Dataset Information

Efficient molecular surface rendering by linear-time pseudo-Gaussian approximation to Lee-Richards surfaces (PGALRS).

ABSTRACT: The PGALRS (pseudo-Gaussian approximation to Lee-Richards surfaces) algorithm is discussed. By modeling electron density with unphysical pseudo-Gaussian atoms, the Lee-Richards surface can be approximated by a contour level of that density in time approximately linear in the number of atoms. Having that contour level, the atoms and residues closest to that surface can be identified in average time O[n(2/3)log(n)] using a NearTree-based nearest neighbor search. If a high-quality Lee-Richards surface is required, then, as a final stage, one of the standard Lee-Richards algorithms can be used but considering only the previously identified surface residues; the typical cost is thereby reduced to O[n(2/3)log(n)], making the overall average time for all the steps O(n). For very large macromolecules, such a reduction in computational burden may be essential to being able to render a meaningful molecular surface. This approach extends the feasible range of application for existing molecular surface software, such as MSMS, to larger macromolecules, especially to macromolecules with more than 50 000 atoms, and can be used as a starting point for surface-based (as opposed to backbone-based) motif identification, e.g. using ProMol.

SUBMITTER: Bernstein HJ

PROVIDER: S-EPMC2839470 | biostudies-literature | 2010 Apr

REPOSITORIES: biostudies-literature

ACCESS DATA

Publications

Efficient molecular surface rendering by linear-time pseudo-Gaussian approximation to Lee-Richards surfaces (PGALRS).

Bernstein Herbert J HJ Craig Paul A PA

Journal of applied crystallography 20100212 Pt 2

The PGALRS (pseudo-Gaussian approximation to Lee-Richards surfaces) algorithm is discussed. By modeling electron density with unphysical pseudo-Gaussian atoms, the Lee-Richards surface can be approximated by a contour level of that density in time approximately linear in the number of atoms. Having that contour level, the atoms and residues closest to that surface can be identified in average time O[n(2/3)log(n)] using a NearTree-based nearest neighbor search. If a high-quality Lee-Richards surf ...[more]

PMID: 20300495

Similar Datasets

Project description:BackgroundStochastic fluctuations in molecular numbers have been in many cases shown to be crucial for the understanding of biochemical systems. However, the systematic study of these fluctuations is severely hindered by the high computational demand of stochastic simulation algorithms. This is particularly problematic when, as is often the case, some or many model parameters are not well known. Here, we propose a solution to this problem, namely a combination of the linear noise approximation with optimisation methods. The linear noise approximation is used to efficiently estimate the covariances of particle numbers in the system. Combining it with optimisation methods in a closed-loop to find extrema of covariances within a possibly high-dimensional parameter space allows us to answer various questions. Examples are, what is the lowest amplitude of stochastic fluctuations possible within given parameter ranges? Or, which specific changes of parameter values lead to the increase of the correlation between certain chemical species? Unlike stochastic simulation methods, this has no requirement for small numbers of molecules and thus can be applied to cases where stochastic simulation is prohibitive.ResultsWe implemented our strategy in the software COPASI and show its applicability on two different models of mitogen-activated kinases (MAPK) signalling -- one generic model of extracellular signal-regulated kinases (ERK) and one model of signalling via p38 MAPK. Using our method we were able to quickly find local maxima of covariances between particle numbers in the ERK model depending on the activities of phospho-MKKK and its corresponding phosphatase. With the p38 MAPK model our method was able to efficiently find conditions under which the coefficient of variation of the output of the signalling system, namely the particle number of Hsp27, could be minimised. We also investigated correlations between the two parallel signalling branches (MKK3 and MKK6) in this model.ConclusionsOur strategy is a practical method for the efficient investigation of fluctuations in biochemical models even when some or many of the model parameters have not yet been fully characterised.

Project description:The objectives of this study were to develop an efficient algorithm for calculating prediction error variances (PEVs) for genomic best linear unbiased prediction (GBLUP) models using the Algorithm for Proven and Young (APY), extend it to single-step GBLUP (ssGBLUP), and apply this algorithm for approximating the theoretical reliabilities for single- and multiple-trait models in ssGBLUP. The PEV with APY was calculated by block sparse inversion, efficiently exploiting the sparse structure of the inverse of the genomic relationship matrix with APY. Single-step GBLUP reliabilities were approximated by combining reliabilities with and without genomic information in terms of effective record contributions. Multi-trait reliabilities relied on single-trait results adjusted using the genetic and residual covariance matrices among traits. Tests involved two datasets provided by the American Angus Association. A small dataset (Data1) was used for comparing the approximated reliabilities with the reliabilities obtained by the inversion of the left-hand side of the mixed model equations. A large dataset (Data2) was used for evaluating the computational performance of the algorithm. Analyses with both datasets used single-trait and three-trait models. The number of animals in the pedigree ranged from 167,951 in Data1 to 10,213,401 in Data2, with 50,000 and 20,000 genotyped animals for single-trait and multiple-trait analysis, respectively, in Data1 and 335,325 in Data2. Correlations between estimated and exact reliabilities obtained by inversion ranged from 0.97 to 0.99, whereas the intercept and slope of the regression of the exact on the approximated reliabilities ranged from 0.00 to 0.04 and from 0.93 to 1.05, respectively. For the three-trait model with the largest dataset (Data2), the elapsed time for the reliability estimation was 11 min. The computational complexity of the proposed algorithm increased linearly with the number of genotyped animals and with the number of traits in the model. This algorithm can efficiently approximate the theoretical reliability of genomic estimated breeding values in ssGBLUP with APY for large numbers of genotyped animals at a low cost.

Dataset Information

Efficient molecular surface rendering by linear-time pseudo-Gaussian approximation to Lee-Richards surfaces (PGALRS).

Publications

Efficient molecular surface rendering by linear-time pseudo-Gaussian approximation to Lee-Richards surfaces (PGALRS).

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure

Tweets