3,554 research outputs found
Flexible protein folding by ant colony optimization
Protein structure prediction is one of the most challenging topics in bioinformatics.
As the protein structure is found to be closely related to its functions,
predicting the folding structure of a protein to judge its functions is meaningful to
the humanity. This chapter proposes a flexible ant colony (FAC) algorithm for solving
protein folding problems (PFPs) based on the hydrophobic-polar (HP) square lattice
model. Different from the previous ant algorithms for PFPs, the pheromones in the
proposed algorithm are placed on the arcs connecting adjacent squares in the lattice.
Such pheromone placement model is similar to the one used in the traveling salesmen
problems (TSPs), where pheromones are released on the arcs connecting the cities.
Moreover, the collaboration of effective heuristic and pheromone strategies greatly
enhances the performance of the algorithm so that the algorithm can achieve good
results without local search methods. By testing some benchmark two-dimensional
hydrophobic-polar (2D-HP) protein sequences, the performance shows that the proposed
algorithm is quite competitive compared with some other well-known methods
for solving the same protein folding problems
Potentials of Mean Force for Protein Structure Prediction Vindicated, Formalized and Generalized
Understanding protein structure is of crucial importance in science, medicine
and biotechnology. For about two decades, knowledge based potentials based on
pairwise distances -- so-called "potentials of mean force" (PMFs) -- have been
center stage in the prediction and design of protein structure and the
simulation of protein folding. However, the validity, scope and limitations of
these potentials are still vigorously debated and disputed, and the optimal
choice of the reference state -- a necessary component of these potentials --
is an unsolved problem. PMFs are loosely justified by analogy to the reversible
work theorem in statistical physics, or by a statistical argument based on a
likelihood function. Both justifications are insightful but leave many
questions unanswered. Here, we show for the first time that PMFs can be seen as
approximations to quantities that do have a rigorous probabilistic
justification: they naturally arise when probability distributions over
different features of proteins need to be combined. We call these quantities
reference ratio distributions deriving from the application of the reference
ratio method. This new view is not only of theoretical relevance, but leads to
many insights that are of direct practical use: the reference state is uniquely
defined and does not require external physical insights; the approach can be
generalized beyond pairwise distances to arbitrary features of protein
structure; and it becomes clear for which purposes the use of these quantities
is justified. We illustrate these insights with two applications, involving the
radius of gyration and hydrogen bonding. In the latter case, we also show how
the reference ratio method can be iteratively applied to sculpt an energy
funnel. Our results considerably increase the understanding and scope of energy
functions derived from known biomolecular structures
Energy Minimization of Discrete Protein Titration State Models Using Graph Theory
There are several applications in computational biophysics which require the
optimization of discrete interacting states; e.g., amino acid titration states,
ligand oxidation states, or discrete rotamer angles. Such optimization can be
very time-consuming as it scales exponentially in the number of sites to be
optimized. In this paper, we describe a new polynomial-time algorithm for
optimization of discrete states in macromolecular systems. This algorithm was
adapted from image processing and uses techniques from discrete mathematics and
graph theory to restate the optimization problem in terms of "maximum
flow-minimum cut" graph analysis. The interaction energy graph, a graph in
which vertices (amino acids) and edges (interactions) are weighted with their
respective energies, is transformed into a flow network in which the value of
the minimum cut in the network equals the minimum free energy of the protein,
and the cut itself encodes the state that achieves the minimum free energy.
Because of its deterministic nature and polynomial-time performance, this
algorithm has the potential to allow for the ionization state of larger
proteins to be discovered
Exploring the Free Energy Landscape: From Dynamics to Networks and Back
The knowledge of the Free Energy Landscape topology is the essential key to
understand many biochemical processes. The determination of the conformers of a
protein and their basins of attraction takes a central role for studying
molecular isomerization reactions. In this work, we present a novel framework
to unveil the features of a Free Energy Landscape answering questions such as
how many meta-stable conformers are, how the hierarchical relationship among
them is, or what the structure and kinetics of the transition paths are.
Exploring the landscape by molecular dynamics simulations, the microscopic data
of the trajectory are encoded into a Conformational Markov Network. The
structure of this graph reveals the regions of the conformational space
corresponding to the basins of attraction. In addition, handling the
Conformational Markov Network, relevant kinetic magnitudes as dwell times or
rate constants, and the hierarchical relationship among basins, complete the
global picture of the landscape. We show the power of the analysis studying a
toy model of a funnel-like potential and computing efficiently the conformers
of a short peptide, the dialanine, paving the way to a systematic study of the
Free Energy Landscape in large peptides.Comment: PLoS Computational Biology (in press
Landscape statistics of the low autocorrelated binary string problem
The statistical properties of the energy landscape of the low autocorrelated
binary string problem (LABSP) are studied numerically and compared with those
of several classic disordered models. Using two global measures of landscape
structure which have been introduced in the Simulated Annealing literature,
namely, depth and difficulty, we find that the landscape of LABSP, except
perhaps for a very large degeneracy of the local minima energies, is
qualitatively similar to some well-known landscapes such as that of the
mean-field 2-spin glass model. Furthermore, we consider a mean-field
approximation to the pure model proposed by Bouchaud and Mezard (1994, J.
Physique I France 4 1109) and show both analytically and numerically that it
describes extremely well the statistical properties of LABSP
Sequence Dependence of Self-Interacting Random Chains
We study the thermodynamic behavior of the random chain model proposed by
Iori, Marinari and Parisi, and how this depends on the actual sequence of
interactions along the chain. The properties of randomly chosen sequences are
compared to those of designed ones, obtained through a simulated annealing
procedure in sequence space. We show that the transition to the folded phase
takes place at a smaller strength of the quenched disorder for designed
sequences. As a result, folding can be relatively fast for these sequences.Comment: 14 pages, uuencoded compressed postscript fil
Dynamics of the Desai-Zwanzig model in multiwell and random energy landscapes
We analyze a variant of the Desai-Zwanzig model [J. Stat. Phys. {\bf 19}1-24 (1978)]. In particular, we study stationary states of the mean field limit for a system of weakly interacting diffusions moving in a multi-well potential energy landscape, coupled via a Curie-Weiss type (quadratic) interaction potential. The location and depth of the local minima of the potential are either deterministic or random. We characterize the structure and nature of bifurcations and phase transitions for this system, by means of extensive numerical simulations and of analytical calculations for an explicitly solvable model. Our numerical experiments are based on Monte Carlo simulations, the numerical solution of the time-dependent nonlinear Fokker-Planck (McKean-Vlasov equation), the minimization of the free energy functional and a continuation algorithm for the stationary solutions
Restart could optimize the probability of success in a Bernoulli trial
Recently noticed ability of restart to reduce the expected completion time of
first-passage processes allows appealing opportunities for performance
improvement in a variety of settings. However, complex stochastic processes
often exhibit several possible scenarios of completion which are not equally
desirable in terms of efficiency. Here we show that restart may have profound
consequences on the splitting probabilities of a Bernoulli-like first-passage
process, i.e. of a process which can end with one of two outcomes. Particularly
intriguing in this respect is the class of problems where a carefully adjusted
restart mechanism maximizes probability that the process will complete in a
desired way. We reveal the universal aspects of this kind of optimal behaviour
by applying the general approach recently proposed for the problem of
first-passage under restart.Comment: 6 pages and 3 figures in the main text + 4 pages of supplementary
informatio
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