27,859 research outputs found
Protein Docking by the Underestimation of Free Energy Funnels in the Space of Encounter Complexes
Similarly to protein folding, the association of two proteins is driven
by a free energy funnel, determined by favorable interactions in some neighborhood of the
native state. We describe a docking method based on stochastic global minimization of
funnel-shaped energy functions in the space of rigid body motions (SE(3)) while accounting
for flexibility of the interface side chains. The method, called semi-definite
programming-based underestimation (SDU), employs a general quadratic function to
underestimate a set of local energy minima and uses the resulting underestimator to bias
further sampling. While SDU effectively minimizes functions with funnel-shaped basins, its
application to docking in the rotational and translational space SE(3) is not
straightforward due to the geometry of that space. We introduce a strategy that uses
separate independent variables for side-chain optimization, center-to-center distance of the
two proteins, and five angular descriptors of the relative orientations of the molecules.
The removal of the center-to-center distance turns out to vastly improve the efficiency of
the search, because the five-dimensional space now exhibits a well-behaved energy surface
suitable for underestimation. This algorithm explores the free energy surface spanned by
encounter complexes that correspond to local free energy minima and shows similarity to the
model of macromolecular association that proceeds through a series of collisions. Results
for standard protein docking benchmarks establish that in this space the free energy
landscape is a funnel in a reasonably broad neighborhood of the native state and that the
SDU strategy can generate docking predictions with less than 5 ïżœ ligand interface Ca
root-mean-square deviation while achieving an approximately 20-fold efficiency gain compared
to Monte Carlo methods
A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments
The computational study of chemical reactions in complex, wet environments is
critical for applications in many fields. It is often essential to study
chemical reactions in the presence of applied electrochemical potentials,
taking into account the non-trivial electrostatic screening coming from the
solvent and the electrolytes. As a consequence the electrostatic potential has
to be found by solving the generalized Poisson and the Poisson-Boltzmann
equation for neutral and ionic solutions, respectively. In the present work
solvers for both problems have been developed. A preconditioned conjugate
gradient method has been implemented to the generalized Poisson equation and
the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the
minimization problem with some ten iterations of a ordinary Poisson equation
solver. In addition, a self-consistent procedure enables us to solve the
non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy
and parallel efficiency, and allow for the treatment of different boundary
conditions, as for example surface systems. The solver has been integrated into
the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be
released as an independent program, suitable for integration in other codes
The LBFGS Quasi-Newtonian Method for Molecular Modeling Prion AGAAAAGA Amyloid Fibrils
Experimental X-ray crystallography, NMR (Nuclear Magnetic Resonance)
spectroscopy, dual polarization interferometry, etc are indeed very powerful
tools to determine the 3-Dimensional structure of a protein (including the
membrane protein); theoretical mathematical and physical computational
approaches can also allow us to obtain a description of the protein 3D
structure at a submicroscopic level for some unstable, noncrystalline and
insoluble proteins. X-ray crystallography finds the X-ray final structure of a
protein, which usually need refinements using theoretical protocols in order to
produce a better structure. This means theoretical methods are also important
in determinations of protein structures. Optimization is always needed in the
computer-aided drug design, structure-based drug design, molecular dynamics,
and quantum and molecular mechanics. This paper introduces some optimization
algorithms used in these research fields and presents a new theoretical
computational method - an improved LBFGS Quasi-Newtonian mathematical
optimization method - to produce 3D structures of Prion AGAAAAGA amyloid
fibrils (which are unstable, noncrystalline and insoluble), from the potential
energy minimization point of view. Because the NMR or X-ray structure of the
hydrophobic region AGAAAAGA of prion proteins has not yet been determined, the
model constructed by this paper can be used as a reference for experimental
studies on this region, and may be useful in furthering the goals of medicinal
chemistry in this field
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