Karen A. Selz

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.

Hydrophobic Free Energy Eigenfunctions of Pore, Channel, and Transporter Proteins Contain β-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.

Entropy conservation as hTμ≈λ̄μ+dμ in neurobiological dynamical systems

That the topological entropy, h(T(m) ), of a C(1 M, of a surface, M, upon which invariant measure(s) m are concentrated, varies as the product of its average leading Lyapunov characteristic exponent, lambda(m), and the Hausdorff dimension of its support, d(m),was proven by Pesin [Russ. Math Surveys 32, 55-114 (1977)] for nonuniform partial hyperbolic systems and by Ledreppier and Young [Ergod. Theor. Dyn. Syst. 2, 109-123 (1982)], and Manning [Ergod. Theor. Dyn. Syst. 1, 451-459 (1981)] for uniformly hyperbolic (Axiom A) diffeomorphisms. When considered in conjunction with the post-Shannon information encoding theorems of Adler [Trans. Am. Math. Soc. 114, 309-319 (1965); Mem. Am. Math. Soc., No. 219 (1979)] and others, this suggests a way to differentiate equal entropy behaviors in systems with varying patterns of dynamical behaviors. Here we show this relation to be useful in the quantitative discrimination among the behaviors of abstract neuronal models and two real, finite time, partially and nonuniformly hyperbolic, brain-related dynamical systems. We observe a trade-off in finite time between two competing dynamical processes, jittery sticking (tending to increase d(m)) and convective escaping (more prominently incrementing lambda(m) (+)). In finite time systems, these changes in combination can statistically conserve the dynamical entropy, h(T(m) ), while altering the Levy characteristic exponent, alpha (describing the tail of the density distribution of observables, rho(x) approximately exp-gammamid R:xmid R:(alpha),1 0.5 implicates sequential correlations and H(*)<0.5 sequential anticorrelation. When the relation h(T(m) )=lambda(m) (+)dm fails, the way it does so provides information about the system. (c) 1997 American Institute of Physics.

The development of nuchal atonia associated with active (REM) sleep in fetal sheep: presence of recurrent fractal organization

The behavioral state of active or rapid eye movement sleep (REMS) is dominant during fetal life and may play an important role in brain development. One marker of this state in fetal sheep is neck nuchal muscle atonia (NA). We observed burst within burst NA patterns suggestive of recurrent fractal organization in continuous 13 day in utero recordings of NA during the third trimester. Consistent with fractal renewal processes, the cumulative mean and standard deviation (SD) diverged over this time and the tail of NA distributions fit a stable Lévy law with exponents that remained invariant over the periods of development examined. The Hurst exponent, a measure of self-affine fractals, indicated that long-range correlations among NA intervals were present throughout development. A conserved complex fractal structure is apparent in NA which may help elucidate ambiguities in defining fetal states as well as some unique properties of fetal REMS.

BERNOULLI PARTITION-EQUIVALENCE OF INTERMITTENT NEURONAL DISCHARGE PATTERNS

The binary partition of the range of values for a series of interspike intervals necessary to generate the growth rate of the longest run equivalent to that observed in a Bernoulli, fair coin sequence was found to discriminate three classes of intermittently firing brain stem neurons more clearly than either the higher statistical moments or the leading Lyapunov exponent.

DISTRIBUTIONS OF LOCAL MANDELBROT-HURST EXPONENTS: MOTOR ACTIVITY IN FETAL RATS OF COCAINIZED MOTHERS AND MANIC-DEPRESSIVE PATIENTS

Intermittency, in which the normalized weight of large fluctuations grows for increasingly longer statistical samples, is seen as irregular bursting activity in time and is characteristic of the behavior of many brain and behavioral systems. This pattern has been related to the brain-stabilizing interplay of the general mechanisms of silence-evoked sensitization and activity-evoked desensitization, which can be found at most levels of neurobiological function and which vary more smoothly and at much longer times than the phasic observables. We use both the global Mandelbrot-Hurst exponent and the distribution of local Mandelbrot-Hurst exponents, in combination with dynamical entropies, to quantitate the property of nonuniform persistence which we treat as both deterministically expansive and statistically diffusive. For example, varying the parameter of the one-dimensional, Manneville-Pomeau intermittency map generated time series which demonstrated systematic changes in these statistical indices of persistence. Relatively small doses of cocaine administered to pregnant rats increased statistical indices of expansiveness and persistence in fetal motor behavior. These techniques also model and characterize a breakdown of statistical scaling in 72-hour time series of the amount of motor activity in some hospitalized manic-depressive patients.

Predicting Peptide−Receptor, Peptide−Protein, and Chaperone−Protein Binding Using Patterns in Amino Acid Hydrophobic Free Energy Sequences†

Much of the current study of protein organization is aimed at understanding emergent polymeric structure in three rather than one dimensions. This is largely because the weak bonds between amino acid side chains in one-dimensional peptide heteropolymers that determine their equilibrium tertiary structures involve large loop interactions between sequentially distant sites. For this reason, searches for sequential patterns seem intuitively irrelevant even though the coding for 3D protein structure is present in the 1D peptide chain, On the other hand, we have found that there are particular circumstances in which matches in sequential patterns in amino acid side chain thermodynamic properties postdict signatory modularity in the tertiary structure of protein families and polypeptide -protein interactions, such as peptide -r ceptor, peptide -membrane transporter, nuclear factor -protein docking, and chaperone -protein binding. Here we describe and justify our computational approach to matching sequential organization, with examples from experimentally demonstrable, polypeptide protein interactions. Using established values for each amino acid’s hydrophobic free energy, “hydrophobicity”, in kcal/mol, derived from their normalized free energy of transfer from nonpolar to polar bulk phases of binary solutions, 34 we study the variations in hydrophobicity along primary sequences and seek matching patterns among them. We analyze this discrete data series using the all-poles power spectrum for shorter polypeptides. For longer polypeptides and proteins, including membrane receptors, relevant protein domains, nuclear factors, and chaperones, we first decompose the data using autocovariance matrices into orthogonal eigenvectors, compose these eigenvectors with the original series to generate eigenfunctions, and then compute their power spectra. We show examples of sequential pattern-matched peptides that postdict binding of a non-peptide (estrogen) receptor, protein (calcineurin) binding to its T-cell nuclear factor (NFAT) docking site, and chaperone (GroEL) binding to one of its target enzyme proteins ( â-lactamase). Polypeptide sequences and the associated proteins that bind them share distinguishing spectral features in their all poles power spectrum. This approach achieves practical significance because inversion of these analytic methods are now being used to successfully design de novo peptides which demonstrated their predicted physiological activity.

Protein binding predictions from amino acid primary sequence hydrophobicity

Abstract A protein is composed of a linear chain of amino acids, called its primary structure. Each amino acid has a measured hydrophobicity that reflects its attraction to or repulsion from a water environment. Going along a proteins amino acid chain the hydrophobicity sequence is analogous to a discrete data series. We analyze this data series with several numerical methods. In this paper, we will focus on decomposing this data series into orthogonal modes and then calculate the power spectrum of these modes. We find that proteins that bind together possess the same distinguishing spectral features in their power spectrum.

Daydreaming, Thought Blocking and Strudels in the Taskless, Resting Human Brain’s Magnetic Fields

The incidence, i(S), and duration, l(S), of transient, intermittent, hierarchical vorticities, strudels, S, in magnetic flux fluctuations, were computed from MEG records. from 91 task‐free resting subjects. The MEG’s i(S) and l(S) manifested characteristic times and entropic sensitivity resembling those reported in psychological studies of daydreaming and task‐unrelated thoughts, TUTs. Transient reduction or absences of strudels can be found in patients with syndromes characterized by thought blocking. Positive ergodic single orbit measures of expansiveness and mixing predict i(S) and l(S). An analogy with the relationship between intermittent pontine‐geniculate‐occipital waves and dreaming is made to strudels with daydreaming. Both can be interpreted as neurophysiological correlates of the spontaneous intrusions into consciousness of the never idle unconscious mind.

A third measure-metastable state in the dynamics of spontaneous shape change in healthy human's white cells.

Human polymorphonuclear leucocytes, PMN, are highly motile cells with average 12-15 µm diameters and prominent, loboid nuclei. They are produced in the bone marrow, are essential for host defense, and are the most populous of white blood cell types. PMN also participate in acute and chronic inflammatory processes, in the regulation of the immune response, in angiogenesis, and interact with tumors. To accommodate these varied functions, their behavior is adaptive, but still definable in terms of a set of behavioral states. PMN morphodynamics have generally involved a non-equilibrium stationary, spheroid Idling state that transitions to an activated, ellipsoid translocating state in response to chemical signals. These two behavioral shape-states, spheroid and ellipsoid, are generally recognized as making up the vocabulary of a healthy PMN. A third, “random” state has occasionally been reported as associated with disease states. I have observed this third, Treadmilling state, in PMN from healthy subjects, the cells demonstrating metastable dynamical behaviors known to anticipate phase transitions in mathematical, physical, and biological systems. For this study, human PMN were microscopically imaged and analyzed as single living cells. I used a microscope with a novel high aperture, cardioid annular condenser with better than 100 nanometer resolution of simultaneous, mixed dark field and intrinsic fluorescent images to record shape changes in 189 living PMNs. Relative radial roundness, R(t), served as a computable order parameter. Comparison of R(t) series of 10 cells in the Idling and 10 in the Treadmilling state reveals the robustness of the “random” appearing Treadmilling state, and the emergence of behaviors observed in the neighborhood of global state transitions, including increased correlation length and variance (divergence), sudden jumps, mixed phases, bimodality, power spectral scaling and temporal slowing. Wavelet transformation of an R(t) series of an Idling to Treadmilling state change, demonstrated behaviors concomitant with the observed transition.