Free energy landscape of a dense hard-sphere system

The topography of the free energy landscape in phase space of a dense hard-sphere system characterized by a discretized free energy functional of the Ramakishnan-Yussouff form is investigated numerically using a specially devised Monte Carlo procedure. We locate a considerable number of glassy local minima of the free energy and analyze the distributions of the free energy at a minimum and an appropriately defined phase-space "distance" between different minima. We find evidence for the existence of pairs of closely related glassy minima("two-level systems"). We also investigate the way the system makes transitions as it moves from the basin of attraction of a minimum to that of another one after a start under nonequilibrium conditions. This allows us to determine the effective height of free energy barriers that separate a glassy minimum from the others. The dependence of the height of free energy barriers on the density is investigated in detail. The general appearance of the free energy landscape resembles that of a putting green: relatively deep minima separated by a fairly flat structure. We discuss the connection of our results with the Vogel-Fulcher law and relate our observations to other work on the glass transition.

Energy landscape view of phase transitions and slow dynamics in thermotropic liquid crystals

Thermotropic liquid crystals are known to display rich phase behavior on temperature variation. Although the nematic phase is orientationally ordered but translationally disordered, a smectic phase is characterized by the appearance of a partial translational order in addition to a further increase in orientational order. In an attempt to understand the interplay between orientational and translational order in the mesophases that thermotropic liquid crystals typically exhibit upon cooling from the high-temperature isotropic phase, we investigate the potential energy landscapes of a family of model liquid crystalline systems. The configurations of the system corresponding to the local potential energy minima, known as the inherent structures, are determined from computer simulations across the mesophases. We find that the depth of the potential energy minima explored by the system along an isochor grows through the nematic phase as temperature drops in contrast to its insensitivity to temperature in the isotropic and smectic phases. The onset of the growth of the orientational order in the parent phase is found to induce a translational order, resulting in a smectic-like layer in the underlying inherent structures; the inherent structures, surprisingly, never seem to sustain orientational order alone if the parent nematic phase is sandwiched between the high-temperature isotropic phase and the low-temperature smectic phase. The Arrhenius temperature dependence of the orientational relaxation time breaks down near the isotropic-nematic transition. We find that this breakdown occurs at a temperature below which the system explores increasingly deeper potential energy minima.

Elucidation of the conformational free energy landscape in H.pylori LuxS and its implications to catalysis

Background: One of the major challenges in understanding enzyme catalysis is to identify the different conformations and their populations at detailed molecular level in response to ligand binding/environment. A detail description of the ligand induced conformational changes provides meaningful insights into the mechanism of action of enzymes and thus its function. Results: In this study, we have explored the ligand induced conformational changes in H. pylori LuxS and the associated mechanistic features. LuxS, a dimeric protein, produces the precursor (4,5-dihydroxy-2,3-pentanedione) for autoinducer-2 production which is a signalling molecule for bacterial quorum sensing. We have performed molecular dynamics simulations on H. pylori LuxS in its various ligand bound forms and analyzed the simulation trajectories using various techniques including the structure network analysis, free energy evaluation and water dynamics at the active site. The results bring out the mechanistic details such as co operativity and asymmetry between the two subunits, subtle changes in the conformation as a response to the binding of active and inactive forms of ligands and the population distribution of different conformations in equilibrium. These investigations have enabled us to probe the free energy landscape and identify the corresponding conformations in terms of network parameters. In addition, we have also elucidated the variations in the dynamics of water co-ordination to the Zn2+ ion in LuxS and its relation to the rigidity at the active sites. Conclusions: In this article, we provide details of a novel method for the identification of conformational changes in the different ligand bound states of the protein, evaluation of ligand-induced free energy changes and the biological relevance of our results in the context of LuxS structure-function. The methodology outlined here is highly generalized to illuminate the linkage between structure and function in any protein of known structure.

Levitation effect and its relationship with the underlying potential energy landscape

Positions of potential energy minima for spherical monatomic sorbates in zeolite NaY have been identified for different sizes of the sorbate. It is found that for small sorbates (sigma less than or equal to 4.96 Angstrom) there are only six adsorption sites per alpha-cage, which are located close to the inner surface of the alpha-cage. For larger sorbates, additional sites of comparable energies appear close to the 12-ring window which forms the bottleneck for intercage diffusion. Minimum energy paths between these sites have been computed. These suggest that the barriers for both intracage and intercage site-to-site migrations are comparable and decrease with increase in sorbate size. Earlier simulation studies on the diffusion of monatomic sorbates in zeolites indicated that there is a dramatic change in the nature of dependence of D on sorbate size around 4.96 Angstrom, for zeolite NaY. Therefore, the present results suggest that the dependence of D on sorbate size and the changes in the potential energy landscape are correlated. The sorbate-zeolite system is characterized by a flatter potential energy landscape when the sorbate size is large. (C) 1999 American Institute of Physics. [S0021-9606(99)51110-0].

Understanding glassy dynamics from the free-energy landscape

Many interesting features of the dynamics of simple liquids near the glass transition may be understood in terms of properties of the free-energy landscape obtained from numerical studies of a model free-energy functional. Main results obtained from this approach are summarized and a list of references to relevant publications is provided. (C) 2002 Elsevier Science B.V. All rights reserved.

Characterization of the dynamics of glass-forming liquids from the properties of the potential energy landscape

We develop a framework for understanding the difference between strong and fragile behavior in the dynamics of glass-forming liquids from the properties of the potential energy landscape. Our approach is based on a master equation description of the activated jump dynamics among the local minima of the potential energy (the so-called inherent structures) that characterize the potential energy landscape of the system. We study the dynamics of a small atomic cluster using this description as well as molecular dynamics simulations and demonstrate the usefulness of our approach for this system. Many of the remarkable features of the complex dynamics of glassy systems emerge from the activated dynamics in the potential energy landscape of the atomic cluster. The dynamics of the system exhibits typical characteristics of a strong supercooled liquid when the system is allowed to explore the full configuration space. This behavior arises because the dynamics is dominated by a few lowest-lying minima of the potential energy and the potential energy barriers between these minima. When the system is constrained to explore only a limited region of the potential energy landscape that excludes the basins of attraction of a few lowest-lying minima, the dynamics is found to exhibit the characteristics of a fragile liquid.

Communication: Benzene dimer-The free energy landscape

Establishing the relative orientation of the two benzene molecules in the dimer has remained an enigmatic challenge. Consensus has narrowed the choice of structures to either a T-shape, that may be tilted, or a parallel displaced arrangement, but the relatively small energy differences makes identifying the global minimum difficult. Here we report an ab initio Car-Parrinello Molecular Dynamics based metadynamics computation of the free-energy landscape of the benzene dimer. Our calculations show that although competing structures may be isoenergetic, free energy always favors a tilted T-shape geometry at all temperatures where the bound benzene dimer exist. (C) 2013 AIP Publishing LLC.

Propensity to Form Amyloid Fibrils Is Encoded as Excitations in the Free Energy Landscape of Monomeric Proteins

Protein aggregation, linked to many of diseases, is initiated when monomers access rogue conformations that are poised to form amyloid fibrils. We show, using simulations of src SH3 domain, that mechanical force enhances the population of the aggregation-prone (N*) states, which are rarely populated under force free native conditions but are encoded in the spectrum of native fluctuations. The folding phase diagrams of SH3 as a function of denaturant concentration (C]), mechanical force (f), and temperature exhibit an apparent two-state behavior, without revealing the presence of the elusive N* states. Interestingly, the phase boundaries separating the folded and unfolded states at all C] and f fall on a master curve, which can be quantitatively described using an analogy to superconductors in a magnetic field. The free energy profiles as a function of the molecular extension (R), which are accessible in pulling experiments, (R), reveal the presence of a native-like N* with a disordered solvent-exposed amino-terminal beta-strand. The structure of the N* state is identical with that found in Fyn SH3 by NMR dispersion experiments. We show that the timescale for fibril formation can be estimated from the population of the N* state, determined by the free energy gap separating the native structure and the N* state, a finding that can be used to assess fibril forming tendencies of proteins. The structures of the N* state are used to show that oligomer formation and likely route to fibrils occur by a domain-swap mechanism in SH3 domain. (C) 2014 Elsevier Ltd. All rights reserved.

Diffusion on a rugged energy landscape with spatial correlations

Rugged energy landscapes find wide applications in diverse fields ranging from astrophysics to protein folding. We study the dependence of diffusion coefficient (D) of a Brownian particle on the distribution width (epsilon) of randomness in a Gaussian random landscape by simulations and theoretical analysis. We first show that the elegant expression of Zwanzig Proc. Natl. Acad. Sci. U.S.A. 85, 2029 (1988)] for D(epsilon) can be reproduced exactly by using the Rosenfeld diffusion-entropy scaling relation. Our simulations show that Zwanzig's expression overestimates D in an uncorrelated Gaussian random lattice - differing by almost an order of magnitude at moderately high ruggedness. The disparity originates from the presence of ``three-site traps'' (TST) on the landscape - which are formed by the presence of deep minima flanked by high barriers on either side. Using mean first passage time formalism, we derive a general expression for the effective diffusion coefficient in the presence of TST, that quantitatively reproduces the simulation results and which reduces to Zwanzig's form only in the limit of infinite spatial correlation. We construct a continuous Gaussian field with inherent correlation to establish the effect of spatial correlation on random walk. The presence of TSTs at large ruggedness (epsilon >> k(B)T) gives rise to an apparent breakdown of ergodicity of the type often encountered in glassy liquids. (C) 2014 AIP Publishing LLC.

Relationship between entropy and diffusion: A statistical mechanical derivation of Rosenfeld expression for a rugged energy landscape

Diffusion-a measure of dynamics, and entropy-a measure of disorder in the system are found to be intimately correlated in many systems, and the correlation is often strongly non-linear. We explore the origin of this complex dependence by studying diffusion of a point Brownian particle on a model potential energy surface characterized by ruggedness. If we assume that the ruggedness has a Gaussian distribution, then for this model, one can obtain the excess entropy exactly for any dimension. By using the expression for the mean first passage time, we present a statistical mechanical derivation of the well-known and well-tested scaling relation proposed by Rosenfeld between diffusion and excess entropy. In anticipation that Rosenfeld diffusion-entropy scaling (RDES) relation may continue to be valid in higher dimensions (where the mean first passage time approach is not available), we carry out an effective medium approximation (EMA) based analysis of the effective transition rate and hence of the effective diffusion coefficient. We show that the EMA expression can be used to derive the RDES scaling relation for any dimension higher than unity. However, RDES is shown to break down in the presence of spatial correlation among the energy landscape values. (C) 2015 AIP Publishing LLC.

Allostery and conformational free energy changes in human tryptophanyl-tRNA synthetase from essential dynamics and structure networks

The interdependence of the concept of allostery and enzymatic catalysis, and they being guided by conformational mobility is gaining increased prominence. However, to gain a molecular level understanding of llostery and hence of enzymatic catalysis, it is of utter importance that the networks of amino acids participating in allostery be deciphered. Our lab has been exploring the methods of network analysis combined with molecular dynamics simulations to understand allostery at molecular level. Earlier we had outlined methods to obtain communication paths and then to map the rigid/flexible regions of proteins through network parameters like the shortest correlated paths, cliques, and communities. In this article, we advance the methodology to estimate the conformational populations in terms of cliques/communities formed by interactions including the side-chains and then to compute the ligand-induced population shift. Finally, we obtain the free-energy landscape of the protein in equilibrium, characterizing the free-energy minima accessed by the protein complexes. We have chosen human tryptophanyl-tRNA synthetase (hTrpRS), a protein esponsible for charging tryptophan to its cognate tRNA during protein biosynthesis for this investigation. This is a multidomain protein exhibiting excellent allosteric communication. Our approach has provided valuable structural as well as functional insights into the protein. The methodology adopted here is highly generalized to illuminate the linkage between protein structure networks and conformational mobility involved in the allosteric mechanism in any protein with known structure.

Temperature dependent free energy surface of polymer folding from equilibrium and quench studies

Langevin dynamics simulation studies have been employed to calculate the temperature dependent free energy surface and folding characteristics of a 500 monomer long linear alkane (polyethylene) chain with a realistic interaction potential. Both equilibrium and temperature quench simulation studies have been carried out. Using the shape anisotropy parameter (S) of the folded molecule as the order parameter, we find a weakly first order phase transition between the high-temperature molten globule and low-temperature rodlike crystalline states separated by a small barrier of the order of k(B)T. Near the melting temperature (580 K), we observe an intriguing intermittent fluctuation with pronounced ``1/f noise characteristics'' between these two states with large difference in shape and structure. We have also studied the possibilities of different pathways of folding to states much below the melting point. At 300 K starting from the all-trans linear configuration, the chain folds stepwise into a very regular fourfold crystallite with very high shape anisotropy. Whereas, when quenched from a high temperature (900 K) random coil regime, we identify a two step transition from the random coiled state to a molten globulelike state and, further, to a anisotropic rodlike state. The trajectory reveals an interesting coupling between the two order parameters, namely, radius of gyration (R-g) and the shape anisotropy parameter (S). The rodlike final state of the quench trajectory is characterized by lower shape anisotropy parameter and significantly larger number of gauche defects as compared to the final state obtained through equilibrium simulation starting from all-trans linear chain. The quench study shows indication of a nucleationlike pathway from the molten globule to the rodlike state involving an underlying rugged energy landscape. (C) 2010 American Institute of Physics. doi:10.1063/1.3509398]

Multidimensional free energy surface of unfolding of HP-36: Microscopic origin of ruggedness

The protein folding funnel paradigm suggests that folding and unfolding proceed as directed diffusion in a multidimensional free energy surface where a multitude of pathways can be traversed during the protein's sojourn from initial to final state. However, finding even a single pathway, with the detail chronicling of intermediates, is an arduous task. In this work we explore the free energy surface of unfolding pathway through umbrella sampling, for a small globular a-helical protein chicken-villin headpiece (HP-36) when the melting of secondary structures is induced by adding DMSO in aqueous solution. We find that the unfolding proceeds through the initial separation or melting of aggregated hydrophobic core that comprises of three phenylalanine residues (Phe7, Phe11, and Phe18). This separation is accompanied by simultaneous melting of the second helix. Unfolding is found to be a multistage process involving crossing of three consecutive minima and two barriers at the initial stage. At a molecular level, Phe18 is observed to reorient itself towards other hydrophobic grooves to stabilize the intermediate states. We identify the configuration of the intermediates and correlate the intermediates with those obtained in our previous works. We also give an estimate of the barriers for different transition states and observe the softening of the barriers with increasing DMSO concentration. We show that higher concentration of DMSO tunes the unfolding pathway by destabilizing the third minimum and stabilizing the second one, indicating the development of a solvent modified, less rugged pathway. The prime outcome of this work is the demonstration that mixed solvents can profoundly transform the nature of the energy landscape and induce unfolding via a modified route. A successful application of Kramer's rate equation correlating the free energy simulation results shows faster rate of unfolding with increasing DMSO concentration. This work perhaps presents the first systematic theoretical study of the effect of a chemical denaturant on the microscopic free energy surface and rates of unfolding of HP-36. (C) 2014 AIP Publishing LLC.

Allostery in tRNA Synthetases Elucidated from MD Simulations and Protein Structure Networks

tRNA synthetases (aaRS) are enzymes crucial in the translation of genetic code. The enzyme accylates the acceptor stem of tRNA by the congnate amino acid bound at the active site, when the anti-codon is recognized by the anti-codon site of aaRS. In a typical aaRS, the distance between the anti-codon region and the amino accylation site is approximately 70 Å. We have investigated this allosteric phenomenon at molecular level by MD simulations followed by the analysis of protein structure networks (PSN) of non-covalent interactions. Specifically, we have generated conformational ensembles by performing MD simulations on different liganded states of methionyl tRNA synthetase (MetRS) from Escherichia coli and tryptophenyl tRNA synthetase (TrpRS) from Human. The correlated residues during the MD simulations are identified by cross correlation maps. We have identified the amino acids connecting the correlated residues by the shortest path between the two selected members of the PSN. The frequencies of paths have been evaluated from the MD snapshots[1]. The conformational populations in different liganded states of the protein have been beautifully captured in terms of network parameters such as hubs, cliques and communities[2]. These parameters have been associated with the rigidity and plasticity of the protein conformations and can be associated with free energy landscape. A comparison of allosteric communication in MetRS and TrpRS [3] elucidated in this study highlights diverse means adopted by different enzymes to perform a similar function. The computational method described for these two enzymes can be applied to the investigation of allostery in other systems.