Influence of noise on the function of a “physiological” neural network

A model neural network with stochastic elements in its millisecond dynamics is investigated. The network consists of neuronal units which are modelled in close analogy to physiological neurons. Dynamical variables of the network are the cellular potentials, axonic currents and synaptic efficacies. The dynamics of the synapses obeys a modified Hebbian rule and, as proposed by v. d. Malsburg (1981, 1985), develop on a time scale of a tenth of a second. In a previous publication (Buhmann and Schulten 1986) we have confirmed that the resulting noiseless autoassociative network is capable of the well-known computational tasks of formal associative networks (Cooper 1973; Kohonen et al. 1984, 1981; Hopfield 1982). In the present paper we demonstrate that random fluctuations of the membrane potential improve the performance of the network. In comparison to a deterministic network a noisy neural network can learn at lower input frequencies and with lower average neural firing rates. The electrical activity of a noisy network is very reminiscent of that observed by physiological recordings. We demonstrate furthermore that associative storage reduces the effective dimension of the phase space in which the electrical activity of the network develops.     

Self-organizing maps: stationary states,metastability and convergence rate

We investigate the effect of various types of neighborhood function on the convergence rates and the presence or absence of metastable stationary states of Kohonen's self-organizing feature map algorithm in one dimension. We demonstrate that the time necessary to form a topographic representation of the unit interval [0, 1] may vary over several orders of magnitude depending on the range and also the shape of the neighborhood function, by which the weight changes of the neurons in the neighborhood of the winning neuron are scaled. We will prove that for neighborhood functions which are convex on an interval given by the length of the Kohonen chain there exist no metastable states. For all other neighborhood functions, metastable states are present and may trap the algorithm during the learning process. For the widely-used Gaussian function there exists a threshold for the width above which metastable states cannot exist. Due to the presence or absence of metastable states, convergence time is very sensitive to slight changes in the shape of the neighborhood function. Fastest convergence is achieved using neighborhood functions which are "convex" over a large range around the winner neuron and yet have large differences in value at neighboring neurons.     

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.     

Factors responsible for the formation of different N-alkylated porphyrins in rat liver microsomal systems exposed to norethindrone. The role of 3 alpha-hydroxysteroid dehydrogenase.

Incubation of rat liver microsomes with norethindrone and a NADPH-generating system leads to the formation of one N-alkylated porphyrin (green pigment, GP1). Administration of this steroid to male rats in vivo results in the formation of three more-polar green pigments (GP2, 3 and 4). A cytosolic protein (green-pigment converting protein) has been purified from rat liver that, when added to liver microsomal mixtures containing norethindrone (0.03 mM) and a NADPH-generating system, results in the formation of all four green pigments (GP1, 2, 3 and 4). Field-desorption mass spectrometry of the purified green pigments gave protonated molecules, [M + H]+, at m/z 905 for GP1, m/z 909 for GP2, m/z 925 for GP3 and 4. The Mr of the purified cytosolic protein on SDS/polyacrylamide-gel electrophoresis or gel filtration was 37000. Polyacrylamide-gel isoelectric focusing gave a pI value of 5.9. Antibodies raised in rabbits against this protein, after preincubation with rat liver cytosol, subsequently prevented the formation of the more-polar norethindrone-induced green pigments (GP2, 3 and 4). The purified protein in the presence of either NADH or NADPH catalysed the reduction of delta 4-ring-reduced norethindrone, 5 alpha-oestran-17 alpha-ethynyl-17 beta-ol-3-one and, with the appropriate cofactor, the oxidation and reduction of steroids lacking the ethynyl function, e.g. androsterone or dihydrotestosterone. Indomethacin inhibited the reduction of dihydrotestosterone by this protein with an I50 (concn. causing 50% inhibition) value of 4.9 microM. From its physical and enzymic properties it is concluded that green-pigment converting protein is the same as 3 alpha-hydroxysteroid dehydrogenase (EC 1.1.1.50).     

Molecular dynamics study of the M412 intermediate of bacteriorhodopsin.

Molecular dynamics simulations have been carried out to study the M412 intermediate of bacteriorhodopsin's (bR) photocycle. The simulations start from two simulated structures for the L550 intermediate of the photocycle, one involving a 13-cis retinal with strong torsions, the other a 13,14-dicis retinal, from which the M412 intermediate is initiated through proton transfer to Asp-85. The simulations are based on a refined structure of bR568 obtained through all-atom molecular dynamics simulations and placement of 16 waters inside the protein. The structures of the L550 intermediates were obtained through simulated photoisomerization and subsequent molecular dynamics, and simulated annealing. Our simulations reveal that the M412 intermediate actually comprises a series of conformations involving 1) a motion of retinal; 2) protein conformational changes; and 3) diffusion and reconfiguration of water in the space between the retinal Schiff base nitrogen and the Asp-96 side group. (1) turns the retinal Schiff base nitrogen from an early orientation toward Asp-85 to a late orientation toward Asp-96; (2) disconnects the hydrogen bond network between retinal and Asp-85 and tilts the helix F of bR, enlarging bR's cytoplasmic channel; (3) adds two water molecules to the three water molecules existing in the cytoplasmic channel at the bR568 stage and forms a proton conduction pathway. The conformational change (2) of the protein involves a 60 degrees bent of the cytoplasmic side of helix F and is induced through a break of a hydrogen bond between Tyr-185 and a water-side group complex in the counterion region.     

Basic steroid saponins from aerial parts of Fritillaria Thunbergii

From the aerial parts of Fritillaria thunbergii, three glycosidal Solanum alkaloids (basic steroid saponins) were isolated together with minor     

Copulation, egg production and sex-ratio in Phytoseiulus persimilis and Amblyseius bibens (Acari: Phytoseiidae)

In Phytoseiulus persimilis Athias-Henriot and Amblyseius bibens Blommers a relation was found between the duration of copulation and the resultant egg production. After 15 min of copulation no eggs were produced but after respectively 30, 60 and 90 min an increasing number of eggs were deposited. In P. persimilis the total number of eggs can be produced after one copulation of long duration but in A. bibens several copulations are necessary for total egg production. Evidence was found that egg deposition depends on the quantity of sperm transferred during insemination. Relatively more males developed from eggs deposited during the first day of egg deposition but males are produced throughout the whole egg-laying period. Females of P. persimilis remain fertile throughout their life until they have deposited their total possible number of eggs. Three to 4 egg-laying periods could be induced by copulations of 30 min duration. At each period relatively more males developed from eggs laid during the first days. Males of P. persimilis were found to be very fertile. The results obtained are discussed in relation to the reproductive strategy of both species.

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Zusammenfassung Bei Phytoseiulus persimilis Athias-Henriot und Amblyseius bibens Blommers wurde ein Zusammenhang gefunden zwischen Kopulationsdauer und der resultierenden Eiproduktion. Nach 15 Minuten Kopulation wurden keine Eier produziert; nach 30, 60 und 90 Minute Kopulation hingegen wurde eine steigende Zahl Eier abgelegt. Bei P. persimilis kann die totale Eizahl nach einer einzigen Kopulation von langer Dauer produziert werden, während bei A. bibens mehrere Kopulationen notwendig sind. Es wurden Anhaltspunkte gefunden, dass die Eizahl von der während der Besamung übertragenen Spermienmenge abhängt. Aus während der ersten Tage der Eiproduktion abgelegten Eiern entwickelten sich relativ mehr Männchen, doch wurden Männchen während der ganzen Eiablageperiode produziert. Weibchen von P. persimilis bleiben während ihres ganzen Lebens, bis sie alle Eier abgelegt haben, fertil. Drei bis vier Eiablageperioden konnten durch Kopulationen von 30 Minuten Dauer induziert werden. Bei jeder Periode entwickelten sich aus den in den ersten Tagen abgelegten Eiern relativ mehr Männchen. Männchen von P. persimilis erwiesen sich als sehr fertil. Die Resultate werden im Zusammenhang mit der Vermehrungsstrategie beider Arten diskutiert.

     

Quantitative field desorption mass spectrometry. V. Discussion of methodology and examples of applications

The possibilities for the application of field desorption mass spectrometry in quantitative analyses are described and evaluated. The advantages of and the sources of errors in the use of different standards as well as in the application of different methods such as photographic detection, single ion monitoring, repetitive scanning, selected ion monitoring, and double ion detection are illustrated by representative examples. Sensitivity and precision of the different techniques are evaluated. Most importantly, the use of stable isotope labelled compounds as internal standards has enabled quantitative determination with good precision, accuracy, and sensitivity. In order to demonstrate the capabilities of the methods, examples of applications are presented and the scope of quantitative analysis with field desorption mass spectrometry is discussed.