Polymer collapse in the presence of hydrodynamic interactions

Monte Carlo Simulations of Polymer Collapse in an Explicit Solvent of Varying Quality

The behavior of a single homopolymer chain in an explicit solvent in a wide range of poor and good solvents was investigated. For this purpose, a two-dimensional coarse-grained model based on a triangular lattice was used. Simulations were carried out by the Monte Carlo method using the Cooperative Motion Algorithm to study high-density systems. The scaling relations of the parameters describing the phase transitions of the chain were determined. For systems with polymer-solvent attraction, significant changes in chain size and shape were observed. This was associated with the mechanism of chain penetration by solvents and the formation of structures via a mechanism called 'Bridging-Induced Attraction', similar to those discovered for three dimensions.

Impact of Hydrodynamic Interactions on the Kinetic Pathway of Protein Folding

Protein folding is a fundamental process critical to cellular function and human health, but it remains a grand challenge in biophysics. Hydrodynamic interaction (HI) plays a vital role in the self-organization of soft and biological materials, yet its role in protein folding is not fully understood despite folding occurring in a fluid environment. Here, we use the fluid particle dynamics method to investigate many-body hydrodynamic couplings between amino acid residues and fluid motion in the folding kinetics of a coarse-grained four-α-helices bundle protein. Our results reveal that HI helps select fast folding pathways to the native state without being kinetically trapped, significantly speeding up the folding kinetics compared to its absence. First, the directional flow along the protein backbone expedites protein collapse. Then, the incompressibility-induced squeezing flow effects retard the accumulation of non-native hydrophobic contacts, thus preventing the protein from being trapped in local energy minima during the conformational search of the native structure. We also find that the significance of HI in folding kinetics depends on temperature, with a pronounced effect under biologically relevant conditions. Our findings suggest that HI, particularly the short-range squeezing effect, may be crucial in avoiding protein misfolding.

Hydrodynamic Effects on the Collapse Kinetics of Flexible Polyelectrolytes

Understanding the collapse kinetics of polyelectrolytes (PEs) is crucial for comprehending various biological and industrial phenomena. Despite occurring in an aqueous environment, previous computational studies have overlooked the influence of hydrodynamic interactions (HIs) facilitated by fluid motion. Here, we directly compute the Navier-Stokes equation to investigate the collapse kinetics of a highly charged flexible PE. Our findings reveal that HI accelerates PE collapse induced by hydrophobicity and multivalent salt. In the case of hydrophobicity, HI induces long-range collective motion of monomers, accelerating the coarsening of local clusters through either Brownian-coagulation-like or evaporation-condensation-like processes, depending on the strength of hydrophobicity with respect to electrostatic interaction. Regarding multivalent salt, HI does not affect the condensation dynamics of multivalent ions but facilitates quicker movement of local dipolar clusters along the PE, thereby expediting the collapse process. These results provide valuable insights into the underlying mechanisms of HI in PE collapse kinetics.

Coil-globule transition in two-dimensional polymer chains in an explicit solvent

The structure of two-dimensional polymer chains in a solvent at different temperatures is still far from being fully understood. Computer simulations of high-density macromolecular systems require the use of appropriate algorithms, and therefore the simulations were carried out using the Cooperative Motion Algorithm. The polymer model studied was exactly two-dimensional, coarse-grained and based on a triangular lattice. The theta temperature and temperature of coil-to-globule transition, and critical exponents were determined. The differences between the structure of such a disk and that of a chain in a dense polymer liquid were shown.

Effects of alignment activity on the collapse kinetics of a flexible polymer

The dynamics of various biological filaments can be understood within the framework of active polymer models. Here we consider a bead-spring model for a flexible polymer chain in which the active interaction among the beads is introduced via an alignment rule adapted from the Vicsek model. Following quenching from the high-temperature coil phase to a low-temperature state point, we study the coarsening kinetics via molecular dynamics (MD) simulations using the Langevin thermostat. For the passive polymer case the low-temperature equilibrium state is a compact globule. The results from our MD simulations reveal that though the globular state is also the typical final state in the active case, the nonequilibrium pathways to arrive at such a state differ from the picture for the passive case due to the alignment interaction among the beads. We notice that deviations from the intermediate "pearl-necklace"-like arrangement, which is observed in the passive case, and the formation of more elongated dumbbell-like structures increase with increasing activity. Furthermore, it appears that while a small active force on the beads certainly makes the coarsening process much faster, there exists a nonmonotonic dependence of the collapse time on the strength of active interaction. We quantify these observations by comparing the scaling laws for the collapse time and growth of pearls with the passive case.

Hydrodynamics of immiscible binary fluids with viscosity contrast: a multiparticle collision dynamics approach

We present a multiparticle collision dynamics (MPC) implementation of layered immiscible fluids A and B of different shear viscosities separated by planar interfaces. The simulated flow profile for imposed steady shear motion and the time-dependent shear stress functions are in excellent agreement with our continuum hydrodynamics results for the composite fluid. The wave-vector dependent transverse velocity auto-correlation functions (TVAF) in the bulk-fluid regions of the layers decay exponentially, and agree with those of single-phase isotropic MPC fluids. In addition, we determine the hydrodynamic mobilities of an embedded colloidal sphere moving steadily parallel or transverse to a fluid-fluid interface, as functions of the distance from the interface. The obtained mobilities are in good agreement with hydrodynamic force multipoles calculations, for a no-slip sphere moving under creeping flow conditions near a clean, ideally flat interface. The proposed MPC fluid-layer model can be straightforwardly implemented, and it is computationally very efficient. Yet, owing to the spatial discretization inherent to the MPC method, the model can not reproduce all hydrodynamic features of an ideally flat interface between immiscible fluids.

Mesoscale modelling of polymer aggregate digestion

We use mesoscale simulations to gain insight into the digestion of biopolymers by studying the break-up dynamics of polymer aggregates (boluses) bound by physical cross-links. We investigate aggregate evolution, establishing that the linking bead fraction and the interaction energy are the main parameters controlling stability with respect to diffusion. We show via a simplified model that chemical breakdown of the constituent molecules causes aggregates that would otherwise be stable to disperse. We further investigate breakdown of biopolymer aggregates in the presence of fluid flow. Shear flow in the absence of chemical breakdown induces three different regimes depending on the flow Weissenberg number ( W i ). i) At W i ≪ 1 , shear flow has a negligible effect on the aggregates. ii) At W i ∼ 1 , the aggregates behave approximately as solid bodies and move and rotate with the flow. iii) At W i ≫ 1 , the energy input due to shear overcomes the attractive cross-linking interactions and the boluses are broken up. Finally, we study bolus evolution under the combined action of shear flow and chemical breakdown, demonstrating a synergistic effect between the two at high reaction rates.

Cluster prevalence in concentrated ring-chain mixtures under shear

Semiflexible ring polymers are known to exhibit clustering behavior and form stacks in concentrated solutions. Recently, weak shear was suggested to re-orient these stacks with flow, a phenomenon more easily visible in more concentrated solutions [Liebetreu et al., ACS Appl. Polym. Mater., 2020, 2(8), 3505-3517, DOI: 10.1021/acsapm.0c00522]. In this work, we investigate the impact of mixing linear chains and rings in a similar system under shear, studying clustering in the presence of semiflexible, rod-like chains. We present a correlation between chain monomer fraction and clustering behavior as linear chains take up less space, thus decreasing the system's effective density and, subsequently, clustering. However, we suggest mixtures with a low chain concentration to maintain or potentially enhance clustering at equilibrium while this effect is destroyed under shear. The mixing of chains and rings may therefore be used to create more strongly organized structures susceptible to reorientation via weak shear.

Nanoparticle transport phenomena in confined flows

Nanoparticles submerged in confined flow fields occur in several technological applications involving heat and mass transfer in nanoscale systems. Describing the transport with nanoparticles in confined flows poses additional challenges due to the coupling between the thermal effects and fluid forces. Here, we focus on the relevant literature related to Brownian motion, hydrodynamic interactions and transport associated with nanoparticles in confined flows. We review the literature on the several techniques that are based on the principles of non-equilibrium statistical mechanics and computational fluid dynamics in order to simultaneously preserve the fluctuation-dissipation relationship and the prevailing hydrodynamic correlations. Through a review of select examples, we discuss the treatments of the temporal dynamics from the colloidal scales to the molecular scales pertaining to nanoscale fluid dynamics and heat transfer. As evident from this review, there, indeed has been little progress made in regard to the accurate modeling of heat transport in nanofluids flowing in confined geometries such as tubes. Therefore the associated mechanisms with such processes remain unexplained. This review has revealed that the information available in open literature on the transport properties of nanofluids is often contradictory and confusing. It has been very difficult to draw definitive conclusions. The quality of work reported on this topic is non-uniform. A significant portion of this review pertains to the treatment of the fluid dynamic aspects of the nanoparticle transport problem. By simultaneously treating the energy transport in ways discussed in this review as related to momentum transport, the ultimate goal of understanding nanoscale heat transport in confined flows may be achieved.

Driven spheres, ellipsoids and rods in explicitly modeled polymer solutions

Understanding the transport of driven nano- and micro-particles in complex fluids is of relevance for many biological and technological applications. Here we perform hydrodynamic multiparticle collision dynamics simulations of spherical and elongated particles driven through polymeric fluids containing different concentrations of polymers. We determine the mean particle velocities which are larger than expected from Stokes law for all particle shapes and polymer densities. Furthermore we measure the fluid flow fields and local polymer density and polymer conformation around the particles. We find that polymer-depleted regions close to the particles are responsible for an apparent tangential slip velocity which accounts for the measured flow fields and transport velocities. A simple two-layer fluid model gives a good match to the simulation results.

Behavior of active filaments near solid-boundary under linear shear flow

The steady-state behavior of a dilute suspension of self-propelled filaments confined between planar walls subjected to Couette-flow is reported herein. The effect of hydrodynamics has been taken into account using a mesoscale simulation approach. We present a detailed analysis of positional and angular probability distributions of filaments with varying propulsive force and shear-flow. The distribution of the centre-of-mass of the filament shows adsorption near the surfaces, which diminishes with the flow. The excess density of filaments decreases with Weissenberg number as Wi-β with an exponent β ≈ 0.8, in the intermediate shear range (1 < Wi < 30). The angular orientational moment also decreases near the wall as Wi-δ with δ ≈ 1/5; the variation in orientational moment near the wall is relatively slower than the bulk. It shows a strong dependence on the propulsive force near the wall, with variation on force as Pe-1/3 for large Pe ≥ 1. The active filament shows orientational preference with flow near the surfaces, which splits into upstream and downstream swimming. The population splitting from a unimodal (propulsive force dominated regime) to bimodal phase (shear dominated regime) is identified in the parameter space of propulsive force and shear flow.

Tethered Semiflexible Polymer under Large Amplitude Oscillatory Shear

The properties of a semiflexible polymer with fixed ends exposed to oscillatory shear flow are investigated by simulations. The two-dimensionally confined polymer is modeled as a linear bead-spring chain, and the interaction with the fluid is described by the Brownian multiparticle collision dynamics approach. For small shear rates, the tethering of the ends leads to a more-or-less linear oscillatory response. However, at high shear rates, we found a strongly nonlinear reaction, with a polymer (partially) wrapped around the fixation points. This leads to an overall shrinkage of the polymer. Dynamically, the location probability of the polymer center-of-mass position is largest on a spatial curve resembling a limaçon, although with an inhomogeneous distribution. We found shear-induced modifications of the normal-mode correlation functions, with a frequency doubling at high shear rates. Interestingly, an even-odd asymmetry for the Cartesian components of the correlation functions appears, with rather similar spectra for odd x- and even y-modes and vice versa. Overall, our simulations yielded an intriguing nonlinear behavior of tethered semiflexible polymers under oscillatory shear flow.

Impact of hydrodynamic interactions on protein folding rates depends on temperature

We investigated the impact of hydrodynamic interactions (HI) on protein folding using a coarse-grained model. The extent of the impact of hydrodynamic interactions, whether it accelerates, retards, or has no effect on protein folding, has been controversial. Together with a theoretical framework of the energy landscape theory (ELT) for protein folding that describes the dynamics of the collective motion with a single reaction coordinate across a folding barrier, we compared the kinetic effects of HI on the folding rates of two protein models that use a chain of single beads with distinctive topologies: a 64-residue α/β chymotrypsin inhibitor 2 (CI2) protein, and a 57-residue β-barrel α-spectrin Src-homology 3 domain (SH3) protein. When comparing the protein folding kinetics simulated with Brownian dynamics in the presence of HI to that in the absence of HI, we find that the effect of HI on protein folding appears to have a "crossover" behavior about the folding temperature. This means that at a temperature greater than the folding temperature, the enhanced friction from the hydrodynamic solvents between the beads in an unfolded configuration results in lowered folding rate; conversely, at a temperature lower than the folding temperature, HI accelerates folding by the backflow of solvent toward the folded configuration of a protein. Additionally, the extent of acceleration depends on the topology of a protein: for a protein like CI2, where its folding nucleus is rather diffuse in a transition state, HI channels the formation of contacts by favoring a major folding pathway in a complex free energy landscape, thus accelerating folding. For a protein like SH3, where its folding nucleus is already specific and less diffuse, HI matters less at a temperature lower than the folding temperature. Our findings provide further theoretical insight to protein folding kinetic experiments and simulations.

Steady state sedimentation of ultrasoft colloids

The structural and dynamical properties of ultra-soft colloids-star polymers-exposed to a uniform external force field are analyzed by applying the multiparticle collision dynamics technique, a hybrid coarse-grain mesoscale simulation approach, which captures thermal fluctuations and long-range hydrodynamic interactions. In the weak-field limit, the structure of the star polymer is nearly unchanged; however, in an intermediate regime, the radius of gyration decreases, in particular transverse to the sedimentation direction. In the limit of a strong field, the radius of gyration increases with field strength. Correspondingly, the sedimentation coefficient increases with increasing field strength, passes through a maximum, and decreases again at high field strengths. The maximum value depends on the functionality of the star polymer. High field strengths lead to symmetry breaking with trailing, strongly stretched polymer arms and a compact star-polymer body. In the weak-field-linear response regime, the sedimentation coefficient follows the scaling relation of a star polymer in terms of functionality and arm length.

The effect of hydrodynamic interactions on nanoparticle diffusion in polymer solutions: a multiparticle collision dynamics study

The diffusion of nanoparticles (NPs) in polymer solutions is studied by a combination of a mesoscale simulation method, multiparticle collision dynamics (MPCD), and molecular dynamics (MD) simulations. We investigate the long-time diffusion coefficient D as well as the subdiffusive behavior in the intermediate time region. The dependencies of both D and subdiffusion factor α on NP size and polymer concentration, respectively, are explicitly calculated. Particular attention is paid to the role of hydrodynamic interaction (HI) in the NP diffusion dynamics. Our simulation results show that the long-time diffusion coefficients satisfy perfectly the scaling relation found by experimental observations. Meanwhile, the subdiffusive factor decreases with the increase in polymer concentration but is of little relevance to the NP size. By parallel simulations with and without HI, we reveal that HI will generally enhance D, while the enhancement effect is non-monotonous with increasing polymer concentration, and it becomes most pronounced at semidilute concentrations. With the aid of a scaling law based on the diffusive activation energy model, we understand that HI affects diffusion through decreasing the diffusive activation energy on the one hand while increasing the effective diffusion size on the other. In addition, HI will certainly influence the subdiffusive behavior of the NP, leading to a larger subdiffusion exponent.

Molecular dynamics of protein A and a WW domain with a united-residue model including hydrodynamic interaction

The folding of the N-terminal part of the B-domain of staphylococcal protein A (PDB ID: 1BDD, a 46-residue three-α-helix bundle) and the formin-binding protein 28 WW domain (PDB ID: 1E0L, a 37-residue three-stranded anti-parallel β protein) was studied by means of Langevin dynamics with the coarse-grained UNRES force field to assess the influence of hydrodynamic interactions on protein-folding pathways and kinetics. The unfolded, intermediate, and native-like structures were identified by cluster analysis, and multi-exponential functions were fitted to the time dependence of the fractions of native and intermediate structures, respectively, to determine bulk kinetics. It was found that introducing hydrodynamic interactions slows down both the formation of an intermediate state and the transition from the collapsed structures to the final native-like structures by creating multiple kinetic traps. Therefore, introducing hydrodynamic interactions considerably slows the folding, as opposed to the results obtained from earlier studies with the use of Gō-like models.

Effects of hydrodynamic interactions on the crystallization of passive and active colloidal systems

Effects of hydrodynamic interactions (HI) on the crystallization of a two-dimensional suspension of colloidal particles have been investigated, by applying a multiscale simulation method combining multiparticle collision dynamics for solvent particles with standard molecular dynamics for the colloids. For a passive system, we find that HI slightly shifts the freezing point to a smaller density, while the equilibrium structure remains nearly unchanged for a given global order parameter. For an active system, however, HI can significantly shift the freezing density to a higher value and the freezing transition becomes more continuous compared to its passive counterpart. This HI-induced shift becomes more remarkable with increasing propelling force. In addition, HI may also enhance the structural heterogeneities in an active system. For both passive and active systems, it is shown that HI can accelerate the relaxation process to their final steady state.

Electrophoretic Mobility of Polyelectrolytes within a Confining Well

We present a numerical study of polyelectrolytes electrophoresing in free solution while squeezed by an axisymmetric confinement force transverse to their net displacement. Hybrid multiparticle collision dynamics and molecular dynamics simulations with mean-field finite Debye layers show that even though the polyelectrolyte chains remain "free-draining" their electrophoretic mobility increases with confinement in nanoconfining potential wells. The primary mechanism leading to the increase in mobility above the free-solution value, despite long-range hydrodynamic screening by counterion layers, is the orientation of polymer segments within Debye layers. The observed length dependence of the electrophoretic mobility arises due to secondary effects of counterion condensation related to confinement compactification.

Derivation of a Markov state model of the dynamics of a protein-like chain immersed in an implicit solvent

A Markov state model of the dynamics of a protein-like chain immersed in an implicit hard sphere solvent is derived from first principles for a system of monomers that interact via discontinuous potentials designed to account for local structure and bonding in a coarse-grained sense. The model is based on the assumption that the implicit solvent interacts on a fast time scale with the monomers of the chain compared to the time scale for structural rearrangements of the chain and provides sufficient friction so that the motion of monomers is governed by the Smoluchowski equation. A microscopic theory for the dynamics of the system is developed that reduces to a Markovian model of the kinetics under well-defined conditions. Microscopic expressions for the rate constants that appear in the Markov state model are analyzed and expressed in terms of a temperature-dependent linear combination of escape rates that themselves are independent of temperature. Excellent agreement is demonstrated between the theoretical predictions of the escape rates and those obtained through simulation of a stochastic model of the dynamics of bond formation. Finally, the Markov model is studied by analyzing the eigenvalues and eigenvectors of the matrix of transition rates, and the equilibration process for a simple helix-forming system from an ensemble of initially extended configurations to mainly folded configurations is investigated as a function of temperature for a number of different chain lengths. For short chains, the relaxation is primarily single-exponential and becomes independent of temperature in the low-temperature regime. The profile is more complicated for longer chains, where multi-exponential relaxation behavior is seen at intermediate temperatures followed by a low temperature regime in which the folding becomes rapid and single exponential. It is demonstrated that the behavior of the equilibration profile as the temperature is lowered can be understood in terms of the number of relaxation modes or "folding pathways" that contribute to the evolution of the state populations.

Structure and rheology of colloidal particle gels: insight from computer simulation

A particle gel is a network of aggregated colloidal particles with soft solid-like mechanical properties. Its structural and rheological properties, and the kinetics of its formation, are dependent on the sizes and shapes of the constituent particles, the volume fraction of the particles, and the nature of the interactions between the particles before, during and after gelation. Particle gels may be permanent or transient depending on whether the colloidal forces between the aggregating particles lead to irreversible bonding or weak reversible interactions. With short-range reversible interactions, network formation is typically associated with phase separation or kinetic arrest due to particle crowding. Much existing knowledge has been derived from computer simulations of idealized model systems containing spherical particles interacting with well-defined pair potentials. The status of current progress is reviewed here by summarizing the underlying methodology and key findings from a range of simulation approaches: Monte Carlo, molecular dynamics, Brownian dynamics, Stokesian dynamics, dissipative particle dynamics, multiparticle collision dynamics, and fluid particle dynamics. Then it is described how the technique of Brownian dynamics simulation, in particular, has provided detailed insight into how different kinds of bonding and weak reversible interactions can affect the aggregate fractal structure, the percolation behaviour, and the small-deformation rheological properties of network-forming colloidal systems. A significant ongoing development has been the establishment and testing of efficient algorithms that are able to capture the subtle dynamic structuring effects that arise from effects of interparticle hydrodynamic interactions. This has led to an appreciation recently of the potentially important role of these particle-particle hydrodynamic effects in controlling the evolving morphology of simulated colloidal aggregates and in defining the location of the sol-gel phase boundary.

Dynamics of self-assembly of model viral capsids in the presence of a fluctuating membrane

A coarse-grained computational model is used to investigate the effect of a fluctuating fluid membrane on the dynamics of patchy-particle assembly into virus capsid-like cores. Results from simulations for a broad range of parameters are presented, showing the effect of varying interaction strength, membrane stiffness, and membrane viscosity. Furthermore, the effect of hydrodynamic interactions is investigated. Attraction to a membrane may promote assembly, including for subunit interaction strengths for which it does not occur in the bulk, and may also decrease single-core assembly time. The membrane budding rate is strongly increased by hydrodynamic interactions. The membrane deformation rate is important in determining the finite-time yield. Higher rates may decrease the entropic penalty for assembly and help guide subunits toward each other but may also block partial cores from being completed. For increasing subunit interaction strength, three regimes with different effects of the membrane are identified.

A molecule-centered method for accelerating the calculation of hydrodynamic interactions in Brownian dynamics simulations containing many flexible biomolecules

Inclusion of hydrodynamic interactions (HIs) is essential in simulations of biological macromolecules that treat the solvent implicitly if the macromolecules are to exhibit correct translational and rotational diffusion. The present work describes the development and testing of a simple approach aimed at allowing more rapid computation of HIs in coarse-grained Brownian dynamics simulations of systems that contain large numbers of flexible macromolecules. The method combines a complete treatment of intramolecular HIs with an approximate treatment of the intermolecular HIs which assumes that the molecules are effectively spherical; all of the HIs are calculated at the Rotne-Prager-Yamakawa level of theory. When combined with Fixman's Chebyshev polynomial method for calculating correlated random displacements, the proposed method provides an approach that is simple to program but sufficiently fast that it makes it computationally viable to include HIs in large-scale simulations. Test calculations performed on very coarse-grained models of the pyruvate dehydrogenase (PDH) E2 complex and on oligomers of ParM (ranging in size from 1 to 20 monomers) indicate that the method reproduces the translational diffusion behavior seen in more complete HI simulations surprisingly well; the method performs less well at capturing rotational diffusion but its discrepancies diminish with increasing size of the simulated assembly. Simulations of residue-level models of two tetrameric protein models demonstrate that the method also works well when more structurally detailed models are used in the simulations. Finally, test simulations of systems containing up to 1024 coarse-grained PDH molecules indicate that the proposed method rapidly becomes more efficient than the conventional BD approach in which correlated random displacements are obtained via a Cholesky decomposition of the complete diffusion tensor.

Modeling of solvent flow effects in enzyme catalysis under physiological conditions

A stochastic model for the dynamics of enzymatic catalysis in explicit, effective solvents under physiological conditions is presented. Analytically-computed first passage time densities of a diffusing particle in a spherical shell with absorbing boundaries are combined with densities obtained from explicit simulation to obtain the overall probability density for the total reaction cycle time of the enzymatic system. The method is used to investigate the catalytic transfer of a phosphoryl group in a phosphoglycerate kinase-ADP-bis phosphoglycerate system, one of the steps of glycolysis. The direct simulation of the enzyme-substrate binding and reaction is carried out using an elastic network model for the protein, and the solvent motions are described by multiparticle collision dynamics which incorporates hydrodynamic flow effects. Systems where solvent-enzyme coupling occurs through explicit intermolecular interactions, as well as systems where this coupling is taken into account by including the protein and substrate in the multiparticle collision step, are investigated and compared with simulations where hydrodynamic coupling is absent. It is demonstrated that the flow of solvent particles around the enzyme facilitates the large-scale hinge motion of the enzyme with bound substrates, and has a significant impact on the shape of the probability densities and average time scales of substrate binding for substrates near the enzyme, the closure of the enzyme after binding, and the overall time of completion of the cycle.

Hydrodynamic fluctuations in thermostatted multiparticle collision dynamics

In this work we study the behavior of mesoscopic fluctuations of a fluid simulated by Multiparticle Collision Dynamics when this is applied together with a local thermostatting procedure that constrains the strength of temperature fluctuations. We consider procedures in which the thermostat interacts with the fluid at every simulation step as well as cases in which the thermostat is applied only at regular time intervals. Due to the application of the thermostat temperature fluctuations are forced to relax to equilibrium faster than they do in the nonthermostatted, constant-energy case. Depending on the interval of application of the thermostat, it is demonstrated that the thermodynamic state changes gradually from isothermal to adiabatic conditions. In order to exhibit this effect we compute from simulations diverse correlation functions of the hydrodynamic fluctuating fields. These correlation functions are compared with those predicted by a linearized hydrodynamic theory of a simple fluid in which a thermostat is applied locally. We find a good agreement between the model and the numerical results, which confirms that hydrodynamic fluctuations in Multiparticle Collision Dynamics in the presence of the thermostat have the properties expected for spontaneous fluctuations in fluids in contact with a heat reservoir.

Effect of confinement on the collapsing mechanism of a flexible polymer chain

In this paper, Brownian dynamics simulation (BDS) studies are executed to demonstrate the distinctive influences of the extent of confinement on the collapsing mechanism and kinetics of a flexible hydrophobic polymer chain in a poor solvent. The collapsing behavior is quantified by the time of collapse, which below a critical dimension of the confinement (h(c)), encounters a drastic reduction with a further strengthening in the degree of confinement. For dimensions greater than this critical one, the collapse occurs through the well-known hydrodynamic interaction (HI) controlled multiple-globule-mediated mechanisms. However, for channel dimensions less than this critical one, the collapse mechanism is drastically altered. Under such circumstances, the collapse gets predominantly controlled by the confinement effects (with negligible contribution of the HIs) and occurs via the formation of a single central globule. This central globule rapidly engulfs the noncondensed polymer segments, and in the process largely hastens up the collapsing event. Under such circumstances, the collapse time is found to decrease linearly with decrements in the channel height. On the contrary, for channel heights greater than h(c), the multiple-globule-mediated collapse is characterized by a collapse time that shows an exponential dependence on the channel height, rapidly attaining a state in which the confinement effect becomes inconsequential and HIs dictate the entire collapsing behavior. We further propose detailed arguments based on physical reasoning as well as free energy estimations to conclusively support the qualitative and quantitative nature of influences of the confinement on the polymer collapse.

An improved coarse-grained model of solvation and the hydrophobic effect

We present a coarse-grained lattice model of solvation thermodynamics and the hydrophobic effect that implements the ideas of Lum-Chandler-Weeks theory [J. Phys. Chem. B 134, 4570 (1999)] and improves upon previous lattice models based on it. Through comparison with molecular simulation, we show that our model captures the length-scale and curvature dependence of solvation free energies with near-quantitative accuracy and 2-3 orders of magnitude less computational effort, and further, correctly describes the large but rare solvent fluctuations that are involved in dewetting, vapor tube formation, and hydrophobic assembly. Our model is intermediate in detail and complexity between implicit-solvent models and explicit-water simulations.

Probing solvation decay length in order to characterize hydrophobicity-induced bead-bead attractive interactions in polymer chains

In this paper, we quantitatively demonstrate that exponentially decaying attractive potentials can effectively mimic strong hydrophobic interactions between monomer units of a polymer chain dissolved in aqueous solvent. Classical approaches to modeling hydrophobic solvation interactions are based on invariant attractive length scales. However, we demonstrate here that the solvation interaction decay length may need to be posed as a function of the relative separation distances and the sizes of the interacting species (or beads or monomers) to replicate the necessary physical interactions. As an illustrative example, we derive a universal scaling relationship for a given solute-solvent combination between the solvation decay length, the bead radius, and the distance between the interacting beads. With our formalism, the hydrophobic component of the net attractive interaction between monomer units can be synergistically accounted for within the unified framework of a simple exponentially decaying potential law, where the characteristic decay length incorporates the distinctive and critical physical features of the underlying interaction. The present formalism, even in a mesoscopic computational framework, is capable of incorporating the essential physics of the appropriate solute-size dependence and solvent-interaction dependence in the hydrophobic force estimation, without explicitly resolving the underlying molecular level details.

Macromolecular dynamics in crowded environments

The structural and dynamical properties of macromolecules in confining or crowded environments are different from those in simple bulk liquids. In this paper, both the conformational and diffusional dynamics of globular polymers are studied in solutions containing fixed spherical obstacles. These properties are studied as a function of obstacle volume fraction and size, as well as polymer chain length. The results are obtained using a hybrid scheme that combines multiparticle collision dynamics of the solvent with molecular dynamics that includes the interactions among the polymer monomers and between the polymer beads and obstacles and solvent molecules. The dynamics accounts for hydrodynamic interactions among the polymer beads and intermolecular forces with the solvent molecules. We consider polymers in poor solvents where the polymer chain adopts a compact globular structure in solution. Our results show that the collapse of the polymer chain to a compact globular state is strongly influenced by the obstacle array. A nonmonotonic variation in the radius of gyration with time is observed and the collapse time scale is much longer than that in simple solutions without obstacles. Hydrodynamic interactions are important at low obstacle volume fractions but are screened at high volume fractions. The diffusion of the globular polymer chain among the obstacles is subdiffusive in character on intermediate time scales where the dynamics explores the local structure of the heterogeneous environment. For large polymer chains in systems with high obstacle volume fractions, the chain adopts bloblike conformations that arise from trapping of portions of the chain in voids among the obstacles.

Hydrodynamic effects on chiral induction

There are few unambiguous reports describing the transfer of chirality from stirring vortices down to the level of electronic transitions. In this tutorial review the methods reported are discussed as well as the structural trends that seem to be necessary conditions in order to detect this phenomenon.

Hydrodynamic selection of the kinetic pathway of a polymer coil-globule transition

Recently, the role of hydrodynamic interactions in the selection of a kinetic pathway for phase transitions has attracted considerable attention. Here we study this problem numerically by taking as an example a coil-globule transition of a single polymer, which is a prototype model of protein folding. When a swollen polymer collapses into a globule state, hydrodynamic interactions accelerate the transition. We find, on the other hand, that when a rather compact polymer collapses into the same final state, hydrodynamic interactions decelerate the transition due to a slow squeezing process of the solvent. We reveal that the degree of the initial enhancement of anisotropy of the polymer configuration determines whether hydrodynamic interactions accelerate or decelerate the collapsing dynamics. We also discuss the possible relevance of squeezing flow effects in protein folding.

Folding and unfolding kinetics of a single semiflexible polymer

We investigate theoretically the kinetics of the folding transition of a single semiflexible polymer. In the folding transition, the growth rate decreases with an increase in the number of monomers in the collapsed domain, suggesting that the main contribution to dissipation is from the motion of the domain. In the unfolding transition, the dynamic scaling exponents 1/8 and 1/4 were determined for the disentanglement and relaxation steps, respectively. We performed Langevin dynamics simulations to test our theory. It is found that our theory is in good agreement with simulations. We also propose the kinetics of the transitions in the presence of a hydrodynamic interaction.

Brownian dynamics simulation of polymer collapse in a poor solvent: influence of implicit hydrodynamic interactions

The effect of solvent on the collapse dynamics of homopolymers is investigated with Brownian dynamics simulations of a non-linear bead-spring chain model incorporating implicit hydrodynamic interactions. Our simulations suggest that the polymer collapse takes place via a three-stage mechanism, namely, formation of pearls, coarsening of pearls and the formation of a compact globule. The collapse pathways from a good solvent state to a poor solvent state are found to be independent of hydrodynamic interactions. On the other hand, hydrodynamic interaction is found to speed up the collapse rate. At a large quench depth (the depth of the Lennard-Jones potential), independent of the presence of hydrodynamic interaction, polymer molecules are found to be trapped in metastable states for long periods before acquiring their native globular state. The exponents characterizing the decay of various properties such as the radius of gyration are determined and compared with the values reported in the literature.