Density fields for branching, stiff networks in rigid confining regions

We develop a formalism to describe the equilibrium distributions for segments of confined branched networks consisting of stiff filaments. This is applicable to certain situations of cytoskeleton in cells, such as for example actin filaments with branching due to the Arp2/3 complex. We develop a grand ensemble formalism that enables the computation of segment density and polarisation profiles within the confines of the cell. This is expressed in terms of the solution to nonlinear integral equations for auxiliary functions. We find three specific classes of behaviour depending on filament length, degree of branching and the ratio of persistence length to the dimensions of the geometry. Our method allows a numerical approach for semi-flexible filaments that are networked.Comment: 15 pages, revise

Entropic competition in polymeric systems under geometrical confinement

Using molecular dynamics simulation, we investigate the effect of confinement on a system that comprises several stiff segmented polymer chains where each chain has similar segments, but length and stiffness of the segments vary among the chains which makes the system inhomogeneous. The translational and orientational entropy loss due to the confinement plays a crucial role in organizing the chains which can be considered as an entropy-driven segregation mechanism to differentiate the components of the system. Due to the inhomogeneity, both weak and strong confinement regimes show the competition in the system and we see segregation of chains as the confining volume is decreased. In the case of strong spherical confinement, a chain at the periphery shows higher angular mobility than other chains, despite being more radially constrained.Comment: 16 pages, 11 figure

Field-theoretical approach to a dense polymer with an ideal binary mixture of clustering centers

We propose a field-theoretical approach to a polymer system immersed in an ideal mixture of clustering centers. The system contains several species of these clustering centers with different functionality, each of which connects a fixed number segments of the chain to each other. The field-theory is solved using the saddle point approximation and evaluated for dense polymer melts using the Random Phase Approximation. We find a short-ranged effective inter-segment interaction with strength dependent on the average segment density and discuss the structure factor within this approximation. We also determine the fractions of linkers of the different functionalities.Comment: 27 pages, 9 figures, accepted on Phys. Rev.

Collective Dynamics of Random Polyampholytes

We consider the Langevin dynamics of a semi-dilute system of chains which are random polyampholytes of average monomer charge $q$ and with a fluctuations in this charge of the size $Q^{-1}$ and with freely floating counter-ions in the surrounding. We cast the dynamics into the functional integral formalism and average over the quenched charge distribution in order to compute the dynamic structure factor and the effective collective potential matrix. The results are given for small charge fluctuations. In the limit of finite $q$ we then find that the scattering approaches the limit of polyelectrolyte solutions.Comment: 13 pages including 6 figures, submitted J. Chem. Phy

Active force maintains the stability of a contractile ring

We investigate a system of sufficiently dense polar actin filaments considered rigid and cross-linked by dimer myosin II protein within the contractile ring. The Langevin dynamics of this system is cast in a functional integral formalism and then transformed into density variables. Using the dynamical Random Phase Approximation (RPA) along with the a one-dimensional Langevin dynamics simulation (LDS), we investigate the structural integrity of the actin bundle network. The active force and the networking force reveal a non-trivial diffusive behaviour of the filaments within the ring. We conclude on when the active and networking forces lead to the contractile ring breaking down. The non-equilibrium active force is predominantly responsible for the prevention of the gaps in the ring