Spectral Analysis of Sequence Variability in Basic-Helix-loop-helix (bHLH) Protein Domains

The basic helix-loop-helix (bHLH) family of transcription factors is used as a paradigm to explore structural implications of periodicity patterns in amino acid sequence variability. A Boltzmann-Shannon entropy profile represents site-by-site amino acid variation in the bHLH domain. Spectral analysis of almost 200 bHLH sequences documents the periodic nature of the bHLH sequence variation. Spectral analyses provide strong evidence that the patterns of amino acid variation in large numbers of sequences conform to the classical α-helix three-dimensional structure periodicity of 3.6 amino acids per turn. Multivariate indices of amino acid physiochemical attributes derived from almost 500 amino acid attributes are used to provide information regarding the underlying causal components of the bHLH sequence variability. Five multivariate attribute indices are used that reflect patterns in i) polarity - hydrophobicity - accessibility, ii) propensity for secondary structures, iii) molecular volume, iv) codon composition and v) electrostatic charge. Multiple regression analyses of the entropy values as dependent variables and the factor score means and variances as independent variables are used to partition variation in entropy values into their underlying causal structural components.