99 research outputs found
Basins of attraction for cascading maps
We study a finite uni-directional array of "cascading" or "threshold coupled"
chaotic maps. Such systems have been proposed for use in nonlinear computing
and have been applied to classification problems in bioinformatics. We describe
some of the attractors for such systems and prove general results about their
basins of attraction. In particular, we show that the basins of attraction have
infinitely many path components. We show that these components always
accumulate at the corners of the domain of the system. For all threshold
parameters above a certain value, we show that they accumulate at a Cantor set
in the interior of the domain. For certain ranges of the threshold, we prove
that the system has many attractors.Comment: 15 pages, 9 figures. To appear in International Journal of
Bifurcations and Chao
Universality and diversity of folding mechanics for three-helix bundle proteins
In this study we evaluate, at full atomic detail, the folding processes of
two small helical proteins, the B domain of protein A and the Villin headpiece.
Folding kinetics are studied by performing a large number of ab initio Monte
Carlo folding simulations using a single transferable all-atom potential. Using
these trajectories, we examine the relaxation behavior, secondary structure
formation, and transition-state ensembles (TSEs) of the two proteins and
compare our results with experimental data and previous computational studies.
To obtain a detailed structural information on the folding dynamics viewed as
an ensemble process, we perform a clustering analysis procedure based on graph
theory. Moreover, rigorous pfold analysis is used to obtain representative
samples of the TSEs and a good quantitative agreement between experimental and
simulated Fi-values is obtained for protein A. Fi-values for Villin are also
obtained and left as predictions to be tested by future experiments. Our
analysis shows that two-helix hairpin is a common partially stable structural
motif that gets formed prior to entering the TSE in the studied proteins. These
results together with our earlier study of Engrailed Homeodomain and recent
experimental studies provide a comprehensive, atomic-level picture of folding
mechanics of three-helix bundle proteins.Comment: PNAS, in press, revised versio
Three-body Interactions Improve the Prediction of Rate and Mechanism in Protein Folding Models
Here we study the effects of many-body interactions on rate and mechanism in
protein folding, using the results of molecular dynamics simulations on
numerous coarse-grained C-alpha-model single-domain proteins. After adding
three-body interactions explicitly as a perturbation to a Go-like Hamiltonian
with native pair-wise interactions only, we have found 1) a significantly
increased correlation with experimental phi-values and folding rates, 2) a
stronger correlation of folding rate with contact order, matching the
experimental range in rates when the fraction of three-body energy in the
native state is ~ 20%, and 3) a considerably larger amount of 3-body energy
present in Chymotripsin inhibitor than other proteins studied.Comment: 9 pages, 2 tables and 5 figure
Investigation of routes and funnels in protein folding by free energy functional methods
We use a free energy functional theory to elucidate general properties of
heterogeneously ordering, fast folding proteins, and we test our conclusions
with lattice simulations. We find that both structural and energetic
heterogeneity can lower the free energy barrier to folding. Correlating
stronger contact energies with entropically likely contacts of a given native
structure lowers the barrier, and anticorrelating the energies has the reverse
effect. Designing in relatively mild energetic heterogeneity can eliminate the
barrier completely at the transition temperature. Sequences with native
energies tuned to fold uniformly, as well as sequences tuned to fold by a
single or a few routes, are rare. Sequences with weak native energetic
heterogeneity are more common; their folding kinetics is more strongly
determined by properties of the native structure. Sequences with different
distributions of stability throughout the protein may still be good folders to
the same structure. A measure of folding route narrowness is introduced which
correlates with rate, and which can give information about the intrinsic biases
in ordering due to native topology. This theoretical framework allows us to
systematically investigate the coupled effects of energy and topology in
protein folding, and to interpret recent experiments which investigate these
effects.Comment: 12 pages, 1 figure, to appear in Proc. Natl. Acad. Sc
Microsecond folding dynamics of the F13W G29A mutant of the B domain of staphylococcal protein A by laser-induced temperature jump
The small size (58 residues) and simple structure of the B domain of staphylococcal protein A (BdpA) have led to this domain being a paradigm for theoretical studies of folding. Experimental studies of the folding of BdpA have been limited by the rapidity of its folding kinetics. We report the folding kinetics of a fluorescent mutant of BdpA (G29A F13W), named F13W*, using nanosecond laser-induced temperature jump experiments. Automation of the apparatus has permitted large data sets to be acquired that provide excellent signal-to-noise ratio over a wide range of experimental conditions. By measuring the temperature and denaturant dependence of equilibrium and kinetic data for F13W*, we show that thermodynamic modeling of multidimensional equilibrium and kinetic surfaces is a robust method that allows reliable extrapolation of rate constants to regions of the folding landscape not directly accessible experimentally. The results reveal that F13W* is the fastest-folding protein of its size studied to date, with a maximum folding rate constant at 0 M guanidinium chloride and 45°C of 249,000 (s-1). Assuming the single-exponential kinetics represent barrier-limited folding, these data limit the value for the preexponential factor for folding of this protein to at least ≈2 x 10(6) s(-1)
Non-Markovian Configurational Diffusion and Reaction Coordinates for Protein Folding
The non-Markovian nature of polymer motions is accounted for in folding
kinetics, using frequency-dependent friction. Folding, like many other problems
in the physics of disordered systems, involves barrier crossing on a correlated
energy landscape. A variational transition state theory (VTST) that reduces to
the usual Bryngelson-Wolynes Kramers approach when the non-Markovian aspects
are neglected is used to obtain the rate, without making any assumptions
regarding the size of the barrier, or the memory time of the friction. The
transformation to collective variables dependent on the dynamics of the system
allows the theory to address the controversial issue of what are ``good''
reaction coordinates for folding.Comment: 9 pages RevTeX, 3 eps-figures included, submitted to PR
Molecular dynamics simulation of polymer helix formation using rigid-link methods
Molecular dynamics simulations are used to study structure formation in
simple model polymer chains that are subject to excluded volume and torsional
interactions. The changing conformations exhibited by chains of different
lengths under gradual cooling are followed until each reaches a state from
which no further change is possible. The interactions are chosen so that the
true ground state is a helix, and a high proportion of simulation runs succeed
in reaching this state; the fraction that manage to form defect-free helices is
a function of both chain length and cooling rate. In order to demonstrate
behavior analogous to the formation of protein tertiary structure, additional
attractive interactions are introduced into the model, leading to the
appearance of aligned, antiparallel helix pairs. The simulations employ a
computational approach that deals directly with the internal coordinates in a
recursive manner; this representation is able to maintain constant bond lengths
and angles without the necessity of treating them as an algebraic constraint
problem supplementary to the equations of motion.Comment: 15 pages, 14 figure
Optimized Folding Simulations of Protein A
We describe optimized parallel tempering simulations of the 46-residue
B-fragment of protein A. Native-like configurations with a root-mean-square
deviation of approximately 3A to the experimentally determined structure
(Protein Data Bank identifier 1BDD) are found. However, at biologically
relevant temperatures such conformations appear with only about 10% frequency
in our simulations. Possible short comings in our energy function are
discussed.Comment: 6 pages, 8 figure
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