Stochastic automaton models for the temporal pattern discrimination of nerve impulse sequences

The application of stochastic automata to the input-output relations of single neurons is considered. For this, some stochastic properties of temporal pattern discrimination in single synaptic cells are used to suggest stochastic automaton models. The models have only three possible states, the active, the absolute refractory and the relative refractory states, which are sufficient for temporal pattern sensitivity. From such an application, it was found that the temporal pattern discriminating structures in the models are similar to those used for experimental data and computer simulation (real-time neuron models). Extensions related to temporal pattern learning are discussed.     

Stochastic models for heterogeneous DNA sequences

The composition of naturally occurring DNA sequences is often strikingly heterogeneous. In this paper, the DNA sequence is viewed as a stochastic process with local compositional properties determined by the states of a hidden Markov chain. The model used is a discrete-state, discreteoutcome version of a general model for non-stationary time series proposed by Kitagawa (1987). A smoothing algorithm is described which can be used to reconstruct the hidden process and produce graphic displays of the compositional structure of a sequence. The problem of parameter estimation is approached using likelihood methods and an EM algorithm for approximating the maximum likelihood estimate is derived. The methods are applied to sequences from yeast mitochondrial DNA, human and mouse mitochondrial DNAs, a human X chromosomal fragment and the complete genome of bacteriophage lambda.     

Stochastic host-parasite interaction models

 We contribute to the discussion of causes and effects of aggregation (overdispersion) of macroparasite counts, focussing particularly upon the effects of clumped infections and parasite-induced host mortality. The simple nonlinear stochastic model for the evolution of the parasite load of a single host, investigated in Isham (1995), is extended to allow three parasite stages (larval, mature and offspring), and to allow durations of these stages to be non-exponentially distributed. As in the earlier work, exact algebraic results are possible, providing insight into the aggregation mechanisms, as long as the only source of interaction between host and parasites is an excess host mortality linearly related to the parasite load. Results are obtained on the distribution of parasite lad and on host survival. In particular, although parasite-induced host mortality is usually thought of as a process that reduces parasite aggregation (Anderson and Gordon 1982), it is shown that, for this model, parasite-induced host mortality cannot cause the index of dispersion to fall below unity. Host heterogeneity and disease control are also discussed. An approximation based on moment assumptions appropriate to a specially-constructed multivariate negative binomial distribution is proposed. This approximation, which is applicable to other processes, and an alternative based on the multivariate normal distribution are compared with exact results. Received: 17 December 1998 / Revised version: 2 June 1999     

Traffic of botulinum toxins A and E in excitatory and inhibitory neurons

Botulinum neurotoxins (BoNTs), proteases specific for the SNARE proteins, are used to study the molecular machinery supporting exocytosis and are used to treat human diseases characterized by cholinergic hyperactivity. The recent extension of the use of BoNTs to central nervous system (CNS) pathologies prompted the study of their traffic in central neurons. We used fluorescent BoNT/A and BoNT/E to study the penetration, the translocation and the catalytic action of these toxins in excitatory and inhibitory neurons. We show that BoNT/A and BoNT/E, besides preferentially inhibiting synaptic vesicle recycling at glutamatergic relative to Gamma-aminobutyric acid (GABA)-ergic neurons, are more efficient in impairing the release of excitatory than inhibitory neurotransmitter from brain synaptosomes. This differential effect does not result from a defective penetration of the toxin in line with the presence of the BoNT/A receptor, synaptic vesicle protein 2 (SV2), in both types of neurons. Interestingly, exogenous expression of SNAP-25 in GABAergic neurons confers sensitivity to BoNT/A. These results indicate that the expression of the toxin substrate, and not the toxin penetration, most likely accounts for the distinct effects of the two neurotoxins at the two types of terminals and support the use of BoNTs for the therapy of CNS diseases caused by the altered activity of selected neuronal populations.     

Dynamics of networks of randomly connected excitatory and inhibitory spiking neurons

Recent advances in the understanding of the dynamics of populations of spiking neurones are reviewed. These studies shed light on how a population of neurones can follow arbitrary variations in input stimuli, how the dynamics of the population depends on the type of noise, and how recurrent connections influence the dynamics. The importance of inhibitory feedback for the generation of irregularity in single cell behaviour is emphasized. Examples of computation that recurrent networks with excitatory and inhibitory cells can perform are then discussed. Maintenance of a network state as an attractor of the system is discussed as a model for working memory function, in both object and spatial modalities. These models can be used to interpret and make predictions about electrophysiological data in the awake monkey.     

Mechanisms of modification of excitatory and inhibitory inputs in various neurons of olivary-cerebellar network

It is known from the experimental data that at different cerebellar neurons there are voltage-dependent Ca2+ channels, NMDA receptors, metabotropic glutamate and GABAB receptors. This receptor arrangement ensures that activation of excitatory and inhibitory input results in changes in activity of protein kinases and phosphatases and subsequent modification of synaptic efficacy. The mechanism of synaptic plasticity is advanced that in accordance with the known experimental data concerning the modification of excitatory and inhibitory inputs to Purkinje cells, granule cells, and deep cerebellar nuclei cells. The mechanism is based on a postulate that phosphorylation/dephosphorylation of AMPA (GABAA) receptors on cerebellar cells causes the LTP/LTD of excitatory (LTD/LTP of inhibitory) transmission. It is assumed that modification rules for Purkinje cells, granule cells, and deep cerebellar nuclei cells, wherein cGMP-dependent protein kinase G is involved in synaptic plasticity, are distinct from those of hippocampal/neocortical cells, wherein cAMP-dependent protein kinase A is involved in synaptic plasticity, since cGMP (cAMP) concentration decreases (increases) with Ca2+ rise.     

Emergence of oscillations and spatio-temporal coherence states in a continuum-model of excitatory and inhibitory neurons

A neural field model of the reaction-diffusion type for the emergence of oscillatory phenomena in visual cortices is proposed. To investigate the joint spatio-temporal oscillatory dynamics in a continuous distribution of excitatory and inhibitory neurons, the coupling among oscillators is modelled as a diffusion process, combined with non-linear point interactions. The model exhibits cooperative activation properties in both time and space, by reacting to volleys of activations at multiple cortical sites with ordered spatio-temporal oscillatory states, similar to those found in the physiological experiments on slow-wave field potentials. The possible use of the resulting spatial distributions of coherent states, as a flexible medium to establish feature association, is discussed.     

The influence of depolarization block on seizure-like activity in networks of excitatory and inhibitory neurons

The inhibitory restraint necessary to suppress aberrant activity can fail when inhibitory neurons cease to generate action potentials as they enter depolarization block. We investigate possible bifurcation structures that arise at the onset of seizure-like activity resulting from depolarization block in inhibitory neurons. Networks of conductance-based excitatory and inhibitory neurons are simulated to characterize different types of transitions to the seizure state, and a mean field model is developed to verify the generality of the observed phenomena of excitatory-inhibitory dynamics. Specifically, the inhibitory population’s activation function in the Wilson-Cowan model is modified to be non-monotonic to reflect that inhibitory neurons enter depolarization block given strong input. We find that a physiological state and a seizure state can coexist, where the seizure state is characterized by high excitatory and low inhibitory firing rate. Bifurcation analysis of the mean field model reveals that a transition to the seizure state may occur via a saddle-node bifurcation or a homoclinic bifurcation. We explain the hysteresis observed in network simulations using these two bifurcation types. We also demonstrate that extracellular potassium concentration affects the depolarization block threshold; the consequent changes in bifurcation structure enable the network to produce the tonic to clonic phase transition observed in biological epileptic networks.     

Characterization of excitatory and inhibitory motor neurons to the human gastric clasp and sling fibers

The aim of this study was to determine the morphology and position of the excitatory and inhibitory motor neurons to the human gastric sling and clasp fibers. Motor neurons were identified by retrograde staining with 1,1'-didodecyl 3,3,3',3'-indocarbocyanine perchlorate (DiI), and choline acetyltransferase (ChAT) or nitric oxide synthase (NOS) immunoreactivity was then determined in these motor neurons. In the sling preparations, 46% of the DiI-stained cells were aboral motor neurons, 43% were local motor neurons, and only 10% were descending motor neurons. Overall, 58% were immunoreactive for ChAT, and 36% for NOS (P = 0.042). Sixty-two percent of local, and 66% of aboral DiI-stained motor neurons were immunoreactive for ChAT. In the clasp preparations, 52% of the DiI-stained cells were descending motor neurons, 45% were local motor neurons, and only 3% were aboral neurons. Overall, 31% were immunoreactive for ChAT and 65% for NOS (P = 0.039). Eighty-five percent of the DiI-stained descending motor neurons were immunoreactive for NOS. All of the cells that were labeled adequately had a single axon and a number of filamentous or flattened lobular dendrites, and fitted into the broad category of Dogiel type I neurons. In conclusion, the majority of the motor neurons to the sling fibers were ChAT-positive excitatory neurons from the myenteric plexus of the stomach and the local region, and to the clasp were predominantly NOS-positive inhibitory neurons from the esophagus.     

Differential Ca(2+) signaling characteristics of inhibitory and excitatory myenteric motor neurons in culture

Physiological studies on functionally identified myenteric neurons are scarce because of technical limitations. We combined retrograde labeling, cell culturing, and fluorescent intracellular Ca(2+) concentration ([Ca(2+)](i)) signaling to study excitatory neurotransmitter responsiveness of myenteric motor neurons. 1, 1-Didodecyl-3,3,3',3'-tetramethyl indocarbocyanine (DiI) was used to label circular muscle motor neurons of the guinea pig ileum. DiI-labeled neurons were easily detectable in cultures prepared from these segments. The excitatory neurotransmitters (10(-5) M) acetylcholine, substance P, and serotonin induced a transient rise in [Ca(2+)](i) in subsets of DiI-labeled neurons (66.7, 56.5, and 84. 3%, respectively). DiI-labeled motor neurons were either inhibitory (23.8%) or excitatory (76.2%) as assessed by staining for nitric oxide synthase or choline acetyltransferase. Compared with excitatory motor neurons, significantly fewer inhibitory neurons in culture responded to acetylcholine (0 vs. 69%) and substance P (12.5 vs. 69.2%). We conclude that combining retrograde labeling and Ca(2+) imaging allows identification of differential receptor expression in functionally identified neurons in culture.     

Adenylate cyclase-mediated modulation of interaction between excitatory and inhibitory synaptic influences on smooth muscles

We found that nonadrenergic inhibitory synaptic potentials (ISP) induced by intramural stimulation in atropine-treated smooth muscles of the guinea-pig large intestine demonstrated no changes upon the influence of an activator of adenylate cyclase, forskolin. This indicates that cAMP-dependent pathways are not involved in the generation of ISP. However, in these muscles with no atropine pretreatment ISP were suppressed by forskolin; intramural stimulation evoked in these smooth muscle cells M-cholinergic excitatory synaptic potentials (ESP) instead of ISP. An increase in the intracellular cAMP concentration due to application of its membrane-penetrating form, dibutyryl-cAMP, did not mimic the above-described effect of forskolin. Hence, it can be supposed that the effect of forskolin on inhibitory synaptic transmission in the atropine-untreated smooth muscles is not related to changes in the intracellular cAMP level; this effect is determined by other mechanisms. The above differences between the effects of forskolin on ISP in the atropine-treated and atropine-untreated smooth muscle strips indicate that the interaction of intracellular signal pathways (probably, through protein G_q/11), which is observed with activation of adenylate cyclase, occurs under conditions of simultaneous activation of M cholinoreceptors and purinoreceptors. The pattern of adenylate cyclase-mediated modulation of inhibitory effects of purinergic neurons on smooth muscles does not allow us to rule out the possibility of involvement of interstitial cells of Cajal as a relay link providing this synaptic effect. Transmission of excitation from cholinergic nerve terminals to smooth muscles is realized without the participation of the interstitial cells of Cajal.Neirofiziologiya/Neurophysiology, Vol. 36, Nos. 5/6, pp. 438–445, September–December, 2004.This revised version was published online in April 2005 with a corrected cover date and copyright year.     

Interconnected biochemical processes in striatal neurons induced by activation of excitatory, inhibitory, and dopamine inputs

Postsynaptic processes induced by glutamate, GABA, and dopamine in dendritic spines of inhibitory striatal neurones, were studied. Some functional features were revealed in striatal neurones activation of two protein kinases, cAMP-dependent PKA and cGMP-dependent PKG; presence of calcium/calmodulin-independent adenylate cyclase; bidirectional changes of the cAMP concentration with dopamine. Rise of the cGMP concentration in striatum seems to be a result of activation of the membrane-bound guanylate cyclase via the GABAb receptors. The findings suggest that the active protein kinases/phosphatases ratio is affected by calcium influx through the NMDA-channels.     

Diazepam binding inhibitor governs neurogenesis of excitatory and inhibitory neurons during embryonic development via GABA signaling

1. Download : Download high-res image (186KB)
2. Download : Download full-size image

     

Stochastic differential equation models for spatially distributed neurons and propagation of chaos for interacting systems.

Distribution or nuclear space-valued stochastic differential equations (SDEs) (diffusions as well as discontinuous equations) are discussed as stochastic models for the behavior of voltage potentials of spatially distributed neurons. A propagation of chaos result is obtained for an interacting system of Hilbert space-valued SDEs.     

Effects of Hebbian learning on the dynamics and structure of random networks with inhibitory and excitatory neurons

The aim of the present paper is to study the effects of Hebbian learning in random recurrent neural networks with biological connectivity, i.e. sparse connections and separate populations of excitatory and inhibitory neurons. We furthermore consider that the neuron dynamics may occur at a (shorter) time scale than synaptic plasticity and consider the possibility of learning rules with passive forgetting. We show that the application of such Hebbian learning leads to drastic changes in the network dynamics and structure. In particular, the learning rule contracts the norm of the weight matrix and yields a rapid decay of the dynamics complexity and entropy. In other words, the network is rewired by Hebbian learning into a new synaptic structure that emerges with learning on the basis of the correlations that progressively build up between neurons. We also observe that, within this emerging structure, the strongest synapses organize as a small-world network. The second effect of the decay of the weight matrix spectral radius consists in a rapid contraction of the spectral radius of the Jacobian matrix. This drives the system through the "edge of chaos" where sensitivity to the input pattern is maximal. Taken together, this scenario is remarkably predicted by theoretical arguments derived from dynamical systems and graph theory.