10 research outputs found
Swelling of two-dimensional polymer rings by trapped particles
The mean area of a two-dimensional Gaussian ring of monomers is known to
diverge when the ring is subject to a critical pressure differential, . In a recent publication [Eur. Phys. J. E 19, 461 (2006)] we have shown
that for an inextensible freely jointed ring this divergence turns into a
second-order transition from a crumpled state, where the mean area scales as
, to a smooth state with . In the current work we
extend these two models to the case where the swelling of the ring is caused by
trapped ideal-gas particles. The Gaussian model is solved exactly, and the
freely jointed one is treated using a Flory argument, mean-field theory, and
Monte Carlo simulations. For fixed number of trapped particles the
criticality disappears in both models through an unusual mechanism, arising
from the absence of an area constraint. In the Gaussian case the ring swells to
such a mean area, , that the pressure exerted by the particles is
at for any . In the freely jointed model the mean area is such that
the particle pressure is always higher than , and consequently
follows a single scaling law, , for any . By contrast,
when the particles are in contact with a reservoir of fixed chemical potential,
the criticality is retained. Thus, the two ensembles are manifestly
inequivalent in these systems.Comment: 8 page
Law of corresponding states for osmotic swelling of vesicles
As solute molecules permeate into a vesicle due to a concentration difference
across its membrane, the vesicle swells through osmosis. The swelling can be
divided into two stages: (a) an "ironing" stage, where the volume-to-area ratio
of the vesicle increases without a significant change in its area; (b) a
stretching stage, where the vesicle grows while remaining essentially
spherical, until it ruptures. We show that the crossover between these two
stages can be represented as a broadened continuous phase transition.
Consequently, the swelling curves for different vesicles and different
permeating solutes can be rescaled into a single, theoretically predicted,
universal curve. Such a data collapse is demonstrated for giant unilamellar
POPC vesicles, osmotically swollen due to the permeation of urea, glycerol, or
ethylene glycol. We thereby gain a sensitive measurement of the solutes'
membrane permeability coefficients, finding a concentration-independent
coefficient for urea, while those of glycerol and ethylene glycol are found to
increase with solute concentration. In addition, we use the width of the
transition, as extracted from the data collapse, to infer the number of
independent bending modes that affect the thermodynamics of the vesicle in the
transition region.Comment: 10 page
Swelling of particle-encapsulating random manifolds
We study the statistical mechanics of a closed random manifold of fixed area
and fluctuating volume, encapsulating a fixed number of noninteracting
particles. Scaling analysis yields a unified description of such swollen
manifolds, according to which the mean volume gradually increases with particle
number, following a single scaling law. This is markedly different from the
swelling under fixed pressure difference, where certain models exhibit
criticality. We thereby indicate when the swelling due to encapsulated
particles is thermodynamically inequivalent to that caused by fixed pressure.
The general predictions are supported by Monte Carlo simulations of two
particle-encapsulating model systems -- a two-dimensional self-avoiding ring
and a three-dimensional self-avoiding fluid vesicle. In the former the
particle-induced swelling is thermodynamically equivalent to the
pressure-induced one whereas in the latter it is not.Comment: 8 pages, 6 figure
Critical swelling of particle-encapsulating vesicles
We consider a ubiquitous scenario where a fluctuating, semipermeable vesicle
is embedded in solution while enclosing a fixed number of solute particles. The
swelling with increasing number of particles or decreasing concentration of the
outer solution exhibits a continuous phase transition from a fluctuating state
to the maximum-volume configuration, whereupon appreciable pressure difference
and surface tension build up. This criticality is unique to
particle-encapsulating vesicles, whose volume and inner pressure both
fluctuate. It implies a universal swelling behavior of such vesicles as they
approach their limiting volume and osmotic lysis.Comment: 4 pages, 1 figur
Increased Concentration of Polyvalent Phospholipids in the Adsorption Domain of a Charged Protein
We studied the adsorption of a charged protein onto an oppositely charged
membrane, composed of mobile phospholipids of differing valence, using a
statistical-thermodynamical approach. A two-block model was employed, one block
corresponding to the protein-affected region on the membrane, referred to as
the adsorption domain, and the other to the unaffected remainder of the
membrane. We calculated the protein-induced lipid rearrangement in the
adsorption domain as arising from the interplay between the electrostatic
interactions in the system and the mixing entropy of the lipids. Equating the
electrochemical potentials of the lipids in the two blocks yields an expression
for the relations among the various lipid fractions in the adsorption domain,
indicating a sensitive dependence of lipid fraction on valence. This expression
is a result of the two-block picture but does not depend on further details of
the protein-membrane interaction. We subsequently calculated the lipid
fractions themselves using the Poisson-Boltzmann theory. We examined the
dependence of lipid enrichment, i.e., the ratio between the lipid fractions
inside and outside the adsorption domain, on various parameters such as ionic
strength and lipid valence. Maximum enrichment was found for lipid valence of
about (-3) to (-4) in physiological conditions. Our results are in qualitative
agreement with recent experimental studies on the interactions between peptides
having a domain of basic residues and membranes containing a small fraction of
the polyvalent phosphatidylinositol 4,5-bisphosphate (PIP2). This study
provides theoretical support for the suggestion that proteins adsorbed onto
membranes through a cluster of basic residues may sequester PIP2 and other
polyvalent lipids.Comment: 25 pages, 12 figure
Algorithms for Molecular Biology Fall Semester, 2001
Introduction 12.1.1 Background Proteins are long chains of Amino Acids (AA). There are 20 di#erent AAs that serve as building blocks for proteins. Each AA has a specific chemical structure which contains a carbon backbone similar to all amino acids and a residue which varies between the AAs. The length of a protein chain can range from 50 to 1000-3000 AA (200 on the average). Proteins are known to have many important functions in the cell, such as enzymatic activity, storage and transport of material, signal transduction, antibodies and more. An important property of a protein is the length and composition of the AA chain. The series can be obtained automatically from the gene that encodes for the protein. Another interesting property is the unique folding. The AA composition of a protein will usually uniquely determine (on specific environment conditions) the 3D structure of the protein (e.g., two proteins with the same AA sequence will have the same 3D structure in natural conditi