Mode matches and their locations in the hydrophobic free energy sequences of peptide ligands and their receptor eigenfunctions

Patterns in sequences of amino acid hydrophobic free energies predict secondary structures in proteins. In protein folding, matches in hydrophobic free energy statistical wavelengths appear to contribute to selective aggregation of secondary structures in “hydrophobic zippers.” In a similar setting, the use of Fourier analysis to characterize the dominant statistical wavelengths of peptide ligands’ and receptor proteins’ hydrophobic modes to predict such matches has been limited by the aliasing and end effects of short peptide lengths, as well as the broad-band, mode multiplicity of many of their frequency (power) spectra. In addition, the sequence locations of the matching modes are lost in this transformation. We make new use of three techniques to address these difficulties: (i) eigenfunction construction from the linear decomposition of the lagged covariance matrices of the ligands and receptors as hydrophobic free energy sequences; (ii) maximum entropy, complex poles power spectra, which select the dominant modes of the hydrophobic free energy sequences or their eigenfunctions; and (iii) discrete, best bases, trigonometric wavelet transformations, which confirm the dominant spectral frequencies of the eigenfunctions and locate them as (absolute valued) moduli in the peptide or receptor sequence. The leading eigenfunction of the covariance matrix of a transmembrane receptor sequence locates the same transmembrane segments seen in n-block-averaged hydropathy plots while leaving the remaining hydrophobic modes unsmoothed and available for further analyses as secondary eigenfunctions. In these receptor eigenfunctions, we find a set of statistical wavelength matches between peptide ligands and their G-protein and tyrosine kinase coupled receptors, ranging across examples from 13.10 amino acids in acid fibroblast growth factor to 2.18 residues in corticotropin releasing factor. We find that the wavelet-located receptor modes in the extracellular loops are compatible with studies of receptor chimeric exchanges and point mutations. A nonbinding corticotropin-releasing factor receptor mutant is shown to have lost the signatory mode common to the normal receptor and its ligand. Hydrophobic free energy eigenfunctions and their transformations offer new quantitative physical homologies in database searches for peptide-receptor matches.

A sampling problem in molecular dynamics simulations of macromolecules.

Correlations in low-frequency atomic displacements predicted by molecular dynamics simulations on the order of 1 ns are undersampled for the time scales currently accessible by the technique. This is shown with three different representations of the fluctuations in a macromolecule: the reciprocal space of crystallography using diffuse x-ray scattering data, real three-dimensional Cartesian space using covariance matrices of the atomic displacements, and the 3N-dimensional configuration space of the protein using dimensionally reduced projections to visualize the extent to which phase space is sampled.

Skeletal matrices, muci, and the origin of invertebrate calcification.

The sudden appearance of calcified skeletons among many different invertebrate taxa at the Precambrian-Cambrian transition may have required minor reorganization of preexisting secretory functions. In particular, features of the skeletal organic matrix responsible for regulating crystal growth by inhibition may be derived from mucous epithelial excretions. The latter would have prevented spontaneous calcium carbonate overcrusting of soft tissues exposed to the highly supersaturated Late Proterozoic ocean [Knoll, A. H., Fairchild, I. J. & Swett, K. (1993) Palaios 8, 512-525], a putative function for which we propose the term "anticalcification." We tested this hypothesis by comparing the serological properties of skeletal water-soluble matrices and mucous excretions of three invertebrates--the scleractinian coral Galaxea fascicularis and the bivalve molluscs Mytilus edulis and Mercenaria mercenaria. Crossreactivities recorded between muci and skeletal water-soluble matrices suggest that these different secretory products have a high degree of homology. Furthermore, freshly extracted muci of Mytilus were found to inhibit calcium carbonate precipitation in solution.