4 research outputs found
A physically meaningful method for the comparison of potential energy functions
In the study of the conformational behavior of complex systems, such as
proteins, several related statistical measures are commonly used to compare two
different potential energy functions. Among them, the Pearson's correlation
coefficient r has no units and allows only semi-quantitative statements to be
made. Those that do have units of energy and whose value may be compared to a
physically relevant scale, such as the root mean square deviation (RMSD), the
mean error of the energies (ER), the standard deviation of the error (SDER) or
the mean absolute error (AER), overestimate the distance between potentials.
Moreover, their precise statistical meaning is far from clear. In this article,
a new measure of the distance between potential energy functions is defined
which overcomes the aforementioned difficulties. In addition, its precise
physical meaning is discussed, the important issue of its additivity is
investigated and some possible applications are proposed. Finally, two of these
applications are illustrated with practical examples: the study of the van der
Waals energy, as implemented in CHARMM, in the Trp-Cage protein (PDB code 1L2Y)
and the comparison of different levels of the theory in the ab initio study of
the Ramachandran map of the model peptide HCO-L-Ala-NH2.Comment: 30 pages, 7 figures, LaTeX, BibTeX. v2: A misspelling in the author's
name has been corrected. v3: A new application of the method has been added
at the end of section 9 and minor modifications have also been made in other
sections. v4: Journal reference and minor corrections adde
Reducing the standard deviation in multiple-assay experiments where the variation matters but the absolute value does not
You measure the value of a quantity x for a number of systems (cells,
molecules, people, chunks of metal, DNA vectors, etc.). You repeat the whole
set of measures in different occasions or assays, which you try to design as
equal to one another as possible. Despite the effort, you find that the results
are too different from one assay to another. As a consequence, some systems'
averages present standard deviations that are too large to render the results
statistically significant. In this work, we present a novel correction method
of very low mathematical and numerical complexity that can reduce the standard
deviation in your results and increase their statistical significance as long
as two conditions are met: inter-system variations of x matter to you but its
absolute value does not, and the different assays display a similar tendency in
the values of x; in other words, the results corresponding to different assays
present high linear correlation. We demonstrate the improvement that this
method brings about on a real cell biology experiment, but the method can be
applied to any problem that conforms to the described structure and
requirements, in any quantitative scientific field that has to deal with data
subject to uncertainty.Comment: Supplementary material at http://bit.ly/14I718
Quantum mechanical calculation of the effects of stiff and rigid constraints in the conformational equilibrium of the Alanine dipeptide
If constraints are imposed on a macromolecule, two inequivalent classical
models may be used: the stiff and the rigid one. This work studies the effects
of such constraints on the Conformational Equilibrium Distribution (CED) of the
model dipeptide HCO-L-Ala-NH2 without any simplifying assumption. We use ab
initio Quantum Mechanics calculations including electron correlation at the MP2
level to describe the system, and we measure the conformational dependence of
all the correcting terms to the naive CED based in the Potential Energy Surface
(PES) that appear when the constraints are considered. These terms are related
to mass-metric tensors determinants and also occur in the Fixman's compensating
potential. We show that some of the corrections are non-negligible if one is
interested in the whole Ramachandran space. On the other hand, if only the
energetically lower region, containing the principal secondary structure
elements, is assumed to be relevant, then, all correcting terms may be
neglected up to peptides of considerable length. This is the first time, as far
as we know, that the analysis of the conformational dependence of these
correcting terms is performed in a relevant biomolecule with a realistic
potential energy function.Comment: 37 pages, 4 figures, LaTeX, BibTeX, AMSTe
Efficient model chemistries for peptides. I. Split-valence Gaussian basis sets and the heterolevel approximation in RHF and MP2
We present an exhaustive study of more than 250 ab initio potential energy
surfaces (PESs) of the model dipeptide HCO-L-Ala-NH2. The model chemistries
(MCs) used are constructed as homo- and heterolevels involving possibly
different RHF and MP2 calculations for the geometry and the energy. The basis
sets used belong to a sample of 39 selected representants from Pople's
split-valence families, ranging from the small 3-21G to the large
6-311++G(2df,2pd). The reference PES to which the rest are compared is the
MP2/6-311++G(2df,2pd) homolevel, which, as far as we are aware, is the more
accurate PES of a dipeptide in the literature. The aim of the study presented
is twofold: On the one hand, the evaluation of the influence of polarization
and diffuse functions in the basis set, distinguishing between those placed at
1st-row atoms and those placed at hydrogens, as well as the effect of different
contraction and valence splitting schemes. On the other hand, the investigation
of the heterolevel assumption, which is defined here to be that which states
that heterolevel MCs are more efficient than homolevel MCs. The heterolevel
approximation is very commonly used in the literature, but it is seldom
checked. As far as we know, the only tests for peptides or related systems,
have been performed using a small number of conformers, and this is the first
time that this potentially very economical approximation is tested in full
PESs. In order to achieve these goals, all data sets have been compared and
analyzed in a way which captures the nearness concept in the space of MCs.Comment: 54 pages, 16 figures, LaTeX, AMSTeX, Submitted to J. Comp. Che