Chapter 5 - Combination of genetic algorithm and generalised-ensemble algorithms for biomolecular simulations

Hybrid parallel tempering and simulated annealing method

Accelerating conformational sampling through changes in molecular mass is an attractive option in biomolecular modeling. Here, we examine the utility and compare the efficiency of hydrogen mass repartitioning (HMR) and light water (LW) models in the context of replica exchange (RE) simulations of an alanine dipeptide. To maintain integrator stability, we introduced scaling of integration steps with RE temperatures and determined their maximum values, assuring the stability of RE simulations. HMR2 and HMR3 models featuring doubled and tripled hydrogen masses and, to a lesser extent, the LW model reproduce the energetic and conformational properties of alanine dipeptide in water compared to the HMR1 reference. This conclusion is based on comparing kinetic and potential energies, free energy landscapes of the peptide, as well as its structural properties, including hydrogen bonding, water counts in the peptide first solvation shell, and RMSD distributions. Thereby, our results demonstrate that both HMR and LW models can be integrated into RE simulations. We then compared HMR and LW models with respect to the computational efforts required to equilibrate alanine dipeptide. HMR2 and HMR3 are up to 4-fold more computationally efficient than the HMR1 reference, whereas LW lags behind being less than a factor of 2 more efficient. As a result, LW efficiency is 2-fold lower than that of HMR3. This outcome means that increasing the integration step provides faster sampling than boosting water diffusion. Even if the computation of long-range interactions is adjusted with the length of the integration step and the step in LW simulations is further increased, the model remains less efficient than HMR3. We considered a hybrid variant of LW, hLW, featuring heavier water and mass repartitioning applied to all hydrogens, affording longer integration steps than LW does. hLW improves computational efficiency and provides more accurate reproduction of energetic and conformational properties of alanine dipeptide than LW. We concluded that HMR3 and hLW models demonstrate good performance in replica exchange simulation, but the former is preferable due to broader applicability and simplicity. hLW remains an excellent alternative to HMR3, but its scope is limited to "water-rich" systems. More generally, our findings suggest that among the two approaches, HMR or decreasing water mass, the former is more effective. Since LW simulations are not currently supported out-of-the-box by the NAMD molecular dynamics program, we implemented a patch enabling LW functionality.

The efficiency of temperature replica exchange (RE) simulations hinge on their ability to enhance conformational sampling at physiological temperatures by taking advantage of more rapid conformational interconversions at higher temperatures. While temperature RE is a parallel simulation technique that is relatively straightforward to implement, kinetics in the RE ensemble is complicated, and there is much to learn about how best to employ RE simulations in computational biophysics. Protein folding rates often slow down above a certain temperature due to entropic bottlenecks. This "anti-Arrhenius" behavior represents a challenge for RE. However, it is far from straightforward to systematically explore the impact of this on RE by brute force molecular simulations, since RE simulations of protein folding are very difficult to converge. To understand some of the basic mechanisms that determine the efficiency of RE, it is useful to study simplified low dimensionality systems that share some of the key characteristics of molecular systems. Results are presented concerning the efficiency of temperature RE on a continuous two-dimensional potential that contains an entropic bottleneck. Optimal efficiency was obtained when the temperatures of the replicas did not exceed the temperature at which the harmonic mean of the folding and unfolding rates is maximized. This confirms a result we previously obtained using a discrete network model of RE. Comparison of the efficiencies obtained using the continuous and discrete models makes it possible to identify non-Markovian effects, which slow down equilibration of the RE ensemble on the more complex continuous potential. In particular, the rate of temperature diffusion and also the efficiency of RE is limited by the time scale of conformational rearrangements within free energy basins.

This paper introduces an improved simulated annealing - parallel simulated annealing with genetic crossover: PSAGC, and uses this method in energy minimization problem of protein structure prediction. Through experiments on three real proteins, PSAGC is proved more effective than SA and PSA, it can achieve conformations which have lower energy values. Then the paper investigates crossover interval and crossover method of PSAGC, and obtains useful conclusions

Replica exchange molecular dynamics is a multicanonical simulation technique commonly used to enhance the sampling of solvated biomolecules on rugged free energy landscapes. While replica exchange is relatively easy to implement, there are many unanswered questions about how to use this technique most efficiently, especially because it is frequently the case in practice that replica exchange simulations are not fully converged. A replica exchange cycle consists of a series of molecular dynamics steps of a set of replicas moving under different Hamiltonians or at different thermodynamic states followed by one or more replica exchange attempts to swap replicas among the different states. How the replica exchange cycle is constructed affects how rapidly the system equilibrates. We have constructed a Markov state model of replica exchange (MSMRE) using long molecular dynamics simulations of a host-guest binding system as an example, in order to study how different implementations of the replica exchange cycle can affect the sampling efficiency. We analyze how the number of replica exchange attempts per cycle, the number of MD steps per cycle, and the interaction between the two parameters affects the largest implied time scale of the MSMRE simulation. The infinite swapping limit is an important concept in replica exchange. We show how to estimate the infinite swapping limit from the diagonal elements of the exchange transition matrix constructed from MSMRE "simulations of simulations" as well as from relatively short runs of the actual replica exchange simulations.

Polyglutamine (polyQ) repeat disorders are caused by the expansion of CAG tracts in certain genes, resulting in transcription of proteins with abnormally long polyQ inserts. When these inserts expand beyond 35-45 glutamines, affected proteins form toxic aggregates, leading to neuron death. Chymotrypsin inhibitor 2 (CI2) with an inserted glutamine repeat has previously been used to model polyQ-mediated aggregation in vitro. However, polyQ insertion lengths in these studies have been kept below the pathogenic threshold. We perform molecular dynamics simulations to study monomer folding dynamics and dimer formation in CI2-polyQ chimeras with insertion lengths of up to 80 glutamines. Our model recapitulates the experimental results of previous studies of chimeric CI2 proteins, showing high folding cooperativity of monomers as well as protein association via domain swapping. Surprisingly, for chimeras with insertion lengths above the pathogenic threshold, monomer folding cooperativity decreases and the dominant mode for dimer formation becomes interglutamine hydrogen bonding. These results support a mechanism for pathogenic polyQ-mediated aggregation, in which expanded polyQ tracts destabilize affected proteins and promote the formation of partially unfolded intermediates. These unfolded intermediates form aggregates through associations by interglutamine interactions.

In this paper, the local search algorithm to improve the searching capability of parallel simulated annealing using genetic crossover (PSA/GAc) for the energy minimization of protein tertiary structures is proposed. Our previous research shows that PSA/GAc is effective for the energy minimization of the small proteins. However, because the energy minimization of larger proteins requires larger number of calculations required to reach the global optimum. In this paper, the local search algorithm to search /spl alpha/-helix efficiently is proposed and is applied to the energy minimization of proteins. Also, for the verification of the algorithm, the test function which has a similar characteristic to the energy functions of proteins that have /spl alpha/-helix structures is proposed. Finally, PSA/GAc with the proposed local search is applied to the same proteins and its capability is discussed. The result indicates that as for the target proteins of this paper, PSA/GAc with local search has obtained the more accurate solutions and additionally, total number of evaluations required to reach the optimum can reduced. From the results, the possibility of effectiveness of proposed local search algorithm on the energy minimization of the proteins with /spl alpha/-helix has been verified.

127 遺伝的交叉を用いた並列シミュレーテッドアニーリングによるタンパク質立体構造予測

Fine-Grained Parallel and Distributed Spatial Stochastic Simulation of Biological Reactions

Parallel tempering, also known as replica exchange molecular dynamics (REMD), has recently been successfully used to study the structure and thermodynamic properties of biomolecules such as peptides and small proteins. For large systems, however, applying REMD can be costly since the number of replicas needed increases as the square root of the number of degrees of freedom in the system. Often, enhanced sampling is only needed for a subset of atoms, such as a loop region of a large protein or a small ligand binding to a receptor. In such applications, it is often reasonable to assume a weak dependence of the structure of the larger region on the instantaneous conformation of the smaller region of interest. For these cases, we derived two variant replica exchange methods, partial replica exchange molecular dynamics (PREMD) and local replica exchange molecular dynamics (LREMD). The Hamiltonian for the system is separated, with replica exchange carried out only for terms involving the subsystem of interest while the remainder of the system is maintained at a single temperature. The number of replicas required for efficient exchange thus depends on the number of degrees of freedom in the fragment needing refinement rather than on the size of the full system. The method can be applied to much larger systems than was previously practical. This also provides a means to preserve the integrity of the structure outside the refinement region without introduction of restraints. LREMD takes this weak coupling approximation a step further, employing only a single representation of the large fragment that simultaneously interacts with all of the replicas of the subsystem of interest. This is obtained by combining replica exchange with the locally enhanced sampling approximation (LES), reducing the computational expense of replica exchange simulations to near that of a single standard molecular dynamics (MD) simulation. Use of LREMD also permits the use of LES without requiring the specification of a single temperature, a known difficulty for standard LES simulations. We tested these two methods on the loop region of an RNA hairpin model system and find significant advantages over standard MD and REMD simulations.

Advances in computational biophysics depend on the development of accurate effective potentials and powerful sampling methods to traverse rugged energy landscapes. We have developed an approach that makes use of the combined power of replica exchange simulations and a network model for kinetics. We carry out replica exchange simulations to generate a very large set of states using an all-atom effective potential function and construct a kinetic model for the folding, using an ansatz that allows kinetic transitions between states based on structural similarity. We are also using replica exchange simulations to study the binding of ligands to proteins such as cytochrome P450. A better understanding of the relationship between the physical kinetics of the systems being studied to their “kinetics” in the replica exchange ensemble is needed to use this new technology to maximum advantage. To illustrate some of the challenges, we will discuss the results using a network model to “simulate” replica exchange simulations of protein folding.KeywordsMonte CarloGeneralize BornImplicit Solvent ModelReplica ExchangeProximal StateThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The nature of analog and digital simulation is different, so they work with two different simulation kernels. Synchronization between these two kernels is an important challenge in the mixed signal simulation subject. In this paper we introduce an algorithm for mixed signal simulation that works based on reducing the analog and digital simulation interaction. When the simulator switches to analog simulation, the analog solver initiates the analog parameters to start analog simulation. Resuming the analog simulation needs some additional steps; we reduce some switching between analog and digital simulation. The efficiency of the new algorithm is shown by some examples.

This work presents a replica exchanging self-guided Langevin dynamics (RXSGLD) simulation method for efficient conformational searching and sampling. Unlike temperature-based replica exchanging simulations, which use high temperatures to accelerate conformational motion, this method uses self-guided Langevin dynamics (SGLD) to enhance conformational searching without the need to elevate temperatures. A RXSGLD simulation includes a series of SGLD simulations, with simulation conditions differing in the guiding effect and/or temperature. These simulation conditions are called stages and the base stage is one with no guiding effect. Replicas of a simulation system are simulated at the stages and are exchanged according to the replica exchanging probability derived from the SGLD partition function. Because SGLD causes less perturbation on conformational distribution than high temperatures, exchanges between SGLD stages have much higher probabilities than those between different temperatures. Therefore, RXSGLD simulations have higher conformational searching ability than temperature based replica exchange simulations. Through three example systems, we demonstrate that RXSGLD can generate target canonical ensemble distribution at the base stage and achieve accelerated conformational searching. Especially for large systems, RXSGLD has remarkable advantages in terms of replica exchange efficiency, conformational searching ability, and system size extensiveness.

In this study, the protein tertiary structure prediction systems on the grid are proposed for progress of the bioinformatics. The prediction is mainly performed by the protein energy minimization. However, this method has many iterated calculation of the protein energy in most cases. To use the grid as the large-scale computing environment would be valuable for this system. In the system, parallel simulated annealing using genetic crossover (PSA/GAc) is a minimization engine and NetSolve is a basic tool to use the grid. In this study, two types of implementations are prepared. The first naive implementation of the system has a critical overhead due to large communication delay over the Internet. The second system, asynchronous crossover model, improves the performance in the second implementation. The details of the system and the experimental results solving C-peptide are shown as an example of grid application.

The replica exchange approach, also called parallel tempering, is gaining popularity for biomolecular simulation. We ask whether the approach is likely to be efficient compared to standard simulation methods for fixed-temperature equilibrium sampling. To examine the issue, we make a number of straightforward observations on how "fast" high-temperature molecular simulations can be expected to run, as well as on how to characterize efficiency in replica exchange. Although our conclusions remain to be fully established, based on a range of results in the literature and some of our own work with a 50-atom peptide, we are not optimistic for the efficiency of replica exchange for canonical sampling of biomolecules.