1,642 research outputs found
Swollen-Collapsed Transition in Random Hetero-Polymers
A lattice model of a hetero-polymer with random hydrophilic-hydrophobic
charges interacting with the solvent is introduced, whose continnuum
counterpart has been proposed by T. Garel, L. Leibler and H. Orland {J. Phys.
II France 4, 2139 (1994)]. The transfer matrix technique is used to study
various constrained annealed systems which approximate at various degrees of
accuracy the original quenched model. For highly hydrophobic chains an ordinary
-point transition is found from a high temperature swollen phase to a
low temperature compact phase. Depending on the type of constrained averages,
at very low temperatures a swollen phase or a coexistence between compact and
swollen phases are found. The results are carefully compared with the
corresponding ones obtained in the continuum limit, and various improvements in
the original calculations are discussed.Comment: 13 pages, 8 figures; revised version with minor changes, accepted for
publication in European Physical Journal
Cluster Derivation of the Parisi Scheme for Disordered Systems
We propose a general quantitative scheme in which systems are given the
freedom to sacrifice energy equi-partitioning on the relevant time-scales of
observation, and have phase transitions by separating autonomously into ergodic
sub-systems (clusters) with different characteristic time-scales and
temperatures. The details of the break-up follow uniquely from the requirement
of zero entropy for the slower cluster. Complex systems, such as the
Sherrington-Kirkpatrick model, are found to minimise their free energy by
spontaneously decomposing into a hierarchy of ergodically equilibrating degrees
of freedom at different (effective) temperatures. This leads exactly and
uniquely to Parisi's replica symmetry breaking scheme. Our approach, which is
somewhat akin to an earlier one by Sompolinsky, gives new insight into the
physical interpretation of the Parisi scheme and its relations with other
approaches, numerical experiments, and short range models. Furthermore, our
approach shows that the Parisi scheme can be derived quantitatively and
uniquely from plausible physical principles.Comment: 6 pages, 3 figures, proceedings of international conference on
"Disordered And Complex Systems", 10-14 July 2000 King's College Londo
Solvable Lattice Gas Models of Random Heteropolymers at Finite Density: II. Dynamics and Transitions to Compact States
In this paper we analyse both the dynamics and the high density physics of
the infinite dimensional lattice gas model for random heteropolymers recently
introduced in \cite{jort}. Restricting ourselves to site-disordered
heteropolymers, we derive exact closed deterministic evolution equations for a
suitable set of dynamic order parameters (in the thermodynamic limit), and use
these to study the dynamics of the system for different choices of the monomer
polarity parameters. We also study the equilibrium properties of the system in
the high density limit, which leads to a phase diagram exhibiting transitions
between swollen states, compact states, and regions with partial
compactification. Our results find excellent verification in numerical
simulations, and have a natural and appealing interpretation in terms of real
heteropolymers.Comment: 12 pages, 8 eps figures, revised version (to be published in EPJ
Magnetization enumerator of real-valued symmetric channels in Gallager error-correcting codes
Using the magnetization enumerator method, we evaluate the practical and
theoretical limitations of symmetric channels with real outputs. Results are
presented for several regular Gallager code constructions.Comment: 5 pages, 1 figure, to appear as Brief Report in Physical Review
Ultrafast electron diffraction using an ultracold source
We present diffraction patterns from micron-sized areas of mono-crystalline
graphite obtained with an ultracold and ultrafast electron source. We show that
high spatial coherence is manifest in the visibility of the patterns even for
picosecond bunches of appreciable charge, enabled by the extremely low source
temperature (~ 10 K). For a larger, ~ 100 um spot size on the sample, spatial
coherence lengths > 10 nm result, sufficient to resolve diffraction patterns of
complex protein crystals. This makes the source ideal for ultrafast electron
diffraction of complex macromolecular structures such as membrane proteins, in
a regime unattainable by conventional photocathode sources. By further reducing
the source size, sub-um spot sizes on the sample become possible with spatial
coherence lengths exceeding 1 nm, enabling ultrafast nano-diffraction for
material science.Comment: 5 pages, 4 figure
Determination of Interaction Potentials of Amino Acids from Native Protein Structures: Test on Simple Lattice Models
We propose a novel method for the determination of the effective interaction
potential between the amino acids of a protein. The strategy is based on the
combination of a new optimization procedure and a geometrical argument, which
also uncovers the shortcomings of any optimization procedure. The strategy can
be applied on any data set of native structures such as those available from
the Protein Data Bank (PDB). In this work, however, we explain and test our
approach on simple lattice models, where the true interactions are known a
priori. Excellent agreement is obtained between the extracted and the true
potentials even for modest numbers of protein structures in the PDB.
Comparisons with other methods are also discussed.Comment: 24 pages, 4 figure
A Solvable Model of Secondary Structure Formation in Random Hetero-Polymers
We propose and solve a simple model describing secondary structure formation
in random hetero-polymers. It describes monomers with a combination of
one-dimensional short-range interactions (representing steric forces and
hydrogen bonds) and infinite range interactions (representing polarity forces).
We solve our model using a combination of mean field and random field
techniques, leading to phase diagrams exhibiting second-order transitions
between folded, partially folded and unfolded states, including regions where
folding depends on initial conditions. Our theoretical results, which are in
excellent agreement with numerical simulations, lead to an appealing physical
picture of the folding process: the polarity forces drive the transition to a
collapsed state, the steric forces introduce monomer specificity, and the
hydrogen bonds stabilise the conformation by damping the frustration-induced
multiplicity of states.Comment: 24 pages, 14 figure
- …