Suman Chakrabarty | National Chemical Laboratory (NCL) (original) (raw)
Papers by Suman Chakrabarty
The pathological forms of prions are known to be a result of misfolding, oligomerization, and agg... more The pathological forms of prions are known to be a result of misfolding, oligomerization, and aggregation of the cellular prion. While the mechanism of misfolding and aggregation in prions has been widely studied using both experimental and computational tools, the structural and energetic characterization of the dimer form have not garnered as much attention. On one hand dimerization can be the first step toward a nucleation-like pathway to aggregation, whereas on the other hand it may also increase the conformational stability preventing self-aggregation. In this work, we have used extensive all-atom replica exchange molecular dynamics simulations of both monomer and dimer forms of a mouse prion protein to understand the structural, dynamic, and thermodynamic stability of dimeric prion as compared to the monomeric form. We show that prion proteins can dimerize spontaneously being stabilized by hydrophobic interactions as well as intermolecular hydrogen bonding and salt bridge formation. We have computed the conformational free energy landscapes for both monomer and dimer forms to compare the thermodynamic stability and misfolding pathways. We observe large conformational heterogeneity among the various modes of interactions between the monomers and the strong intermolecular interactions may lead to as high as 20% β-content. The hydrophobic regions in helix-2, surrounding coil regions, terminal regions along with the natively present β-sheet region appear to actively participate in prion−prion intermolecular interactions. Dimerization seems to considerably suppress the inherent dynamic instability observed in monomeric prions, particularly because the regions of structural frustration constitute the dimer interface. Further, we demonstrate an interesting reversible coupling between the Q160-G131 interaction (which leads to inhibition of β-sheet extension) and the G131-V161 H-bond formation.
The properties of water in a confined environment can be drastically different than the bulk wate... more The properties of water in a confined environment can be drastically different than the bulk water. In a confined system, e.g. the interior of a reverse micelle, there exist at least two distinct regions namely ''interfacial water'' characterized by markedly slower dynamics, and ''core water'', which may resemble bulk water for a larger size of the water pool. Using atomistic molecular dynamics simulations, we systematically investigate the presence of bulk-like water in AOT reverse micelles (RMs) with varying size given by w 0 = [H 2 O]/[AOT] = 10, 15 and 20. In order to understand the effect of the negatively charged interface of the RM, we have performed control studies for the model systems of water-in-oil (isooctane) nanodroplets with the same size of the water pool as the RM systems. In order to quantify the deviations from bulk-like behavior, we have used three kinds of structural order parameters, namely (i) number density to probe the local translational ordering, (ii) tetrahedral order and hydrogen bond distribution to probe the local orientational ordering, and (iii) dipolar orientation relative to the radial vector to capture the global orientational ordering of the water dipoles. We demonstrate that the size of the ''core water'' region that resembles bulk water decreases in the above order, i.e. orientational order parameters of water molecules are perturbed by the charged interface to a larger length scale as compared to the translational order. We have compared the translational and rotational dynamics of the water molecules for the interfacial and core regions to find that the slower dynamics persists even for the core water for the size range that we have studied although to a much lesser extent as compared to the interfacial water. Moreover, we demonstrate that the hydrophobic interface in the water-in-oil nanodroplets has a much weaker effect on the structure and dynamics of the confined water molecules as compared to the anionic RMs. Thus, the major contribution towards the structural ordering and slow dynamics of water in a charged RM system would originate from the strong electrostatic and hydrogen bonded interactions with the interface, and not due to the spatial confinement effect.
We present a comparative study of the glass forming ability of binary systems with varying compos... more We present a comparative study of the glass forming ability of binary systems with varying composition, where the systems have similar global crystalline structure (CsCl+fcc). Biased Monte Carlo simulations using umbrella sampling technique show that the free energy cost to create a CsCl nucleus increases as the composition of the smaller particles is decreased. We find that systems with comparatively lower free energy cost to form CsCl nucleus exhibit more pronounced pre-crystalline demixing near the liquid/crystal interface. The structural frustration between the CsCl and fcc crystal demands this demixing. We show that closer to the equimolar mixture, the entropic penalty for demixing is lower and a glass forming system may crystallize when seeded with a nucleus. This entropic penalty as a function of composition shows a non-monotonic behaviour with a maximum at a composition similar to the well known Kob-Anderson (KA) model. Although the KA model shows the maximum entropic penalty and thus maximum frustration against CsCl formation, it also shows a strong tendency towards crystallization into fcc lattice of the larger "A" particles which can be explained from the study of the energetics. Thus for systems closer to the equimolar mixture although it is the requirement of demixing which provides their stability against crystallization, for KA model it is not demixing but slow dynamics and the presence of the "B" particles make it a good glass former. The locally favoured structure around "B" particles is quite similar to the CsCl structure and the incompatibility of CsCl and fcc hinders the fcc structure growth in the KA model. Although the glass forming binary systems studied here are quite similar, differing only in composition, we find that their glass forming ability cannot be attributed to a single phenomenon. Published by AIP Publishing. [http://dx.
It has been suggested that the structure and thermodynamics of the water molecules in the hydrati... more It has been suggested that the structure and thermodynamics of the water molecules in the hydration layer of simple hydrophobic solutes undergo an order−disorder transition around a nanometer length-scale of the solute size. Using extensive atomistic molecular dynamics (MD) and replica exchange molecular dynamics (REMD) simulation studies, we have probed this order−disorder transition around model hydrophobic solutes of varying size and shape (spherical, planar, and linear), as well as flexible hydrophobic homopolymer chains (n-alkanes), where the conformational fluctuations are likely to create both spatial and temporal heterogeneity on the solvent accessible surface. We have explored the structural response of the water molecules in the hydration shell due to the local variations of the length-scale (or curvature) upon hydrophobic collapse and/or local conformational changes of these polymers. We have shown that the tetrahedral order of the water molecules in the hydration shell is practically independent of the polymer size in the extended state of the polymer due to the availability of a subnanometer cross-sectional length-scale, allowing the water molecules to form hydrogen bonds around the polymer chain. Beyond a certain length of the polymer chains, the collapsed states (associated with larger solute length-scale) start to induce disorder in the surface water molecules. We demonstrate that the local structure (both local number density and tetrahedral order) of the hydration layer is dynamically coupled to the local topology of the polymer. Thus, we envisage that in a flexible (bio)polymer, the hydration shell properties will be sensitive to the local conformational state of the molecule (both spatially and temporally), and the overall observed water structure and dynamics will be dependent on the topological/chemical heterogeneity, and the timescale of fluctuations in the local curvature (length-scale) of the solvent accessible surface. Moreover, we have demonstrated the direct coupling between the local density fluctuations of water and the local hydrophobic collapse of the polymer. For the extended state of the polymer, the local solvent density fluctuation is practically independent of the solute coordinate (lengthscale), and the hydrophobic collapse of the polymer is prompted by a "local dewetting" process induced by these fluctuations.
Glycopolypeptide-based polymersomes have promising applications as vehicles for targeted drug del... more Glycopolypeptide-based polymersomes have promising applications as vehicles for targeted drug delivery because they are capable of encapsulating different pharmaceuticals of diverse polarity as well as interacting with specific cell surfaces due to their hollow structural morphology and bioactive surfaces. We have synthesized glycopolypeptide-b-poly(propylene oxide) by ROP of glyco-N-carboxyanhydride (NCA) using the hydrophobic amine-terminated poly(propylene oxide) (PPO) as the initiator. This block copolymer is composed of an FDA-approved PPO hydrophobic block in conjugation with hydrophilic glycopolypeptides which are expected to be biocompatible. We demonstrate the formation of glycopolypeptide-based polymersomes from the self-assembly of glycopolypeptide-b-poly(propylene oxide) in which the presence of an ordered helical glycopolypeptide segment is required for their self-assembly into spherical nanoscale (∼50 nm) polymersomes. The polymersomes were characterized in detail using a variety of techniques such as TEM, AFM, cryo-SEM, and light-scattering measurements. As a model for drugs, both hydrophobic (RBOE) and hydrophilic (calcein) dyes have been incorporated within the polymersomes from solution. To substantiate the simultaneous entrapment of the two dyes, spectrally resolved fluorescence microscopy was performed on the glycopeptide polymersomes cast on a glass substrate. We show that it is possible to visualize individual nanoscale polymersomes and effectively probe the dyes’ colocalization and energy-transfer behaviors therein as well as investigate the variation in dual-dye encapsulation over a large number of single polymersomes. Finally, we show that the galactose moieties present on the surface can specifically recognize lectin RCA120, which reveals that the polymersomes’ surface is indeed biologically active.
J. Chem. Phys., 2013
In this work we explore the interplay between crystallization and glass transition in different b... more In this work we explore the interplay between crystallization and glass transition in different binary mixtures by changing their inter-species interaction length and also the composition. We find that only those systems which form bcc crystal in the equimolar mixture and whose global structure for larger x A (x A = 0.6, where x A is the mole fraction of the bigger particles) is a mixed fcc + bcc phase, do not crystallize at this higher composition. However, the systems whose equimolar structure is a variant of fcc (NaCl type crystal) and whose global structure at larger x A is a mixed NaCl + fcc phase, crystallize easily to this mixed structure. We find that the stability against crystallization of this “bcc zone” is due to the frustration between the locally preferred structure (LPS) and the mixed bcc + fcc crystal. Our study suggests that when the global structure is a mixed crystal where a single species contributes to both the crystal forms and where the two crystal forms have large difference in some order parameter related to that species then this induces frustration between the LPS and the global structure. This frustration makes the systems good glass former. When x A is further increased (0.70 ⩽ x A < 0.90) the systems show a tendency towards mixed fcc crystal formation. However, the “bcc zone” even for this higher composition is found to be sitting at the bottom of a V shaped phase diagram formed by two different variants of the fcc crystal structure, leading to its stability against crystallization.
J. Phys. Chem. B, 2013
Understanding the nature of the free-energy surfaces for phosphate hydrolysis is a prerequisite f... more Understanding the nature of the free-energy surfaces for phosphate hydrolysis is a prerequisite for understanding the corresponding key chemical reactions in biology. Here, the challenge has been to move to careful ab initio QM/MM (QM(ai)/MM) free-energy calculations, where obtaining converging results is very demanding and computationally expensive. This work describes such calculations, focusing on the free-energy surface for the hydrolysis of phosphate monoesters, paying special attention to the comparison between the one water (1W) and two water (2W) paths for the proton-transfer (PT) step. This issue has been explored before by energy minimization with implicit solvent models and by nonsystematic QM/MM energy minimization, as well as by nonsystematic free-energy mapping. However, no study has provided the needed reliable 2D (3D) surfaces that are necessary for reaching concrete conclusions. Here we report a systematic evaluation of the 2D (3D) free-energy maps for several relevant systems, comparing the results of QM(ai)/MM and QM(ai)/implicit solvent surfaces, and provide an advanced description of the relevant energetics. It is found that the 1W path for the hydrolysis of the methyl diphosphate (MDP) trianion is 6–9 kcal/mol higher than that the 2W path. This difference becomes slightly larger in the presence of the Mg2+ ion because this ion reduces the pKa of the conjugated acid form of the phosphate oxygen that accepts the proton. Interestingly, the BLYP approach (which has been used extensively in some studies) gives a much smaller difference between the 1W and 2W activation barriers. At any rate, it is worth pointing out that the 2W transition state for the PT is not much higher that the common plateau that serves as the starting point of both the 1W and 2W PT paths. Thus, the calculated catalytic effects of proteins based on the 2W PT mechanistic model are not expected to be different from the catalytic effects predicted using the 1W PT mechanistic model, which was calibrated on the observed barrier in solution and in which the TS charge distribution was similar to the that of the plateau (as was done in all of our previous EVB studies).
PROTEINS: Structure, Function, and Bioinformatics, 2013
Consistent description of the effect of internal water in proteins has been a major challenge for... more Consistent description of the effect of internal water in proteins has been a major challenge for both simulation and experimental studies. Describing this effect has been particularly important and elusive in cases of charges in protein interiors. Here, we present a new microscopic method that provides an efficient way for simulating the energetics of water insertion. Instead of performing explicit Monte Carlo (MC) moves on the insertion process, which generally involves an enormous number of rejected attempts, our method is based on generating trial configurations with excess amount of internal water, estimating the relevant free energy by the linear response approximation, and then using a postprocessing MC treatment to filter out a limited number of configurations from a large possible set. Our approach is validated on particularly challenging test cases including the pKa of the V66D mutation in Staphylococcal nuclease, Glu286 in cytochrome c oxidase (CcO) and the energetics of a protonated water molecule in the D channel of CcO. The new postprocessing method allows us to reproduce the relevant energetics of highly unstable charges in protein interiors using fully microscopic calculations and provides a substantial improvement over regular microscopic free energy estimates. This advance established the effectiveness of our water insertion strategy in challenging cases that have not been addressed successfully by other microscopic methods. Furthermore, our study provides a new exciting view on the crucial effect of water penetration in key biological systems as well as a new view on the nature of the dielectric in protein interiors.
Proc. Natl. Acad. Sci. U.S.A., 2012
Understanding the detailed mechanism of the activation of voltage-gated ion channels has been a p... more Understanding the detailed mechanism of the activation of voltage-gated ion channels has been a problem of great current interest. Reliable molecular simulations of voltage effects present a major challenge because meaningful converging microscopic simulations are not yet available and macroscopic treatments involve major uncertainties regarding the dielectric constant used and other key features. The current work has overcome some of the above challenges by using our recently developed coarse-grained (CG) model in simulating the activation of the Kv1.2 channel. The CG model has allowed us to explore problems that cannot be addressed at present by fully microscopic simulations, while providing insights on some features that are not usually considered in continuum models, including the distribution of the electrolytes between the membrane and the electrodes during the activation process and thus the nature of the gating current. Furthermore, the clear connection to microscopic descriptions combined with the power of CG modeling offers a powerful tool for exploring the energy balance between the protein conformational energy and the interaction with the external potential in voltage-activated channels. Our simulations have reproduced the observed experimental trend of the gating charge and, most significantly, the correct trend in the free energies, where the closed channel is more stable at negative potential and the open channel is more stable at positive potential. Moreover, we provide a unique view of the activation landscape and the time dependence of the activation process.
The relationship between the membrane voltage and the gating of voltage activated ion channels an... more The relationship between the membrane voltage and the gating of voltage activated ion channels and other systems have been a problem of great current interest. Unfortunately, reliable molecular simulations of external voltage effects present a major challenge, since meaningful converging microscopic simulations are not yet available and macroscopic treatments involve major uncertainties in terms of the dielectric used and other key features. This work extends our coarse grained (CG) model to simulations of membrane/protein systems under external potential. Special attention has been devoted to a consistent modeling of the effect of external potential due to the electrodes, emphasizing semimacroscopic description of the electrolytes in the solution regions between the membranes and the electrodes, as well as the coupling between the combined potential from the electrodes and electrolytes, and the protein ionization states. We also provide a clear connection to microscopic treatment of the electrolytes and thus can explore possible conceptual problems that are hard to resolve by other current approaches. For example, we obtain a clear description of the charge distribution in the entire electrolyte system, including near the electrodes in membrane/electrodes systems (where continuum models do not seem to provide the relevant results). Furthermore, the present treatment provides an insight on the distribution of the electrolyte charges before and after equilibration across the membrane, and thus on the nature of the gating charge. The different aspects of the model have been carefully validated by considering problems ranging for the simple Debye–Huckel, Gouy–Chapman models to the evaluation of the electrolyte distribution between two electrodes, as well as the effect of extending the simulation system by periodic replicas. Overall the clear connection to microscopic descriptions combined with the power of the CG modeling seems to offer a powerful tool for exploring the balance between the protein conformational energy and the interaction with the external potential in voltage activated channels. With this in mind we present a preliminary study of the gating charge in the voltage activated Kv1.2 channel, using the actual change in the electrolyte charge distribution rather than the conventional macroscopic estimate. We also discuss other special features of the model, which include the ability to capture the effect of changes in the protonation states of the protein residues during the open to close voltage induced transition. This article is part of a Special Issue entitled: Membrane protein structure and function.
Cytochrome c oxidase (CytcO) is a membrane-bound enzyme, which catalyzes the reduction of di-oxyg... more Cytochrome c oxidase (CytcO) is a membrane-bound enzyme, which catalyzes the reduction of di-oxygen to water and uses a major part of the free energy released in this reaction to pump protons across the membrane. In the Rhodobacter sphaeroides aa3 CytcO all protons that are pumped across the membrane, as well as one half of the protons that are used for O2 reduction, are transferred through one specific intraprotein proton pathway, which holds a highly conserved Glu286 residue. Key questions that need to be addressed in order to understand the function of CytcO at a molecular level are related to the timing of proton transfers from Glu286 to a “pump site” and the catalytic site, respectively. Here, we have investigated the temperature dependencies of the H/D kinetic-isotope effects of intramolecular proton-transfer reactions in the wild-type CytcO as well as in two structural CytcO variants, one in which proton uptake from solution is delayed and one in which proton pumping is uncoupled from O2 reduction. These processes were studied for two specific reaction steps linked to transmembrane proton pumping, one that involves only proton transfer (peroxy–ferryl, P → F, transition) and one in which the same sequence of proton transfers is also linked to electron transfer to the catalytic site (ferryl–oxidized, F → O, transition). An analysis of these reactions in the framework of theory indicates that that the simpler, P → F reaction is rate-limited by proton transfer from Glu286 to the catalytic site. When the same proton-transfer events are also linked to electron transfer to the catalytic site (F → O), the proton-transfer reactions might well be gated by a protein structural change, which presumably ensures that the proton-pumping stoichiometry is maintained also in the presence of a transmembrane electrochemical gradient. Furthermore, the present study indicates that a careful analysis of the temperature dependence of the isotope effect should help us in gaining mechanistic insights about CytcO.
Gaining detailed understanding of the energetics of the proton-pumping process in cytochrome c ox... more Gaining detailed understanding of the energetics of the proton-pumping process in cytochrome c oxidase (CcO) is a problem of great current interest. Despite promising mechanistic proposals, so far, a physically consistent model that would reproduce all the relevant barriers needed to create a working pump has not been presented. In addition, there are major problems in elucidating the origin of key mutational effects and in understanding the nature of the apparent pKa values associated with the pH dependencies of specific proton transfer (PT) reactions in CcO. This work takes a key step in resolving the above problems, by considering mutations, such as the Asn139Asp replacement, that blocks proton pumping without affecting PT to the catalytic site. We first introduce a formulation that makes it possible to relate the apparent pKa of Glu286 to different conformational states of this residue. We then use the new formulation along with the calculated pKa values of Glu286 at these different conformations to reproduce the experimentally observed apparent pKa of the residue. Next, we take the X-ray structures of the native and Asn139Asp mutant of the Paracoccus denitrificans CcO (N131D in this system) and reproduce for the first time the change in the primary PT pathways (and other key features) based on simulations that start with the observed structural changes. We also consider the competition between proton transport to the catalytic site and the pump site, as a function of the bulk pH, as well as the H/D isotope effect, and use this information to explore the relative height of the two barriers. The paper emphasizes the crucial role of energy-based considerations that include the PT process, and the delicate control of PT in CcO.
We find that at a mole fraction 0.05 of DMSO (x_DMSO = 0.05) in aqueous solution, a linear hydroc... more We find that at a mole fraction 0.05 of DMSO (x_DMSO = 0.05) in aqueous solution, a linear hydrocarbon chain of intermediate length (n = 30–40) adopts the most stable collapsed conformation. In pure water, the same chain exhibits an intermittent oscillation between the collapsed and the extended coiled conformations. Even when the mole fraction of DMSO in the bulk is 0.05, the concentration of the same in the first hydration layer around the hydrocarbon of chain length 30 (n = 30) is as large as 17%. Formation of such hydrophobic environment around the hydrocarbon chain may be viewed as the reason for the collapsed conformation gaining additional stability. We find a second anomalous behavior to emerge near x_DMSO = 0.15, due to a chain-like aggregation of the methyl groups of DMSO in water that lowers the relative concentration of the DMSO molecules in the hydration layer. We further find that as the concentration of DMSO is gradually increased, it progressively attains the extended coiled structure as the stable conformation. Although Flory–Huggins theory (for binary mixture solvent) fails to predict the anomaly at x_DMSO = 0.05, it seems to capture the essence of the anomaly at 0.15.
Langevin dynamics simulation studies have been employed to calculate the temperature dependent fr... more 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.
We demonstrate a chain length dependent crossover in the structural properties of linear hydrocar... more We demonstrate a chain length dependent crossover in the structural properties of linear hydrocarbon (n-alkane) chains using detailed atomistic simulations in explicit water. We identify a number of exotic structures of the polymer chain through energy minimization of representative snapshots collected from molecular dynamics trajectory. While the collapsed state is ring-like (circular) for small chains (CnH2n+2; n <= 20) and spherical for very long ones (n = 100), we find the emergence of ordered helical structures at intermediate lengths (n similar to 40). We find different types of disordered helices and toroid-like structures at n = 60. We also report a sharp transition in the stability of the collapsed state as a function of the chain length through relevant free energy calculations. While the collapsed state is only marginally metastable for C20H42, a clear bistable free energy surface emerges only when the chain is about 30 monomers long. For n = 30, the polymer exhibits an intermittent oscillation between the collapsed and the coil structures, characteristic of two stable states separated by a small barrier.
We study the nucleation of liquid phase from a supersaturated vapor in two dimensions, where the ... more We study the nucleation of liquid phase from a supersaturated vapor in two dimensions, where the particles interact through Lennard-Jones (LJ) pairwise potential. Using different Monte Carlo simulation methods, we calculate the free energy barrier for nucleation, the line tension, and bulk densities of equilibrium liquid and vapor phases, and also investigate the size and shape of the critical nucleus. The study is carried out at an intermediate level of supersaturation (away from the spinodal limit). In two dimensions, a surprisingly large cutoff (rc>=7.0sigma, sigma is the diameter of LJ particles) in the truncation of the LJ potential is required to obtain converged results. A lower cutoff [typically 2.5sigma which is generally sufficient in three dimensional (3D) studies] leads to a substantial error in the values of the line tension, nucleation barrier, and characteristics of the critical cluster. It is found that in two dimensions, the classical nucleation theory (CNT) fails to provide a reliable estimate of the free energy barrier. It underestimates the barrier by as much as 50% at the saturation ratio S=1.1 (defined as S=P/PC, where PC is the coexistence pressure) and at the reduced temperature T*=0.427 (defined as T*=kBT/epsilon, where epsilon is the depth of the potential well). Interestingly, CNT has been found to overestimate the nucleation free energy barrier in 3D systems near the triple point. In fact, the agreement of the calculated nucleation rate with CNT is much worse in two dimensions than in three dimensions. The reason for the inadequacy of the CNT can be attributed to the noncircular nature of the critical clusters. Although the shape becomes increasingly circular and the clusters become more compact with increase in cutoff radius, an appreciable noncircular nature remains even without any cutoff to make the simple CNT inaccurate.
We have constructed a multidimensional free energy surface of nucleation of the liquid phase from... more We have constructed a multidimensional free energy surface of nucleation of the liquid phase from the parent supercooled and supersaturated vapor phase near the gas-liquid spinodal. In particular, we remove the Becker-Doring constraint of having only one growing cluster in the system. Close to the spinodal, the free energy, as a function of the size of the largest cluster, develops surprisingly a minimum at a subcritical cluster size. It is this minimum at intermediate size that is found to be responsible for the barrier towards further growth of the nucleus at large supersaturation. An alternative free energy pathway involving the participation of many subcritical clusters is found near the spinodal where the growth of the nucleus is promoted by a coalescence mechanism. The growth of the stable phase becomes collective and spatially diffuse, and the significance of a “critical nucleus” is lost for deeper quenches.
Orientational dynamics in a liquid crystalline system near the isotropic-nematic (IN) phase trans... more Orientational dynamics in a liquid crystalline system near the isotropic-nematic (IN) phase transition is studied using molecular dynamics simulations of the well-known Lebwohl-Lasher model. As the IN transition temperature is approached from the isotropic side, we find that the decay of the orientational time correlation functions (OTCF) slows down noticeably, giving rise to a power law decay at intermediate time scales. The angular velocity time correlation function also exhibits a rather pronounced power law decay near the IN boundary. In the mean squared angular displacement at comparable time scales, we observe the emergence of a subdiffusive regime which is followed by a superdiffusive regime before the onset of the long-time diffusive behavior. We observe signature of dynamical heterogeneity through pronounced non-Gaussian behavior in orientational motion particularly at lower temperatures. This behavior closely resembles what is usually observed in supercooled liquids. We obtain the free energy as a function of orientational order parameter by the use of the transition matrix Monte Carlo method. The free energy surface is flat for the system considered here and the barrier between isotropic and nematic phases is vanishingly small for this weakly first-order phase transition, hence allowing large scale, collective, and correlated orientational density fluctuations. This might be responsible for the observed power law decay of the OTCFs.
We observe a surprisingly general power law decay at short to intermediate times in orientational... more We observe a surprisingly general power law decay at short to intermediate times in orientational relaxation in a variety of model systems (both calamitic and discotic, and also lattice) for thermotropic liquid crystals. As all these systems transit across the isotropic-nematic phase boundary, two power law relaxation regimes, separated by a plateau, emerge, giving rise to a steplike feature (well known in glassy liquids) in the single-particle second-rank orientational time correlation function. In contrast to its probable dynamical origin in supercooled liquids, we show that the power law here can originate from the thermodynamic fluctuations of the orientational order parameter, driven by the rapid growth in the second-rank orientational correlation length.
The pathological forms of prions are known to be a result of misfolding, oligomerization, and agg... more The pathological forms of prions are known to be a result of misfolding, oligomerization, and aggregation of the cellular prion. While the mechanism of misfolding and aggregation in prions has been widely studied using both experimental and computational tools, the structural and energetic characterization of the dimer form have not garnered as much attention. On one hand dimerization can be the first step toward a nucleation-like pathway to aggregation, whereas on the other hand it may also increase the conformational stability preventing self-aggregation. In this work, we have used extensive all-atom replica exchange molecular dynamics simulations of both monomer and dimer forms of a mouse prion protein to understand the structural, dynamic, and thermodynamic stability of dimeric prion as compared to the monomeric form. We show that prion proteins can dimerize spontaneously being stabilized by hydrophobic interactions as well as intermolecular hydrogen bonding and salt bridge formation. We have computed the conformational free energy landscapes for both monomer and dimer forms to compare the thermodynamic stability and misfolding pathways. We observe large conformational heterogeneity among the various modes of interactions between the monomers and the strong intermolecular interactions may lead to as high as 20% β-content. The hydrophobic regions in helix-2, surrounding coil regions, terminal regions along with the natively present β-sheet region appear to actively participate in prion−prion intermolecular interactions. Dimerization seems to considerably suppress the inherent dynamic instability observed in monomeric prions, particularly because the regions of structural frustration constitute the dimer interface. Further, we demonstrate an interesting reversible coupling between the Q160-G131 interaction (which leads to inhibition of β-sheet extension) and the G131-V161 H-bond formation.
The properties of water in a confined environment can be drastically different than the bulk wate... more The properties of water in a confined environment can be drastically different than the bulk water. In a confined system, e.g. the interior of a reverse micelle, there exist at least two distinct regions namely ''interfacial water'' characterized by markedly slower dynamics, and ''core water'', which may resemble bulk water for a larger size of the water pool. Using atomistic molecular dynamics simulations, we systematically investigate the presence of bulk-like water in AOT reverse micelles (RMs) with varying size given by w 0 = [H 2 O]/[AOT] = 10, 15 and 20. In order to understand the effect of the negatively charged interface of the RM, we have performed control studies for the model systems of water-in-oil (isooctane) nanodroplets with the same size of the water pool as the RM systems. In order to quantify the deviations from bulk-like behavior, we have used three kinds of structural order parameters, namely (i) number density to probe the local translational ordering, (ii) tetrahedral order and hydrogen bond distribution to probe the local orientational ordering, and (iii) dipolar orientation relative to the radial vector to capture the global orientational ordering of the water dipoles. We demonstrate that the size of the ''core water'' region that resembles bulk water decreases in the above order, i.e. orientational order parameters of water molecules are perturbed by the charged interface to a larger length scale as compared to the translational order. We have compared the translational and rotational dynamics of the water molecules for the interfacial and core regions to find that the slower dynamics persists even for the core water for the size range that we have studied although to a much lesser extent as compared to the interfacial water. Moreover, we demonstrate that the hydrophobic interface in the water-in-oil nanodroplets has a much weaker effect on the structure and dynamics of the confined water molecules as compared to the anionic RMs. Thus, the major contribution towards the structural ordering and slow dynamics of water in a charged RM system would originate from the strong electrostatic and hydrogen bonded interactions with the interface, and not due to the spatial confinement effect.
We present a comparative study of the glass forming ability of binary systems with varying compos... more We present a comparative study of the glass forming ability of binary systems with varying composition, where the systems have similar global crystalline structure (CsCl+fcc). Biased Monte Carlo simulations using umbrella sampling technique show that the free energy cost to create a CsCl nucleus increases as the composition of the smaller particles is decreased. We find that systems with comparatively lower free energy cost to form CsCl nucleus exhibit more pronounced pre-crystalline demixing near the liquid/crystal interface. The structural frustration between the CsCl and fcc crystal demands this demixing. We show that closer to the equimolar mixture, the entropic penalty for demixing is lower and a glass forming system may crystallize when seeded with a nucleus. This entropic penalty as a function of composition shows a non-monotonic behaviour with a maximum at a composition similar to the well known Kob-Anderson (KA) model. Although the KA model shows the maximum entropic penalty and thus maximum frustration against CsCl formation, it also shows a strong tendency towards crystallization into fcc lattice of the larger "A" particles which can be explained from the study of the energetics. Thus for systems closer to the equimolar mixture although it is the requirement of demixing which provides their stability against crystallization, for KA model it is not demixing but slow dynamics and the presence of the "B" particles make it a good glass former. The locally favoured structure around "B" particles is quite similar to the CsCl structure and the incompatibility of CsCl and fcc hinders the fcc structure growth in the KA model. Although the glass forming binary systems studied here are quite similar, differing only in composition, we find that their glass forming ability cannot be attributed to a single phenomenon. Published by AIP Publishing. [http://dx.
It has been suggested that the structure and thermodynamics of the water molecules in the hydrati... more It has been suggested that the structure and thermodynamics of the water molecules in the hydration layer of simple hydrophobic solutes undergo an order−disorder transition around a nanometer length-scale of the solute size. Using extensive atomistic molecular dynamics (MD) and replica exchange molecular dynamics (REMD) simulation studies, we have probed this order−disorder transition around model hydrophobic solutes of varying size and shape (spherical, planar, and linear), as well as flexible hydrophobic homopolymer chains (n-alkanes), where the conformational fluctuations are likely to create both spatial and temporal heterogeneity on the solvent accessible surface. We have explored the structural response of the water molecules in the hydration shell due to the local variations of the length-scale (or curvature) upon hydrophobic collapse and/or local conformational changes of these polymers. We have shown that the tetrahedral order of the water molecules in the hydration shell is practically independent of the polymer size in the extended state of the polymer due to the availability of a subnanometer cross-sectional length-scale, allowing the water molecules to form hydrogen bonds around the polymer chain. Beyond a certain length of the polymer chains, the collapsed states (associated with larger solute length-scale) start to induce disorder in the surface water molecules. We demonstrate that the local structure (both local number density and tetrahedral order) of the hydration layer is dynamically coupled to the local topology of the polymer. Thus, we envisage that in a flexible (bio)polymer, the hydration shell properties will be sensitive to the local conformational state of the molecule (both spatially and temporally), and the overall observed water structure and dynamics will be dependent on the topological/chemical heterogeneity, and the timescale of fluctuations in the local curvature (length-scale) of the solvent accessible surface. Moreover, we have demonstrated the direct coupling between the local density fluctuations of water and the local hydrophobic collapse of the polymer. For the extended state of the polymer, the local solvent density fluctuation is practically independent of the solute coordinate (lengthscale), and the hydrophobic collapse of the polymer is prompted by a "local dewetting" process induced by these fluctuations.
Glycopolypeptide-based polymersomes have promising applications as vehicles for targeted drug del... more Glycopolypeptide-based polymersomes have promising applications as vehicles for targeted drug delivery because they are capable of encapsulating different pharmaceuticals of diverse polarity as well as interacting with specific cell surfaces due to their hollow structural morphology and bioactive surfaces. We have synthesized glycopolypeptide-b-poly(propylene oxide) by ROP of glyco-N-carboxyanhydride (NCA) using the hydrophobic amine-terminated poly(propylene oxide) (PPO) as the initiator. This block copolymer is composed of an FDA-approved PPO hydrophobic block in conjugation with hydrophilic glycopolypeptides which are expected to be biocompatible. We demonstrate the formation of glycopolypeptide-based polymersomes from the self-assembly of glycopolypeptide-b-poly(propylene oxide) in which the presence of an ordered helical glycopolypeptide segment is required for their self-assembly into spherical nanoscale (∼50 nm) polymersomes. The polymersomes were characterized in detail using a variety of techniques such as TEM, AFM, cryo-SEM, and light-scattering measurements. As a model for drugs, both hydrophobic (RBOE) and hydrophilic (calcein) dyes have been incorporated within the polymersomes from solution. To substantiate the simultaneous entrapment of the two dyes, spectrally resolved fluorescence microscopy was performed on the glycopeptide polymersomes cast on a glass substrate. We show that it is possible to visualize individual nanoscale polymersomes and effectively probe the dyes’ colocalization and energy-transfer behaviors therein as well as investigate the variation in dual-dye encapsulation over a large number of single polymersomes. Finally, we show that the galactose moieties present on the surface can specifically recognize lectin RCA120, which reveals that the polymersomes’ surface is indeed biologically active.
J. Chem. Phys., 2013
In this work we explore the interplay between crystallization and glass transition in different b... more In this work we explore the interplay between crystallization and glass transition in different binary mixtures by changing their inter-species interaction length and also the composition. We find that only those systems which form bcc crystal in the equimolar mixture and whose global structure for larger x A (x A = 0.6, where x A is the mole fraction of the bigger particles) is a mixed fcc + bcc phase, do not crystallize at this higher composition. However, the systems whose equimolar structure is a variant of fcc (NaCl type crystal) and whose global structure at larger x A is a mixed NaCl + fcc phase, crystallize easily to this mixed structure. We find that the stability against crystallization of this “bcc zone” is due to the frustration between the locally preferred structure (LPS) and the mixed bcc + fcc crystal. Our study suggests that when the global structure is a mixed crystal where a single species contributes to both the crystal forms and where the two crystal forms have large difference in some order parameter related to that species then this induces frustration between the LPS and the global structure. This frustration makes the systems good glass former. When x A is further increased (0.70 ⩽ x A < 0.90) the systems show a tendency towards mixed fcc crystal formation. However, the “bcc zone” even for this higher composition is found to be sitting at the bottom of a V shaped phase diagram formed by two different variants of the fcc crystal structure, leading to its stability against crystallization.
J. Phys. Chem. B, 2013
Understanding the nature of the free-energy surfaces for phosphate hydrolysis is a prerequisite f... more Understanding the nature of the free-energy surfaces for phosphate hydrolysis is a prerequisite for understanding the corresponding key chemical reactions in biology. Here, the challenge has been to move to careful ab initio QM/MM (QM(ai)/MM) free-energy calculations, where obtaining converging results is very demanding and computationally expensive. This work describes such calculations, focusing on the free-energy surface for the hydrolysis of phosphate monoesters, paying special attention to the comparison between the one water (1W) and two water (2W) paths for the proton-transfer (PT) step. This issue has been explored before by energy minimization with implicit solvent models and by nonsystematic QM/MM energy minimization, as well as by nonsystematic free-energy mapping. However, no study has provided the needed reliable 2D (3D) surfaces that are necessary for reaching concrete conclusions. Here we report a systematic evaluation of the 2D (3D) free-energy maps for several relevant systems, comparing the results of QM(ai)/MM and QM(ai)/implicit solvent surfaces, and provide an advanced description of the relevant energetics. It is found that the 1W path for the hydrolysis of the methyl diphosphate (MDP) trianion is 6–9 kcal/mol higher than that the 2W path. This difference becomes slightly larger in the presence of the Mg2+ ion because this ion reduces the pKa of the conjugated acid form of the phosphate oxygen that accepts the proton. Interestingly, the BLYP approach (which has been used extensively in some studies) gives a much smaller difference between the 1W and 2W activation barriers. At any rate, it is worth pointing out that the 2W transition state for the PT is not much higher that the common plateau that serves as the starting point of both the 1W and 2W PT paths. Thus, the calculated catalytic effects of proteins based on the 2W PT mechanistic model are not expected to be different from the catalytic effects predicted using the 1W PT mechanistic model, which was calibrated on the observed barrier in solution and in which the TS charge distribution was similar to the that of the plateau (as was done in all of our previous EVB studies).
PROTEINS: Structure, Function, and Bioinformatics, 2013
Consistent description of the effect of internal water in proteins has been a major challenge for... more Consistent description of the effect of internal water in proteins has been a major challenge for both simulation and experimental studies. Describing this effect has been particularly important and elusive in cases of charges in protein interiors. Here, we present a new microscopic method that provides an efficient way for simulating the energetics of water insertion. Instead of performing explicit Monte Carlo (MC) moves on the insertion process, which generally involves an enormous number of rejected attempts, our method is based on generating trial configurations with excess amount of internal water, estimating the relevant free energy by the linear response approximation, and then using a postprocessing MC treatment to filter out a limited number of configurations from a large possible set. Our approach is validated on particularly challenging test cases including the pKa of the V66D mutation in Staphylococcal nuclease, Glu286 in cytochrome c oxidase (CcO) and the energetics of a protonated water molecule in the D channel of CcO. The new postprocessing method allows us to reproduce the relevant energetics of highly unstable charges in protein interiors using fully microscopic calculations and provides a substantial improvement over regular microscopic free energy estimates. This advance established the effectiveness of our water insertion strategy in challenging cases that have not been addressed successfully by other microscopic methods. Furthermore, our study provides a new exciting view on the crucial effect of water penetration in key biological systems as well as a new view on the nature of the dielectric in protein interiors.
Proc. Natl. Acad. Sci. U.S.A., 2012
Understanding the detailed mechanism of the activation of voltage-gated ion channels has been a p... more Understanding the detailed mechanism of the activation of voltage-gated ion channels has been a problem of great current interest. Reliable molecular simulations of voltage effects present a major challenge because meaningful converging microscopic simulations are not yet available and macroscopic treatments involve major uncertainties regarding the dielectric constant used and other key features. The current work has overcome some of the above challenges by using our recently developed coarse-grained (CG) model in simulating the activation of the Kv1.2 channel. The CG model has allowed us to explore problems that cannot be addressed at present by fully microscopic simulations, while providing insights on some features that are not usually considered in continuum models, including the distribution of the electrolytes between the membrane and the electrodes during the activation process and thus the nature of the gating current. Furthermore, the clear connection to microscopic descriptions combined with the power of CG modeling offers a powerful tool for exploring the energy balance between the protein conformational energy and the interaction with the external potential in voltage-activated channels. Our simulations have reproduced the observed experimental trend of the gating charge and, most significantly, the correct trend in the free energies, where the closed channel is more stable at negative potential and the open channel is more stable at positive potential. Moreover, we provide a unique view of the activation landscape and the time dependence of the activation process.
The relationship between the membrane voltage and the gating of voltage activated ion channels an... more The relationship between the membrane voltage and the gating of voltage activated ion channels and other systems have been a problem of great current interest. Unfortunately, reliable molecular simulations of external voltage effects present a major challenge, since meaningful converging microscopic simulations are not yet available and macroscopic treatments involve major uncertainties in terms of the dielectric used and other key features. This work extends our coarse grained (CG) model to simulations of membrane/protein systems under external potential. Special attention has been devoted to a consistent modeling of the effect of external potential due to the electrodes, emphasizing semimacroscopic description of the electrolytes in the solution regions between the membranes and the electrodes, as well as the coupling between the combined potential from the electrodes and electrolytes, and the protein ionization states. We also provide a clear connection to microscopic treatment of the electrolytes and thus can explore possible conceptual problems that are hard to resolve by other current approaches. For example, we obtain a clear description of the charge distribution in the entire electrolyte system, including near the electrodes in membrane/electrodes systems (where continuum models do not seem to provide the relevant results). Furthermore, the present treatment provides an insight on the distribution of the electrolyte charges before and after equilibration across the membrane, and thus on the nature of the gating charge. The different aspects of the model have been carefully validated by considering problems ranging for the simple Debye–Huckel, Gouy–Chapman models to the evaluation of the electrolyte distribution between two electrodes, as well as the effect of extending the simulation system by periodic replicas. Overall the clear connection to microscopic descriptions combined with the power of the CG modeling seems to offer a powerful tool for exploring the balance between the protein conformational energy and the interaction with the external potential in voltage activated channels. With this in mind we present a preliminary study of the gating charge in the voltage activated Kv1.2 channel, using the actual change in the electrolyte charge distribution rather than the conventional macroscopic estimate. We also discuss other special features of the model, which include the ability to capture the effect of changes in the protonation states of the protein residues during the open to close voltage induced transition. This article is part of a Special Issue entitled: Membrane protein structure and function.
Cytochrome c oxidase (CytcO) is a membrane-bound enzyme, which catalyzes the reduction of di-oxyg... more Cytochrome c oxidase (CytcO) is a membrane-bound enzyme, which catalyzes the reduction of di-oxygen to water and uses a major part of the free energy released in this reaction to pump protons across the membrane. In the Rhodobacter sphaeroides aa3 CytcO all protons that are pumped across the membrane, as well as one half of the protons that are used for O2 reduction, are transferred through one specific intraprotein proton pathway, which holds a highly conserved Glu286 residue. Key questions that need to be addressed in order to understand the function of CytcO at a molecular level are related to the timing of proton transfers from Glu286 to a “pump site” and the catalytic site, respectively. Here, we have investigated the temperature dependencies of the H/D kinetic-isotope effects of intramolecular proton-transfer reactions in the wild-type CytcO as well as in two structural CytcO variants, one in which proton uptake from solution is delayed and one in which proton pumping is uncoupled from O2 reduction. These processes were studied for two specific reaction steps linked to transmembrane proton pumping, one that involves only proton transfer (peroxy–ferryl, P → F, transition) and one in which the same sequence of proton transfers is also linked to electron transfer to the catalytic site (ferryl–oxidized, F → O, transition). An analysis of these reactions in the framework of theory indicates that that the simpler, P → F reaction is rate-limited by proton transfer from Glu286 to the catalytic site. When the same proton-transfer events are also linked to electron transfer to the catalytic site (F → O), the proton-transfer reactions might well be gated by a protein structural change, which presumably ensures that the proton-pumping stoichiometry is maintained also in the presence of a transmembrane electrochemical gradient. Furthermore, the present study indicates that a careful analysis of the temperature dependence of the isotope effect should help us in gaining mechanistic insights about CytcO.
Gaining detailed understanding of the energetics of the proton-pumping process in cytochrome c ox... more Gaining detailed understanding of the energetics of the proton-pumping process in cytochrome c oxidase (CcO) is a problem of great current interest. Despite promising mechanistic proposals, so far, a physically consistent model that would reproduce all the relevant barriers needed to create a working pump has not been presented. In addition, there are major problems in elucidating the origin of key mutational effects and in understanding the nature of the apparent pKa values associated with the pH dependencies of specific proton transfer (PT) reactions in CcO. This work takes a key step in resolving the above problems, by considering mutations, such as the Asn139Asp replacement, that blocks proton pumping without affecting PT to the catalytic site. We first introduce a formulation that makes it possible to relate the apparent pKa of Glu286 to different conformational states of this residue. We then use the new formulation along with the calculated pKa values of Glu286 at these different conformations to reproduce the experimentally observed apparent pKa of the residue. Next, we take the X-ray structures of the native and Asn139Asp mutant of the Paracoccus denitrificans CcO (N131D in this system) and reproduce for the first time the change in the primary PT pathways (and other key features) based on simulations that start with the observed structural changes. We also consider the competition between proton transport to the catalytic site and the pump site, as a function of the bulk pH, as well as the H/D isotope effect, and use this information to explore the relative height of the two barriers. The paper emphasizes the crucial role of energy-based considerations that include the PT process, and the delicate control of PT in CcO.
We find that at a mole fraction 0.05 of DMSO (x_DMSO = 0.05) in aqueous solution, a linear hydroc... more We find that at a mole fraction 0.05 of DMSO (x_DMSO = 0.05) in aqueous solution, a linear hydrocarbon chain of intermediate length (n = 30–40) adopts the most stable collapsed conformation. In pure water, the same chain exhibits an intermittent oscillation between the collapsed and the extended coiled conformations. Even when the mole fraction of DMSO in the bulk is 0.05, the concentration of the same in the first hydration layer around the hydrocarbon of chain length 30 (n = 30) is as large as 17%. Formation of such hydrophobic environment around the hydrocarbon chain may be viewed as the reason for the collapsed conformation gaining additional stability. We find a second anomalous behavior to emerge near x_DMSO = 0.15, due to a chain-like aggregation of the methyl groups of DMSO in water that lowers the relative concentration of the DMSO molecules in the hydration layer. We further find that as the concentration of DMSO is gradually increased, it progressively attains the extended coiled structure as the stable conformation. Although Flory–Huggins theory (for binary mixture solvent) fails to predict the anomaly at x_DMSO = 0.05, it seems to capture the essence of the anomaly at 0.15.
Langevin dynamics simulation studies have been employed to calculate the temperature dependent fr... more 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.
We demonstrate a chain length dependent crossover in the structural properties of linear hydrocar... more We demonstrate a chain length dependent crossover in the structural properties of linear hydrocarbon (n-alkane) chains using detailed atomistic simulations in explicit water. We identify a number of exotic structures of the polymer chain through energy minimization of representative snapshots collected from molecular dynamics trajectory. While the collapsed state is ring-like (circular) for small chains (CnH2n+2; n <= 20) and spherical for very long ones (n = 100), we find the emergence of ordered helical structures at intermediate lengths (n similar to 40). We find different types of disordered helices and toroid-like structures at n = 60. We also report a sharp transition in the stability of the collapsed state as a function of the chain length through relevant free energy calculations. While the collapsed state is only marginally metastable for C20H42, a clear bistable free energy surface emerges only when the chain is about 30 monomers long. For n = 30, the polymer exhibits an intermittent oscillation between the collapsed and the coil structures, characteristic of two stable states separated by a small barrier.
We study the nucleation of liquid phase from a supersaturated vapor in two dimensions, where the ... more We study the nucleation of liquid phase from a supersaturated vapor in two dimensions, where the particles interact through Lennard-Jones (LJ) pairwise potential. Using different Monte Carlo simulation methods, we calculate the free energy barrier for nucleation, the line tension, and bulk densities of equilibrium liquid and vapor phases, and also investigate the size and shape of the critical nucleus. The study is carried out at an intermediate level of supersaturation (away from the spinodal limit). In two dimensions, a surprisingly large cutoff (rc>=7.0sigma, sigma is the diameter of LJ particles) in the truncation of the LJ potential is required to obtain converged results. A lower cutoff [typically 2.5sigma which is generally sufficient in three dimensional (3D) studies] leads to a substantial error in the values of the line tension, nucleation barrier, and characteristics of the critical cluster. It is found that in two dimensions, the classical nucleation theory (CNT) fails to provide a reliable estimate of the free energy barrier. It underestimates the barrier by as much as 50% at the saturation ratio S=1.1 (defined as S=P/PC, where PC is the coexistence pressure) and at the reduced temperature T*=0.427 (defined as T*=kBT/epsilon, where epsilon is the depth of the potential well). Interestingly, CNT has been found to overestimate the nucleation free energy barrier in 3D systems near the triple point. In fact, the agreement of the calculated nucleation rate with CNT is much worse in two dimensions than in three dimensions. The reason for the inadequacy of the CNT can be attributed to the noncircular nature of the critical clusters. Although the shape becomes increasingly circular and the clusters become more compact with increase in cutoff radius, an appreciable noncircular nature remains even without any cutoff to make the simple CNT inaccurate.
We have constructed a multidimensional free energy surface of nucleation of the liquid phase from... more We have constructed a multidimensional free energy surface of nucleation of the liquid phase from the parent supercooled and supersaturated vapor phase near the gas-liquid spinodal. In particular, we remove the Becker-Doring constraint of having only one growing cluster in the system. Close to the spinodal, the free energy, as a function of the size of the largest cluster, develops surprisingly a minimum at a subcritical cluster size. It is this minimum at intermediate size that is found to be responsible for the barrier towards further growth of the nucleus at large supersaturation. An alternative free energy pathway involving the participation of many subcritical clusters is found near the spinodal where the growth of the nucleus is promoted by a coalescence mechanism. The growth of the stable phase becomes collective and spatially diffuse, and the significance of a “critical nucleus” is lost for deeper quenches.
Orientational dynamics in a liquid crystalline system near the isotropic-nematic (IN) phase trans... more Orientational dynamics in a liquid crystalline system near the isotropic-nematic (IN) phase transition is studied using molecular dynamics simulations of the well-known Lebwohl-Lasher model. As the IN transition temperature is approached from the isotropic side, we find that the decay of the orientational time correlation functions (OTCF) slows down noticeably, giving rise to a power law decay at intermediate time scales. The angular velocity time correlation function also exhibits a rather pronounced power law decay near the IN boundary. In the mean squared angular displacement at comparable time scales, we observe the emergence of a subdiffusive regime which is followed by a superdiffusive regime before the onset of the long-time diffusive behavior. We observe signature of dynamical heterogeneity through pronounced non-Gaussian behavior in orientational motion particularly at lower temperatures. This behavior closely resembles what is usually observed in supercooled liquids. We obtain the free energy as a function of orientational order parameter by the use of the transition matrix Monte Carlo method. The free energy surface is flat for the system considered here and the barrier between isotropic and nematic phases is vanishingly small for this weakly first-order phase transition, hence allowing large scale, collective, and correlated orientational density fluctuations. This might be responsible for the observed power law decay of the OTCFs.
We observe a surprisingly general power law decay at short to intermediate times in orientational... more We observe a surprisingly general power law decay at short to intermediate times in orientational relaxation in a variety of model systems (both calamitic and discotic, and also lattice) for thermotropic liquid crystals. As all these systems transit across the isotropic-nematic phase boundary, two power law relaxation regimes, separated by a plateau, emerge, giving rise to a steplike feature (well known in glassy liquids) in the single-particle second-rank orientational time correlation function. In contrast to its probable dynamical origin in supercooled liquids, we show that the power law here can originate from the thermodynamic fluctuations of the orientational order parameter, driven by the rapid growth in the second-rank orientational correlation length.