Selective permeability in gels: Beyond the solution-diffusion model

Permeability, a measure of potential transport of macromolecules through crowded media such as hydrogels, determines important control parameters in bio-soft functional material applications, e.g., for filtration, drug release, and transport of reactants in responsive nano-reactors. Tuning permeability is thus of great importance since it enables selective barrier crossings in molecular transport. We develop a model of semi- flexible cross-linked polymer gel networks by means of extensive coarse-grained simulations and scaling theories. The gel system consists of randomly formed tetra- functional network regions and also bulk regions where the macromolecular cosolutes diffuse in both regions, enabling a quantitative study of partitioning, diffusivity, and permeability. The gel undergoes a sharp volume transition upon changing inter- and intra-particle interactions, yielding a rich topology of the partitioning phase landscape which is highly correlated with the cosolute diffusivity. Moreover, we find that resultant permeability is largely maximized or minimized at an optimal gel density and inter-particle couplings between the networks and the cosolutes. This nontrivial phenomenon is triggered by a competition between partitioning and diffusion, resulting in a large anti-correlation. It is revealed that permeability can be highly selective by tuning the coupling interactions and the solvent quality. By applying external driving forces, we show this selectiveness of permeability beyond the linear response regime based on the solution-diffusion model. Finally we present scaling theories for partitioning, diffusion and thus permeability in crowded systems.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. Vicerrectorado de Investigación de la UM

How a single stretched polymer responds coherently to a minute oscillation in fluctuating environments: An entropic stochastic resonance

Within the cell, biopolymers are often situated in constrained, fluid environments, e.g., cytoskeletal networks, stretched DNAs in chromatin. It is of paramount importance to understand quantitatively how they, utilizing their flexibility, optimally respond to a minute signal, which is, in general, temporally fluctuating far away from equilibrium. To this end, we analytically study viscoelastic response and associated stochastic resonance in a stretched single semi-flexible chain to an oscillatory force or electric field. Including hydrodynamic interactions between chain segments, we evaluate dynamics of the polymer extension in coherent response to the force or field. We find power amplification factor of the response at a noise-strength (temperature) can attain the maximum that grows as the chain length increases, indicative of an entropic stochastic resonance (ESR). In particular for a charged chain under an electric field, we find that the maximum also occurs at an optimal chain length, a new feature of ESR. The hydrodynamic interaction is found to enhance the power amplification, representing unique polymer cooperativity which the fluid background imparts despite its overdamping nature. For the slow oscillatory force, the resonance behavior is explained by the chain undulation of the longest wavelength. This novel ESR phenomenon suggests how a biopolymer self-organizes in an overdamping environment, utilizing its flexibility and thermal fluctuations

The mean shape of transition and first-passage paths

We calculate the mean shape of transition paths and first-passage paths based on the one-dimensional Fokker-Planck equation in an arbitrary free energy landscape including a general inhomogeneous diffusivity profile. The transition path ensemble is the collection of all paths that do not revisit the start position $x_A$ and that terminate when first reaching the final position $x_B$. In contrast, a first-passage path can revisit but not cross its start position $x_A$ before it terminates at $x_B$. Our theoretical framework employs the forward and backward Fokker-Planck equations as well as first-passage, passage, last-passage and transition-path time distributions, for which we derive the defining integral equations. We show that the mean time at which the transition path ensemble visits an intermediate position $x$ is equivalent to the mean first-passage time of reaching the starting position $x_A$ from $x$ without ever visiting $x_B$. The mean shape of first-passage paths is related to the mean shape of transition paths by a constant time shift. Since for large barrier height $U$ the mean first-passage time scales exponentially in $U$ while the mean transition path time scales linearly inversely in $U$, the time shift between first-passage and transition path shapes is substantial. We present explicit examples of transition path shapes for linear and harmonic potentials and illustrate our findings by trajectories generated from Brownian dynamics simulations

Elasticity-based polymer sorting in active fluids: A Brownian dynamics study

While the dynamics of polymer chains in equilibrium media is well understood by now, the polymer dynamics in active non-equilibrium environments can be very different. Here we study the dynamics of polymers in a viscous medium containing self-propelled particles in two dimensions by using Brownian dynamics simulations. We find that the polymer center of mass exhibits a superdiffusive motion at short to intermediate times and the motion turns normal at long times, but with a greatly enhanced diffusivity. Interestingly, the long time diffusivity shows a non-monotonic behavior as a function of the chain length and stiffness. We analyze how the polymer conformation and the accumulation of the self-propelled particles, and therefore the directed motion of the polymer, are correlated. At the point of maximal polymer diffusivity, the polymer has preferentially bent conformations maintained by the balance between the chain elasticity and the propelling force generated by the active particles. We also consider the barrier crossing dynamics of actively-driven polymers in a double-well potential. The barrier crossing times are demonstrated to have a peculiar non-monotonic dependence, related to that of the diffusivity. This effect can be potentially utilized for sorting of polymers from solutions in \textit{in vitro} experiments.Comment: 11 pages, 7 figure

Genome-wide analysis to predict protein sequence variations that change phosphorylation sites or their corresponding kinases

We define phosphovariants as genetic variations that change phosphorylation sites or their interacting kinases. Considering the essential role of phosphorylation in protein functions, it is highly likely that phosphovariants change protein functions and may constitute a proportion of the mechanisms by which genetic variations cause individual differences or diseases. We categorized phosphovariants into three subtypes and developed a system that predicts them. Our method can be used to screen important polymorphisms and help to identify the mechanisms of genetic diseases