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.

Motor-driven Dynamics of Cytoskeletal FIlaments in Motility Assays

We model analytically the dynamics of a cytoskeletal filament in a motility assay. The filament is described as rigid rod free to slide in two dimensions. The motor proteins consist of polymeric tails tethered to the plane and modeled as linear springs and motor heads that bind to the filament. As in related models of rigid and soft two-state motors, the binding/unbinding dynamics of the motor heads and the dependence of the transition rates on the load exerted by the motor tails play a crucial role in controlling the filament's dynamics. Our work shows that the filament effectively behaves as a self-propelled rod at long times, but with non-Markovian noise sources arising from the coupling to the motor binding/unbinding dynamics. The effective propulsion force of the filament and the active renormalization of the various friction and diffusion constants are calculated in terms of microscopic motor and filament parameters. These quantities could be probed by optical force microscopy.Comment: 13 pages, 8 figures, 1 Tabl

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

Filament networks using theoretical physics

Kristian Müller-Nedebock’s association with Stellenbosch began when his parents moved the family here from his place of birth, Eshowe, in KwaZulu-Natal. With predilections for libraries, Lego and Latin, his pursuit of drama, music and experimental construction and electronics projects at home pointed toward a future academic career. Eventually, after enthusing about many disciplines, conversations with inspirational academics at Stellenbosch University led Kristian to settle on the study of physics. Following his B.Sc. and honours degrees, with a focus on theoretical physics, Kristian received a scholarship from the Emanuel Bradlow Foundation to pursue Ph.D. studies as a member of St John’s College, Cambridge. It was at the University of Cambridge, under the supervision of Professor Sir Sam Edwards at the Cavendish Laboratory, that he commenced studying aspects of the networks that are also the topic of this inaugural lecture. But he also attended many superb concerts played on period instruments, punted on the Cam and discovered that May Week occurs in June. Kristian subsequently moved to Mainz, Germany, as a post-doctoral researcher. There he derived equations for the behaviours of various types of polyelectrolytes and polyampholytes – electrically charged polymers. (It is perhaps also there that his accent became completely untraceable for most listeners.) During this period an unexpected encounter in Paris eventually led to the sequence of events that culminated with his appointment in the Physics Department at Stellenbosch University. Kristian spends his time tracing and assembling the mathematical-physical threads for filaments as they are found in cells. His theatre is the lecture hall. He has taught at the African Institute for Mathematical Sciences. He is currently serving on the council of the South African Institute of Physics, which also awarded him the Silver Jubilee Medal in 2003. Every so often he still uses a smidgeon of Latin