Efficiency of exchange schemes in replica exchange

Accelerating Solvent Dynamics with Replica Exchange for Improved Free Energy Sampling

Molecular reactions in solution typically involve solvent exchange; for example, a surface must partly desolvate for a molecule to adsorb onto it. When these reactions are simulated, slow solvent dynamics can limit the sampling of configurations and reduce the accuracy of free energy estimates. Here, we combine Hamiltonian replica exchange (HREX) with well-tempered metadynamics (WTMD) to accelerate the sampling of solvent configurations orthogonal to the collective variable space. We compute the formation free energy of a carbonate vacancy in the calcite-water interface and find that the combination of WTMD with HREX significantly improves the sampling relative to WTMD without HREX.

Fuzzy Drug Targets: Disordered Proteins in the Drug-Discovery Realm

Intrinsically disordered proteins (IDPs) and regions (IDRs) form a large part of the eukaryotic proteome. Contrary to the structure-function paradigm, the disordered proteins perform a myriad of functions in vivo. Consequently, they are involved in various disease pathways and are plausible drug targets. Unlike folded proteins, that have a defined structure and well carved out drug-binding pockets that can guide lead molecule selection, the disordered proteins require alternative drug-development methodologies that are based on an acceptable picture of their conformational ensemble. In this review, we discuss various experimental and computational techniques that contribute toward understanding IDP "structure" and describe representative pursuances toward IDP-targeting drug development. We also discuss ideas on developing rational drug design protocols targeting IDPs.

Thermodynamic Signatures of Structural Transitions and Dissociation of Charged Colloidal Clusters: A Parallel Tempering Monte Carlo Study

Computational simulation of colloidal systems make use of empirical interaction potentials that are founded in well-established theory. In this work, we have performed parallel tempering Monte Carlo (PTMC) simulations to calculate heat capacity and to assess structural transitions, which may occur in charged colloidal clusters whose effective interactions are described by a sum of pair potentials with attractive short-range and repulsive long-range components. Previous studies on these systems have shown that the global minimum structure varies from spherical-type shapes for small-size clusters to Bernal spiral and “beaded-necklace” shapes at intermediate and larger sizes, respectively. In order to study both structural transitions and dissociation, we have organized the structures appearing in the PTMC calculations by three sets according to their energy: (i) low-energy structures, including the global minimum; (ii) intermediate-energy “beaded-necklace” motifs; (iii) high-energy linear and branched structures that characterize the dissociative clusters. We observe that, depending on the cluster, either peaks or shoulders on the heat–capacity curve constitute thermodynamics signatures of dissociation and structural transitions. The dissociation occurs at T=0.20 for all studied clusters and it is characterized by the appearance of a significant number of linear structures, while the structural transitions corresponding to unrolling the Bernal spiral are quite dependent on the size of the colloidal system.

Tempering of Au nanoclusters: capturing the temperature-dependent competition among structural motifs

A computational approach to determine the equilibrium structures of nanoclusters in the whole temperature range from 0 K to melting is developed. Our approach relies on Parallel Tempering Molecular Dynamics (PTMD) simulations complemented by Harmonic Superposition Approximation (HSA) calculations and global optimization searches, thus combining the accuracy of global optimization and HSA in describing the low-energy part of configuration space, together with the PTMD thorough sampling of high-energy configurations. This combined methodology is shown to be instrumental towards revealing the temperature-dependent structural motifs in Au nanoclusters of sizes 90, 147, and 201 atoms. The reported phenomenology is particularly rich, displaying a size- and temperature-dependent competition between the global energy minimum and other structural motifs. In the case of Au₉₀ and Au₁₄₇, the global minimum is also the dominant structure at finite temperatures. In contrast, the Au₂₀₁ cluster undergoes a solid-solid transformation at low temperature (<200 K). Results indicate that PTMD and HSA very well agree at intermediate temperatures, between 300 and 400 K. For higher temperatures, PTMD gives an accurate description of equilibrium, while HSA fails in describing the melting range. On the other hand, HSA is more efficient in catching low-temperature structural transitions. Finally, we describe the elusive structures close to the melting region which can present complex and defective geometries, that are otherwise difficult to characterize through experimental imaging.

Exploring Protocols to Build Reservoirs to Accelerate Temperature Replica Exchange MD Simulations

Temperature replica exchange molecular dynamics (REMD) is a widely used enhanced sampling method for accelerating biomolecular simulations. During the past 2 decades, several variants of REMD have been developed to further improve the rate of conformational sampling of REMD. One such variant, reservoir REMD (RREMD), was shown to improve the rate of conformational sampling by around 5-20×. Despite the significant increase in the sampling speed, RREMD methods have not been widely used because of the difficulties in building the reservoir and also because of the code not being available on the graphics processing units (GPUs). In this work, we ported the Amber RREMD code onto GPUs making it 20× faster than the central processing unit code. Then, we explored protocols for building Boltzmann-weighted reservoirs as well as non-Boltzmann reservoirs and tested how each choice affects the accuracy of the resulting RREMD simulations. We show that, using the recommended protocols outlined here, RREMD simulations can accurately reproduce Boltzmann-weighted ensembles obtained by much more expensive conventional temperature-based REMD simulations, with at least 15× faster convergence rates even for larger proteins (>50 amino acids) compared to conventional REMD.

de Almeida M, Marques JMC, Prudente FV. A thermodynamic view on the microsolvation of ions by rare gas: application to Li+ with argon

Parallel tempering Monte Carlo calculations on the Li⁺Ar_n microsolvation clusters have shown that the two peaks appearing in the heat capacity curve as a function of temperature correspond to the melting of the second and first solvation shells.

A generalized linear response framework for expanded ensemble and replica exchange simulations

Expanded ensemble simulation is a powerful technique for enhancing sampling over a range of thermodynamic parameters. However, although the premise is relatively simple, running successful simulations in practice still presents something of an ad hoc challenge. Three main difficulties exist: (1) the selection of the thermodynamic states, (2) the selection of the sampling weights, and (3) efficient sampling of the expanded parameter space. Here we consider these problems in the context of a pairwise linear response approach to the work fluctuation theorem. The approach offers comprehensive tactics for addressing the three difficulties and can be used as either an alternative or a complement to replica exchange simulations. Importantly, the results are trivially implemented for multi-dimensional parameter spaces and they recover results from the literature aimed at the special cases of simulated/parallel tempering and replica exchange umbrella sampling. Illustrative examples are shown using the NAMD simulation engine.

Conformational Dynamics and Stability of U-Shaped and S-Shaped Amyloid β Assemblies

Alzheimer’s disease is the most fatal neurodegenerative disorder characterized by the aggregation and deposition of Amyloid β (Aβ) oligomers in the brain of patients. Two principal variants of Aβ exist in humans: Aβ_1–40 and Aβ_1–42. The former is the most abundant in the plaques, while the latter is the most toxic species and forms fibrils more rapidly. Interestingly, fibrils of Aβ_1–40 peptides can only assume U-shaped conformations while Aβ_1–42 can also arrange as S-shaped three-stranded chains, as recently discovered. As alterations in protein conformational arrangement correlate with cell toxicity and speed of disease progression, it is important to characterize, at molecular level, the conformational dynamics of amyloid fibrils. In this work, Replica Exchange Molecular Dynamics simulations were carried out to compare the conformational dynamics of U-shaped and S-shaped Aβ_17–42 small fibrils. Our computational results provide support for the stability of the recently proposed S-shaped model due to the maximized interactions involving the C-terminal residues. On the other hand, the U-shaped motif is characterized by significant distortions resulting in a more disordered assembly. Outcomes of our work suggest that the molecular architecture of the protein aggregates might play a pivotal role in formation and conformational stability of the resulting fibrils.

Free energy landscape of siRNA-polycation complexation: Elucidating the effect of molecular geometry, polymer flexibility, and charge neutralization

The success of medical threatments with DNA and silencing interference RNA is strongly related to the design of efficient delivery technologies. Cationic polymers represent an attractive strategy to serve as nucleic-acid carriers with the envisioned advantages of efficient complexation, low cost, ease of production, well-defined size, and low polydispersity index. However, the balance between efficacy and toxicity (safety) of these polymers is a challenge and in need of improvement. With the aim of designing more effective polycationic-based gene carriers, many parameters such as carrier morphology, size, molecular weight, surface chemistry, and flexibility/rigidity ratio need to be taken into consideration. In the present work, the binding mechanism of three cationic polymers (polyarginine, polylysine and polyethyleneimine) to a model siRNA target is computationally investigated at the atomistic level. In order to better understand the polycationic carrier-siRNA interactions, replica exchange molecular dynamic simulations were carried out to provide an exhaustive exploration of all the possible binding sites, taking fully into account the siRNA flexibility together with the presence of explicit solvent and ions. Moreover, well-tempered metadynamics simulations were employed to elucidate how molecular geometry, polycation flexibility, and charge neutralization affect the siRNA-polycations free energy landscape in term of low-energy binding modes and unbinding free energy barriers. Significant differences among polymer binding modes have been detected, revealing the advantageous binding properties of polyarginine and polylysine compared to polyethyleneimine.

Molecular determinants for the thermodynamic and functional divergence of uniporter GLUT1 and proton symporter XylE

GLUT1 facilitates the down-gradient translocation of D-glucose across cell membrane in mammals. XylE, an Escherichia coli homolog of GLUT1, utilizes proton gradient as an energy source to drive uphill D-xylose transport. Previous studies of XylE and GLUT1 suggest that the variation between an acidic residue (Asp27 in XylE) and a neutral one (Asn29 in GLUT1) is a key element for their mechanistic divergence. In this work, we combined computational and biochemical approaches to investigate the mechanism of proton coupling by XylE and the functional divergence between GLUT1 and XylE. Using molecular dynamics simulations, we evaluated the free energy profiles of the transition between inward- and outward-facing conformations for the apo proteins. Our results revealed the correlation between the protonation state and conformational preference in XylE, which is supported by the crystal structures. In addition, our simulations suggested a thermodynamic difference between XylE and GLUT1 that cannot be explained by the single residue variation at the protonation site. To understand the molecular basis, we applied Bayesian network models to analyze the alteration in the architecture of the hydrogen bond networks during conformational transition. The models and subsequent experimental validation suggest that multiple residue substitutions are required to produce the thermodynamic and functional distinction between XylE and GLUT1. Despite the lack of simulation studies with substrates, these computational and biochemical characterizations provide unprecedented insight into the mechanistic difference between proton symporters and uniporters.

We seek to address one intriguing question, the mechanistic distinction between active proton-coupled symporters and passive uniporters that are related in evolution. Proton-coupled symporters harness the transmembrane proton gradient to drive the substrate transport, while uniporters can only facilitate the passive substrate translocation. In this work, we focus on two sugar transporters GLUT1 and XylE, which belong to symporters and uniporters respectively but have high sequence similarity. We first applied molecular dynamics simulations to characterize the thermodynamic behaviors of apo GLUT1 and XylE, which are supposed to provide prominent details of mechanisms. From the identified difference in thermodynamics, we concluded that neutralizing protonation site in XylE is insufficient for its conversion to GLUT1 analog. To pinpoint extra elements contributing to their evolutionary divergence, we developed a novel network modeling scheme based on Bayesian network which shows impressive predictive power on residue mutations. Our models suggested the detailed mechanism of proton coupling in XylE and molecular basis of symporter/uniporter discrepancy. Furthermore, the modeling scheme could help to guide the design of biomolecules for desired functions.

Conformation transitions of a single polyelectrolyte chain in a poor solvent: a replica-exchange lattice Monte-Carlo study

The thermodynamic behaviors of a strongly charged polyelectrolyte chain in a poor solvent are studied using replica-exchange Monte-Carlo simulations on a lattice model, focusing on the effects of finite chain length and the solvent quality on the chain conformation and conformation transitions. The neutralizing counterions and solvent molecules are considered explicitly. The thermodynamic quantities that vary continuously with temperature over a wide range are computed using the multiple histogram reweighting method. Our results suggest that the strength of the short-range hydrophobic interaction, the chain length, and the temperature of the system, characterized by ε, N, and T, respectively, are important parameters that control the conformations of a charged chain. When ε is moderate, the competition between the electrostatic energy and the short-range hydrophobic interaction leads to rich conformations and conformation transitions for a longer chain with a fixed length. Our results have unambiguously demonstrated the stability of the n-pearl-necklace structures, where n has a maximum value and decreases with decreasing temperature. The maximum n value increases with increasing chain length. Our results have also demonstrated the first-order nature of the conformation transitions between the m-pearl and the (m-1)-pearl necklaces. With the increase of ε, the transition temperature increases and the first-order feature becomes more pronounced. It is deduced that at the thermodynamic limit of infinitely long chain length, the conformational transitions between the m-pearl and the (m-1)-pearl necklaces may remain first order when ε > 0 and m = 2 or 3. Pearl-necklace conformations cannot be observed when either ε is too large or N is too small. To observe a pearl-necklace conformation, the T value needs to be carefully chosen for simulations performed at only a single temperature.

Thermodynamic and kinetic stability of the Josephin Domain closed arrangement: evidences from replica exchange molecular dynamics

BACKGROUND

Molecular phenomena driving pathological aggregation in neurodegenerative diseases are not completely understood yet. Peculiar is the case of Spinocerebellar Ataxia 3 (SCA3) where the conformational properties of the AT-3 N-terminal region, also called Josephin Domain (JD), play a key role in the first step of aggregation, having the JD an amyloidogenic propensity itself. For this reason, unraveling the intimate relationship between JD structural features and aggregation tendency may lead to a step forward in understanding the pathology and rationally design a cure. In this connection, computational modeling has demonstrated to be helpful in exploring the protein molecular dynamics and mechanism of action.

RESULTS

Conformational dynamics of the JD is here finely investigated by replica exchange molecular dynamics simulations able to sample the microsecond time scale and to provide both a thermodynamic and kinetic description of the protein conformational changes. Accessible structural conformations of the JD have been identified in: open, intermediate and closed like arrangement. Data indicated the closed JD arrangement as the most likely protein arrangement. The protein transition from closed toward intermediate/open states was characterized by a rate constant higher than 700 ns. This result also explains the inability of classical molecular dynamics to explore transitions from closed to open JD configuration on a time scale of hundreds of nanoseconds.

CONCLUSION

This work provides the first kinetic estimation of the JD transition pathway from open-like to closed-like arrangement and vice-versa, indicating the closed-like arrangement as the most likely configuration for a JD in water environment. More widely, the importance of our results is also underscored considering that the ability to provide a kinetic description of the protein conformational changes is a scientific challenge for both experimental and theoretical approaches to date.

REVIEWERS

This article was reviewed by Oliviero Carugo, Bojan Zagrovic.

An explicit-solvent conformation search method using open software

Computer modeling is a popular tool to identify the most-probable conformers of a molecule. Although the solvent can have a large effect on the stability of a conformation, many popular conformational search methods are only capable of describing molecules in the gas phase or with an implicit solvent model. We have developed a work-flow for performing a conformation search on explicitly-solvated molecules using open source software. This method uses replica exchange molecular dynamics (REMD) to sample the conformational states of the molecule efficiently. Cluster analysis is used to identify the most probable conformations from the simulated trajectory. This work-flow was tested on drug molecules α-amanitin and cabergoline to illustrate its capabilities and effectiveness. The preferred conformations of these molecules in gas phase, implicit solvent, and explicit solvent are significantly different.

Intermediate Thermodynamic States Contribute Equally to Free Energy Convergence: A Demonstration with Replica Exchange

We investigate the relationship between the number of intermediate thermodynamic states along a pathway and the precision of free energy estimates. With a sufficient number of states, the asymptotic variance collapses as a function of the total sample size. Our analytical result is corroborated by replica exchange molecular dynamics simulations of model systems in which the neighbor exchange rate exceeds 35%. Precision collapse is also observed in heat capacity estimates based on the multistate Bennett acceptance ratio. In contrast to the relaxation and mean first-passage times, the autocorrelation time of state indices is found to be relevant to free energy convergence.

Simulations in generalized ensembles through noninstantaneous switches

Generalized-ensemble simulations, such as replica exchange and serial generalized-ensemble methods, are powerful simulation tools to enhance sampling of free energy landscapes in systems with high energy barriers. In these methods, sampling is enhanced through instantaneous transitions of replicas, i.e., copies of the system, between different ensembles characterized by some control parameter associated with thermodynamical variables (e.g., temperature or pressure) or collective mechanical variables (e.g., interatomic distances or torsional angles). An interesting evolution of these methodologies has been proposed by replacing the conventional instantaneous (trial) switches of replicas with noninstantaneous switches, realized by varying the control parameter in a finite time and accepting the final replica configuration with a Metropolis-like criterion based on the Crooks nonequilibrium work (CNW) theorem. Here we revise these techniques focusing on their correlation with the CNW theorem in the framework of Markovian processes. An outcome of this report is the derivation of the acceptance probability for noninstantaneous switches in serial generalized-ensemble simulations, where we show that explicit knowledge of the time dependence of the weight factors entering such simulations is not necessary. A generalized relationship of the CNW theorem is also provided in terms of the underlying equilibrium probability distribution at a fixed control parameter. Illustrative calculations on a toy model are performed with serial generalized-ensemble simulations, especially focusing on the different behavior of instantaneous and noninstantaneous replica transition schemes.

Exploring biomolecular dynamics and interactions using advanced sampling methods

Molecular dynamics (MD) and Monte Carlo (MC) simulations have emerged as a valuable tool to investigate statistical mechanics and kinetics of biomolecules and synthetic soft matter materials. However, major limitations for routine applications are due to the accuracy of the molecular mechanics force field and due to the maximum simulation time that can be achieved in current simulations studies. For improving the sampling a number of advanced sampling approaches have been designed in recent years. In particular, variants of the parallel tempering replica-exchange methodology are widely used in many simulation studies. Recent methodological advancements and a discussion of specific aims and advantages are given. This includes improved free energy simulation approaches and conformational search applications.

Parameterization of the Hamiltonian Dielectric Solvent (HADES) Reaction-Field Method for the Solvation Free Energies of Amino Acid Side-Chain Analogs

Optimization of the Hamiltonian dielectric solvent (HADES) method for biomolecular simulations in a dielectric continuum is presented with the goal of calculating accurate absolute solvation free energies while retaining the model's accuracy in predicting conformational free-energy differences. The solvation free energies of neutral and polar amino acid side-chain analogs calculated by using HADES, which may optionally include nonpolar contributions, were optimized against experimental data to reach a chemical accuracy of about 0.5 kcal mol(-1). The new parameters were evaluated for charged side-chain analogs. The HADES results were compared with explicit-solvent, generalized Born, Poisson-Boltzmann, and QM-based methods. The potentials of mean force (PMFs) between pairs of side-chain analogs obtained by using HADES and explicit-solvent simulations were used to evaluate the effects of the improved parameters optimized for solvation free energies on intermolecular potentials.

Theory of Adaptive Optimization for Umbrella Sampling

We present a theory of adaptive optimization for umbrella sampling. With the analytical bias force constant obtained from the constrained thermodynamic length along the reaction coordinate, the windows are distributed to optimize the overlap between neighbors. Combining with the replica exchange method, we propose a method of adaptive window exchange umbrella sampling. The efficiency gain in sampling by the present method originates from the optimal window distribution, in which windows are concentrated to the region where the free energy is steep, as well as consequently improved random walk.

Computational Recipe for Efficient Description of Large-Scale Conformational Changes in Biomolecular Systems

Characterizing large-scale structural transitions in biomolecular systems poses major technical challenges to both experimental and computational approaches. On the computational side, efficient sampling of the configuration space along the transition pathway remains the most daunting challenge. Recognizing this issue, we introduce a knowledge-based computational approach toward describing large-scale conformational transitions using (i) nonequilibrium, driven simulations combined with work measurements and (ii) free energy calculations using empirically optimized biasing protocols. The first part is based on designing mechanistically relevant, system-specific reaction coordinates whose usefulness and applicability in inducing the transition of interest are examined using knowledge-based, qualitative assessments along with nonequilirbrium work measurements which provide an empirical framework for optimizing the biasing protocol. The second part employs the optimized biasing protocol resulting from the first part to initiate free energy calculations and characterize the transition quantitatively. Using a biasing protocol fine-tuned to a particular transition not only improves the accuracy of the resulting free energies but also speeds up the convergence. The efficiency of the sampling will be assessed by employing dimensionality reduction techniques to help detect possible flaws and provide potential improvements in the design of the biasing protocol. Structural transition of a membrane transporter will be used as an example to illustrate the workings of the proposed approach.

Electrostatics of proteins in dielectric solvent continua. II. Hamiltonian reaction field dynamics

In Paper I of this work [S. Bauer, G. Mathias, and P. Tavan, J. Chem. Phys. 140, 104102 (2014)] we have presented a reaction field (RF) method, which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of polarizable molecular mechanics (MM) force fields. Building upon these results, here we suggest a method for linearly scaling Hamiltonian RF/MM molecular dynamics (MD) simulations, which we call "Hamiltonian dielectric solvent" (HADES). First, we derive analytical expressions for the RF forces acting on the solute atoms. These forces properly account for all those conditions, which have to be self-consistently fulfilled by RF quantities introduced in Paper I. Next we provide details on the implementation, i.e., we show how our RF approach is combined with a fast multipole method and how the self-consistency iterations are accelerated by the use of the so-called direct inversion in the iterative subspace. Finally we demonstrate that the method and its implementation enable Hamiltonian, i.e., energy and momentum conserving HADES-MD, and compare in a sample application on Ac-Ala-NHMe the HADES-MD free energy landscape at 300 K with that obtained in Paper I by scanning of configurations and with one obtained from an explicit solvent simulation.

The Microscopic Physical Cause for the Density Maximum of Liquid Water

The existence of a density maximum at 277 K is probably the most prominent anomaly among the many very special thermodynamic properties of liquid water. While usually attributed to so-called hydrogen bonding, the microscopic physical cause of this prominent anomaly is still elusive. Here we show that the density anomaly is caused by those short-range electrostatic forces, which are generated by the quadrupole and higher moments of the charge distributions present in liquid-phase water molecules. This conclusion derives from 20 ns replica exchange molecular-dynamics simulations with closely related polarizable four-, five-, and six-point water models. As soon as the model complexity suffices to represent the higher electrostatic moments with sufficient accuracy, the density temperature profile n(T) calculated for T ∈ [250,320] K at the standard pressure 1 bar locks in to the experimental observation. The corresponding six-point model is, therefore, the most simple available cartoon for liquid-phase water molecules.

Microcanonical thermostatistics of coarse-grained proteins with amyloidogenic propensity

The formation of fibrillar aggregates seems to be a common characteristic of polypeptide chains, although the observation of these aggregates may depend on appropriate experimental conditions. Partially folded intermediates seem to have an important role in the generation of protein aggregates, and a mechanism for this fibril formation considers that these intermediates also correspond to metastable states with respect to the fibrillar ones. Here, using a coarse-grained (CG) off-lattice model, we carry out a comparative analysis of the thermodynamic aspects characterizing the folding transition with respect to the propensity for aggregation of four different systems: two isoforms of the amyloid β-protein, the Src SH3 domain, and the human prion proteins (hPrP). Microcanonical analysis of the data obtained from replica exchange method is conducted to evaluate the free-energy barrier and latent heat in these models. The simulations of the amyloid β isoforms and Src SH3 domain indicated that the folding process described by this CG model is related to a negative specific heat, a phenomenon that can only be verified in the microcanonical ensemble in first-order phase transitions. The CG simulation of the hPrP heteropolymer yielded a continuous folding transition. The absence of a free-energy barrier and latent heat favors the presence of partially unfolded conformations, and in this context, this thermodynamic aspect could explain the reason why the hPrP heteropolymer is more aggregation-prone than the other heteropolymers considered in this study. We introduced the hydrophobic radius of gyration as an order parameter and found that it can be used to obtain reliable information about the hydrophobic packing and the transition temperatures in the folding process.

Advanced replica-exchange sampling to study the flexibility and plasticity of peptides and proteins

Molecular dynamics (MD) simulations are ideally suited to investigate protein and peptide plasticity and flexibility simultaneously at high spatial (atomic) and high time resolution. However, the applicability is still limited by the force field accuracy and by the maximum simulation time that can be routinely achieved in current MD simulations. In order to improve the sampling the replica-exchange (REMD) methodology has become popular and is now the most widely applied advanced sampling approach. Many variants of the REMD method have been designed to reduce the computational demand or to enhance sampling along specific sets of conformational variables. An overview on recent methodological advances and discussion of specific aims and advantages of the approaches will be given. Applications in the area of free energy simulations and advanced sampling of intrinsically disordered peptides and proteins will also be discussed. This article is part of a Special Issue entitled: The emerging dynamic view of proteins: Protein plasticity in allostery, evolution and self-assembly.

Two Dimensional Window Exchange Umbrella Sampling for Transmembrane Helix Assembly

The method of window exchange umbrella sampling molecular dynamics (WEUSMD) with a pre-optimized parameter set was recently used to obtain the most probable conformations and the energetics of transmembrane (TM) helix assembly of a generic TM sequence. When applied to glycophorin A TM domain (GpA-TM) using the restraint potentials along the helix-helix distance, however, tight interfacial packing of GpA-TM resulted in insufficient conformational sampling at short helix-helix separation. This sampling issue is addressed by extending the WEUSMD into two dimensions with the restraint potentials along the helix-helix distance and crossing angle. The two-dimensional WEUSMD results demonstrate that the incomplete sampling in the one-dimensional WEUSMD arises from high barriers along the crossing angle between the GpA-TM helices. Together with the faster convergence in both the assembled conformations and the potential of mean force, the 2D-WEUSMD can be a general and efficient approach in computational studies of TM helix assembly.

Transmembrane helix assembly by window exchange umbrella sampling

A method of window exchange umbrella sampling molecular dynamics simulation is employed for transmembrane helix assembly. An analytical expression for the average acceptance probability between neighboring windows is derived and combined with the first passage time optimization method to predetermine a parameter set in an optimal range. With the parameter set, the method provides a substantially more efficient sampling of helix-helix interfaces together with the potential of mean force along the helix-helix distance of a transmembrane helix-dimer model, compared to the umbrella sampling method.

Conformation transitions of a polyelectrolyte chain: a replica-exchange Monte-Carlo study

The thermodynamic behavior of a strongly charged polyelectrolyte chain immersed in a salt-free solution is studied using replica-exchange Monte-Carlo simulations. The results reveal that the chain can assume a variety of conformations, and it undergoes two phase transitions upon cooling. The first transition is identified as a continuous counterion condensation transition while the second one as a first-order coil-globule transition. In the globular state, the counterions and the charged chain segments are densely packed forming a three-dimensional Wigner crystal.