378 research outputs found
Collapse of Randomly Linked Polymers
We consider polymers in which M randomly selected pairs of monomers are
restricted to be in contact. Analytical arguments and numerical simulations
show that an ideal (Gaussian) chain of N monomers remains expanded as long as
M<<N. This result is inconsistent with results obtained from free energy
considerations by Brygelson and Thirumalai (PRL76, 542 (1996)).Comment: 1 page, 1 postscript figure, LaTe
Is Heteropolymer Freezing Well Described by the Random Energy Model?
It is widely held that the Random Energy Model (REM) describes the freezing
transition of a variety of types of heteropolymers. We demonstrate that the
hallmark property of REM, statistical independence of the energies of states
over disorder, is violated in different ways for models commonly employed in
heteropolymer freezing studies. The implications for proteins are also
discussed.Comment: 4 pages, 3 eps figures To appear in Physical Review Letters, May 199
Energy landscapes, supergraphs, and "folding funnels" in spin systems
Dynamical connectivity graphs, which describe dynamical transition rates
between local energy minima of a system, can be displayed against the
background of a disconnectivity graph which represents the energy landscape of
the system. The resulting supergraph describes both dynamics and statics of the
system in a unified coarse-grained sense. We give examples of the supergraphs
for several two dimensional spin and protein-related systems. We demonstrate
that disordered ferromagnets have supergraphs akin to those of model proteins
whereas spin glasses behave like random sequences of aminoacids which fold
badly.Comment: REVTeX, 9 pages, two-column, 13 EPS figures include
Folding in two-dimenensional off-lattice models of proteins
Model off-lattice sequences in two dimensions are constructed so that their
native states are close to an on-lattice target. The Hamiltonian involves the
Lennard-Jones and harmonic interactions. The native states of these sequences
are determined with a high degree of certainty through Monte Carlo processes.
The sequences are characterized thermodynamically and kinetically. It is shown
that the rank-ordering-based scheme of the assignment of contact energies
typically fails in off-lattice models even though it generates high stability
of on-lattice sequences. Similar to the on-lattice case, Go-like modeling, in
which the interaction potentials are restricted to the native contacts in a
target shape, gives rise to good folding properties. Involving other contacts
deteriorates these properties.Comment: REVTeX, 9 pages, 8 EPS figure
Statics, metastable states and barriers in protein folding: A replica variational approach
Protein folding is analyzed using a replica variational formalism to
investigate some free energy landscape characteristics relevant for dynamics. A
random contact interaction model that satisfies the minimum frustration
principle is used to describe the coil-globule transition (characterized by
T_CG), glass transitions (by T_A and T_K) and folding transition (by T_F).
Trapping on the free energy landscape is characterized by two characteristic
temperatures, one dynamic, T_A the other static, T_K (T_A> T_K), which are
similar to those found in mean field theories of the Potts glass. 1)Above T_A,
the free energy landscape is monotonous and polymer is melted both dynamically
and statically. 2)Between T_A and T_K, the melted phase is still dominant
thermodynamically, but frozen metastable states, exponentially large in number,
appear. 3)A few lowest minima become thermodynamically dominant below T_K,
where the polymer is totally frozen. In the temperature range between T_A and
T_K, barriers between metastable states are shown to grow with decreasing
temperature suggesting super-Arrhenius behavior in a sufficiently large system.
Due to evolutionary constraints on fast folding, the folding temperature T_F is
expected to be higher than T_K, but may or may not be higher than T_A. Diverse
scenarios of the folding kinetics are discussed based on phase diagrams that
take into account the dynamical transition, as well as the static ones.Comment: 41 pages, LaTeX, 9 EPS figure
What does the potential energy landscape tell us about the dynamics of supercooled liquids and glasses?
For a model glass-former we demonstrate via computer simulations how
macroscopic dynamic quantities can be inferred from a PEL analysis. The
essential step is to consider whole superstructures of many PEL minima, called
metabasins, rather than single minima. We show that two types of metabasins
exist: some allowing for quasi-free motion on the PEL (liquid-like), the others
acting as traps (solid-like). The activated, multi-step escapes from the latter
metabasins are found to dictate the slowing down of dynamics upon cooling over
a much broader temperature range than is currently assumed
Scaling of folding properties in simple models of proteins
Scaling of folding properties of proteins is studied in a toy system -- the
lattice Go model with various two- and three- dimensional geometries of the
maximally compact native states. Characteristic folding times grow as power
laws with the system size. The corresponding exponents are not universal.
Scaling of the thermodynamic stability also indicates size-related
deterioration of the folding properties.Comment: REVTeX, 4 pages, 4 EPS figures, PRL (in press
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