2,346 research outputs found
Sequential Monte Carlo Methods for Protein Folding
We describe a class of growth algorithms for finding low energy states of
heteropolymers. These polymers form toy models for proteins, and the hope is
that similar methods will ultimately be useful for finding native states of
real proteins from heuristic or a priori determined force fields. These
algorithms share with standard Markov chain Monte Carlo methods that they
generate Gibbs-Boltzmann distributions, but they are not based on the strategy
that this distribution is obtained as stationary state of a suitably
constructed Markov chain. Rather, they are based on growing the polymer by
successively adding individual particles, guiding the growth towards
configurations with lower energies, and using "population control" to eliminate
bad configurations and increase the number of "good ones". This is not done via
a breadth-first implementation as in genetic algorithms, but depth-first via
recursive backtracking. As seen from various benchmark tests, the resulting
algorithms are extremely efficient for lattice models, and are still
competitive with other methods for simple off-lattice models.Comment: 10 pages; published in NIC Symposium 2004, eds. D. Wolf et al. (NIC,
Juelich, 2004
Long Proteins with Unique Optimal Foldings in the H-P Model
It is widely accepted that (1) the natural or folded state of proteins is a
global energy minimum, and (2) in most cases proteins fold to a unique state
determined by their amino acid sequence. The H-P (hydrophobic-hydrophilic)
model is a simple combinatorial model designed to answer qualitative questions
about the protein folding process. In this paper we consider a problem
suggested by Brian Hayes in 1998: what proteins in the two-dimensional H-P
model have unique optimal (minimum energy) foldings? In particular, we prove
that there are closed chains of monomers (amino acids) with this property for
all (even) lengths; and that there are open monomer chains with this property
for all lengths divisible by four.Comment: 22 pages, 18 figure
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
Growth Algorithms for Lattice Heteropolymers at Low Temperatures
Two improved versions of the pruned-enriched-Rosenbluth method (PERM) are
proposed and tested on simple models of lattice heteropolymers. Both are found
to outperform not only the previous version of PERM, but also all other
stochastic algorithms which have been employed on this problem, except for the
core directed chain growth method (CG) of Beutler & Dill. In nearly all test
cases they are faster in finding low-energy states, and in many cases they
found new lowest energy states missed in previous papers. The CG method is
superior to our method in some cases, but less efficient in others. On the
other hand, the CG method uses heavily heuristics based on presumptions about
the hydrophobic core and does not give thermodynamic properties, while the
present method is a fully blind general purpose algorithm giving correct
Boltzmann-Gibbs weights, and can be applied in principle to any stochastic
sampling problem.Comment: 9 pages, 9 figures. J. Chem. Phys., in pres
A Hybrid Monte Carlo Ant Colony Optimization Approach for Protein Structure Prediction in the HP Model
The hydrophobic-polar (HP) model has been widely studied in the field of
protein structure prediction (PSP) both for theoretical purposes and as a
benchmark for new optimization strategies. In this work we introduce a new
heuristics based on Ant Colony Optimization (ACO) and Markov Chain Monte Carlo
(MCMC) that we called Hybrid Monte Carlo Ant Colony Optimization (HMCACO). We
describe this method and compare results obtained on well known HP instances in
the 3 dimensional cubic lattice to those obtained with standard ACO and
Simulated Annealing (SA). All methods were implemented using an unconstrained
neighborhood and a modified objective function to prevent the creation of
overlapping walks. Results show that our methods perform better than the other
heuristics in all benchmark instances.Comment: In Proceedings Wivace 2013, arXiv:1309.712
Structure optimization in an off-lattice protein model
We study an off-lattice protein toy model with two species of monomers
interacting through modified Lennard-Jones interactions. Low energy
configurations are optimized using the pruned-enriched-Rosenbluth method
(PERM), hitherto employed to native state searches only for off lattice models.
For 2 dimensions we found states with lower energy than previously proposed
putative ground states, for all chain lengths . This indicates that
PERM has the potential to produce native states also for more realistic protein
models. For , where no published ground states exist, we present some
putative lowest energy states for future comparison with other methods.Comment: 4 pages, 2 figure
Is protein folding problem really a NP-complete one ? First investigations
To determine the 3D conformation of proteins is a necessity to understand
their functions or interactions with other molecules. It is commonly admitted
that, when proteins fold from their primary linear structures to their final 3D
conformations, they tend to choose the ones that minimize their free energy. To
find the 3D conformation of a protein knowing its amino acid sequence,
bioinformaticians use various models of different resolutions and artificial
intelligence tools, as the protein folding prediction problem is a NP complete
one. More precisely, to determine the backbone structure of the protein using
the low resolution models (2D HP square and 3D HP cubic), by finding the
conformation that minimize free energy, is intractable exactly. Both the proof
of NP-completeness and the 2D prediction consider that acceptable conformations
have to satisfy a self-avoiding walk (SAW) requirement, as two different amino
acids cannot occupy a same position in the lattice. It is shown in this
document that the SAW requirement considered when proving NP-completeness is
different from the SAW requirement used in various prediction programs, and
that they are different from the real biological requirement. Indeed, the proof
of NP completeness and the predictions in silico consider conformations that
are not possible in practice. Consequences of this fact are investigated in
this research work.Comment: Submitted to Journal of Bioinformatics and Computational Biology,
under revie
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