Pseudochemotaxis in inhomogeneous active Brownian systems

We study dynamical properties of confined, self-propelled Brownian particles in an inhomogeneous activity profile. Using Brownian dynamics simulations, we calculate the probability to reach a fixed target and the mean first passage time to the target of an active particle. We show that both these quantities are strongly influenced by the inhomogeneous activity. When the activity is distributed such that high-activity zone is located between the target and the starting location, the target finding probability is increased and the passage time is decreased in comparison to a uniformly active system. Moreover, for a continuously distributed profile, the activity gradient results in a drift of active particle up the gradient bearing resemblance to chemotaxis. Integrating out the orientational degrees of freedom, we derive an approximate Fokker-Planck equation and show that the theoretical predictions are in very good agreement with the Brownian dynamics simulations.Comment: 7 pages, 5 figure

Facilitated diffusion of DNA-binding proteins

The diffusion-controlled limit of reaction times for site-specific DNA-binding proteins is derived from first principles. We follow the generally accepted concept that a protein propagates via two competitive modes, a three-dimensional diffusion in space and a one-dimensional sliding along the DNA. However, our theoretical treatment of the problem is new. The accuracy of our analytical model is verified by numerical simulations. The results confirm that the unspecific binding of protein to DNA, combined with sliding, is capable to reduce the reaction times significantly.Comment: 4 pages, 2 figures Nov 22 2005 - accepted for PR

Modelling diffusional transport in the interphase cell nucleus

In this paper a lattice model for diffusional transport of particles in the interphase cell nucleus is proposed. Dense networks of chromatin fibers are created by three different methods: randomly distributed, non-interconnected obstacles, a random walk chain model, and a self avoiding random walk chain model with persistence length. By comparing a discrete and a continuous version of the random walk chain model, we demonstrate that lattice discretization does not alter particle diffusion. The influence of the 3D geometry of the fiber network on the particle diffusion is investigated in detail, while varying occupation volume, chain length, persistence length and walker size. It is shown that adjacency of the monomers, the excluded volume effect incorporated in the self avoiding random walk model, and, to a lesser extent, the persistence length, affect particle diffusion. It is demonstrated how the introduction of the effective chain occupancy, which is a convolution of the geometric chain volume with the walker size, eliminates the conformational effects of the network on the diffusion, i.e., when plotting the diffusion coefficient as a function of the effective chain volume, the data fall onto a master curve.Comment: 9 pages, 8 figure

Facilitated diffusion of DNA-binding proteins: Simulation of large systems

The recently introduced method of excess collisions (MEC) is modified to estimate diffusion-controlled reaction times inside systems of arbitrary size. The resulting MEC-E equations contain a set of empirical parameters, which have to be calibrated in numerical simulations inside a test system of moderate size. Once this is done, reaction times of systems of arbitrary dimensions are derived by extrapolation, with an accuracy of 10 to 15 percent. The achieved speed up, when compared to explicit simulations of the reaction process, is increasing proportional to the extrapolated volume of the cell.Comment: 8 pages, 4 figures, submitted to J. Chem. Phy

Nanoparticle Loading of Unentangled Polymers Induces Entanglement-Like Relaxation Modes and a Broad Sol-Gel Transition

We combine molecular dynamics simulations, imaging and data analysis, and the Green−Kubo summation formula for the relaxation modulus G(t) to elicit the structure and rheology of unentangled polymer−nanoparticle composites distinguished by small NPs and strong NP−monomer attraction, εNPM ≫ kBT. A reptation-like plateau emerges in G(t) beyond a terminal relaxation time scale as the volume fraction, cNP, of NPs increases, coincident with a structure transition. A condensed phase of NP-aggregates forms, tightly interlaced with thin sheets of polymer chains, the remaining phase consisting of free chains void of NPs. Rouse mode analyses are applied to the two individual phases, revealing that long-wavelength Rouse modes in the aggregate phase are the source of reptation-like relaxation. Imaging reveals chain motion confined within the thin sheets between NPs and exhibits a 2D analogue of classical reptation. In the NP-free phase, Rouse modes relax indistinguishable from a neat polymer melt. The Fourier transform of G(t) reveals a sol−gel transition across a broad frequency spectrum, tuned by cNP and εNPM above critical thresholds, below which all structure and rheological transitions vanish

Chain stiffness effect on the properties of topological polymer brushes and the penetration by free chains using MD simulation

Molecular dynamic simulations are carried out to study the static and dynamic properties of topological polymer brushes by taking into account chain stiffness and their topological feature. It is found that chain stiffness plays an important role in topological polymer brushes, and there exists scaling laws for the radius of gyration against chain stiffness and topological feature, indicating that bending interaction is as important as topological constraint. An empirical finitely extensible nonlinear elastic force in terms of chain stiffness and topological features is also obtained by fitting related parameters. A simulation on the invasion of free polymer chains from environment into a ring polymer brush shows that under pressure, such kind of penetration depends largely on chain stiffness, in contrast to the minor influence of topological structure, which seems to be suppressed

Chain stiffness boosts active nanoparticle transport in polymer networks

Recent advances in technologies such as nanomanufacturing and nanorobotics have opened new pathways for the design of active nanoparticles (NPs) capable of penetrating biolayers for biomedical applications, e.g., for drug delivery. The coupling and feedback between active NP motility (with large stochastic increments relative to passive NPs) and the induced nonequilibrium deformation and relaxation responses of the polymer network, spanning scales from the NP to the local structure of the network, remain to be clarified. Using molecular dynamics simulations, combined with a Rouse mode analysis of network chains and position and velocity autocorrelation functions of the NPs, we demonstrate that the mobility of active NPs within cross-linked, concentrated polymer networks is a monotonically increasing function of chain stiffness, contrary to passive NPs, for which chain stiffness suppresses mobility. In flexible networks, active NPs exhibit a behavior similar to passive NPs, with a boost in mobility proportional to the self-propulsion force. These results are suggestive of design strategies for active NP penetration of stiff biopolymer matrices