65 research outputs found
Fractal Analysis of Protein Potential Energy Landscapes
The fractal properties of the total potential energy V as a function of time
t are studied for a number of systems, including realistic models of proteins
(PPT, BPTI and myoglobin). The fractal dimension of V(t), characterized by the
exponent \gamma, is almost independent of temperature and increases with time,
more slowly the larger the protein. Perhaps the most striking observation of
this study is the apparent universality of the fractal dimension, which depends
only weakly on the type of molecular system. We explain this behavior by
assuming that fractality is caused by a self-generated dynamical noise, a
consequence of intermode coupling due to anharmonicity. Global topological
features of the potential energy landscape are found to have little effect on
the observed fractal behavior.Comment: 17 pages, single spaced, including 12 figure
Efficient Dynamic Importance Sampling of Rare Events in One Dimension
Exploiting stochastic path integral theory, we obtain \emph{by simulation}
substantial gains in efficiency for the computation of reaction rates in
one-dimensional, bistable, overdamped stochastic systems. Using a well-defined
measure of efficiency, we compare implementations of ``Dynamic Importance
Sampling'' (DIMS) methods to unbiased simulation. The best DIMS algorithms are
shown to increase efficiency by factors of approximately 20 for a
barrier height and 300 for , compared to unbiased simulation. The
gains result from close emulation of natural (unbiased), instanton-like
crossing events with artificially decreased waiting times between events that
are corrected for in rate calculations. The artificial crossing events are
generated using the closed-form solution to the most probable crossing event
described by the Onsager-Machlup action. While the best biasing methods require
the second derivative of the potential (resulting from the ``Jacobian'' term in
the action, which is discussed at length), algorithms employing solely the
first derivative do nearly as well. We discuss the importance of
one-dimensional models to larger systems, and suggest extensions to
higher-dimensional systems.Comment: version to be published in Phys. Rev.
The inevitable QSAR renaissance
QSAR approaches, including recent advances in 3D-QSAR, are advantageous during the lead optimization phase of drug discovery and complementary with bioinformatics and growing data accessibility. Hints for future QSAR practitioners are also offered
Allosteric Transitions of Supramolecular Systems Explored by Network Models: Application to Chaperonin GroEL
Identification of pathways involved in the structural transitions of biomolecular
systems is often complicated by the transient nature of the conformations
visited across energy barriers and the multiplicity of paths accessible in the
multidimensional energy landscape. This task becomes even more challenging in
exploring molecular systems on the order of megadaltons. Coarse-grained models
that lend themselves to analytical solutions appear to be the only possible
means of approaching such cases. Motivated by the utility of elastic network
models for describing the collective dynamics of biomolecular systems and by the
growing theoretical and experimental evidence in support of the intrinsic
accessibility of functional substates, we introduce a new method,
adaptive anisotropic network model (aANM),
for exploring functional transitions. Application to bacterial chaperonin GroEL
and comparisons with experimental data, results from action minimization
algorithm, and previous simulations support the utility of aANM
as a computationally efficient, yet physically plausible, tool for unraveling
potential transition pathways sampled by large complexes/assemblies. An
important outcome is the assessment of the critical inter-residue interactions
formed/broken near the transition state(s), most of which involve conserved
residues
Multi-Scaled Explorations of Binding-Induced Folding of Intrinsically Disordered Protein Inhibitor IA3 to its Target Enzyme
Biomolecular function is realized by recognition, and increasing evidence shows that recognition is determined not only by structure but also by flexibility and dynamics. We explored a biomolecular recognition process that involves a major conformational change – protein folding. In particular, we explore the binding-induced folding of IA3, an intrinsically disordered protein that blocks the active site cleft of the yeast aspartic proteinase saccharopepsin (YPrA) by folding its own N-terminal residues into an amphipathic alpha helix. We developed a multi-scaled approach that explores the underlying mechanism by combining structure-based molecular dynamics simulations at the residue level with a stochastic path method at the atomic level. Both the free energy profile and the associated kinetic paths reveal a common scheme whereby IA3 binds to its target enzyme prior to folding itself into a helix. This theoretical result is consistent with recent time-resolved experiments. Furthermore, exploration of the detailed trajectories reveals the important roles of non-native interactions in the initial binding that occurs prior to IA3 folding. In contrast to the common view that non-native interactions contribute only to the roughness of landscapes and impede binding, the non-native interactions here facilitate binding by reducing significantly the entropic search space in the landscape. The information gained from multi-scaled simulations of the folding of this intrinsically disordered protein in the presence of its binding target may prove useful in the design of novel inhibitors of aspartic proteinases
Quasi-continuous Interpolation Scheme for Pathways between Distant Configurations
A quasi-continuous interpolation (QCI) scheme is introduced for characterizing physically realistic initial pathways from which to initiate transition state searches and construct kinetic transition networks. Applications are presented for peptides, proteins, and a morphological transformation in an atomic cluster. The first step in each case involves end point alignment, and we describe the use of a shortest augmenting path algorithm for optimizing permutational isomers. The QCI procedure then employs an interpolating potential, which preserves the covalent bonding framework for the biomolecules and includes repulsive terms between unconstrained atoms. This potential is used to identify an interpolating path by minimizing contributions from a connected set of images, including terms corresponding to minima in the interatomic distances between them. This procedure detects unphysical geometries in the line segments between images. The most difficult cases, where linear interpolation would involve chain crossings, are treated by growing the structure an atom at a time using the interpolating potential. To test the QCI procedure, we carry through a series of benchmark calculations where the initial interpolation is coupled to explicit transition state searches to produce complete pathways between specified local minima.This work was supported by the Engineering and Physical Sciences Research Council [grant number EP/H042660/1]This document is the unedited Author’s version of a Submitted Work that was subsequently accepted for publication in the Journal of Chemical Theory and Computation, copyright © American Chemical Society after peer review. To access the final edited and published work see http://dx.doi.org/10.1021/ct300483
A two-step target binding and selectivity support vector machines approach for virtual screening of dopamine receptor subtype-selective ligands
10.1371/journal.pone.0039076PLoS ONE76
Some aspects of the Liouville equation in mathematical physics and statistical mechanics
This paper presents some mathematical aspects of Classical Liouville theorem
and we have noted some mathematical theorems about its initial value problem.
Furthermore, we have implied on the formal frame work of Stochastic Liouville
equation (SLE)
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