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

Hitting times in turbulent diffusion due to multiplicative noise

We study a distribution of times of the first arrivals to absorbing targets in turbulent diffusion, which is due to a multiplicative noise. Two examples of dynamical systems with a multiplicative noise are studied. The first one is a random process according to inhomogeneous diffusion, which is also known as a geometric Brownian motion in the Black-Scholes model. The second model is due to a random processes on a two-dimensional comb, where inhomogeneous advection is possible only along the backbone, while Brownian diffusion takes place inside the branches. It is shown that in both cases turbulent diffusion takes place as the one-dimensional random process with the log-normal distribution in the presence of absorbing targets, which are characterized by the Lévy-Smirnov distribution for the first hitting times.

Dissipative Lévy random searches: universal behavior at low target density

We investigate the problem of survival at the very low target-density limit and report on a second-order phase transition for one-dimensional random searches in which the energy cost of locomotion is a function of the distance traveled by the searcher. Surprisingly, from analytical calculations (also tested numerically) we find identical critical exponents for arbitrary energy cost functions. We conclude that there is a single universality class that describes this process.

Wavelet Analysis of Protein Motion

As high-throughput molecular dynamics simulations of proteins become more common and the databases housing the results become larger and more prevalent, more sophisticated methods to quickly and accurately mine large numbers of trajectories for relevant information will have to be developed. One such method, which is only recently gaining popularity in molecular biology, is the continuous wavelet transform, which is especially well-suited for time course data such as molecular dynamics simulations. We describe techniques for the calculation and analysis of wavelet transforms of molecular dynamics trajectories in detail and present examples of how these techniques can be useful in data mining. We demonstrate that wavelets are sensitive to structural rearrangements in proteins and that they can be used to quickly detect physically relevant events. Finally, as an example of the use of this approach, we show how wavelet data mining has led to a novel hypothesis related to the mechanism of the protein γδ resolvase.

A WAVELET APPROACH FOR THE ANALYSIS OF FOLDING TRAJECTORY OF PROTEIN TRP-CAGE

Understanding how protein folds into a functional native structure is arguably one of the most challenging problems remaining in computational biology. Currently, the protein folding mechanism is often characterized by calculating the free energy landscape in terms of various reaction coordinates such as the fraction of native contacts, the radius of gyration, the RMS deviation from the native and so on. In this paper, we present a wavelet approach towards understanding the global state changes during protein folding. The approach is based on the wavelet analysis on the trajectories of various reaction coordinates to identify the significant intermediate states or structural motifs in the folding process. We demonstrate through an example protein Trp-cage that this approach extracts crucial information about protein folding intermediate states as well as the time correlation among these states. Furthermore, the current approach reveals a meaningful structural pattern that had been overlooked in previous works, which provides a better understanding of the folding mechanism as well as the limitation of the current force fields.

How landscape heterogeneity frames optimal diffusivity in searching processes

Theoretical and empirical investigations of search strategies typically have failed to distinguish the distinct roles played by density versus patchiness of resources. It is well known that motility and diffusivity of organisms often increase in environments with low density of resources, but thus far there has been little progress in understanding the specific role of landscape heterogeneity and disorder on random, non-oriented motility. Here we address the general question of how the landscape heterogeneity affects the efficiency of encounter interactions under global constant density of scarce resources. We unveil the key mechanism coupling the landscape structure with optimal search diffusivity. In particular, our main result leads to an empirically testable prediction: enhanced diffusivity (including superdiffusive searches), with shift in the diffusion exponent, favors the success of target encounters in heterogeneous landscapes.

Using support vector machines to distinguish enzymes: approached by incorporating wavelet transform

The enzymatic attributes of newly found protein sequences are usually determined either by biochemical analysis of eukaryotic and prokaryotic genomes or by microarray chips. These experimental methods are both time-consuming and costly. With the explosion of protein sequences registered in the databanks, it is highly desirable to develop an automated method to identify whether a given new sequence belongs to enzyme or non-enzyme. The discrete wavelet transform (DWT) and support vector machine (SVM) have been used in this study for distinguishing enzyme structures from non-enzymes. The networks have been trained and tested on two datasets of proteins with different wavelet basis functions, decomposition scales and hydrophobicity data types. Maximum accuracy has been obtained using SVM with a wavelet function of Bior2.4, a decomposition scale j=5, and Kyte-Doolittle hydrophobicity scales. The results obtained by the self-consistency test, jackknife test and independent dataset test are encouraging, which indicates that the proposed method can be employed as a useful assistant technique for distinguishing enzymes from non-enzymes.

Single-mutation-induced stability loss in protein lysozyme

Recent NMR experiments have revealed that a single residue mutation W62G on protein hen's-egg white lysozyme can cause a dramatic loss of long-range interactions and protein stability; however, the molecular mechanism for this surprising phenomenon is not completely clear. In this mini-review, we have summarized some of our recent work on the molecular mechanism with large-scale molecular modelling, and also utilized a new wavelet method to analyse the local structural clusters present in both the wild-type and mutant folding trajectories. These extensive MD (Molecular Dynamics) simulations (10+ μs) were performed in 8 M urea, mimicking the experimental condition. Detailed analyses revealed that the Trp62 residue is the key to a co-operative long-range interaction within the wild-type protein: it acts as a bridge between neighbouring basic residues, mainly arginine residues, through π-type hydrogen bonds or π-cation interactions to form an Arg-Trp-Arg ‘sandwich-like’ local structure. The local cluster near Trp62 further extends its interaction to other clusters, such as the one near Trp111, through Arg112, which is involved in such an Arg-Trp-Arg bridging structure, thus achieving the long-range interactions for the wild-type. On the other hand, the mutant does not have this bridging effect and forms much less local clusters or contacts, and therefore results in a much less stable structure. Overall, these findings not only support the general conclusions of the experiment, but also provide a detailed but somewhat different molecular picture of the disruption of the long-range interactions.

Clustering of protein structures using hydrophobic free energy and solvent accessibility of proteins

The hydrophobic free energy and solvent accessibility of amino acids are used to study the relationship between the primary structure and structural classification of large proteins. A measure representation and a Z curve representation of protein sequences are proposed. Fractal analysis of the measure and Z curve representations of proteins and multifractal analysis of their hydrophobic free energy and solvent accessibility sequences indicate that the protein sequences possess correlations and multifractal scaling. The parameters from the fractal and multifractal analyses on these sequences are used to construct some parameter spaces. Each protein is represented by a point in these spaces. A method is proposed to distinguish and cluster proteins from the alpha, beta, alpha + beta, and alpha/beta structural classes in these parameter spaces. Fisher's linear discriminant algorithm is used to give a quantitative assessment of our clustering on the selected proteins. Numerical results indicate that the discriminant accuracies are satisfactory. In particular, they reach 94.12% and 88.89% in separating proteins from {alpha, alpha + beta, alpha/beta} proteins in a three-dimensional space.

Algorithmically designed peptides ameliorate behavioral defects in animal model of ADHD by an allosteric mechanism

This study exemplifies the use of three ADHD-relevant methodological innovations. (1) The use of novel, patented, computational peptide design techniques to generate peptides targeting the extra-cellular and para-transmembrane amino acid loops of the putatively ADHD-involved, D(2) dopamine receptor, D(2)DAR; (2) experimental evidence that these peptides in L-amino acid/ortho ordered or D-amino acid/reverse ordered (retro-inverso), D(2)DAR, hydrophobic eigenmode matched forms, evoked positive allosteric and indirect agonist influences on in vitro stably receptor transfected CHO and LtK cells and on in vivo, brain mediated activity; (3) a representative 15 residue all-D-amino acid, D(2) mode matched peptide, given parenterally, was found to "repair" a key aberrant ADHD behavioral characteristic in a standard animal model of ADHD, the Spontaneously Hypertensive Rat, SHR, relative to its progenitor species control, the Wistar-Kyoto rat, WKY. The representative, retro-inverso peptide, all-D-LLYKNKPRYPKRNRE, reversed SHR's relative deficiency in sensory motor gating (pre-pulse inhibition, PPI) while leaving SHR's nonselective attention (rearings), impulsive behavior (time in center), and activity level (timed total motor behavior) unchanged. Amphetamine also reversed SHRs sensory gating defect, but with significant increases in nonselective attention, impulsivity and hyperactivity. These preliminary results suggest the possibility of a new, "softer" pharmacological approach to ADHD: hydrophobic mode matched peptide allosteric augmentation of the activity of indigenous dopamine with respect to D(2)DAR mediated function, in place of stimulant drug-induced presynaptic dopamine release or impairment of dopamine uptake.

Designing allosteric peptide ligands targeting a globular protein

Patented signal analytic algorithms applied to hydrophobically transformed, numerical amino acid sequences have previously been used to design short, protein-targeted, L or D retro-inverso peptides. These peptides have demonstrated allosteric and/or indirect agonist effects on a variety of G-protein and tyrosine kinase coupled membrane receptors with 30% to over 80% hit rates. Here we extend these approaches to a globular protein target. We designed eight peptide ligands targeting an ELISA antibody responsive protein, beta-galactosidase, betaGAL. Three of the eight 14mer peptides allosterically activated betaGAL with ELISA methodology. Using Bayesian statistics, this 38% hit rate would have occurred 2 x 10(-9) by chance. These peptides demonstrated binding site competitive or noncompetitive interactions, suggesting allosteric site multiplicity with respect to their betaGAL binding-mediated ELISA signal. Kinetic studies demonstrated the temperature dependence of the betaGAL peptide binding functions. Using the van't Hoff relation, we found evidence for enthalpy-entropy compensation. This relation is often found for hydrophobic interactions in aqueous media, and is consistent with the postulated hydrophobic series encoding underlying our protein-targeted, peptide design methods. It appears that our algorithmic, hydrophobic autocovariance eigenvector template approach to the design of allosteric peptides targeting membrane receptors may also be applicable to the design of peptide ligands targeting nonmembrane involved globular proteins.

Designing human m1 muscarinic receptor-targeted hydrophobic eigenmode matched peptides as functional modulators

A new proprietary de novo peptide design technique generated ten 15-residue peptides targeting and containing the leading nontransmembrane hydrophobic autocorrelation wavelengths, "modes", of the human m(1) muscarinic cholinergic receptor, m(1)AChR. These modes were also shared by the m(4)AChR subtype (but not the m(2), m(3), or m(5) subtypes) and the three-finger snake toxins that pseudoirreversibly bind m(1)AChR. The linear decomposition of the hydrophobically transformed m(1)AChR amino acid sequence yielded ordered eigenvectors of orthogonal hydrophobic variational patterns. The weighted sum of two eigenvectors formed the peptide design template. Amino acids were iteratively assigned to template positions randomly, within hydrophobic groups. One peptide demonstrated significant functional indirect agonist activity, and five produced significant positive allosteric modulation of atropine-reversible, direct-agonist-induced cellular activation in stably m(1)AChR-transfected Chinese hamster ovary cells, reflected in integrated extracellular acidification responses. The peptide positive allosteric ligands produced left-shifts and peptide concentration-response augmentation in integrated extracellular acidification response asymptotic sigmoidal functions and concentration-response behavior in Hill number indices of positive cooperativity. Peptide mode specificity was suggested by negative crossover experiments with human m(2)ACh and D(2) dopamine receptors. Morlet wavelet transformation of the leading eigenvector-derived, m(1)AChR eigenfunctions locates seven hydrophobic transmembrane segments and suggests possible extracellular loop locations for the peptide-receptor mode-matched, modulatory hydrophobic aggregation sites.

Cellular and behavioral effects of D2 dopamine receptor hydrophobic eigenmode-targeted peptide ligands

Patterns in G-protein-coupled receptors' hydrophobically transformed amino-acid sequences can be computationally characterized as hierarchies of autocorrelation waves, "hydrophobic eigenmodes", using autocovariance matrix decomposition and all poles power spectral and wavelet transformations. L- or D-amino acid (retro-inverso) 12-18 residue peptides targeting these modes can be designed using eigenvector templates derived from these computations. In all, 12 human long-form D(2) dopamine receptor eigenmode-targeted 15 mer peptides were designed, synthesized, and shown to modulate and/or indirectly activate the extracellular acidification response, EAR, in stably receptor-transfected CHO and LtK cells, with an 83% hit rate. Representative L- and D-amino-acid retro-inverso peptides injected bilaterally in the nucleus accumbens demonstrated changes in rat exploratory behavior and prepulse inhibition similar to those observed following parenteral amphetamine. In contrast with geometric models used for ligand design, such as pharmacophores, the hydrophobic eigenmode approach to lead modulatory peptide design targets hydrophobic eigenmode-bearing subsequences, including those not visible from X-ray and NMR studies such as extracellular segments and loops.

New cell attachment peptide sequences from conserved epitopes in the carboxy termini of fibrinogen

Fibrinogen seems to contribute significantly to cell binding and recruitment into wounds besides its major role in clot formation. We describe 19- to 21-mer cell-binding (haptotactic) peptides from the C-termini of fibrinogen beta-chain (Cbeta), the extended alphaE chain, and near the C-terminal of the gamma-chain. When these peptides were covalently bound to a biologically inert matrix such as Sepharose beads (SB), they elicited beads attachment to cells, mostly of mesenchymal origin (including fibroblasts, endothelial cells, and smooth muscle cells) as well as some transformed cell lines. Based on such haptotactic activity, these peptides were termed "haptides." By contrast, peptides homologous to fibrinogen C-termini alpha- and gamma-chains elicited no such activity. The haptide Cbeta could not block the interaction of fibroblasts with antibodies directed against integrins beta(1), alpha(v), alpha(v)beta(1), alpha(v)beta(3), and alphaIIbeta(3). Moreover, GRGDS peptide could not inhibit enhanced cell binding to SB-Cbeta, as expected from an integrin-mediated process. In soluble form the haptides were accumulated in cells with nonsaturable kinetics without any toxic or proproliferative effects in concentrations up to 80 microM. These findings suggest that the conserved haptidic sequences within fibrin(ogen) can be associated with the adhesion and migration of cells into fibrin clots and may have a significant role in normal wound healing and in various pathological conditions.

Recurrence quantification analysis reveals interaction partners in paramyxoviridae envelope glycoproteins

The paramyxovirus envelope fuses with the host cell membrane by cooperative interaction of two transmembrane glycoproteins: the hemagglutinin neuraminidase (HN) and the fusion (F) glycoprotein. The interaction appears to be finely regulated, as both proteins must derive from the same viral species to obtain a functional interaction. Because HN and F do not form stable complexes, this interaction is poorly characterized. This article demonstrates that a modification of a classical bioinformatic method based on the co-evolution of interacting partners can detect the specificity of the HN and F interaction. The proposed approach relies on a relatively new nonlinear signal analysis technique, recurrence quantification analysis (RQA), applied to the hydrophobicity sequences of viral proteins. This technique is able to shed light on the interaction between HN and F proteins in the virus-cell fusion and, more generally, permits the quantitative comparison of nonhomologue protein systems. On the contrary, the same co-evolution approach, based on the classical sequence alignment procedure, was unable to discriminate interacting partners from the general strict correlation existing between the evolution of viral proteins as a whole. The cooperation between HN and F in the fusion process is thus demonstrated by a bioinformatic, purely sequence-dependent, perspective.

Nonlinear methods in the analysis of protein sequences: a case study in rubredoxins

Two computational methods widely used in time series analysis were applied to protein sequences, and their ability to derive structural information not directly accessible through classical sequence comparisons methods was assessed. The primary structures of 19 rubredoxins of both mesophilic and thermophilic bacteria, coded with hydrophobicity values of amino acid residues, were considered as time series and were analyzed by 1) recurrence quantification analysis and 2) spectral analysis of the sequence major eigenfunctions. The results of the two methods agreed to a large extent and generated a classification consistent with known 3D structural characteristics of the studied proteins. This classification separated in a clearcut manner a thermophilic protein from mesophilic proteins. The classification of primary structures given by the two dynamical methods was demonstrated to be basically different from classification stemming from classical sequence homology metrics. Moreover, on a more detailed scale, the method was able to discriminate between thermophilic and mesophilic proteins from a set of chimeric sequences generated from the mixing of a mesophilic (Rubr Clopa) and a thermophilic (Rubr Pyrfu) protein. Overall, our results point to a new way of looking at protein sequence comparisons.

Hydrophobic free energy eigenfunctions of pore, channel, and transporter proteins contain beta-burst patterns

Hydropathy plots are often used in place of missing physical data to model transmembrane proteins that are difficult to crystallize. The sequential maxima of their graphs approximate the number and locations of transmembrane segments, but potentially useful additional information about sequential hydrophobic variation is lost in this smoothing procedure. To explore a broader range of hydrophobic variations without loss of the transmembrane segment-relevant sequential maxima, we utilize a sequence of linear decompositions and transformations of the n-length hydrophobic free energy sequences, Hi, i = 1...n, of proteins. Constructions of hydrophobic free energy eigenfunctions, psil, from M-lagged, M x M autocovariance matrices, CM, were followed by their all-poles, maximum entropy power spectral, Somega(psil), and Mexican Hat wavelet, Wa,b(psil), transformations. These procedures yielded graphs indicative of inverse frequencies, omega-1, and sequence locations of hydrophobic modes suggestive of secondary and supersecondary protein structures. The graphs of these computations discriminated between Greek Key, Jelly Role, and Up and Down categories of antiparallel beta-barrel proteins. With these methods, examples of porins, connexins, hexose transporters, nuclear membrane proteins, and potassium but not sodium channels appear to belong to the Up and Down antiparallel beta-barrel variety.

Mode matches in hydrophobic free energy eigenfunctions predict peptide-protein interactions

The dominant statistical hydrophobic free energy inverse frequencies amino acid wavelengths as hydrophobic modes, of neurotensin (NT), cholescystokinin (CCK), the human dopamine D2 receptor [(DA)D2], and the human dopamine transporter (DAT) were determined using orthogonal decomposition of the autocovariance matrices of their amino acid sequences as hydrophobic free energy equivalents in kcal/mol. The leading eigenvalues-associated eigenvectors were convolved with the original series to construct eigenfunctions. Eigenfunctions were further analyzed using discrete trigonometric wavelet and all poles, maximum entropy power spectral transformations. This yielded clean representations of the dominant hydrophobic free energy modes, most of which are otherwise lost in the smoothing of hydropathy plots or contaminated by end effects and multimodality in conventional Fourier transformations. Mode matches were found between NT and (DA)D2 and between CCK and DAT, but not the converse. These mode matches successfully predicted the nonlinear kinetic interactions of NT-(DA)D2 in contrast with CCK-(DA) D2 on 3H-spiperone binding to (DA) D2, and by CCK-DAT but not NT-DAT on [N-methyl-3H]-WIN 35,428 binding to DAT in (DA)D2 and DAT cDNA stably transfected cell lines without known NT or CCK receptors. Computation of the dominant modes of hydrophobic free energy eigenfunctions may help predict functionally relevant peptide-membrane protein interactions, even across neurotransmitter families.