687 research outputs found
Raft Instability of Biopolymer Gels
Following recent X-ray diffraction experiments by Wong, Li, and Safinya on
biopolymer gels, we apply Onsager excluded volume theory to a nematic mixture
of rigid rods and strong ``'' cross-linkers obtaining a long-ranged,
highly anisotropic depletion attraction between the linkers. This attraction
leads to breakdown of the percolation theory for this class of gels, to
breakdown of Onsager's second-order virial method, and to formation of
heterogeneities in the form of raft-like ribbons.Comment: 5 pages, 4 figure
Scaling Laws of Polyelectrolyte Adsorption
Adsorption of charged polymers (polyelectrolytes) from a semi-dilute solution
to a charged surface is investigated theoretically. We obtain simple scaling
laws for (i) the amount of polymer adsorbed to the surface, Gamma, and (ii) the
width of the adsorbed layer D, as function of the fractional charge per monomer
p and the salt concentration c_b. For strongly charged polyelectrolytes (p<1)
in a low-salt solution, both Gamma and D scale as p^{-1/2}. In salt-rich
solutions D~c_b^{1/2}/p whereas the scaling behavior of Gamma depends on the
strength of the polymer charge. For weak polyelectrolytes (p<<1) we find that
Gamma~p/c_b^{1/2} while for strong polyelectrolytes Gamma~c_b^{1/2}/p. Our
results are in good agreement with adsorption experiments and with numerical
solutions of mean-field equations.Comment: 13 pages, RevTex + epsf, 9 postscript figures; minor correction
Random Polyelectrolytes and Polyampholytes in Solution
The behavior of polyelectrolytes and polyampholytes in semi-dilute solutions
is investigated theoretically. Various statistical charge distributions along
the polyelectrolyte chains are considered: smeared, annealed, permuted and
quenched. Annealed polyampholytes are also considered. Path integral
formulation was used to derive mean field free energies for the different
models. Self-consistent field equation is obtained for the polymer order
parameter and a Poisson-Boltzmann like equation for the electrostatic
potential. The random phase approximation is used to calculate the
monomer-monomer structure factor S(q) for the different statistical charge
distribution models. We show that in the annealed model, fluctuations of the
the monomer charges contribute to the electrostatic screening in addition to
the free ions in the solution. The strength of this screening depends on the
variance of the monomer charge distribution and is especially important for
polyampholytes in bad solvent conditions where the mesophase separation is
enhanced. The ratio between the variance and the net average charge determines
whether polyampholytes behave as polyelectrolytes or as neutral chains.Comment: 18 pages, 5 figures, submitted to Eur. Phys. J.
Inter-filament Attractions Narrow the Length Distribution of Actin Filaments
We show that the exponential length distribution that is typical of actin
filaments under physiological conditions dramatically narrows in the presence
of (i) crosslinker proteins (ii) polyvalent counterions or (iii) depletion
mediated attractions. A simple theoretical model shows that in equilibrium,
short-range attractions enhance the tendency of filaments to align parallel to
each other, eventually leading to an increase in the average filament length
and a decrease in the relative width of the distribution of filament lengths.Comment: 5 pages, 4 figure
Structural Polymorphism of the Cytoskeleton: A Model of Linker-Assisted Filament Aggregation
The phase behavior of charged rods in the presence of inter-rod linkers is
studied theoretically as a model for the equilibrium behavior underlying the
organization of actin filaments by linker proteins in the cytoskeleton. The
presence of linkers in the solution modifies the effective inter-rod
interaction and can lead to inter-filament attraction. Depending on the
system's composition and physical properties such as linker binding energies,
filaments will either orient perpendicular or parallel to each other, leading
to network-like or bundled structures. We show that such a system can have one
of three generic phase diagrams, one dominated by bundles, another by networks,
and the third containing both bundle and network-like phases. The first two
diagrams can be found over a wide range of interaction energies, while the
third occurs only for a narrow range. These results provide theoretical
understanding of the classification of linker proteins as bundling proteins or
crosslinking proteins. In addition, they suggest possible mechanisms by which
the cell may control cytoskeletal morphology.Comment: 17 pages, 3 figure
Bending Moduli of Charged Membranes Immersed in Polyelectrolyte Solutions
We study the contribution of polyelectrolytes in solution to the bending
moduli of charged membranes. Using the Helfrich free energy, and within the
mean-field theory, we calculate the dependence of the bending moduli on the
electrostatics and short-range interactions between the membrane and the
polyelectrolyte chains. The most significant effect is seen for strong
short-range interactions and low amounts of added salt where a substantial
increase in the bending moduli of order is obtained. From short-range
repulsive membranes, the polyelectrolyte contribution to the bending moduli is
small, of order up to at most . For weak short-range
attraction, the increase in membrane rigidity is smaller and of less
significance. It may even become negative for large enough amounts of added
salt. Our numerical results are obtained by solving the adsorption problem in
spherical and cylindrical geometries. In some cases the bending moduli are
shown to follow simple scaling laws.Comment: 16 pages, 6 figure
Polyelectrolyte multilayer formation: electrostatics and short-range interactions
We investigate the phenomenon of multilayer formation via layer-by-layer
deposition of alternating charge polyelectrolytes. Using mean-field theory, we
find that a strong short-range attraction between the two types of polymer
chains is essential for the formation of multilayers. The dependence of the
required short-range attraction on the polymer charge fraction and salt
concentration is calculated. For weak short-range attraction between any two
adjacent layers, the adsorbed amount (per added layer) decays as the distance
from the surface increases, until the chains stop adsorbing altogether. For
strong short-range attraction, the adsorbed amount per layer increases after an
initial decrease, and finally it stabilizes in the form of a polyelectrolyte
multilayer that can be repeated many times.Comment: 8 pages, 7 figure
- …