301 research outputs found
An Analytical Approach to the Protein Designability Problem
We present an analytical method for determining the designability of protein
structures. We apply our method to the case of two-dimensional lattice
structures, and give a systematic solution for the spectrum of any structure.
Using this spectrum, the designability of a structure can be estimated. We
outline a heirarchy of structures, from most to least designable, and show that
this heirarchy depends on the potential that is used.Comment: 16 pages 4 figure
Localization in simple multiparticle catalytic absorption model
We consider the phase transition in the system of n simultaneously developing
random walks on the halfline x>=0. All walks are independent on each others in
all points except the origin x=0, where the point well is located. The well
depth depends on the number of particles simultaneously staying at x=0. We
consider the limit n>>1 and show that if the depth growth faster than 3/2 n
ln(n) with n, then all random walks become localized simultaneously at the
origin. In conclusion we discuss the connection of that problem with the phase
transition in the copolymer chain with quenched random sequence of monomers
considered in the frameworks of replica approach.Comment: 17 pages in LaTeX, 5 PostScript figures; submitted to J.Phys.(A):
Math. Ge
Free Energy Self-Averaging in Protein-Sized Random Heteropolymers
Current theories of heteropolymers are inherently macrpscopic, but are
applied to folding proteins which are only mesoscopic. In these theories, one
computes the averaged free energy over sequences, always assuming that it is
self-averaging -- a property well-established only if a system with quenched
disorder is macroscopic. By enumerating the states and energies of compact 18,
27, and 36mers on a simplified lattice model with an ensemble of random
sequences, we test the validity of the self-averaging approximation. We find
that fluctuations in the free energy between sequences are weak, and that
self-averaging is a valid approximation at the length scale of real proteins.
These results validate certain sequence design methods which can exponentially
speed up computational design and greatly simplify experimental realizations.Comment: 4 pages, 3 figure
Two-Dimensional Polymers with Random Short-Range Interactions
We use complete enumeration and Monte Carlo techniques to study
two-dimensional self-avoiding polymer chains with quenched ``charges'' .
The interaction of charges at neighboring lattice sites is described by . We find that a polymer undergoes a collapse transition at a temperature
, which decreases with increasing imbalance between charges. At the
transition point, the dependence of the radius of gyration of the polymer on
the number of monomers is characterized by an exponent , which is slightly larger than the similar exponent for homopolymers. We
find no evidence of freezing at low temperatures.Comment: 4 two-column pages, 6 eps figures, RevTex, Submitted to Phys. Rev.
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
Origin of Native Driving Force in Protein Folding
We derive an expression with four adjustable parameters that reproduces well
the 20x20 Miyazawa-Jernigan potential matrix extracted from known protein
structures. The numerical values of the parameters can be approximately
computed from the surface tension of water, water-screened dipole interactions
between residues and water and among residues, and average exposures of
residues in folded proteins.Comment: LaTeX file, Postscript file; 4 pages, 1 figure (mij.eps), 2 table
Folding, Design and Determination of Interaction Potentials Using Off-Lattice Dynamics of Model Heteropolymers
We present the results of a self-consistent, unified molecular dynamics study
of simple model heteropolymers in the continuum with emphasis on folding,
sequence design and the determination of the interaction parameters of the
effective potential between the amino acids from the knowledge of the native
states of the designed sequences.Comment: 8 pages, 3 Postscript figures, uses RevTeX. Submitted to Physical
Review Letter
Nucleation phenomena in protein folding: The modulating role of protein sequence
For the vast majority of naturally occurring, small, single domain proteins
folding is often described as a two-state process that lacks detectable
intermediates. This observation has often been rationalized on the basis of a
nucleation mechanism for protein folding whose basic premise is the idea that
after completion of a specific set of contacts forming the so-called folding
nucleus the native state is achieved promptly. Here we propose a methodology to
identify folding nuclei in small lattice polymers and apply it to the study of
protein molecules with chain length N=48. To investigate the extent to which
protein topology is a robust determinant of the nucleation mechanism we compare
the nucleation scenario of a native-centric model with that of a sequence
specific model sharing the same native fold. To evaluate the impact of the
sequence's finner details in the nucleation mechanism we consider the folding
of two non- homologous sequences. We conclude that in a sequence-specific model
the folding nucleus is, to some extent, formed by the most stable contacts in
the protein and that the less stable linkages in the folding nucleus are solely
determined by the fold's topology. We have also found that independently of
protein sequence the folding nucleus performs the same `topological' function.
This unifying feature of the nucleation mechanism results from the residues
forming the folding nucleus being distributed along the protein chain in a
similar and well-defined manner that is determined by the fold's topological
features.Comment: 10 Figures. J. Physics: Condensed Matter (to appear
Reversible stretching of homopolymers and random heteropolymers
We have analyzed the equilibrium response of chain molecules to stretching.
For a homogeneous sequence of monomers, the induced transition from compact
globule to extended coil below the -temperature is predicted to be
sharp. For random sequences, however, the transition may be smoothed by a
prevalence of necklace-like structures, in which globular regions and coil
regions coexist in a single chain. As we show in the context of a random
copolymer, preferential solvation of one monomer type lends stability to such
structures. The range of stretching forces over which necklaces are stable is
sensitive to chain length as well as sequence statistics.Comment: 14 pages, 4 figure
- …