Looking at structure, stability, and evolution of proteins through the principal eigenvector of contact matrices and hydrophobicity profiles

Ugo Bastolla; Markus Porto; H. Eduardo Roman; Michele Vendruscolo

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Looking at structure, stability, and evolution of proteins through the principal eigenvector of contact matrices and hydrophobicity profiles

Ugo Bastolla·Markus Porto·H. Eduardo Roman·Michele Vendruscolo

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Abstract

We review and further develop an analytical model that describes how thermodynamic constraints on the stability of the native state influence protein evolution in a site-specific manner. To this end, we represent both protein sequences and protein structures as vectors: Structures are represented by the principal eigenvector (PE) of the protein contact matrix, a quantity that resembles closely the effective connectivity of each site; Sequences are represented through the ``interactivity'' of each amino acid type, using novel parameters that are correlated with hydropathy scales. These interactivity parameters are more strongly correlated than the other hydropathy scales that we examine with: (1) The change upon mutations of the unfolding free energy of proteins with two-states thermodynamics; (2) Genomic properties as the genome-size and the genome-wide GC content; (3) The main eigenvectors of the substitution matrices. The evolutionary average of the interactivity vector correlates very strongly with the PE of a protein structure. Using this result, we derive an analytic expression for site-specific distributions of amino acids across protein families in the form of Boltzmann distributions whose ``inverse temperature'' is a function of the PE component. We show that our predictions are in agreement with site-specific amino acid distributions obtained from the Protein Data Bank, and we determine the mutational model that best fits the observed site-specific amino acid distributions. Interestingly, the optimal model almost minimizes the rate at which deleterious mutations are eliminated by natural selection.

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Ugo Bastolla, Markus Porto, H. Eduardo Roman, Michele Vendruscolo. 2004-12-02. Looking at structure, stability, and evolution of proteins through the principal eigenvector of contact matrices and hydrophobicity profiles. https://arxiv.org/abs/q-bio/0412004

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