Hidden Thermodynamic Information in Protein Amino Acid Mutation Tables

📝 Abstract

We combine the standard 1992 20x20 substitution matrix based on block alignment, BLOSUM62, with the standard 1982 amino acid hydropathicity scale KD as well as the modern 2007 hydropathicity scale MZ, and compare the results. The 20-parameter KD and MZ hydropathicity scales have different thermodynamic character, corresponding to first and second order transitions. The KD and MZ comparisons show that the mutation rates reflect quantitative iteration of qualitative amino acid phobic and philic binary 2x10 properties that define quaternary 4x5 subgroups (but not quinary 5x4 subgroups), with the modern MZ bioinformatic scale giving much better results. The quaternary 5 mer MZ 4x5 subgroups are called mutons (Mu5).

💡 Analysis

We combine the standard 1992 20x20 substitution matrix based on block alignment, BLOSUM62, with the standard 1982 amino acid hydropathicity scale KD as well as the modern 2007 hydropathicity scale MZ, and compare the results. The 20-parameter KD and MZ hydropathicity scales have different thermodynamic character, corresponding to first and second order transitions. The KD and MZ comparisons show that the mutation rates reflect quantitative iteration of qualitative amino acid phobic and philic binary 2x10 properties that define quaternary 4x5 subgroups (but not quinary 5x4 subgroups), with the modern MZ bioinformatic scale giving much better results. The quaternary 5 mer MZ 4x5 subgroups are called mutons (Mu5).

📄 Content

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Hidden Thermodynamic Information in Protein Amino Acid Mutation Tables V. Sachdeva and J. C. Phillips Dept. of Physics and Astronomy, Rutgers University, Piscataway, N. J., 08854

                                                           Abstract 

We combine the standard 1992 20x20 substitution matrix based on block alignment, BLOSUM62, with the standard 1982 amino acid hydropathicity scale KD as well as the modern 2007 hydropathicity scale MZ, and compare the results. The 20-parameter KD and MZ hydropathicity scales have different thermodynamic character, corresponding to first- and second-order transitions. The KD and MZ comparisons show that the mutation rates reflect quantitative iteration of qualitative amino acid – phobic and -philic binary 2x10 properties that define quaternary 4x5 subgroups (but not quinary 5x4 subgroups), with the modern MZ bioinformatic scale giving much better results. The quaternary 5-mer MZ 4x5 subgroups are called mutons (Mu5).

Protein amino acid sequences (aas) are rich in information, especially when combined with structural data. There are many Web-based tools for analyzing aas, but by far the most utilized is BLAST (Basic Local Alignment Search Tool), which compares two given sequences, or searches for sequences similar to a given sequence. The original BLAST paper [1] was the most highly cited paper published in the 1990s. A key BLAST element is the “substitution matrix”, which assigns a score for aligning any possible pair of residues, and identifies “positive” mutations between similar aas. The BLOSUM62 matrix (available online) is the default for most BLAST programs [2]. It obtains mutation rates Γ of aa pairs from protein blocks (distantly related but conserved regions), which leads to accurate homological lists of functionally similar protein blocks. Competing effects of hydrophobic and hydrophilic segments of a given protein have long been known to be the primary driving force behind the folding of protein chains into protein globules. There are secondary effects associated with longitudinal hydrogen bonding (α helices) and transverse hydrogen bonding (β strands), and even weaker charge effects, but in most proteins the dominant physico-chemical factor in a kinetic property such as aggregation [3] is hydropathic interactions.
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Hydropathic interactions determine globular shapes and are manifested biochemically in many ways, which has led to many tables of aa hydropathicity Ψ. Here we will compare results obtained with the standard 1982 table, Ψ(KD) (17K citations)[4], and the modern 2007 Ψ(MZ) table, based on fractals and self-organized criticality [5]. The KD table is related to first-order effects (unfolding of globular proteins from water to air), while the MZ table describes second-order conformational changes in globular surface differential geometry [3]. Our analysis of the BLOSUM62 matrix will enable us to decide whether block homologies are primarily first- or second-order thermodynamically. There is already a large literature on general aspects of biological evolution and statistical physics [6], which aim to go beyond phylogenetic trees based on point mutations (much less effective than blocks [2]). Explicit applications help to bring these general considerations into sharper perspective. The biomedically important area of viruses and vaccines is best quantified using epitopes [7,8], which are similar to but still different from blocks, which are best suited to describing self-sustaining proteins [9]. Mutational rates can be used to compare two aspects of different hydropathicity scales Ψ(aa), their discrete hierarchical ordering of 20 amino acids, with 20! possible orderings, or the continuum spacings between ordered amino acids. The MZ and KD orderings [5] can be divided into groups (hydropathic scale blocks), with the two obvious choices for replacing binary 2x10 =2x(2x5) by 4x5 = (2x2)x5, or quaternary 4 x 5aa blocks (denoted by Mut5), or quinary 5 x 4aa blocks (Mut4). The most hydrophobic Mut5α blocks, extracted from the BLOSUM62 matrix, are shown for the MZ and KD scales in Fig. 1. These groups could display the tendency of amino acids to mutate into other amino acids within their subgroup with similar hydropathicity. One often sees qualitative comparisons of mutation rates of hydro (phobic,philic) aa, but with Mut groups one can make quantitative comparisons. One averages the mutational off-diagonal group matrix elements, and compares those averages with the hydropathic width of each group (defined as Ψ(first aa) - Ψ(last aa)). The wider the subgroup, the more Ψ phase space is available for internal mutations. This idea can be tested at the simple 2x10 hydrophobic/hydrophilic level, for Ω = (Mut4α + Mut4β) - (Mut4γ + Mut4δ). With the MZ scale Ω = -1.2 (as one might have expected, exposed hydrophilic aa mutate much more often than buried hydrophobic aa), but with the KD scale Ω = 0.2

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