Correlations in one-dimensional fully developed chaos

Correlations in the baker map and the tent map as examples of one-dimensional, fully developed chaos are considered. It is shown, utilizing symbolic dynamical systems derived from these maps, that the vanishing second-order correlation function is not sufficient to guarantee uncorrelatedness. Importance of the higher-order, especially third-order, correlation functions is emphasized for chaotic systems. In search of the quantities that grasp correlational behaviors as a whole in chaotic systems, it is proposed to use the fixed-separation correlation integral, which is a modified quantity of the usual correlation integral devised to calculate the fractal dimension of strange attractors, for these maps. It is shown that the new quantity contains all the even-number orders of autocorrelation function that are commonly considered.     

Noise-induced neural impulses

The firing pattern of neural pulses often show the following features: the shapes of individual pulses are nearly identical and frequency independent; the firing frequency can vary over a broad range; the time period between pulses shows a stochastic scatter. This behaviour cannot be understood on the basis of a deterministic non-linear dynamic process, e.g. the Bonhoeffer-van der Pol model. We demonstrate in this paper that a noise term added to the Bonhoeffer-van der Pol model can reproduce the firing patterns of neurons very well. For this purpose we have considered the Fokker-Planck equation corresponding to the stochastic Bonhoeffer-van der Pol model. This equation has been solved by a new Monte Carlo algorithm. We demonstrate that the ensuing distribution functions represent only the global characteristics of the underlying force field: lines of zero slope which attract nearby trajectories prove to be the regions of phase space where the distributions concentrate their amplitude. Since there are two such lines the distributions are bimodal representing repeated fluctuations between two lines of zero slope. Even in cases where the deterministic Bonhoeffer-van der Pol model does not show limit cycle behaviour the stochastic system produces a limit cycle. This cycle can be identified with the firing of neural pulses.     

Numerical solution of a nonlinear advance-delay-differential equation from nerve conduction theory

A functional differential equation which is nonlinear and involves forward and backward deviating arguments is solved numerically. The equation models conduction in a myelinated nerve axon in which the myelin completely insulates the membrane, so that the potential change jumps from node to node. The equation is of first order with boundary values given at t=±. The problem is approximated via a difference scheme which solves the problem on a finite interval by utilizing an asymptotic representation at the endpoints, cubic interpolation and iterative techniques to approximate the delays, and a continuation method to start the procedure. The procedure is tested on a class of problems which are solvable analytically to access the scheme's accuracy and stability, then applied to the problem that models propagation in a myelinated axon. The solution's dependence on various model parameters of physical interest is studied. This is the first numerical study of myelinated nerve conduction in which the advance and delay terms are treated explicitly.Supported in part by NSF Grant MCS8301724 and by a Biomedical Research Support Grant 2SO7RR0706618 from NIH     

Molecular basis for the special properties of proteins and enzymes from Halobacterium marismortui

Abstract Three proteins from Halobacterium marismortui , malate dehydrogenase (hMDH), glutamate dehydrogenase (hGDH) and ferredoxin (hFD) were purified and characterized with respect to their molecular masses, amino acid composition and, for hFD only, primary structure. Striking features of halophilic proteins are: the high excess of acidic over basic residues; acidic clusters in the sequence. Low-salt concentration causes inactivation and changes in structural parameters of hMDH and hGDH. Reactivation of hMDH involves long-lived stable intermediates. The salt concentration optimum of enzymic activity is independent of salt nature. The high capacity of halophilic proteins to retain water and salt is due to unique molecular properties, studied by physico-chemical techniques.     

The relationship between NADPH-dependent lipid peroxidation and degradation of cytochrome P-450 in adrenal cortex mitochondria

The relationship between NADPH-dependent lipid peroxidation and the degradation of cytochrome P-450 has been studied in bovine adrenal cortex mitochondria. Malondialdehyde formation is accompanied by a corresponding decrease in total cytochrome P-450 content. Inhibitors of lipid peroxidation also prevent the loss of cytochrome P-450, further demonstrating a direct relationship between NADPH-dependent lipid peroxidation and degradation of P-450. To differentiate between cytochrome P-450(11)beta and P-450scc, steroid-induced difference spectra were used to evaluate P-450 degradation. These measurements provide the first evidence that both P-450's are degraded during NADPH-dependent lipid peroxidation with P-450(11)beta being much more susceptible to this process.     

Interaction of nucleic acids with the DNA-dependent RNA polymerases of Drosophila

The interaction between the three Drosophila DNA-dependent RNA polymerases (EC 2.7.7.6) and the DNA template or the RNA product was investigated by photochemical cross-linking and binding studies, using RNA polymerase subunits immobilized on nitro-cellulose filters. It can be shown that the two largest subunits are responsible for the binding of the enzymes to both template and newly-synthesized RNA.     

Structure and ultrastructure of the frog motor endplate

Summary The frog motor endplate in its simplest form consists of an elongated, slender nerve ending embedded in a gutter-like depression of the sarcolemma. This nerve terminal contains the usual synaptic organelles. It is covered by a thin coating of Schwann cell cytoplasm which embraces the terminal with thin finger-like processes from both sides, thereby sub-dividing it into 300–1000 regularly spaced compartments. The individual synaptic compartments correspond to the strings of varicosities or grape-like configurations of motor nerve terminals in endplates of other species and in the cerebral neuropil of vertebrates.Each compartment contains one or more bar-like densities of the presynaptic membrane, active zones, which are associated with the attachment sites between synaptic vesicles and plasmalemma. Active zones have a regular transverse arrangement and occur at specific loci opposite the junctional folds. The attachment sites for synaptic vesicles are at the edges of the bars which are bilaterally delineated by a double row of 10 nm particles attached to the A-face. The structural appearance of vesicle attachment sites in freeze-etch replicas corresponds to that of micropinocytosis. The active zones are often fragmented and the frequency of their association with vesicle attachment sites is highly variable.The junctional folds are characterized by specific sites in which intramembranous particle aggregations occur at relatively high packing density (7500/m²). These sites are located opposite the active zones at the juxtaneural lips, a location where one would expect ACh-sensitive receptors on the postsynaptic membrane.This work was supported by the Deutsche Forschungsgemeinschaft (Sonderforschungsbereich 38, Projekt N), The Swiss National Foundation for Scientific Research (Grants Nr. 3 82372 and 3 77472) and the Dr. Eric Slack-Gyr Foundation Zürich.     

The ultrastructure of the sinus gland of Carcinus maenas (Crustacea: Decapoda)

Summary The sinus gland of Carcinus maenas consists of the swollen axonal endings of the neurosecretory cells of the major ganglia and acts as a storage release centre for the membrane bound neurosecretory material. These neurosecretory granules fall into five different types based on size and electron density. Their contents are released by exocytosis of the primary granules or smaller units budded from the primary granules.I thank Professor E. Naylor for his constant advice and Professor E. W. Knight-Jones, Department of Zoology, University College, Swansea, for the provision of laboratory facilities. I am grateful to the Science Research Council for the financial support. Finally, I thank the Electron Microscope Unit, Southampton General Hospital, where the work was completed.