27 research outputs found
Freezing Transition of Random Heteropolymers Consisting of an Arbitrary Set of Monomers
Mean field replica theory is employed to analyze the freezing transition of
random heteropolymers comprised of an arbitrary number () of types of
monomers. Our formalism assumes that interactions are short range and
heterogeneity comes only from pairwise interactions, which are defined by an
arbitrary matrix. We show that, in general, there exists a
freezing transition from a random globule, in which the thermodynamic
equilibrium is comprised of an essentially infinite number polymer
conformations, to a frozen globule, in which equilibrium ensemble is dominated
by one or very few conformations. We also examine some special cases of
interaction matrices to analyze the relationship between the freezing
transition and the nature of interactions involved.Comment: 30 pages, 1 postscript figur
Deviations from the mean field predictions for the phase behaviour of random copolymers melts
We investigate the phase behaviour of random copolymers melts via large scale
Monte Carlo simulations. We observe macrophase separation into A and B--rich
phases as predicted by mean field theory only for systems with a very large
correlation lambda of blocks along the polymer chains, far away from the
Lifshitz point. For smaller values of lambda, we find that a locally
segregated, disordered microemulsion--like structure gradually forms as the
temperature decreases. As we increase the number of blocks in the polymers, the
region of macrophase separation further shrinks. The results of our Monte Carlo
simulation are in agreement with a Ginzburg criterium, which suggests that mean
field theory becomes worse as the number of blocks in polymers increases.Comment: 6 pages, 4 figures, Late
Mechanical response of random heteropolymers
We present an analytical theory for heteropolymer deformation, as exemplified
experimentally by stretching of single protein molecules. Using a mean-field
replica theory, we determine phase diagrams for stress-induced unfolding of
typical random sequences. This transition is sharp in the limit of infinitely
long chain molecules. But for chain lengths relevant to biological
macromolecules, partially unfolded conformations prevail over an intermediate
range of stress. These necklace-like structures, comprised of alternating
compact and extended subunits, are stabilized by quenched variations in the
composition of finite chain segments. The most stable arrangements of these
subunits are largely determined by preferential extension of segments rich in
solvophilic monomers. This predicted significance of necklace structures
explains recent observations in protein stretching experiments. We examine the
statistical features of select sequences that give rise to mechanical strength
and may thus have guided the evolution of proteins that carry out mechanical
functions in living cells.Comment: 10 pages, 6 figure
Sequence randomness and polymer collapse transitions
Contrary to expectations based on Harris' criterion, chain disorder with
frustration can modify the universality class of scaling at the theta
transition of heteropolymers. This is shown for a model with random two-body
potentials in 2D on the basis of exact enumeration and accurate Monte Carlo
results. When frustration grows beyond a certain finite threshold, the
temperature below which disorder becomes relevant coincides with the theta one
and scaling exponents definitely start deviating from those valid for
homopolymers.Comment: 4 pages, 4 eps figure
Adsorption-like Collapse of Diblock Copolymers
A linear copolymer made of two reciprocally attracting N-monomer blocks
collapses to a compact phase through a novel transition, whose exponents are
determined with extensive MC simulations in two and three dimensions. In the
former case, an identification with the statistical geometry of suitable
percolation paths allows to predict that the number of contacts between the
blocks grows like . In the compact phase the blocks are mixed and, in
two dimensions, also zipped, in such a way to form a spiral, double chain
structure.Comment: 4 pages, 5 Postscript figure
Embedding a Native State into a Random Heteropolymer Model: The Dynamic Approach
We study a random heteropolymer model with Langevin dynamics, in the
supersymmetric formulation. Employing a procedure similar to one that has been
used in static calculations, we construct an ensemble in which the affinity of
the system for a native state is controlled by a "selection temperature" T0. In
the limit of high T0, the model reduces to a random heteropolymer, while for
T0-->0 the system is forced into the native state. Within the Gaussian
variational approach that we employed previously for the random heteropolymer,
we explore the phases of the system for large and small T0. For large T0, the
system exhibits a (dynamical) spin glass phase, like that found for the random
heteropolymer, below a temperature Tg. For small T0, we find an ordered phase,
characterized by a nonzero overlap with the native state, below a temperature
Tn \propto 1/T0 > Tg. However, the random-globule phase remains locally stable
below Tn, down to the dynamical glass transition at Tg. Thus, in this model,
folding is rapid for temperatures between Tg and Tn, but below Tg the system
can get trapped in conformations uncorrelated with the native state. At a lower
temperature, the ordered phase can also undergo a dynamical glass transition,
splitting into substates separated by large barriers.Comment: 19 pages, revtex, 6 figure