264 research outputs found
Diffusive Dynamics of the Reaction Coordinate for Protein Folding Funnels
The quantitative description of model protein folding kinetics using a
diffusive collective reaction coordinate is examined. Direct folding kinetics,
diffusional coefficients and free energy profiles are determined from Monte
Carlo simulations of a 27-mer, 3 letter code lattice model, which corresponds
roughly to a small helical protein. Analytic folding calculations, using simple
diffusive rate theory, agree extremely well with the full simulation results.
Folding in this system is best seen as a diffusive, funnel-like process.Comment: LaTeX 12 pages, figures include
A New Monte Carlo Algorithm for Protein Folding
We demonstrate that the recently proposed pruned-enriched Rosenbluth method
(P. Grassberger, Phys. Rev. E 56 (1997) 3682) leads to extremely efficient
algorithms for the folding of simple model proteins. We test them on several
models for lattice heteropolymers, and compare to published Monte Carlo
studies. In all cases our algorithms are faster than all previous ones, and in
several cases we find new minimal energy states. In addition to ground states,
our algorithms give estimates for the partition sum at finite temperatures.Comment: 4 pages, Latex incl. 3 eps-figs., submitted to Phys. Rev. Lett.,
revised version with changes in the tex
Flat histogram simulation of lattice polymer systems
We demonstrate the use of a new algorithm called the Flat Histogram sampling
algorithm for the simulation of lattice polymer systems. Thermodynamics
properties, such as average energy or entropy and other physical quantities
such as end-to-end distance or radius of gyration can be easily calculated
using this method. Ground-state energy can also be determined. We also explore
the accuracy and limitations of this method.
Key words: Monte Carlo algorithms, flat histogram sampling, HP model, lattice
polymer systemsComment: 7 RevTeX two-column page
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
Modeling study on the validity of a possibly simplified representation of proteins
The folding characteristics of sequences reduced with a possibly simplified
representation of five types of residues are shown to be similar to their
original ones with the natural set of residues (20 types or 20 letters). The
reduced sequences have a good foldability and fold to the same native structure
of their optimized original ones. A large ground state gap for the native
structure shows the thermodynamic stability of the reduced sequences. The
general validity of such a five-letter reduction is further studied via the
correlation between the reduced sequences and the original ones. As a
comparison, a reduction with two letters is found not to reproduce the native
structure of the original sequences due to its homopolymeric features.Comment: 6 pages with 4 figure
Coarse grained description of the protein folding
We consider two- and three-dimensional lattice models of proteins which were
characterized previously. We coarse grain their folding dynamics by reducing it
to transitions between effective states. We consider two methods of selection
of the effective states. The first method is based on the steepest descent
mapping of states to underlying local energy minima and the other involves an
additional projection to maximally compact conformations. Both methods generate
connectivity patterns that allow to distinguish between the good and bad
folders. Connectivity graphs corresponding to the folding funnel have few loops
and are thus tree-like. The Arrhenius law for the median folding time of a
16-monomer sequence is established and the corresponding barrier is related to
easily identifiable kinetic trap states.Comment: REVTeX, 9 pages, 15 EPS figures, to appear in Phys. Rev.
Dynamical chaos and power spectra in toy models of heteropolymers and proteins
The dynamical chaos in Lennard-Jones toy models of heteropolymers is studied
by molecular dynamics simulations. It is shown that two nearby trajectories
quickly diverge from each other if the heteropolymer corresponds to a random
sequence. For good folders, on the other hand, two nearby trajectories may
initially move apart but eventually they come together. Thus good folders are
intrinsically non-chaotic. A choice of a distance of the initial conformation
from the native state affects the way in which a separation between the twin
trajectories behaves in time. This observation allows one to determine the size
of a folding funnel in good folders. We study the energy landscapes of the toy
models by determining the power spectra and fractal characteristics of the
dependence of the potential energy on time. For good folders, folding and
unfolding trajectories have distinctly different correlated behaviors at low
frequencies.Comment: 8 pages, 9 EPS figures, Phys. Rev. E (in press
Designability of lattice model heteropolymers
Protein folds are highly designable, in the sense that many sequences fold to
the same conformation. In the present work we derive an expression for the
designability in a 20 letter lattice model of proteins which, relying only on
the Central Limit Theorem, has a generality which goes beyond the simple model
used in its derivation. This expression displays an exponential dependence on
the energy of the optimal sequence folding on the given conformation measured
with respect to the lowest energy of the conformational dissimilar structures,
energy difference which constitutes the only parameter controlling
designability. Accordingly, the designability of a native conformation is
intimately connected to the stability of the sequences folding to them.Comment: in press on Phys. Rev.
- …