Rajesh K. Murarka

Isomerization dynamics in viscous liquids: Microscopic investigation of the coupling and decoupling of the rate to and from solvent viscosity and dependence on the intermolecular potential

A detailed investigation of viscosity dependence of the isomerization rate is carried out for continuous potentials by using a fully microscopic, self-consistent mode-coupling theory calculation of both the friction on the reactant and the viscosity of the medium. In this calculation we avoid approximating the short time response by the Enskog limit, which overestimates the friction at high frequencies. The isomerization rate is obtained by using the Grote–Hynes formula. The viscosity dependence of the rate has been investigated for a large number of thermodynamic state points. Since the activated barrier crossing dynamics probes the high-frequency frictional response of the liquid, the barrier crossing rate is found to be sensitive to the nature of the reactant–solvent interaction potential. When the solute–solvent interaction is modeled by a 6–12 Lennard-Jones potential, we find that over a large variation of viscosity (η), the rate (k) can indeed be fitted very well to a fractional viscosity dependence...

Diffusion of small light particles in a solvent of large massive molecules

We study the diffusion of small light particles in a solvent which consists of large heavy particles. The intermolecular interactions are chosen to approximately mimic a water�sucrose (or water�polysaccharide) mixture. Both computer simulation and mode coupling theoretical (MCT) calculations have been performed for a solvent-to-solute size ratio 5 and for a large variation of the mass ratio, keeping the mass of the solute fixed. Even in the limit of large mass ratio the solute motion is found to remain surprisingly coupled to the solvent dynamics. Interestingly, at intermediate values of the mass ratio, the self-intermediate scattering function of the solute, Fs(k,t) (where k is the wave number and t is the time), develops a stretching at long time which could be fitted to a stretched exponential function with a k-dependent exponent,\beta . For very large mass ratio, we find the existence of two stretched exponentials separated by a power law type plateau. The analysis of the trajectory shows the coexistence of both hopping and continuous motions for both the solute and the solvent particles. It is found that for mass ratio 5, the MCT calculations of the self-diffusion underestimates the simulated value by about 20%, which appears to be reasonable because the conventional form of the MCT does not include the hopping mode. However, for larger mass ratio, MCT appears to breakdown more severely. The breakdown of the MCT for large mass ratio can be connected to a similar breakdown near the glass transition.

Single particle and collective hydration dynamics for hydrophobic and hydrophilic peptides

We have conducted extensive molecular dynamics simulations to study the single particle and collective dynamics of water in solutions of N-acetyl-glycine-methylamide, a model hydrophilic protein backbone, and N-acetyl-leucine-methylamide, a model (amphiphilic) hydrophobic peptide, as a function of peptide concentration. Various analytical models commonly used in the analysis of incoherent quasielastic neutron scattering (QENS), are tested against the translational and rotational intermediate scattering function, the mean square displacement of the water molecule center of mass, and fits to the second-order rotational correlation function of water evaluated directly from the simulation data. We find that while the agreement between the model-free analysis and analytical QENS models is quantitatively poor, the qualitative feature of dynamical heterogeneity due to caging is captured well by all approaches. The center of mass collective and single particle intermediate scattering functions of water calculated for these peptide solutions show that the crossover from collective to single particle-dominated motions occurs at a higher value of Q for high concentration solutions relative to low concentration because of the greater restriction in movement of water molecules due to confinement. Finally, we have shown that at the same level of confinement of the two peptides, the aqueous amphiphilic amino acid solution shows the strongest deviation between single particle and collective dynamics relative to the hydrophilic amino acid, indicating that chemical heterogeneity induces even greater spatial heterogeneity in the water dynamics.

Activation of Corticotropin-Releasing Factor 1 Receptor: Insights from Molecular Dynamics Simulations

G-protein-coupled receptors (GPCRs) constitute the largest family of membrane-bound proteins involved in translation of extracellular signals into intracellular responses. They regulate diverse physiological and pathophysiological processes, and hence, they are prime drug targets for therapeutic intervention. In spite of the recent advancements in membrane protein crystallography, limited information is available on the molecular signatures of activation of GPCRs. Although few studies have been reported for class A GPCRs, the activation mechanism of class B GPCRs remains unexplored. Corticotropin-releasing factor 1 receptor (CRF1R), a class B GPCR, is associated with various disease conditions including stress, anxiety, and irritable bowel syndrome. Here, we report the activation of CRF1R using accelerated molecular dynamics simulations of the apo receptor. The breakage of His155(2.50)-Glu209(3.50) and Glu209(3.50)-Thr316(6.42) interactions is found to be crucial in transition of the receptor to its active conformation. Compared to the inactive crystal structure, major structural rearrangements occurred in the intracellular region of the transmembrane (TM) domain upon activation: TM3 twisted away from TM2, and an opening of the G-protein binding site occurred as a result of the outward movements of TM5 and TM6 from the helical bundle. Further, an inward tilt of TM7 toward the helical core is observed at the extracellular side, in agreement with recent findings (Coin et al. Cell 2013, 155, 1258-1269), where it is proposed that this movement helps in establishing favorable interactions with peptide agonist. Moreover, different allosteric pathways in the inactive and active states are identified using the correlations in torsion angle space. The inactive state is found to be less dynamic as compared to the putative active state of the receptor. Results from the current study could present a model for class B GPCRs activation and aid in the design of CRF1R modulators against brain and metabolic disorders.

Diffusion and viscosity in a supercooled polydisperse system

We have carried out extensive molecular dynamics simulations of a supercooled polydisperse Lennard-Jones liquid with large variations in temperature at a fixed pressure. The particles in the system are considered to be polydisperse in both size and mass. The temperature dependence of dynamical properties such as the viscosity (eta) and the self-diffusion coefficients (D(i)) of different size particles is studied. Both viscosity and diffusion coefficients show super-Arrhenius temperature dependence and fit well to the well-known Vogel-Fulcher-Tammann equation. Within the temperature range investigated, the value of Angells fragility parameter (D approximately 1.4) classifies the present system as a very fragile liquid. The critical temperature for diffusion (T(D(i))(o)) increases with the size of the particles. The critical temperature for viscosity (T(eta)(o)) is larger than that for diffusion, and sizable deviations appear for the smaller size particles, implying a decoupling of translational diffusion from viscosity in deeply supercooled liquids. Indeed, the diffusion shows markedly non-Stokesian behavior at low temperatures where a highly nonlinear dependence on size is observed. An inspection of the trajectories of the particles shows that at low temperatures the motions of both the smallest and largest size particles are discontinuous (jump type). However, the crossover from continuous Brownian to large length hopping motion takes place at shorter time scales for the smaller size particles.

Local composition fluctuations in strongly nonideal binary mixtures

We study the static and dynamical aspects of small length scale composition fluctuations in strongly nonideal binary mixtures of two different type by isothermal–isobaric (NPT) ensemble molecular dynamics simulations. Both the two models studied consider strong attractive interaction between dissimilar species which discourage the phase seperation in the binary mixtures. We find that the joint probability distribution of the composition fluctuations within molecular sized volumes is nearly Gaussian. However, the distributions are rather broad in both the binary mixtures. This is to be contrasted with the density fluctuation which is nearly negligible. Spontaneous fluctuation in one component is found to be anticorrelated with the fluctuations in it’s counterpart. The investigation of the dynamical correlation functions of the fluctuations reveal nonexponential relaxation with a slow long time tail. The cross-correlation function relaxes at a slower rate than the two pure correlations.

Conformational changes and allosteric communications in human serum albumin due to ligand binding

It is well recognized that knowledge of structure alone is not sufficient to understand the fundamental mechanism of biomolecular recognition. Information of dynamics is necessary to describe motions involving relevant conformational states of functional importance. We carried out principal component analysis (PCA) of structural ensemble, derived from 84 crystal structures of human serum albumin (HSA) with different ligands and/or different conditions, to identify the functionally important collective motions, and compared with the motions along the low-frequency modes obtained from normal mode analysis of the elastic network model (ENM) of unliganded HSA. Significant overlap is observed in the collective motions derived from PCA and ENM. PCA and ENM analysis revealed that ligand selects the most favored conformation from accessible equilibrium structures of unliganded HSA. Further, we analyzed dynamic network obtained from molecular dynamics simulations of unliganded HSA and fatty acids- bound HSA. Our results show that fatty acids-bound HSA has more robust community network with several routes to communicate among different parts of the protein. Critical nodes (residues) identified from dynamic network analysis are in good agreement with allosteric residues obtained from sequence-based statistical coupling analysis method. This work underscores the importance of intrinsic structural dynamics of proteins in ligand recognition and can be utilized for the development of novel drugs with optimum activity.

Structural Ensemble of CD4 Cytoplasmic Tail (402–419) Reveals a Nearly Flat Free-Energy Landscape with Local α-Helical Order in Aqueous Solution

The human cluster determinant 4 (CD4), expressed primarily on the surface of T helper cells, serves as a coreceptor in T-cell receptor recognition of MHC II antigen complexes. Besides its cellular functions, CD4 serves as a primary receptor of human immunodeficiency virus (HIV) type 1. The cytoplasmic tail of CD4 (residues 402-419) is known to be involved in direct interaction with the HIV-1 proteins Vpu and Nef. These two viral accessory proteins (Vpu and Nef) downregulate CD4 in HIV-1 infected cells by multiple strategies and make the body susceptible to all forms of infections. In this work, we carried out extensive replica exchange molecular dynamics simulations in explicit water with three popular protein force fields Amber ff99SB, Amber ff99SB*-ILDN, and CHARMM36 to characterize the equilibrium conformational ensemble of CD4-tail (402-419) and further validated the simulated ensembles with known NMR data. We found that ff99SB*-ILDN gives a better description of the structural ensemble of this peptide compared with ff99SB and CHARMM36. The peptide adopts multiple distinct conformations with varying degree of residual secondary structures. In particular, we observed 28, 7, and 5% average α-helical, β-strand, and 3(10)-helix content, respectively, for ff99SB*-ILDN. The peptide chain shows the tendency of helix formation in a cooperative manner, seeding at residues 407-410, and subsequently extending toward both ends of the chain. Furthermore, we constructed Markov state model (MSM) from large-scale molecular dynamics simulations to study the dynamics of transitions between different metastable states explored by this peptide. The mean first passage times computed from MSM indicate rapid interconversion of these states, and the time scales of transitions range from several nanoseconds to hundreds of microseconds. Our results show good agreement with experimental data and could help to understand the key molecular mechanisms of T-cell activation and HIV-mediated receptor interference.

Separation of time scale and coupling in the motion governed by the coarse-grained and fine degrees of freedom in a polypeptide backbone

The relevance of describing complex systems by simple coarse-grained models lies in the separation of time scales between the coarse-grained and fine or secondary degrees of freedom that are averaged out when going from an all-atom to the coarse-grained description. In this study, we propose a simple toy model with the aim of studying the variations with time, in a polypeptide backbone, of the coarse-grained (the pseudodihedral angle between subsequent Calpha atoms) and the secondary degrees of freedom (torsional angles for rotation of the peptide groups about the virtual Calpha...Calpha bonds). Microcanonical and Langevin dynamics simulations carried out for this model system with a full potential (which is a function of both the coarse-grained and secondary degrees of freedom) show that, although the main motions associated with the coarse-grained degrees of freedom are low-frequency motions, the motions of the secondary degrees of freedom involve both high- and low-frequency modes in which the higher-frequency mode is superposed on the lower-frequency mode that follows the motions of the coarse-grained degrees of freedom. We found that the ratio of the frequency of the high-to low-frequency modes is from about 3:1 to about 6:1. The correlation coefficients, calculated along the simulation trajectory between these two types of degrees of freedom, indeed show a strong correlation between the fast and slow motions of the secondary and coarse-grained variables, respectively. To complement the findings of the toy-model calculations, all-atom Langevin dynamics simulations with the AMBER 99 force field and generalized Born (GB) solvation were carried out on the terminally blocked Ala10 polypeptide. The coupling in the motions of the secondary and coarse-grained degrees of freedom, as revealed in the toy-model calculations, is also observed for the Ala10 polypeptide. However, in contrast to that of the toy-model calculations, we observed that the higher-frequency modes of the secondary degrees of freedom are spread over a wide range of frequencies in Ala10. We also observed that the correlations between the secondary and coarse-grained degrees of freedom decrease with increasing temperature. This rationalizes the use of a temperature-dependent cumulant-based potential, such as our united-residue (UNRES) energy function for polypeptide chains, as an effective potential energy. To determine the effect of the coupling in the motions of the secondary and coarse-grained degrees of freedom on the dynamics of the latter, we also carried out microcanonical and Langevin dynamics simulations for the reduced toy model with a UNRES potential or potential of mean force (PMF) (obtained by averaging the energy surface of the toy model over the secondary degrees of freedom), and compared the results to those with the full-model system (the potential of which is a function of both the coarse-grained and secondary degrees of freedom). We found that, apparently, the coupling in the motions of the secondary and coarse-grained degrees of freedom, and averaging out the secondary degrees of freedom, does not have any implications in distorting the time scale of the coarse-grained degrees of freedom. This implies that the forces that act on the coarse-grained degrees of freedom are the same, whether they arise from the full potential or from the UNRES potential (PMF), and one can still apply the naive approach of simply using the PMF in the Lagrange equations of motion for the coarse-grained degrees of freedom of a polypeptide backbone to describe their dynamics. This suggests that the coupling between the degrees of freedom of the solvent and those of a polypeptide backbone, rather than averaging out the secondary backbone degrees of freedom, is responsible for the time-scale distortion in the coarse-grained dynamics of a polypeptide backbone.

Heterogeneous relaxation in supercooled liquids: a density functional theory analysis

Recent time domain experiments which allow selective study of the relaxation of slower subpopulations among the distributions of local, inhomogeneous regions, have shown the existence of a length scale (∼2–3 nm) beyond which the liquid behaves like a homogeneous liquid. Here we use the density functional theory to calculate the probability of creating a soft localized density fluctuation (density droplet). Theoretical calculation shows that the free energy penalty for creating a local inhomogeneity of small size is much less than that for a large size and that a dense supercooled system is unlikely to sustain inhomogeneity of a length, lf, which is larger than 5σ, where σ is the molecular diameter. We have calculated both the equilibrium and the nonequilibrium (subsequent to photobleaching) orientational correlation functions with the theoretically obtained inhomogeneous distributions. The nonequilibrium distribution relaxes at a slower rate. A simple two state exchange model has been used to mimic the re...