55 research outputs found
Protein sequence and structure: Is one more fundamental than the other?
We argue that protein native state structures reside in a novel "phase" of
matter which confers on proteins their many amazing characteristics. This phase
arises from the common features of all globular proteins and is characterized
by a sequence-independent free energy landscape with relatively few low energy
minima with funnel-like character. The choice of a sequence that fits well into
one of these predetermined structures facilitates rapid and cooperative
folding. Our model calculations show that this novel phase facilitates the
formation of an efficient route for sequence design starting from random
peptides.Comment: 7 pages, 4 figures, to appear in J. Stat. Phy
Ground-state properties of tubelike flexible polymers
In this work we investigate structural properties of native states of a
simple model for short flexible homopolymers, where the steric influence of
monomeric side chains is effectively introduced by a thickness constraint. This
geometric constraint is implemented through the concept of the global radius of
curvature and affects the conformational topology of ground-state structures. A
systematic analysis allows for a thickness-dependent classification of the
dominant ground-state topologies. It turns out that helical structures,
strands, rings, and coils are natural, intrinsic geometries of such tubelike
objects
Master equation approach to protein folding
The dynamics of two 12-monomer heteropolymers on the square lattice is
studied exactly within the master equation approach. The time evolution
of the occupancy of the native state is determined. At low temperatures,
the median folding time follows the Arrhenius law and is governed by the
longest relaxation time. For both good and bad folders, significant kinetic
traps appear in the folding funnel and the kinetics of the two kinds of folders
are quite similar. What distinguishes between the good and bad folders are
the differences in their thermodynamic stabilities.За допомогою методу керуючого рівняння точно проаналізована динаміка двох 12-мономерних гетерополімерів на квадратній гратці.
Визначена часова еволюція зайнятості нативного стану. При низьких температурах середній час скручування підлягає закону Ареніуса і визначається найдовшим часом релаксації. Для білків, що добре скручуються, з’являються суттєві кінетичні пастки у наборі послідовних конформацій, у той час як для білків, що погано скручуються,
пастки присутні також і в ділянках, що не відповідають нативній конформації
Some asymptotic properties of duplication graphs
Duplication graphs are graphs that grow by duplication of existing vertices,
and are important models of biological networks, including protein-protein
interaction networks and gene regulatory networks. Three models of graph growth
are studied: pure duplication growth, and two two-parameter models in which
duplication forms one element of the growth dynamics. A power-law degree
distribution is found to emerge in all three models. However, the parameter
space of the latter two models is characterized by a range of parameter values
for which duplication is the predominant mechanism of graph growth. For
parameter values that lie in this ``duplication-dominated'' regime, it is shown
that the degree distribution either approaches zero asymptotically, or
approaches a non-zero power-law degree distribution very slowly. In either
case, the approach to the true asymptotic degree distribution is characterized
by a dependence of the scaling exponent on properties of the initial degree
distribution. It is therefore conjectured that duplication-dominated,
scale-free networks may contain identifiable remnants of their early structure.
This feature is inherited from the idealized model of pure duplication growth,
for which the exact finite-size degree distribution is found and its asymptotic
properties studied.Comment: 19 pages, including 3 figure
On the low-temperature phase of the three-state antiferromagnetic Potts model on the simple cubic lattice
The three-state antiferromagnetic Potts model on the simple cubic lattice is
investigated using the cluster variation method in the cube and the star-cube
approximations. The broken-sublattice-symmetry phase is found to be stable in
the whole low-temperature region, contrary to previous results obtained using a
modified cluster variation method. The tiny free energy difference between the
broken-sublattice-symmetry and the permutationally-symmetric-sublattices phases
is calculated in the two approximations and turns out to be smaller in the
(more accurate) star-cube approximation than in the cube one.Comment: 4 pages REVTeX + 2 PostScript figures, to be published in Phys. Rev.
E as a Rapid Communicatio
A real space renormalization group approach to spin glass dynamics
The slow non-equilibrium dynamics of the Edwards-Anderson spin glass model on
a hierarchical lattice is studied by means of a coarse-grained description
based on renormalization concepts. We evaluate the isothermal aging properties
and show how the occurrence of temperature chaos is connected to a gradual loss
of memory when approaching the overlap length. This leads to rejuvenation
effects in temperature shift protocols and to rejuvenation--memory effects in
temperature cycling procedures with a pattern of behavior parallel to
experimental observations.Comment: 4 pages, 4 figure
Minimal H\"older regularity implying finiteness of integral Menger curvature
We study two families of integral functionals indexed by a real number . One family is defined for 1-dimensional curves in and the other one
is defined for -dimensional manifolds in . These functionals are
described as integrals of appropriate integrands (strongly related to the
Menger curvature) raised to power . Given we prove that
regularity of the set (a curve or a manifold), with implies finiteness of both curvature functionals
( in the case of curves). We also show that is optimal by
constructing examples of functions with graphs of infinite
integral curvature
Phase Diagram of the BCC S=1/2 Heisenberg Antiferromagnet with First and Second Neighbor Exchange
We use linked-cluster series expansions, both at T=0 and high temperature, to
analyse the phase structure of the spin-\half Heisenberg antiferromagnet with
competing first and second-neighbor interactions on the 3-dimensional
body-centred-cubic lattice. At zero temperature we find a first-order quantum
phase transition at between AF (Ne\'el)
and AF ordered phases. The high temperature series yield quite accurate
estimates of the bounding critical line for the AF phase, and an apparent
critical line for the AF phase, with a bicritical point at , . The possibility that this latter transition is
first-order cannot be excluded.Comment: 10 pages, 4 figure
Ordered phase and scaling in models and the three-state antiferromagnetic Potts model in three dimensions
Based on a Renormalization-Group picture of symmetric models in three
dimensions, we derive a scaling law for the order parameter in the
ordered phase. An existing Monte Carlo calculation on the three-state
antiferromagnetic Potts model, which has the effective symmetry, is shown
to be consistent with the proposed scaling law. It strongly supports the
Renormalization-Group picture that there is a single massive ordered phase,
although an apparently rotationally symmetric region in the intermediate
temperature was observed numerically.Comment: 5 pages in REVTEX, 2 PostScript figure
Growing dynamics of Internet providers
In this paper we present a model for the growth and evolution of Internet providers. The model reproduces the data observed for the Internet connection as probed by tracing routes from different computers. This problem represents a paramount case of study for growth processes in general, but can also help in the understanding the properties of the Internet. Our main result is that this network can be reproduced by a self-organized interaction between users and providers that can rearrange in time. This model can then be considered as a prototype model for the class of phenomena of aggregation processes in social networks
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