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.

Exploring the folding free energy surface of a three-helix bundle protein

The multidimensional free energy surface for a small fast folding helical protein is explored based on first-principle calculations. The model represents the 46-residue segment from fragment B of staphylococcal protein A. The relationship between collapse and tertiary structure formation, and the order of collapse and secondary structure formation, are investigated. We find that the initial collapse process gives rise to a transition state with about 30% of the native tertiary structure and 50–70% of the native helix content. We also observe two distinct distributions of native helix in this collapsed state (Rg ≈ 12 Å), one with about 20% of the native helical hydrogen bonds, the other with near 70%. The former corresponds to a local minimum. The barrier from this metastable state to the native state is about 2 kBT. In the latter case, folding is essentially a downhill process involving topological assembly. In addition, the order of formation of secondary structure among the three helices is examined. We observe cooperative formation of the secondary structure in helix I and helix II. Secondary structure in helix III starts to form following the formation of certain secondary structure in both helix I and helix II. Comparisons of our results with those from theory and experiment are made.

Rapid chemical kinetic techniques for investigations of neurotransmitter receptors expressed in Xenopus oocytes

Xenopus laevis oocytes have been used extensively during the past decade to express and study neurotransmitter receptors of various origins and subunit composition and also to express and study receptors altered by site-specific mutations. Interpretations of the effects of structural differences on receptor mechanisms were, however, hampered by a lack of rapid chemical reaction techniques suitable for use with oocytes. Here we describe flow and photolysis techniques, with 2-ms and 100-μs time resolution, respectively, for studying neurotransmitter receptors in giant (≈20-μm diameter) patches of oocyte membranes, using muscle and neuronal acetylcholine receptors as examples. With these techniques, we find that the muscle receptor in BC3H1 cells and the same receptor expressed in oocytes have comparable kinetic properties. This finding is in contrast to previous studies and raises questions regarding the interpretations of the many studies of receptors expressed in oocytes in which an insufficient time resolution was available. The results obtained indicate that the rapid reaction techniques described here, in conjunction with the oocyte expression system, will be useful in answering many outstanding questions regarding the structure and function of diverse neurotransmitter receptors.

Spectral diffusion and the energy landscape of a protein

We present a novel type of spectral diffusion experiment in the millikelvin range to characterize the energy landscape of a protein as compared with that of a glass. We measure the time evolution of spectral holes for more than 300 hr after well-defined initial nonequilibrium conditions. We show that the model of noninteracting two-level systems can describe spectral diffusion in the glass, but fails for the protein. Our results further demonstrate that randomness in the energy landscape of a protein shows features of organization. There are “deep minimum” states separated by barriers, the heights of which we are able to estimate. The energy landscape of a glass is featureless by comparison.

Symmetry and the energy landscapes of biomolecules

The role of symmetry in the folding of proteins is discussed using energy landscape theory. An analytical argument shows it is much easier to find sequences with funneled energy landscape capable of fast folding if the structure is symmetric. The analogy with phase transitions of small clusters with magic numbers is discussed.