Hot crystals of thermo-responsive particles with temperature dependent diameter in the presence of a temperature gradient.

Structure formation under non-equilibrium steady state conditions is poorly understood. A non-equilibrium steady state can be achieved in a system by maintaining a temperature gradient. A class of cross-linked microgel particles, such as poly-N-iso-propylacrylamide, is reported to increase in size due to the adsorption of water as the temperature decreases. Here, we study thermo-responsive particles with a temperature sensitive diameter in the presence of a temperature gradient, using molecular dynamics simulations with the Langevin thermostat. We find long-ranged structural order using bond order parameters in both cold and hot regions of the system beyond a certain diameter ratio of the cold and hot particles. This is due to an increase in packing and pressure in both regions. Our observations might be useful in understanding ordered structures under extreme conditions of a non-equilibrium steady state.

Conformational fluctuations in the molten globule state of α-lactalbumin.

A molten globule (MG) state is an intermediate state of a protein observed during the unfolding of the native structure. The MG state of the protein is induced by various denaturing agents (like urea), extreme pH, pressure, and heat. Experiments suggest that the MG state of some proteins is functionally relevant even if there is no well-defined tertiary structure. Earlier experimental and theoretical studies show that the MG state of a protein is dynamic in nature, where conformational states are interconverted on nanosecond time scales. These observations lead us to study and compare the conformational fluctuations of the MG state to those of intrinsic disordered proteins (IDPs). We consider a milk protein, α-lactalbumin (aLA), which shows an MG state at low pH upon removal of the calcium (Ca2+) ion. We use the constant pH molecular dynamics (CpHMD) simulation to maintain the protonation state of titratable residues at a low pH during the simulation. We use the dihedral principal component analysis, the density based clustering method, and the machine learning technique to identify the conformational fluctuations. We observe metastable states in the MG state. The residues containing the essential coordinates responsible for metastability belong to a stable helix in the crystal structure, but most of them prefer unstructured or bent conformation in the MG state. These residues control the exposure of the putative binding residues for fatty acids. Thus, the MG state of a protein behaves as an intrinsic disorder protein, although the disorder here is induced by external conditions.

Viscoelastic response of fluid trapped between two dissimilar van der Waals surfaces.

Employing grand canonical Monte-Carlo and molecular dynamics simulations, the viscoelastic response of trapped fluid under molecularly thin confinement by walls having different wall-fluid interaction strengths, is investigated. With increase in slit asymmetry, given by the ratio of interaction strengths of the wall having strong wall-fluid interaction to that of the wall with weak wall-fluid interaction, a crossover in effective density of the fluid film, from rarer (R) to denser (D) than the bulk density is observed. Upon increasing asymmetry further, the dense fluid (F) layers undergo bond-orientational (S) ordering. The variation of viscoelastic relaxation time with scaled asymmetry shows a universal behavior, independent of slit width, with two distinct regimes. Below a critical value of asymmetry, the viscoelastic relaxation time is a slowly varying function of asymmetry, comparable with the structural relaxation time. Beyond the critical asymmetry, on the other hand, viscoelastic response time shows a sharp increase upon increasing asymmetry, deviating markedly from the structural relaxation time. Interestingly the critical asymmetry value is found to correlate with R to D crossover. The microscopic origin of the two-regime universal behavior of viscoelastic response time is found to stem from the fact that below critical asymmetry, the overall viscoelastic behaviour of the slit is dominated by that of the fast relaxing layer close to the weakly attracting surface, while above the critical asymmetry, the relaxation behaviour is guided by the dense fluid layer adjacent to the strongly attracting wall. In vicinity of fluid to ordering transition, the loss and storage moduli merge for low frequencies as in gel-like mechanical behaviour. The storage modulus takes over the loss modulus in the phase co-existence region even before the long ranged order sets in. Our findings bear important implications for fluid transport in hetero-structured geometry in nanotechnology.

A long-range order in a thermally driven system with temperature-dependent interactions.

Aggregation of macro-molecules under an external force is far from being understood. An important driving situation is achieved by temperature difference. Inter-particle interactions in metallic nanoparticles with ligand capping are reported to be sensitive to temperature and the zeta potential of the particles being reduced in the cold region. Such particles form aggregates in the cold region of the system in the presence of temperature difference. Here we study the aggregation of particles in the presence of temperature difference with temperature-dependent interaction parameters using Brownian dynamics simulation. The particle interaction and particle diffusion are considered to be sensitive to the local temperature. We identify a long-range structural order in the cold region of the system using the Avrami equation for crystal growth kinetics. Our observations might be useful in designing ordered structures with macro-molecules under non-equilibrium steady-state conditions.

Length-scales of dynamic heterogeneity in a driven binary colloid.

Here we study the characteristic length scales in an aqueous suspension of a symmetric oppositely charged colloid subjected to a uniform electric field by Brownian dynamics simulations. We consider the in-plane structure in the presence of a sufficiently strong electric field where the like charges in the system form macroscopic lanes. We construct spatial correlation functions characterizing the structural order and that of particles of different mobilities in the plane transverse to the electric field at a given time. We call these functions equal time density correlation functions (ETDCFs). The ETDCFs between particles of different charges, irrespective of mobilities, are the structural ETDCFs, while those between particles of different mobilities are the dynamic ETDCFs. We extract the characteristic length of correlation by fitting the envelopes of the ETDCFs to exponential dependences. We find that the correlation length scales of the structural ETDCFs and the dynamic ETDCFs of the slow particles increase with time in a concurrent manner. This suggests that the clustering of particles tends to build up dynamically correlated slow particles in the plane transverse to the lanes. The ETDCFs can be measured for colloidal systems by directly following the particle motion by video-microscopy and may be useful to understand the patterns out of equilibrium.

Dynamics of water trapped in transition metal oxide-graphene nano-confinement.

Motivated by practical implementation of transition-metal oxide-graphene heterostructures, we use all atom molecular dynamics simulations to study dynamics of water in a nano slit bounded by a transition metal oxide surface, namely, TiO2 termination of SrTiO3, and graphene. The resultant asymmetric, strong confinement produces square ice-like crystallites of water pinned at TiO2 surface and drives enhanced hydrophobicity of graphene via the proximity effect to the hydrophilic TiO2 surface. This importantly brings in dynamic heterogeneity, both in translational and rotational degrees of freedom, due to coupling between the slow relaxing, strongly adsorbed water layer at the hydrophilic oxide surface, and faster relaxation of subsequent water layers. The heterogeneity is signalled in the ruggedness of the effective free energy landscapes. We discuss possible implications of our findings in drug delivery.

In-silico studies on conformational stability of flagellin-receptor complexes.

Flagellin is a protein, responsible for virulent activities of bacteria. The host cell surface receptor protein TLR5 is known to interact with flagellin in order to activate immune response. However, the underlying microscopic details of this immune response are still elusive. In this study, we report on conformational stability of flagellin of two different organisms known as fliC and flaD in bilayer with reference to water. We find that both the flagellin is conformationally more stable in bilayer than in water. We also observe that fliC-TLR5 and flaD-TLR5 complexes are conformationally stable when the extracellular domain of the protein binds to conserved D1 domain of both fliC and flaD, although the binding interface between fliC-TLR5 and flaD-TLR5 is not identical. Our studies suggest that this might lead to differences in coreceptor bindings involved in immune response and thus have potential application in pharmaceutical developments. AbbreviationsA2Aadenosine receptorDPPCdipalmitoyl phosphatidylcholineecdextracellular domainecl2extracellular loop 2eLRRextracellular Leucine rich repeat domainflaDflagellin of Vibrio choleraefliCflagellin of Salmonella typhimuriumHPVhyper-variableMDmolecular dynamicsRMSDroot means squared deviationTIRtoll-interleukin receptorTLR5toll like receptor 5VPAC1vasoactive intestinal peptide receptorCommunicated by Ramaswamy H. Sarma.

Heterogeneity of dynamics in a modulated colloidal liquid.

We study the dynamics of a system of two dimensional colloidal particles subjected to a spatially periodic external potential using Brownian dynamics simulations. We characterize the dynamics in the system by the mean square displacements and the self-van Hove function. The static density plots suggest that system gets into modulated liquid phase in presence of the external potential. We find that diffusion coefficients, obtained from long time mean sqaure displacements, decay exponentially with increasing potential strength. The self-van Hove functions computed from the distribution of particle displacemets in a given time interval show non-gaussian behaviour in directions both parallel and transverse to the external modulation. This suggests heterogeneous dynamics and is supported by particle mobilities and residence times.

Structural and dynamic responses of calcium ion binding loop residues in metallo-proteins.

Conformational changes in bio-molecular systems are fundamental to several biological processes. It is important to study changes in responses of underlying microscopic variables, like dihedral angles as conformational change takes place. We perform all-atom simulations and modelling via Langevin equation to illustrate the changes in structural and dynamic responses of dihedral angles of calcium ion binding residues of different proteins in metal ion free (apo) and bound (holo) states. The equilibrium distributions of dihedral angles in apo- and holo-states represent structural response. Our studies show the presence of dihedrals with multiple peaks (isomeric states) separated by barrier heights is more frequent in apo- than in holo-state. The relaxation time-scale of dihedral fluctuations is found to increase linearly with decreasing barrier height due to more frequent barrier re-crossing events. The slow kinetic response of the dihedrals also contributes to slowing down of macro-scale fluctuations, which may be useful to understand kinetics of various bio-molecular processes.

Allostery in Orai1 binding to calmodulin revealed from conformational thermodynamics.

Here, we study microscopic mechanism of complex formation between Ca2+-bound calmodulin (holoCaM) and Orai1 that regulates Ca2+-dependent inactivation process in eukaryotic cells. We compute conformational thermodynamic changes in holoCaM with respect to complex of Orai1 bound to C-terminal domain of holoCaM using histograms of dihedral angles of the proteins over trajectories from molecular dynamics simulations. Our analysis shows that the N-terminal domain residues L4, T5, Q41, N42, T44 and E67 of holoCaM get destabilized and disordered due to Orai1 binding to C-terminal domain of calmodulin affect the N-terminal domain residues. Among these residues, polar T44, having maximum destabilization and disorder via backbone fluctuations, shows the largest change in solvent exposure. This suggests that N-terminal domain is allosterically regulated via T44 by the binding of Orai1 to the C-terminal domain.

Dynamic signature of ligand binding over a protein surface.

We study the motion of Zn^{2+} in the presence of ubiquitin by all-atom molecular-dynamics simulations. We observe that unlike normal diffusive liquid, metal ions show an exponential tail in the self-van Hove function (self-vHf). Moreover, the metal ions are trapped strongly by acidic residues which form a binding pocket over the protein surface. The exponential tail disappears by mutation of trapping residues, suggesting that the tail appears due to trapped motion of the ions. The mean-squared displacements, however, in all the cases show linear dependence on time. Our model establishes that ligand binding generically results in an exponential tail of self-vHf. The self-vHf may give an approach to find binding pockets over a protein surface.

Transient dynamical responses of a charged binary colloid in an electric field.

In a model system of oppositely charged colloids we study via Brownian dynamics simulation the dynamical response as the system approaches steady states upon application of a constant electric field. The system is known to form patterns of like charges in the transverse plane to the field that are elongated along the field as lanes. We show that an increase in structural heterogeneity leads to non-Gaussian tails in the probability distribution of particle displacements [self van Hove functions (self-vHfs)]. The self-diffusion coefficient depends upon the time of the observations and consequently indicates aging in the system. However, the anomalies in the self-vHfs and diffusion do not appear during the melting of the structures.

Molecular dynamics studies on conformational thermodynamics of Orai1-calmodulin complex.

Molecular understanding of bio-macromolecular binding is a challenging task due to large sizes of the molecules and presence of variety of interactions. Here, we study the molecular mechanism of calmodulin (CaM) binding to Orai1 that regulates Ca2+-dependent inactivation process in eukaryotic cells. Although experimental observations indicate that Orai1 binds to the C-terminal of Ca2+-loaded CaM, it is not decisive if N-domain of CaM interacts with Orai1. We address the issue of interaction of different domains of CaM with Orai1 using conformational thermodynamic changes, computed from histograms of dihedral angles over simulated trajectories of CaM, CaM-binding domain of Orai1 and complexes of CaM with Orai1. The changes for all residues of both C and N terminal domains of CaM upon Orai1 binding are compared. Our analysis shows that Orai1binds to both C-terminal and N-terminal domains of CaM, indicating 1:2 stoichiometry. The Orai1 binding to N-terminal domain of CaM is less stable than that to the C-terminal domain. The binding residues are primarily hydrophobic. These observations are in qualitative agreement to the experiments. The conformational thermodynamic changes thus provide a useful computational tool to provide atomic details of interactions in bio-macromolecular binding.

Spatio-temporal coordination among functional residues in protein.

The microscopic basis of communication among the functional sites in bio-macromolecules is a fundamental challenge in uncovering their functions. We study the communication through temporal cross-correlation among the binding sites. We illustrate via Molecular Dynamics simulations the properties of the temporal cross-correlation between the dihedrals of a small protein, ubiquitin which participates in protein degradation in eukaryotes. We show that the dihedral angles of the residues possess non-trivial temporal cross-correlations with asymmetry with respect to exchange of the dihedrals, having peaks at low frequencies with time scales in nano-seconds and an algebraic tail with a universal exponent for large frequencies. We show the existence of path for temporally correlated degrees of freedom among the functional residues. We explain the qualitative features of the cross-correlations through a general mathematical model. The generality of our analysis suggests that temporal cross-correlation functions may provide convenient theoretical framework to understand bio-molecular functions on microscopic basis.

Static and dynamic properties of two-dimensional Coulomb clusters.

We study the temperature dependence of static and dynamic responses of Coulomb interacting particles in two-dimensional confinements across the crossover from solid- to liquid-like behaviors. While static correlations that investigate the translational and bond orientational order in the confinements show the footprints of hexatic-like phase at low temperatures, dynamics of the particles slow down considerably in this phase, reminiscent of a supercooled liquid. Using density correlations, we probe long-lived heterogeneities arising from the interplay of the irregularity in the confinement and long-range Coulomb interactions. The relaxation at multiple time scales show stretched-exponential decay of spatial correlations in irregular traps. Temperature dependence of characteristic time scales, depicting the structural relaxation of the system, show striking similarities with those observed for the glassy systems, indicating that some of the key signatures of supercooled liquids emerge in confinements with lower spatial symmetries.

Conformational thermodynamics guided structural reconstruction of biomolecular fragments.

Computational prediction of structure for macromolecular fragments is a formidable challenge. Here we show that the differences in conformational thermodynamics, computed using the equilibrium distribution of dihedral angles from molecular dynamics simulation, can identify the better model for the missing residues in the metal ion free (apo) skeletal muscle Troponin C (TnC). We use the model to understand Troponin I interaction with calcium (Ca(2+)) ion bound TnC. Our method to compare conformational thermodynamics between different models can be easily generalized to any macromolecule to understand the structure and function even if experimental structures are not resolved.

Quantum Chemical Studies on Stability and Chemical Activities in Calcium Ion Bound Calmodulin Loops.

Quantum chemical (QC) calculations for macromolecules require truncation of the molecule, highlighting the portion of interest due to heavy computation cost. As a result, an estimation of the effects of truncation is important to interpret the energy spectrum of such calculations. We perform density functional theory based QC calculations on calcium ion bound EF-hand loops of Calmodulin isolated from the crystal structure in an implicit solvent. We find that the terminal contributions of neutral capping are negligible across the entire ground-state energy spectrum. The coordination energy range and the nature of hybridization of the coordination state molecular orbitals remain qualitatively similar across these loops. While the HOMO and LUMO of loops in the N-terminal domain are dominated by the acidic aspartates, and the polar/hydrophobic residues, respectively, these levels of the C-terminal domain loops show strong localized electron density on the phenyl rings of the tyrosines. The Fukui index calculation identifies the hydroxyl oxygen in the phenyl ring of Y99 as a potent nucleophile. Our analysis indicates a general way of interpreting the electronic energy spectra to understand stability and functions of large biomolecules where the truncation of the molecule and, hence, the terminal capping effects are inevitable.

A microscopic insight from conformational thermodynamics to functional ligand binding in proteins.

We show that the thermodynamics of metal ion-induced conformational changes aid to understand the functions of protein complexes. This is illustrated in the case of a metalloprotein, alpha-lactalbumin (aLA), a divalent metal ion binding protein. We use the histograms of dihedral angles of the protein, generated from all-atom molecular dynamics simulations, to calculate conformational thermodynamics. The thermodynamically destabilized and disordered residues in different conformational states of a protein are proposed to serve as binding sites for ligands. This is tested for ß-1,4-galactosyltransferase (ß4GalT) binding to the Ca(2+)-aLA complex, in which the binding residues are known. Among the binding residues, the C-terminal residues like aspartate (D) 116, glutamine (Q) 117, tryptophan (W) 118 and leucine (L) 119 are destabilized and disordered and can dock ß4GalT onto Ca(2+)-aLA. No such thermodynamically favourable binding residues can be identified in the case of the Mg(2+)-aLA complex. We apply similar analysis to oleic acid binding and predict that the Ca(2+)-aLA complex can bind to oleic acid through the basic histidine (H) 32 of the A2 helix and the hydrophobic residues, namely, isoleucine (I) 59, W60 and I95, of the interfacial cleft. However, the number of destabilized and disordered residues in Mg(2+)-aLA are few, and hence, the oleic acid binding to Mg(2+)-bound aLA is less stable than that to the Ca(2+)-aLA complex. Our analysis can be generalized to understand the functionality of other ligand bound proteins.

Cross-over between central and non-central conservative effective forces in a modulated colloidal fluid.

We study by Monte Carlo simulations the effective forces between two particles dispersed in a two-dimensional colloidal fluid, modulated in one direction by a spatially periodic external potential. When the modulation strength exceeds the strength of interaction between the dispersed and dispersing particles, the anisotropic effective forces, show cross-over between central and non-central nature, although the effective forces remain conservative. The non-central nature of the effective forces depends on the orientation of the separation vector between the dispersed particles with respect to the modulation direction.

Microscopic mechanisms of confinement-induced slow solvation.

Several studies show that the dynamics of solvent molecules around a solute slows down in a nanoscale confined geometry compared to the bulk condition. Here we perform numerical simulations to investigate the microscopic mechanisms of such slowing down. We show a substantial slowing down of solvation dynamics around a solute in strong solvophilic confinements due to suppression of fluid diffusion in the presence of solvophilic walls, along with restricted solvent dynamics due to geometrical constraints. The solvation in strong solvophobic confinements becomes slower than the same in the bulk as well, but not as significantly as in the solvophilic case. This is due to the competition between restriction in solvent dynamics and faster in-plane solvent diffusion. We place our findings in perspective of various solvation dominated chemical processes in nanoconfined geometry.