Arnold J. Mandell

Phase transition behavior of a linear macromolecule threading a membrane

The problem of a polymer molecule whose two ends reside on opposite sides of a membrane or partition separating two solutions is solved exactly in the limit of no self-excluded volume. The monomers can go from one side of the membrane to the other only by threading serially through one hole in the membrane. The ends can be free, confined to run freely on the membrane surfaces, or be fixed to specific points on the membrane. It is found that the equilibrium thermodynamic phase transition is first order in all cases so that slight changes in pH, ionic strength, or temperature can move the polymer from being completely on one side of the membrane to being completely on the other side. Application to two biological problems are suggested: (1) the breaching of cell walls by the nuclear material of T2 bacteriophages, and (2) the transport of drugs that are affixed to these translocating polymers. The relation of this newly discovered transition to four other phase transitions that occur in isolated macromolecul...

Wavelet transformation of protein hydrophobicity sequences suggests their memberships in structural families

The amino acids of representative proteins were transformed into sequences of hydrophobic free energies per residue, the values derived from equilibrium partitions between aqueous and hydrocarbon phases of a binary solvent. The distributions of the amplitudes of the sequential fluctuations in hydrophobic free energy were then examined with respect to location and scale using Morlet wavelet transformations. Graphs of the wavelet coefficients imaginary parts discriminated among proteins whose tertiary structures are dominated by helices, sheets or their combination, using protein X-ray structures and X-ray fractal dimensions as reference criteria.

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.

Nonlinear Dynamical Patterns as Personality Theory for Neurobiology and Psychiatry

ADVANCES in the theory of nonlinear differential equations and their statistical representations have yielded a powerful, qualitatively descriptive yet quantitative language that captures characteristic patterns of behavior (what the psychoanalyst Roy Schafer calls continuity, coherence, and consistency of action) that has begun to influence studies of complex systems in motion as diverse in specifics as signatory patterns of discharge of neurochemically defined single neurons and the dynamical structures characteristic of a particular composers music. What might be called personality theories of neurobiological dynamics have arisen to replace neurobiological theories of personality. It is in this way that rigorously proven and powerful general mathematical insights have changed the face of determinism in research in brain and behavior. Two examples: (1) Very complicated looking behavior of neurobiological forced-dissipative (expanding and contracting) systems over time take place on low dimensional abstract surfaces on which only a few underlying abstract parameters control the action. (2) Independent of specific details (chemical, electrical, and/or behavioral), there exist a relatively few fundamental categories of behavior in time and transitions, among them a property called universality. Results from this new theoretical, in contrast with experimental, reductionism yield analogies with and new approaches to historically important dynamic ideas about personality and character patterns that are equally relevant to micro and macrocomplex systems such as neural membrane receptor proteins and individual personality styles. Research findings achieved over the past decade and a half in our laboratory and others in neurochemistry, neurophysiology, and animal and human behavior, as well as the results of a new demonstration experiment involving the prediction of dynamical category membership from abstract expressive motion in humans, are used to exemplify this use of a quantitative dynamic category theory across disciplinary levels in brain and behavior. Multiple measures of complexity adapted from current research in the statistical properties of chaos on unobtrusively observed and reconstructed orbits on the computer screen made by non-premorbid subjects executing content-free, computer-game-like tasks with a mouse, were used to reliably differentiate the signatures of two Axis II diagnoses as established using SCID-II criteria. Whereas the techniques of nonlinear systems have achieved some success in quantifying and stimulating the dynamical styles of relatively local phenomena such as the spontaneous behavior of neuronal membrane conductances, single neurons, neural networks, and field electrical events, we think that the real power of these techniques lies in their quantitative description and statistical prediction of global patterns of behavior of entire systems. For example, since the late 1970s our work has shown that these measures could be used to discriminate categories of drug action and dose when applied to patterns of rat exploratory behavior in space and time. The combination of abstract generality and quantitative precision of these methods suggests their usefulness as a cross-disciplinary language for fields like psychiatry that deal with complicated behavior of both neurobiological elements and the whole person.

Novel methods for storage stability and release of Bacillus spores

Bacillus subtilis spores were immobilized in activated charcoal and tapioca and filled with acacia gum. These formulations were tested for spore stability during storage at temperatures ranging from 40°C to 90°C and for bacterial release. Thermodynamic analysis showed that immobilization of spores in acacia gum significantly increased their viability compared with unprotected spores. The viability was further increased when suspensions of spores in acacia gum were added to granules of charcoal and tapioca. The number of the spores released after storage was also increased when spores were treated with acacia gum prior to immobilization in tapioca and charcoal. Formulations of Bacillus spores with acacia gum and porous carriers (charcoal and tapioca) prolong the anticipated shelf‐life of spores even under ambient temperature and provide slow and steady bacterial release consistent with their high viability.

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.

Spatiotemporal imaging of complexity

What are the functional neuroimaging measurements required for more fully characterizing the events and locations of neocortical activity? A prime assumption has been that modulation of cortical activity will inevitably be reflected in changes in energy utilization (for the most part) changes of glucose and oxygen consumption. Are such a measures complete and sufficient? More direct measures of cortical electrophysiological activity show event or task-related modulation of amplitude or band-limited oscillatory power. Using magnetoencephalography (MEG), these measures have been shown to correlate well with energy utilization sensitive BOLD fMRI. In this paper, we explore the existence of state changes in electrophysiological cortical activity that can occur independently of changes in averaged amplitude, source power or indices of metabolic rates. In addition, we demonstrate that such state changes can be described by applying a new measure of complexity, rank vector entropy (RVE), to source waveform estimates from beamformer-processed MEG. RVE is a non-parametric symbolic dynamic informational entropy measure that accommodates the wide dynamic range of measured brain signals while resolving its temporal variations. By representing the measurements by their rank values, RVE overcomes the problem of defining embedding space partitions without resorting to signal compression. This renders RVE-independent of absolute signal amplitude. In addition, this approach is robust, being relatively free of tunable parameters. We present examples of task-free and task-dependent MEG demonstrating that RVE provides new information by uncovering hidden dynamical structure in the apparent turbulent (or chaotic) dynamics of spontaneous cortical activity.

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.