Protein local conformations arise from a mixture of Gaussian distributions

Abstract

The classical approaches for protein structure prediction rely either on homology of the protein sequence with a template structure or on ab initio calculations for energy minimization. These methods suffer from disadvantages such as the lack of availability of homologous template structures or intractably large conformational search space, respectively. The recently proposed fragment library based approaches first predict the local structures,which can be used in conjunction with the classical approaches of protein structure prediction. The accuracy of the predictions is dependent on the quality of the fragment library. In this work, we have constructed a library of local conformation classes purely based on geometric similarity. The local conformations are represented using Geometric Invariants, properties that remain unchanged under transformations such as translation and rotation, followed by dimension reduction via principal component analysis. The local conformations are then modeled as a mixture of Gaussian probability distribution functions (PDF). Each one of the Gaussian PDF's corresponds to a conformational class with the centroid representing the average structure of that class. We find 46 classes when we use an octapeptide as a unit of local conformation. The protein 3-D structure can now be described as a sequence of local conformational classes. Further, it was of interest to see whether the local conformations can be predicted from the amino acid sequences. To that end,we have analyzed the correlation between sequence features and the conformational classes.

Protein sequence and structure alignments within one framework

“…Generally, these use a structure classification and then see which sequence patterns fit to each structure motif (or vice versa ). They also require some similarity measure between clusters [ 35 - 38 , 54 , 77 - 81 ]. The methodology here is based on a mixture model which can treat all these properties simultaneously and this leads to a very different kind of result.…”

Tolerance Interval for the Mixture Normal Distribution Based on Generalized Extreme Value Theory

“…Mixture normal distributions have been successfully used to address diverse data problems, such as research on the evaluation of nuclear power plant safety [8], assessment of the debrisoquin and dextromethorphan phenotyping tests [9], examination of the ventricular size in schizophrenia [10], prediction of protein local conformations [11], fitting the asset returns data in portfolio optimization problems [12], modeling rainfall drop size distribution in southern England [13], and analysis of wireless channels [14].…”