4,718 research outputs found
Stochastic kinetics of viral capsid assembly based on detailed protein structures
We present a generic computational framework for the simulation of viral
capsid assembly which is quantitative and specific. Starting from PDB files
containing atomic coordinates, the algorithm builds a coarse grained
description of protein oligomers based on graph rigidity. These reduced protein
descriptions are used in an extended Gillespie algorithm to investigate the
stochastic kinetics of the assembly process. The association rates are obtained
from a diffusive Smoluchowski equation for rapid coagulation, modified to
account for water shielding and protein structure. The dissociation rates are
derived by interpreting the splitting of oligomers as a process of graph
partitioning akin to the escape from a multidimensional well. This modular
framework is quantitative yet computationally tractable, with a small number of
physically motivated parameters. The methodology is illustrated using two
different viruses which are shown to follow quantitatively different assembly
pathways. We also show how in this model the quasi-stationary kinetics of
assembly can be described as a Markovian cascading process in which only a few
intermediates and a small proportion of pathways are present. The observed
pathways and intermediates can be related a posteriori to structural and
energetic properties of the capsid oligomers
Evolution of sparsity and modularity in a model of protein allostery
The sequence of a protein is not only constrained by its physical and
biochemical properties under current selection, but also by features of its
past evolutionary history. Understanding the extent and the form that these
evolutionary constraints may take is important to interpret the information in
protein sequences. To study this problem, we introduce a simple but physical
model of protein evolution where selection targets allostery, the functional
coupling of distal sites on protein surfaces. This model shows how the
geometrical organization of couplings between amino acids within a protein
structure can depend crucially on its evolutionary history. In particular, two
scenarios are found to generate a spatial concentration of functional
constraints: high mutation rates and fluctuating selective pressures. This
second scenario offers a plausible explanation for the high tolerance of
natural proteins to mutations and for the spatial organization of their least
tolerant amino acids, as revealed by sequence analyses and mutagenesis
experiments. It also implies a faculty to adapt to new selective pressures that
is consistent with observations. Besides, the model illustrates how several
independent functional modules may emerge within a same protein structure,
depending on the nature of past environmental fluctuations. Our model thus
relates the evolutionary history and evolutionary potential of proteins to the
geometry of their functional constraints, with implications for decoding and
engineering protein sequences
Learning effective amino acid interactions through iterative stochastic techniques
The prediction of the three-dimensional structures of the native state of
proteins from the sequences of their amino acids is one of the most important
challenges in molecular biology. An essential ingredient to solve this problem
within coarse-grained models is the task of deducing effective interaction
potentials between the amino acids. Over the years several techniques have been
developed to extract potentials that are able to discriminate satisfactorily
between the native and non-native folds of a pre-assigned protein sequence. In
general, when these potentials are used in actual dynamical folding
simulations, they lead to a drift of the native structure outside the
quasi-native basin. In this study, we present and validate an approach to
overcome this difficulty. By exploiting several numerical and analytical tools
we set up a rigorous iterative scheme to extract potentials satisfying a
pre-requisite of any viable potential: the stabilization of proteins within
their native basin (less than 3-4 \AA cRMS). The scheme is flexible and is
demonstrated to be applicable to a variety of parametrizations of the energy
function and provides, in each case, the optimal potentials.Comment: Revtex 17 pages, 10 eps figures. Proteins: Structure, Function and
Genetics (in press
Protein folding using contact maps
We present the development of the idea to use dynamics in the space of
contact maps as a computational approach to the protein folding problem. We
first introduce two important technical ingredients, the reconstruction of a
three dimensional conformation from a contact map and the Monte Carlo dynamics
in contact map space. We then discuss two approximations to the free energy of
the contact maps and a method to derive energy parameters based on perceptron
learning. Finally we present results, first for predictions based on threading
and then for energy minimization of crambin and of a set of 6 immunoglobulins.
The main result is that we proved that the two simple approximations we studied
for the free energy are not suitable for protein folding. Perspectives are
discussed in the last section.Comment: 29 pages, 10 figure
Determination of Interaction Potentials of Amino Acids from Native Protein Structures: Test on Simple Lattice Models
We propose a novel method for the determination of the effective interaction
potential between the amino acids of a protein. The strategy is based on the
combination of a new optimization procedure and a geometrical argument, which
also uncovers the shortcomings of any optimization procedure. The strategy can
be applied on any data set of native structures such as those available from
the Protein Data Bank (PDB). In this work, however, we explain and test our
approach on simple lattice models, where the true interactions are known a
priori. Excellent agreement is obtained between the extracted and the true
potentials even for modest numbers of protein structures in the PDB.
Comparisons with other methods are also discussed.Comment: 24 pages, 4 figure
Computational complexity of the landscape I
We study the computational complexity of the physical problem of finding
vacua of string theory which agree with data, such as the cosmological
constant, and show that such problems are typically NP hard. In particular, we
prove that in the Bousso-Polchinski model, the problem is NP complete. We
discuss the issues this raises and the possibility that, even if we were to
find compelling evidence that some vacuum of string theory describes our
universe, we might never be able to find that vacuum explicitly.
In a companion paper, we apply this point of view to the question of how
early cosmology might select a vacuum.Comment: JHEP3 Latex, 53 pp, 2 .eps figure
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