Universal scaling of the diffusivity of dendrimers in a semidilute solution of linear polymers.

The static and dynamic properties of dendrimers in semidilute solutions of linear chains of comparable size are investigated using Brownian dynamics simulations. The radius of gyration and diffusivity of a wide variety of low generation dendrimers and linear chains in solution follow universal scaling laws independent of their topology. Analysis of the shape functions and internal density of dendrimers shows that they are more spherical than linear chains and have a dense core. At intermediate times, dendrimers become subdiffusive, with an exponent higher than that previously reported for nanoparticles in semidilute polymer solutions. The long-time diffusivity of dendrimers does not follow theoretical predictions for nanoparticles. We propose a new scaling law for the long-time diffusion coefficients of dendrimers which accounts for the fact that, unlike nanoparticles, dendrimers shrink with an increase in background solution concentration. Analysis of the properties of a special case of a higher functionality dendrimer shows a transition from polymer-like to nanoparticle-like behaviour.

How important are fluctuations in the treatment of internal friction in polymers?

The Rouse model with internal friction (RIF), a widely used theoretical framework to interpret the effects of internal friction on conformational transitions in biomolecules, is shown to be an approximate treatment that is based on preaveraging internal friction. By comparison with Brownian dynamics simulations of an exact coarse-grained model that incorporates fluctuations in internal friction, the accuracy of the preaveraged model predictions is examined both at and away from equilibrium. While the two models predict intrachain autocorrelations that approach each other for long enough chain segments, they differ in their predictions for shorter segments. Furthermore, the two models differ qualitatively in their predictions for the chain extension and viscosity in shear flow, which is taken to represent a prototypical out-of-equilibrium condition.

Computing 3D Chromatin Configurations from Contact Probability Maps by Inverse Brownian Dynamics.

The three-dimensional (3D) organization of chromatin, on the length scale of a few genes, is crucial in determining the functional state-accessibility and amount of gene expression-of the chromatin. Recent advances in chromosome conformation capture experiments provide partial information on the chromatin organization in a cell population, namely the contact count between any segment pairs, but not on the interaction strength that leads to these contact counts. However, given the contact matrix, determining the complete 3D organization of the whole chromatin polymer is an inverse problem. In this work, a novel inverse Brownian dynamics method based on a coarse-grained bead-spring chain model has been proposed to compute the optimal interaction strengths between different segments of chromatin such that the experimentally measured contact count probability constraints are satisfied. Applying this method to the α-globin gene locus in two different cell types, we predict the 3D organizations corresponding to active and repressed states of chromatin at the locus. We show that the average distance between any two segments of the region has a broad distribution and cannot be computed as a simple inverse relation based on the contact probability alone. The results presented for multiple normalization methods suggest that all measurable quantities may crucially depend on the nature of normalization. We argue that by experimentally measuring predicted quantities, one may infer the appropriate form of normalization.

Universality of the collapse transition of sticky polymers.

The universality of the swelling of the radius of gyration of a homopolymer relative to its value in the θ state, independent of polymer-solvent chemistry, in the crossover regime between θ and athermal solvent conditions, is well known. Here we study, by Brownian dynamics, a polymer model where a subset of monomers is labelled as "stickers". The mutual interaction of the stickers is more attractive than those of the other ("backbone") monomers, and has an additional important characteristic of "functionality" φ, i.e., the maximum number of stickers that can locally bind to a given sticker. A saturated bond formed in this manner remains bound until it breaks due to thermal fluctuations, a requirement which can be viewed as an additional Boolean degree of freedom that describes the bonding. This, in turn, makes the question of the order of the collapse transition a non-trivial one. Nevertheless, for the parameters that we have studied (in particular, φ = 1), we find a standard second-order θ collapse, using a renormalised solvent quality parameter that takes into account the increased average attraction due to the presence of stickers. We examine the swelling of the radius of gyration of such a sticky polymer relative to its value in the altered θ state, using a novel potential to model the various excluded volume interactions that occur between the monomers on the chain. We find that the swelling of such sticky polymers is identical to the universal swelling of homopolymers in the thermal crossover regime. Additionally, for our model, the Kuhn segment length under θ conditions is found to be the same for chains with and without stickers.

Rheological consequences of wet and dry friction in a dumbbell model with hydrodynamic interactions and internal viscosity.

The effect of fluctuating internal viscosity and hydrodynamic interactions on a range of rheological properties of dilute polymer solutions is examined using a finitely extensible dumbbell model for a polymer. Brownian dynamics simulations are used to compute both transient and steady state viscometric functions in shear flow. The results enable a careful differentiation of the influence, on rheological properties, of solvent-mediated friction from that of a dissipative mechanism that is independent of solvent viscosity. In particular, hydrodynamic interactions have a significant influence on the magnitude of the stress jump at the inception of shear flow, and on the transient viscometric functions, but a negligible effect on the steady state viscometric functions at high shear rates. Zero-shear rate viscometric functions of free-draining dumbbells remain essentially independent of the internal viscosity parameter, as predicted by the Gaussian approximation, but the inclusion of hydrodynamic interactions induces a dependence on both the hydrodynamic interaction and the internal viscosity parameter. Large values of the internal viscosity parameter lead to linear viscoelastic predictions that mimic the behavior of rigid dumbbell solutions. On the other hand, steady-shear viscometric functions at high shear rates differ in general from those for rigid dumbbells, depending crucially on the finite extensibility of the dumbbell spring.

Nicotine and cigarette smoke modulate Nrf2-BDNF-dopaminergic signal and neurobehavioral disorders in adult rat cerebral cortex.

BACKGROUND: Nicotine and cigarette smoking (CS) are associated with addiction behavior, drug-seeking, and abuse. However, the mechanisms that mediate this association especially, the role of brain-derived neurotrophic factor (BDNF), dopamine (DA), and nuclear factor erythroid 2-related factor 2 (Nrf2) signaling in the cerebral cortex, are not fully known. Therefore, we hypothesized that overexpression of BDNF and DA, and suppression of Nrf2 contribute to several pathological and behavioral alterations in adult cerebral cortex. Methodology/Principal Observations: We treated Wistar rats with different doses of oral nicotine and passive CS for 4-week (short-term) and 12-week (long-term) duration, where doses closely mimic the human smoking scenario. Our result showed dose-dependent association of anxiogenic and depressive behavior, and cognitive interference with neurodegeneration and DNA damage in the cerebral cortex upon exposure to nicotine/CS as compared to the control. Further, the results are linked to upregulation of oxidative stress, overexpression of BDNF, DA, and DA marker, tyrosine hydroxylase (TH), with concomitant downregulation of ascorbate and Nrf2 expression in the exposed cerebral cortex when compared with the control. CONCLUSION/SIGNIFICANCE: Overall, our data strongly suggest that the intervention of DA and BDNF, and depletion of antioxidants are important factors during nicotine/CS-induced cerebral cortex pathological changes leading to neurobehavioral impairments, which could underpin the novel therapeutic approaches targeted at tobacco smoking/nicotine's neuropsychological disorders including cognition and drug addiction.

Equilibrium binding energies from fluctuation theorems and force spectroscopy simulations.

Brownian dynamics simulations are used to study the detachment of a particle from a substrate. Although the model is simple and generic, we attempt to map its energy, length and time scales onto a specific experimental system, namely a bead that is weakly bound to a cell and then removed by an optical tweezer. The external driving force arises from the combined optical tweezer and substrate potentials, and thermal fluctuations are taken into account by a Brownian force. The Jarzynski equality and Crooks fluctuation theorem are applied to obtain the equilibrium free energy difference between the final and initial states. To this end, we sample non-equilibrium work trajectories for various tweezer pulling rates. We argue that this methodology should also be feasible experimentally for the envisioned system. Furthermore, we outline how the measurement of a whole free energy profile would allow the experimentalist to retrieve the unknown substrate potential by means of a suitable deconvolution. The influence of the pulling rate on the accuracy of the results is investigated, and umbrella sampling is used to obtain the equilibrium probability of particle escape for a variety of trap potentials.

Size, shape, and diffusivity of a single Debye-Hückel polyelectrolyte chain in solution.

Brownian dynamics simulations of a coarse-grained bead-spring chain model, with Debye-Hückel electrostatic interactions between the beads, are used to determine the root-mean-square end-to-end vector, the radius of gyration, and various shape functions (defined in terms of eigenvalues of the radius of gyration tensor) of a weakly charged polyelectrolyte chain in solution, in the limit of low polymer concentration. The long-time diffusivity is calculated from the mean square displacement of the centre of mass of the chain, with hydrodynamic interactions taken into account through the incorporation of the Rotne-Prager-Yamakawa tensor. Simulation results are interpreted in the light of the Odjik, Skolnick, Fixman, Khokhlov, and Khachaturian blob scaling theory (Everaers et al., Eur. Phys. J. E 8, 3 (2002)) which predicts that all solution properties are determined by just two scaling variables-the number of electrostatic blobs X and the reduced Debye screening length, Y. We identify three broad regimes, the ideal chain regime at small values of Y, the blob-pole regime at large values of Y, and the crossover regime at intermediate values of Y, within which the mean size, shape, and diffusivity exhibit characteristic behaviours. In particular, when simulation results are recast in terms of blob scaling variables, universal behaviour independent of the choice of bead-spring chain parameters, and the number of blobs X, is observed in the ideal chain regime and in much of the crossover regime, while the existence of logarithmic corrections to scaling in the blob-pole regime leads to non-universal behaviour.

Significance of thermal fluctuations and hydrodynamic interactions in receptor-ligand-mediated adhesive dynamics of a spherical particle in wall-bound shear flow.

The dynamics of adhesion of a spherical microparticle to a ligand-coated wall, in shear flow, is studied using a Langevin equation that accounts for thermal fluctuations, hydrodynamic interactions, and adhesive interactions. Contrary to the conventional assumption that thermal fluctuations play a negligible role at high Péclet numbers, we find that for particles with low surface densities of receptors, rotational diffusion caused by fluctuations about the flow and gradient directions aids in bond formation, leading to significantly greater adhesion on average, compared to simulations where thermal fluctuations are completely ignored. The role of wall hydrodynamic interactions on the steady-state motion of a particle, when the particle is close to the wall, has also been explored. At high Péclet numbers, the shear induced force that arises due to the stresslet part of the Stokes dipole plays a dominant role, reducing the particle velocity significantly and affecting the states of motion of the particle. The coupling between the translational and rotational degrees of freedom of the particle, brought about by the presence of hydrodynamic interactions, is found to have no influence on the binding dynamics. On the other hand, the drag coefficient, which depends on the distance of the particle from the wall, plays a crucial role at low rates of bond formation. A significant difference in the effect of both the shear force and the position-dependent drag force on the states of motion of the particle is observed when the Péclet number is small.

Optimization of a Brownian-dynamics algorithm for semidilute polymer solutions.

Simulating the static and dynamic properties of semidilute polymer solutions with Brownian dynamics (BD) requires the computation of a large system of polymer chains coupled to one another through excluded-volume and hydrodynamic interactions. In the presence of periodic boundary conditions, long-ranged hydrodynamic interactions are frequently summed with the Ewald summation technique. By performing detailed simulations that shed light on the influence of several tuning parameters involved both in the Ewald summation method, and in the efficient treatment of Brownian forces, we develop a BD algorithm in which the computational cost scales as O(N(1.8)), where N is the number of monomers in the simulation box. We show that Beenakker's original implementation of the Ewald sum, which is only valid for systems without bead overlap, can be modified so that θ solutions can be simulated by switching off excluded-volume interactions. A comparison of the predictions of the radius of gyration, the end-to-end vector, and the self-diffusion coefficient by BD, at a range of concentrations, with the hybrid lattice Boltzmann-molecular dynamics (LB-MD) method shows excellent agreement between the two methods. In contrast to the situation for dilute solutions, the LB-MD method is shown to be significantly more computationally efficient than the current implementation of BD for simulating semidilute solutions. We argue, however, that further optimizations should be possible.

Dynamic crossover scaling in polymer solutions.

The crossover region in the phase diagram of polymer solutions, in the regime above the overlap concentration, is explored by Brownian dynamics simulations to map out the universal crossover scaling functions for the gyration radius and the single-chain diffusion constant. Scaling considerations, our simulation results, and recently reported data on the polymer contribution to the viscosity obtained from rheological measurements on DNA systems support the assumption that there are simple relations between these functions, such that they can be inferred from one another.

Implicit and explicit solvent models for the simulation of a single polymer chain in solution: Lattice Boltzmann versus Brownian dynamics.

We present a comparative study of two computer simulation methods to obtain static and dynamic properties of dilute polymer solutions. The first approach is a recently established hybrid algorithm based on dissipative coupling between molecular dynamics and lattice Boltzmann (LB), while the second is standard Brownian dynamics (BD) with fluctuating hydrodynamic interactions. Applying these methods to the same physical system (a single polymer chain in a good solvent in thermal equilibrium) allows us to draw a detailed and quantitative comparison in terms of both accuracy and efficiency. It is found that the static conformations of the LB model are distorted when the box length L is too small compared to the chain size. Furthermore, some dynamic properties of the LB model are subject to an L(-1) finite-size effect, while the BD model directly reproduces the asymptotic L-->infinity behavior. Apart from these finite-size effects, it is also found that in order to obtain the correct dynamic properties for the LB simulations, it is crucial to properly thermalize all the kinetic modes. Only in this case, the results are in excellent agreement with each other, as expected. Moreover, Brownian dynamics is found to be much more efficient than lattice Boltzmann as long as the degree of polymerization is not excessively large.

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.

Rheological observation of glassy dynamics of dilute polymer solutions near the coil-stretch transition in elongational flows.

It has long been conjectured that the macroscopic dynamics of dilute polymer solutions may exhibit a glasslike slowdown caused by ergodicity breaking, in the vicinity of the coil-stretch transition in elongational flows. We report experimental observations using a filament stretching rheometer that confirm the existence of such glassy states. It is observed that different time-dependent elongational strain-rate profiles lead to a pronounced history dependence and aging effects within a narrow range of strain rates. The results have a direct bearing on the analysis and design of processes employing dilute polymer solutions, such as ink-jet printing, surface coating, and turbulent-drag reduction.

Universal consequences of the presence of excluded volume interactions in dilute polymer solutions undergoing shear flow.

The role of solvent quality in determining the universal material properties of dilute polymer solutions undergoing steady simple shear flow is examined. A bead-spring chain representation of the polymer molecule is used, and the influence of solvent molecules on polymer conformations is modelled by a narrow Gaussian excluded volume potential that acts pairwise between the beads of the chain. Brownian dynamics simulations data, acquired for chains of finite length, and extrapolated to the limit of infinite chain length, are shown to be model independent. This feature of the narrow Gaussian potential, which leads to results identical to a delta-function repulsive potential, enables the prediction of both universal crossover scaling functions and asymptotic behavior in the excluded volume limit. Universal viscometric functions, obtained by this procedure, are found to exhibit increased shear thinning with increasing solvent quality. In the excluded volume limit, they are found to obey power law scaling with the characteristic shear rate beta, in close agreement with previously obtained renormalization group results. The presence of excluded volume interactions is also shown to lead to a weakening of the alignment of the polymer chain with the flow direction.