830 research outputs found
Genetic Algorithm Optimization of Point Charges in Force Field Development: Challenges and Insights
Evolutionary methods, such as genetic algorithms (GAs), provide powerful tools for optimization of the force field parameters, especially in the case of simultaneous fitting of the force field terms against extensive reference data. However, GA fitting of the nonbonded interaction parameters that includes point charges has not been explored in the literature, likely due to numerous difficulties with even a simpler problem of the least-squares fitting of the atomic point charges against a reference molecular electrostatic potential (MEP), which often demonstrates an unusually high variation of the fitted charges on buried atoms. Here, we examine the performance of the GA approach for the least-squares MEP point charge fitting, and show that the GA optimizations suffer from a magnified version of the classical buried atom effect, producing highly scattered yet correlated solutions. This effect can be understood in terms of the linearly independent, natural coordinates of the MEP fitting problem defined by the eigenvectors of the least-squares sum Hessian matrix, which are also equivalent to the eigenvectors of the covariance matrix evaluated for the scattered GA solutions. GAs quickly converge with respect to the high-curvature coordinates defined by the eigenvectors related to the leading terms of the multipole expansion, but have difficulty converging with respect to the low-curvature coordinates that mostly depend on the buried atom charges. The performance of the evolutionary techniques dramatically improves when the point charge optimization is performed using the Hessian or covariance matrix eigenvectors, an approach with a significant potential for the evolutionary optimization of the fixed-charge biomolecular force fields
Electrostatic Point Charge Fitting as an Inverse Problem: Revealing the Underlying Ill-Conditioning
Atom-centered point charge model of the molecular electrostatics---a major
workhorse of the atomistic biomolecular simulations---is usually parameterized
by least-squares (LS) fitting of the point charge values to a reference
electrostatic potential, a procedure that suffers from numerical instabilities
due to the ill-conditioned nature of the LS problem. Here, to reveal the
origins of this ill-conditioning, we start with a general treatment of the
point charge fitting problem as an inverse problem, and construct an
analytically soluble model with the point charges spherically arranged
according to Lebedev quadrature naturally suited for the inverse electrostatic
problem. This analytical model is contrasted to the atom-centered point-charge
model that can be viewed as an irregular quadrature poorly suited for the
problem. This analysis shows that the numerical problems of the point charge
fitting are due to the decay of the curvatures corresponding to the
eigenvectors of LS sum Hessian matrix. In part, this ill-conditioning is
intrinsic to the problem and related to decreasing electrostatic contribution
of the higher multipole moments, that are, in the case of Lebedev grid model,
directly associated with the Hessian eigenvectors. For the atom-centered model,
this association breaks down beyond the first few eigenvectors related to the
high-curvature monopole and dipole terms; this leads to even wider spread-out
of the Hessian curvature values. Using these insights, it is possible to
alleviate the ill-conditioning of the LS point-charge fitting without
introducing external restraints and/or constraints. Also, as the analytical
Lebedev grid PC model proposed here can reproduce multipole moments up to a
given rank, it may provide a promising alternative to including explicit
multipole terms in a force field
Similarities Between Classical Timelike Geodesics in a Naked Reissner-Nordstrom Singularity Background and the Behaviour of Electrons in Quantum Theory
It is generally assumed that naked singularities must be physically excluded,
as they could otherwise introduce unpredictable influences in their future null
cones. Considering geodesics for a naked Reissner-Nordstrom singularity, it is
found that the singularity is effectively clothed by its repulsive nature.
Regarding electron as naked singularity, the size of the clothed singularity
(electron) turns out to be classical electro-magnetic radius of the electron,
to an observer falling freely from infinity, initially at rest. The size
shrinks for an observer falling freely from infinity, with a positive initial
velocity. For geodetic parameters corresponding to negative energy there are
trapped geodesics. The similarity of this picture with that arising in the
Quantum Theory is discussed.Comment: 8 pages, 6 figure
On the definition of matter collineations
It is shown that when the stress-energy tensor of a spacetime is diagonal and
is written in the mixed form, its collineations admit infinite dimensional Lie
algebras except possibly in the case when the tensor depends on all the
spacetime coordinates. The result can be extended for more general second rank
tensors
Conformal Ricci collineations of static spherically symmetric spacetimes
Conformal Ricci collineations of static spherically symmetric spacetimes are
studied. The general form of the vector fields generating conformal Ricci
collineations is found when the Ricci tensor is non-degenerate, in which case
the number of independent conformal Ricci collineations is \emph{fifteen}; the
maximum number for 4-dimensional manifolds. In the degenerate case it is found
that the static spherically symmetric spacetimes always have an infinite number
of conformal Ricci collineations. Some examples are provided which admit
non-trivial conformal Ricci collineations, and perfect fluid source of the
matter
Uniqueness of Flat Spherically Symmetric Spacelike Hypersurfaces Admitted by Spherically Symmetric Static Spactimes
It is known that spherically symmetric static spacetimes admit a foliation by
{\deg}at hypersurfaces. Such foliations have explicitly been constructed for
some spacetimes, using different approaches, but none of them have proved or
even discussed the uniqueness of these foliations. The issue of uniqueness
becomes more important due to suitability of {\deg}at foliations for studying
black hole physics. Here {\deg}at spherically symmetric spacelike hy-
persurfaces are obtained by a direct method. It is found that spherically
symmetric static spacetimes admit {\deg}at spherically symmetric hypersurfaces,
and that these hypersurfaces are unique up to translation under the time- like
Killing vector. This result guarantees the uniqueness of {\deg}at spherically
symmetric foliations for such spacetimes.Comment: 10 page
Spherically Symmetric Gravitational Collapse
In this paper, we discuss gravitational collapse of spherically symmetric
spacetimes. We derive a general formalism by taking two arbitrary spherically
symmetric spacetimes with . Israel's junction conditions are used to
develop this formalism. The formulae for extrinsic curvature tensor are
obtained. The general form of the surface energy-momentum tensor depending on
extrinsic curvature tensor components is derived. This leads us to the surface
energy density and the tangential pressure. The formalism is applied to two
known spherically symmetric spacetimes. The results obtained show the regions
for the collapse and expansion of the shell.Comment: 12 pages, 4 figures, accepted for publication in Mod. Phys. Lett.
Foliation of the Kottler-Schwarzschild-De Sitter Spacetime by Flat Spacelike Hypersurfaces
There exist Kruskal like coordinates for the Reissner-Nordstrom (RN) black
hole spacetime which are regular at coordinate singularities. Non existence of
such coordinates for the extreme RN black hole spacetime has already been
shown. Also the Carter coordinates available for the extreme case are not
manifestly regular at the coordinate singularity, therefore, a numerical
procedure was developed to obtain free fall geodesics and flat foliation for
the extreme RN black hole spacetime. The Kottler-Schwarzschild-de Sitter
(KSSdS) spacetime geometry is similar to the RN geometry in the sense that,
like the RN case, there exist non-singular coordinates when there are two
distinct coordinate singularities. There are no manifestly regular coordinates
for the extreme KSSdS case. In this paper foliation of all the cases of the
KSSdS spacetime by flat spacelike hypersurfaces is obtained by introducing a
non-singular time coordinate.Comment: 12 pages, 4 figure
Protein Control of S-Nitrosothiol Reactivity: Interplay of Antagonistic Resonance Structures
There is currently great interest in S-nitrosothiols (RSNOs) because formation of protein-based RSNOs—protein S-nitrosation—has been recently recognized as a major pathway of the biological function of nitric oxide, NO. Despite the growing number of S-nitrosated proteins identified in vivo, enzymatic processes that control reactions of biological RSNOs are still not well understood. In this article, we use a range of models to computationally demonstrate that specific interactions of RSNOs with charged and polar residues in proteins can result in dramatic modification of RSNO structure, stability, and reactivity. This unprecedented sensitivity of the −SNO group toward interactions with charged species is related to their unusual electronic structure that can be elegantly expressed in terms of antagonistic resonance structures. We propose a ‘ligand effect map’ (LEM) approach as an efficient way to estimate the environment effects on the −SNO groups in proteins without performing electronic structure calculations. Furthermore, the calculated 15N NMR signatures of these specific interactions suggest that 15N NMR spectroscopy can be an effective technique to identify and study these interactions experimentally. Overall, the results of this study suggest that RSNO reactions in vivo should be tightly controlled by the protein environment via modulation of the RSNO electronic structure
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