16 research outputs found
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 and with a fluctuations in
this charge of the size 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 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