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 quantitative model for membrane fusion based on low-energy intermediates

The energetics of a fusion pathway is considered, starting from the contact site where two apposed membranes each locally protrude (as “nipples”) toward each other. The equilibrium distance between the tips of the two nipples is determined by a balance of physical forces: repulsion caused by hydration and attraction generated by fusion proteins. The energy to create the initial stalk, caused by bending of cis monolayer leaflets, is much less when the stalk forms between nipples rather than parallel flat membranes. The stalk cannot, however, expand by bending deformations alone, because this would necessitate the creation of a hydrophobic void of prohibitively high energy. But small movements of the lipids out of the plane of their monolayers allow transformation of the stalk into a modified stalk. This intermediate, not previously considered, is a low-energy structure that can reconfigure into a fusion pore via an additional intermediate, the prepore. The lipids of this latter structure are oriented as in a fusion pore, but the bilayer is locally compressed. All membrane rearrangements occur in a discrete local region without creation of an extended hemifusion diaphragm. Importantly, all steps of the proposed pathway are energetically feasible.

Use of binding energy by an RNA enzyme for catalysis by positioning and substrate destabilization.

A fundamental catalytic principle for protein enzymes in the use of binding interactions away from the site of chemical transformation for catalysis. We have compared the binding and reactivity of a series of oligonucleotide substrates and products of the Tetrahymena ribozyme, which catalyzes a site-specific phosphodiester cleavage reaction: CCCUCUpA+G<-->CCCUCU-OH+GpA. The results suggest that this RNA enzyme, like protein enzymes, can utilize binding interactions to achieve substantial catalysis via entropic fixation and substrate destabilization. The stronger binding of the all-ribose oligonucleotide product compared to an analog with a terminal 3' deoxyribose residue gives an effective concentration of 2200 M for the 3' hydroxyl group, a value approaching those obtained with protein enzymes and suggesting the presence of a structurally well defined active site capable of precise positioning. The stabilization from tertiary binding interactions is 40-fold less for the oligonucleotide substrate than the oligonucleotide product, despite the presence of the reactive phosphoryl group in the substrate. This destabilization is accounted for by a model in which tertiary interactions away from the site of bond cleavage position the electron-deficient 3' bridging phosphoryl oxygen of the oligonucleotide substrate next to an electropositive Mg ion. As the phosphodiester bond breaks and this 3' oxygen atom develops a negative charge in the transition state, the weak interaction of the substrate with Mg2+ becomes strong. These strategies of "substrate destabilization" and "transition state stabilization" provide estimated rate enhancements of approximately 280- and approximately 60-fold, respectively. Analogous substrate destabilization by a metal ion or hydrogen bond donor may be used more generally by RNA and protein enzymes catalyzing reactions of phosphate esters.