Modified replica exchange simulation methods for local structure refinement

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.     

Hamiltonian replica‐exchange simulations with adaptive biasing of peptide backbone and side chain dihedral angles

A Hamiltonian Replica‐Exchange Molecular Dynamics (REMD) simulation method has been developed that employs a two‐dimensional backbone and one‐dimensional side chain biasing potential specifically to promote conformational transitions in peptides. To exploit the replica framework optimally, the level of the biasing potential in each replica was appropriately adapted during the simulations. This resulted in both high exchange rates between neighboring replicas and improved occupancy/flow of all conformers in each replica. The performance of the approach was tested on several peptide and protein systems and compared with regular MD simulations and previous REMD studies. Improved sampling of relevant conformational states was observed for unrestrained protein and peptide folding simulations as well as for refinement of a loop structure with restricted mobility of loop flanking protein regions. © 2013 Wiley Periodicals, Inc.     

Solvophobic and steric effects of side groups on polymer folding: molecular modeling studies of amine-functionalized m-poly(phenyleneethynylene) foldamers in aqueous solution

The folding behavior of five different amine-functionalized m-poly(phenyleneethynylene) (m-PPE) oligomers containing 24 phenyl rings (12 residues, where a residue includes 2 phenyl rings) in water was examined by using a combination of molecular dynamics (MD) and replica exchange molecular dynamics (REMD) simulation techniques. The REMD method employed the highly parallelized GROMACS MD software and a modified OPLS-AA force field to simulate 44 replicas of each solvated system in parallel, with temperatures ranging from 300 to 577 K. Our results showed that the REMD method was more effective in predicting the helical conformation of the m-PPE in water, from an extended structure, than canonical MD methods in the same simulation time. Furthermore, we observed from canonical MD simulations of the explicitly solvated helical m-PPEs at 300 K that the radius of gyration, average helix inner diameter, and average helix pitch of the helical structure all pass through a minima when the side group is R = OC(2)H(5) as R is changed from R = H through OC(4)H(9).     

Convergence and sampling efficiency in replica exchange simulations of peptide folding in explicit solvent

Replica exchange methods (REMs) are increasingly used to improve sampling in molecular dynamics (MD) simulations of biomolecular systems. However, despite having been shown to be very effective on model systems, the application of REM in complex systems such as for the simulation of protein and peptide folding in explicit solvent has not been objectively tested in detail. Here we present a comparison of conventional MD and temperature replica exchange MD (T-REMD) simulations of a beta-heptapeptide in explicit solvent. This system has previously been shown to undergo reversible folding on the time scales accessible to MD simulation and thus allows a direct one-to-one comparison of efficiency. The primary properties compared are the free energy of folding and the relative populations of different conformers as a function of temperature. It is found that to achieve a similar degree of precision T-REMD simulations starting from a random set of initial configurations were approximately an order of magnitude more computationally efficient than a single 800 ns conventional MD simulation for this system at the lowest temperature investigated (275 K). However, whereas it was found that T-REMD simulations are more than four times more efficient than multiple independent MD simulations at one temperature (300 K) the actual increase in conformation sampling was only twofold. The overall gain in efficiency using REMD resulted primarily from the ordering of different conformational states over temperature, as opposed to a large increase of conformational sampling. It is also shown that in this system exchanges are accepted primarily based on (random) fluctuations within the solvent and are not strongly correlated with the instantaneous peptide conformation raising questions in regard to the efficiency of T-REMD in larger systems.     

On achieving experimental accuracy from molecular dynamics simulations of flexible molecules: aqueous glycerol

The rotational isomeric states (RIS) of glycerol at infinite dilution have been characterized in the aqueous phase via a 1 micros conventional molecular dynamics (MD) simulation, a 40 ns enhanced sampling replica exchange molecular dynamics (REMD) simulation, and a reevaluation of the experimental NMR data. The MD and REMD simulations employed the GLYCAM06/AMBER force field with explicit treatment of solvation. The shorter time scale of the REMD sampling method gave rise to RIS and theoretical scalar 3J(HH) coupling constants that were comparable to those from the much longer traditional MD simulation. The 3J(HH) coupling constants computed from the MD methods were in excellent agreement with those observed experimentally. Despite the agreement between the computed and the experimental J-values, there were variations between the rotamer populations computed directly from the MD data and those derived from the experimental NMR data. The experimentally derived populations were determined utilizing limiting J-values from an analysis of NMR data from substituted ethane molecules and may not be completely appropriate for application in more complex molecules, such as glycerol. Here, new limiting J-values have been derived via a combined MD and quantum mechanical approach and were used to decompose the experimental 3J(HH) coupling constants into population distributions for the glycerol RIS.     

Exchange frequency in replica exchange molecular dynamics

The effect of the exchange-attempt frequency on sampling efficiency is studied in replica exchange molecular dynamics (REMD). We show that sampling efficiency increases with increasing exchange-attempt frequency. This conclusion is contrary to a commonly expressed view in REMD. Five peptides (1-21 residues long) are studied with a spectrum of exchange-attempt rates. Convergence rates are gauged by comparing ensemble properties between fixed length test REMD simulations and longer reference simulations. To show the fundamental correlation between exchange frequency and convergence time, a simple model is designed and studied, displaying the same basic behavior of much more complex systems.     

Convergence of replica exchange molecular dynamics

Replica exchange molecular dynamics (REMD) method is one of the generalized-ensemble algorithms which performs random walk in energy space and helps a system to escape from local energy traps. In this work, we studied the accuracy and efficiency of REMD by examining its ability to reproduce the results of multiple extended conventional molecular dynamics (MD) simulations and to enhance conformational sampling. Two sets of REMD simulations with different initial configurations, one from the fully extended and the other from fully helical conformations, were conducted on a fast-folding 21-amino-acid peptide with a continuum solvent model. Remarkably, the two REMD simulation sets started to converge even within 1.0 ns, despite their dramatically different starting conformations. In contrast, the conventional MD within the same time and with identical starting conformations did not show obvious signs of convergence. Excellent convergence between the REMD sets for T>300 K was observed after 14.0 ns REMD simulations as measured by the average helicity and free-energy profiles. We also conducted a set of 45 MD simulations at nine different temperatures with each trajectory simulated to 100.0 and 200.0 ns. An excellent agreement between the REMD and the extended MD simulation results was observed for T>300 K, showing that REMD can accurately reproduce long-time MD results with high efficiency. The autocorrelation times of the calculated helicity demonstrate that REMD can significantly enhance the sampling efficiency by 14.3+/-6.4, 35.1+/-0.2, and 71.5+/-20.4 times at, respectively, approximately 360, approximately 300, and approximately 275 K in comparison to the regular MD. Convergence was less satisfactory at low temperatures (T<300 K) and a slow oscillatory behavior suggests that longer simulation time was needed to reach equilibrium. Other technical issues, including choice of exchange frequency, were also examined.     

Convergence of folding free energy landscapes via application of enhanced sampling methods in a distributed computing environment

We have implemented the serial replica exchange method (SREM) and simulated tempering (ST) enhanced sampling algorithms in a global distributed computing environment. Here we examine the helix-coil transition of a 21 residue alpha-helical peptide in explicit solvent. For ST, we demonstrate the efficacy of a new method for determining initial weights allowing the system to perform a random walk in temperature space based on short trial simulations. These weights are updated throughout the production simulation by an adaptive weighting method. We give a detailed comparison of SREM, ST, as well as standard MD and find that SREM and ST give equivalent results in reasonable agreement with experimental data. In addition, we find that both enhanced sampling methods are much more efficient than standard MD simulations. The melting temperature of the Fs peptide with the AMBER99phi potential was calculated to be about 310 K, which is in reasonable agreement with the experimental value of 334 K. We also discuss other temperature dependent properties of the helix-coil transition. Although ST has certain advantages over SREM, both SREM and ST are shown to be powerful methods via distributed computing and will be applied extensively in future studies of complex bimolecular systems.     

Coupling of replica exchange simulations to a non-Boltzmann structure reservoir

Computing converged ensemble properties remains challenging for large biomolecules. Replica exchange molecular dynamics (REMD) can significantly increase the efficiency of conformational sampling by using high temperatures to escape kinetic traps. Several groups, including ours, introduced the idea of coupling replica exchange to a pre-converged, Boltzmann-populated reservoir, usually at a temperature higher than that of the highest temperature replica. This procedure reduces computational cost because the long simulation times needed for extensive sampling are only carried out for a single temperature. However, a weakness of the approach is that the Boltzmann-weighted reservoir can still be difficult to generate. We now present the idea of employing a non-Boltzmann reservoir, whose structures can be generated through more efficient conformational sampling methods. We demonstrate that the approach is rigorous and derive a correct statistical mechanical exchange criterion between the reservoir and the replicas that drives Boltzmann-weighted probabilities for the replicas. We test this approach on the trpzip2 peptide and demonstrate that the resulting thermal stability profile is essentially indistinguishable from that obtained using very long (>100 ns) standard REMD simulations. The convergence of this reservoir-aided REMD is significantly faster than for regular REMD. Furthermore, we demonstrate that modification of the exchange criterion is essential; REMD simulations using a standard exchange function with the non-Boltzmann reservoir produced incorrect results.     

Coulomb replica‐exchange method: Handling electrostatic attractive and repulsive forces for biomolecules

We propose a new type of the Hamiltonian replica‐exchange method (REM) for molecular dynamics (MD) and Monte Carlo simulations, which we refer to as the Coulomb REM (CREM). In this method, electrostatic charge parameters in the Coulomb interactions are exchanged among replicas while temperatures are exchanged in the usual REM. By varying the atom charges, the CREM overcomes free‐energy barriers and realizes more efficient sampling in the conformational space than the REM. Furthermore, this method requires only a smaller number of replicas because only the atom charges of solute molecules are used as exchanged parameters. We performed Coulomb replica‐exchange MD simulations of an alanine dipeptide in explicit water solvent and compared the results with those of the conventional canonical, replica exchange, and van der Waals REMs. Two force fields of AMBER parm99 and AMBER parm99SB were used. As a result, the CREM sampled all local‐minimum free‐energy states more frequently than the other methods for both force fields. Moreover, the Coulomb, van der Waals, and usual REMs were applied to a fragment of an amyloid‐β peptide (Aβ) in explicit water solvent to compare the sampling efficiency of these methods for a larger system. The CREM sampled structures of the Aβ fragment more efficiently than the other methods. We obtained β‐helix, α‐helix, 3₁₀‐helix, β‐hairpin, and β‐sheet structures as stable structures and deduced pathways of conformational transitions among these structures from a free‐energy landscape. © 2012 Wiley Periodicals, Inc.     

Ergodicity and model quality in template‐restrained canonical and temperature/Hamiltonian replica exchange coarse‐grained molecular dynamics simulations of proteins

Molecular simulations restrained to single or multiple templates are commonly used in protein‐structure modeling. However, the restraints introduce additional barriers, thus impairing the ergodicity of simulations, which can affect the quality of the resulting models. In this work, the effect of restraint types and simulation schemes on ergodicity and model quality was investigated by performing template‐restrained canonical molecular dynamics (MD), multiplexed replica‐exchange molecular dynamics, and Hamiltonian replica exchange molecular dynamics (HREMD) simulations with the coarse‐grained UNRES force field on nine selected proteins, with pseudo‐harmonic log‐Gaussian (unbounded) or Lorentzian (bounded) restraint functions. The best ergodicity was exhibited by HREMD. It has been found that non‐ergodicity does not affect model quality if good templates are used to generate restraints. However, when poor‐quality restraints not covering the entire protein are used, the improved ergodicity of HREMD can lead to significantly improved protein models. © 2017 Wiley Periodicals, Inc.     

An improved replica-exchange sampling method: temperature intervals with global energy reassignment

In a molecular dynamics (MD) simulation, representative sampling over the entire phase space is desired to obtain an accurate canonical distribution at a given temperature. For large molecules, such as proteins, this is problematic because systems tend to become trapped in local energy minima. The extensively used replica-exchange molecular dynamics (REMD) simulation technique overcomes this kinetic-trapping problem by allowing Boltzmann-weighted configuration exchange processes to occur between numerous thermally adjacent and compositionally identical simulations that are thermostated at sequentially higher temperatures. While the REMD method provides much better sampling than conventional MD, there are two substantial difficulties that are inherent in its application: (1) the large number of replicas that must be used to span a designated temperature range and (2) the subsequent long time required for configurations sampled at high temperatures to exchange down for potential inclusion within the low-temperature ensemble of interest. In this work, a new method based on temperature intervals with global energy reassignment (TIGER) is presented that overcomes both of these problems. A TIGER simulation is conducted as a series of short heating-sampling-quenching cycles. At the end of each cycle, the potential energies of all replicas are simultaneously compared at the same temperature using a Metropolis sampling method and then globally reassigned to the designated temperature levels. TIGER is compared with regular MD and REMD methods for the alanine dipeptide in water. The results indicate that TIGER increases sampling efficiency while substantially reducing the number of central processing units required for a comparable conventional REMD simulation.     

Efficient evaluation of sampling quality of molecular dynamics simulations by clustering of dihedral torsion angles and Sammon mapping

A direct conformational clustering and mapping approach for peptide conformations based on backbone dihedral angles has been developed and applied to compare conformational sampling of Met-enkephalin using two molecular dynamics (MD) methods. Efficient clustering in dihedrals has been achieved by evaluating all combinations resulting from independent clustering of each dihedral angle distribution, thus resolving all conformational substates. In contrast, Cartesian clustering was unable to accurately distinguish between all substates. Projection of clusters on dihedral principal component (PCA) subspaces did not result in efficient separation of highly populated clusters. However, representation in a nonlinear metric by Sammon mapping was able to separate well the 48 highest populated clusters in just two dimensions. In addition, this approach also allowed us to visualize the transition frequencies between clusters efficiently. Significantly, higher transition frequencies between more distinct conformational substates were found for a recently developed biasing-potential replica exchange MD simulation method allowing faster sampling of possible substates compared to conventional MD simulations. Although the number of theoretically possible clusters grows exponentially with peptide length, in practice, the number of clusters is only limited by the sampling size (typically much smaller), and therefore the method is well suited also for large systems. The approach could be useful to rapidly and accurately evaluate conformational sampling during MD simulations, to compare different sampling strategies and eventually to detect kinetic bottlenecks in folding pathways.     

Computational study on the structural diversity of amyloid Beta Peptide (abeta(10-35)) oligomers

We studied the oligomerization of Alzheimer amyloid beta peptide (Abeta) using a replica exchange molecular dynamics (REMD) simulation. The simulation was performed with Abeta(10-35) dimers, trimers, and tetramers. Extensive REMD simulations illustrated several possible oligomer conformations. As the size of the oligomer increased from a dimer to a tetramer, the number of possible configurations was reduced. We identified all the possible conformations for each oligomer and characterized their temperature dependence. It was found that the detailed structures of the oligomers, which may act as folding intermediates, are highly sensitive to the parameters of the simulation environment such as temperature and concentration. Structural diversities of Abeta oligomers suggest multiple pathways of the aggregation process.     

GENESIS 1.1: A hybrid‐parallel molecular dynamics simulator with enhanced sampling algorithms on multiple computational platforms

GENeralized‐Ensemble SImulation System (GENESIS) is a software package for molecular dynamics (MD) simulation of biological systems. It is designed to extend limitations in system size and accessible time scale by adopting highly parallelized schemes and enhanced conformational sampling algorithms. In this new version, GENESIS 1.1, new functions and advanced algorithms have been added. The all‐atom and coarse‐grained potential energy functions used in AMBER and GROMACS packages now become available in addition to CHARMM energy functions. The performance of MD simulations has been greatly improved by further optimization, multiple time‐step integration, and hybrid (CPU + GPU) computing. The string method and replica‐exchange umbrella sampling with flexible collective variable choice are used for finding the minimum free‐energy pathway and obtaining free‐energy profiles for conformational changes of a macromolecule. These new features increase the usefulness and power of GENESIS for modeling and simulation in biological research. © 2017 Wiley Periodicals, Inc.     

Amyloid beta-peptide oligomerization in silico: dimer and trimer

Soluble oligomers of Alzheimer's amyloid beta protein (Abeta) may act as effectors of neurotoxicity in early stages of Alzheimer's disease. Detailed information about the structure of Abeta in atomistic level and the dynamics of assembly of monomeric Abeta into oligomeric structures is rather elusive. We have performed replica exchange molecular dynamics (REMD) simulations on the formation of the dimer and trimer of Abeta10-35 peptide. We have observed spontaneous formation of several basic structural units that may act as a template or an intermediate for further aggregation of Alzheimer's Abeta protein. Various conformers, including interlocking structures of experimentally known bend double beta strands, are identified.     

Multidimensional umbrella sampling and replica‐exchange molecular dynamics simulations for structure prediction of transmembrane helix dimers

Structural information of a transmembrane (TM) helix dimer is useful in understanding molecular mechanisms of important biological phenomena such as signal transduction across the cell membrane. Here, we describe an umbrella sampling (US) scheme for predicting the structure of a TM helix dimer in implicit membrane using the interhelical crossing angle and the TM–TM relative rotation angles as the reaction coordinates. This scheme conducts an efficient conformational search on TM–TM contact interfaces, and its robustness is tested by predicting the structures of glycophorin A (GpA) and receptor tyrosine kinase EphA1 (EphA1) TM dimers. The nuclear magnetic resonance (NMR) structures of both proteins correspond to the global free‐energy minimum states in their free‐energy landscapes. In addition, using the landscape of GpA as a reference, we also examine the protocols of temperature replica‐exchange molecular dynamics (REMD) simulations for structure prediction of TM helix dimers in implicit membrane. A wide temperature range in REMD simulations, for example, 250–1000 K, is required to efficiently obtain a free‐energy landscape consistent with the US simulations. The interhelical crossing angle and the TM–TM relative rotation angles can be used as reaction coordinates in multidimensional US and be good measures for conformational sampling of REMD simulations. © 2013 Wiley Periodicals, Inc.     

Computation of Absolute Hydration and Binding Free Energy with Free Energy Perturbation Distributed Replica-Exchange Molecular Dynamics (FEP/REMD)

Distributed Replica (REPDSTR) is a powerful parallelization technique enabling simulations of a group of replicas in a parallel/parallel fashion, where each replica is distributed to different nodes of a large cluster [Theor. Chem. Acc. 109: 140 (2003)]. Here, we use the framework provided by REPDSTR to combine a staged free energy perturbation protocol with different values of the thermodynamic coupling parameters with replica-exchange molecular dynamics (FEP/REMD. The structure of REPDSTR, which allows multiple parallel input/output (I/O), facilitates the treatment of replica-exchange to couple the N window simulations. As a result, each of the N synchronous window simulations benefit from the sampling carried out by the N-1 others. As illustrative examples of the FEP/REMD strategy, calculations of the absolute hydration and binding free energy of small molecules were performed using the biomolecular simulation program CHARMM adapted for the IBM Blue Gene/P platform. The computations show that a FEP/REMD strategy significantly improves the sampling and accelerate the convergence of absolute free energy computations.     

Folding and thermodynamic studies of Trp-cage based on polarized force field

Two replica exchange molecular dynamics (REMD) simulations were carried out to study the thermodynamics of a 20-residue Trp-cage folding based on a newly developed polarized protein-specific charge (PPC). Starting from a fully extended conformation, Trp-cage native conformation was successfully sampled using REMD based on a 3-step PPC update. Next, the obtained Trp-cage folded conformation was then used to calculate the PPC in which another REMD was performed to explore the thermodynamic stability of Trp-cage. The theoretical melting temperature T _m of ≈325 K was found to be in close agreement with experimental melting temperature, T _m of 315 K. This indicates that the PPC was correctly predicting the temperature dependence. The current study provides a direct proof of how electrostatic polarization affects protein folding.