: protein folding, molecular cluster structure searches, and chemical reactions. The combination of integrated tempering sampling and a trajectory sampling method allows the calculation of rate constants and reaction pathways without predefined collective coordinates.

Coil-to-globule transitions of homopolymers and multiblock copolymers.

We study the coil-to-globule transitions of both homopolymers and multiblock copolymers using integrated tempering sampling method, which is a newly proposed enhanced sampling method that can efficiently sample the energy space with low computational costs. For homopolymers, the coil-to-globule structure transition temperatures (Ttr) are identified by the radius of gyration of the chain. The transition temperature shows a primary scaling dependence on the chain length (N) with Ttr ∼ N(-1/2). For multiblock copolymers, the coil-to-globule transition can be identified as first order, depending on the block size and the difference in attractive interactions of blocks. The influence of mutating a small portion of strongly attractive blocks to weakly attractive blocks on the coil-to-globule transition is found to be related to the position of the mutation.

Understanding the microsolvation of salts in molecular clusters

The solvation of salts in water and salt–water interactions are important for understanding a large variety of chemical, biological, and atmospheric processes. In this perspective, we summarize our recent studies on the theoretical modeling of salt–water clusters. In these studies, the integrated tempering sampling method was used for structure search and density functional theory was used to optimize the low‐energy configurations. The microsolvation mechanisms of three alkali–halide ion pairs in clusters are discussed. We also discuss the implications of these studies to our understanding of corresponding bulk solutions. © 2014 Wiley Periodicals, Inc.

Combine umbrella sampling with integrated tempering method for efficient and accurate calculation of free energy changes of complex energy surface.

Umbrella sampling is an efficient method for the calculation of free energy changes of a system along well-defined reaction coordinates. However, when there exist multiple parallel channels along the reaction coordinate or hidden barriers in directions perpendicular to the reaction coordinate, it is difficult for conventional umbrella sampling to reach convergent sampling within limited simulation time. Here, we propose an approach to combine umbrella sampling with the integrated tempering sampling method. The umbrella sampling method is applied to chemically more relevant degrees of freedom that possess significant barriers. The integrated tempering sampling method is used to facilitate the sampling of other degrees of freedom which may possess statistically non-negligible barriers. The combined method is applied to two model systems, butane and ACE-NME molecules, and shows significantly improved sampling efficiencies as compared to standalone conventional umbrella sampling or integrated tempering sampling approaches. Further analyses suggest that the enhanced performance of the new method come from the complemented advantages of umbrella sampling with a well-defined reaction coordinate and integrated tempering sampling in orthogonal space. Therefore, the combined approach could be useful in the simulation of biomolecular processes, which often involves sampling of complex rugged energy landscapes.

Integrated Hamiltonian Sampling: A Simple and Versatile Method for Free Energy Simulations and Conformational Sampling

Motivated by specific applications and the recent work of Gao and co-workers on integrated tempering sampling (ITS), we have developed a novel sampling approach referred to as integrated Hamiltonian sampling (IHS). IHS is straightforward to implement and complementary to existing methods for free energy simulation and enhanced configurational sampling. The method carries out sampling using an effective Hamiltonian constructed by integrating the Boltzmann distributions of a series of Hamiltonians. By judiciously selecting the weights of the different Hamiltonians, one achieves rapid transitions among the energy landscapes that underlie different Hamiltonians and therefore an efficient sampling of important regions of the conformational space. Along this line, IHS shares similar motivations as the enveloping distribution sampling (EDS) approach of van Gunsteren and co-workers, although the ways that distributions of different Hamiltonians are integrated are rather different in IHS and EDS. Specifically, we report efficient ways for determining the weights using a combination of histogram flattening and weighted histogram analysis approaches, which make it straightforward to include many end-state and intermediate Hamiltonians in IHS so as to enhance its flexibility. Using several relatively simple condensed phase examples, we illustrate the implementation and application of IHS as well as potential developments for the near future. The relation of IHS to several related sampling methods such as Hamiltonian replica exchange molecular dynamics and λ-dynamics is also briefly discussed.

Discriminating trpzip2 and trpzip4 peptides’ folding landscape using the two-dimensional infrared spectroscopy: A simulation study

We analyzed, based on the theoretical spectroscopic modeling, how the differences in the folding landscapes of two β-hairpin peptides trpzip2 and trpzip4 are reflected in their thermal unfolding infrared measurements. The isotope-edited equilibrium FTIR and two dimensional infrared spectra of the two peptides were calculated, using the nonlinear exciton propagation method, at a series of temperatures. The spectra calculations were based on the configuration distributions generated using the GB(OBC) implicit solvent MD simulation and the integrated tempering sampling technique. Conformational analysis revealed the different local thermal stabilities for these two peptides, which suggested the different folding landscapes. Our study further suggested that the ellipticities of the isotope peaks in the coherent IR signals are more sensitive to these local stability differences compared with other spectral features such as the peak intensities. Our technique can thus be combined with the relevant experimental measurements to achieve a better understanding of the peptide folding behaviors.