Mechanisms of phase synchronization in neural even cyclic inhibitory networks

The mechanisms of synchronization have been studied in a mathematical model of the neurodynamics of navigation behavior that is based on even cyclic inhibitory networks. The following factors that affect the synchronized activity of the information units of the network have been highlighted: the weights of interunit connections, the duration of network activity, and the amplitude, duration, and timing of input signals.     

Mechanisms of frequency and pattern control in the neural rhythm generators

The locomotive motion in animals is produced in some central neural units, and basically no sensory signal from peripheral receptors is necessary to induce it. The rhythm generators do not only produce rhythms but also alter their frequencies and patterns. This paper presents some methematical models of the neural rhythm generators and discusses various aspects of the frequency and pattern control in them.     

Gamma神经振荡产生机制及其功能研究进展

Gamma神经振荡的频率在30～100 Hz之间,存在于动物和人类大脑的多个区域,如丘脑、体感皮层以及海马等部位,在各个尺度水平上都可被检测到.抑制性中间神经元组成的神经网络是产生此高频节律性活动的主要条件之一.皮层的gamma神经振荡与丘脑-皮层系统有关.Gamma神经振荡具有易化突触可塑性和调节神经网络的作用,主要参与感觉特征绑定、选择性注意以及记忆等高级功能.     

Reverberations and control of neural networks

Summary The simulation of neural networks, such as the brain cortex, which have a diffuse and rather uniform structure quite unlike the simple block-structure of extant computers, leads naturally to the study of functions and principles which only in part fall within the scope of Automata Theory. Systems of decision equations must be studied with a view especially to obtaining practical means for the prevision and computation of diffuse reverberations of wanted general characteristics, with the exclusion of all others. This amounts to deriving constraints on the allowed variability of the couplings among elements during learning processes, failing which the behavior of the simulator would become uncontrollable for practical purposes. A simple mathematical treatment is presented, which essentially linearizes these problems by an appropriate use of matrix algebra and permits a straightforward study of the wanted conditions, as well as of the controlling elements which may have to be added to the network.This work has been performed in part at the Laboratoire de Physique Théorique et Hautes Energies, Faculté des Sciences de Paris.This work has been performed with the joint sponsorship of the U.S.A.F. and their European Office of Aerospace Research under contracts no. AF EOAR 66-25 and AF 33(615)-2786.We wish to express our sincere thanks to Dr. F. Lauria for many illuminated discussions; and to Prof. M. Lévy for his kind hospitality at the Laboratoire de physique Théorique, in Paris, where part of this research was made.     

Multicellular model for intercellular synchronization in circadian neural networks

We developed a multicellular model characterized by a high degree of heterogeneity to investigate possible mechanisms that underlie circadian network synchronization and rhythmicity in the suprachiasmatic nucleus (SCN). We populated a two-dimensional grid with 400 model neurons coupled via γ-aminobutyric acid (GABA) and vasoactive intestinal polypeptide (VIP) neurotransmitters through a putative Ca²⁺ mediated signaling cascade to investigate their roles in gene expression and electrical firing activity of cell populations. As observed experimentally, our model predicted that GABA would affect the amplitude of circadian oscillations but not synchrony among individual oscillators. Our model recapitulated experimental findings of decreased synchrony and average periods, loss of rhythmicity, and reduced circadian amplitudes as VIP signaling was eliminated. In addition, simulated increases of VIP reduced periodicity and synchrony. We therefore postulated a physiological range of VIP within which the system is able to produce sustained and synchronized oscillations. Our model recapitulated experimental findings of diminished amplitudes and periodicity with decreasing intracellular Ca²⁺ concentrations, suggesting that such behavior could be due to simultaneous decrease of individual oscillation amplitudes and population synchrony. Simulated increases in Cl⁻ levels resulted in increased Cl⁻ influx into the cytosol, a decrease of inhibitory postsynaptic currents, and ultimately a shift of GABA-elicited responses from inhibitory to excitatory. The simultaneous reduction of IPSCs and increase in membrane resting potential produced GABA dose-dependent increases in firing rates across the population, as has been observed experimentally. By integrating circadian gene regulation and electrophysiology with intracellular and intercellular signaling, we were able to develop the first (to our knowledge) multicellular model that allows the effects of clock genes, electrical firing, Ca²⁺, GABA, and VIP on circadian system behavior to be predicted.     

Mathematical model for the self-organization of neural networks

Mutual inhibition between neurons combined with a learning principle similar to that proposed by Hebb is shown to secure a powerful selforganizing property for neural networks. Numerical analysis reveals that the system investigated always organizes itself into the same final state from any arbitrarily chosen initial state.     

Cardiovascular control with artificial neural networks

This paper describes the use of artificial neural networks to model cardiovascular autonomic control in a study of the hemodynamic changes associated with space flight. Cardiovascular system models were created including four parameters: heart rate, contractility, peripheral resistance, and venous tone. Artificial neural networks were then designed and trained. A technique known as backpropagation networking was used and the results of the application of this technique to heart rate control are presented and discussed.     

A model for impulse frequency modulation used in neural encoding

The impulse rate at the output of a neural encoder can be interpreted as the sum of the mean impulse rate plus a noise component. From literature models are known which describe the transient phenomena of the encoder as far as the mean impulse rate is concerned. In this paper in addition the noise phenomenon is treated by a model which is in agreement with results derived from measurements. This model consists of two parts, a multiplicative and an additive estimator. The first one is similar to the automatic gain control system known from literature. This system estimates the amplification of the impulse rate due to the step input of the neural encoder. Multiplying the impulse rate with the inverse of this factor inhibits the change of the impulse rate. The second estimator calculates the step size of the impulse rate which is subtracted from the output of the encoder. Again the change of the impulse rate is inhibited. The comparison of the impulse rates simulated by the model and given by published measurements shows a good agreement for the properties of the mean impulse rate and the variance of the imposed noise.     

Sequential configuration model for firing patterns in local neural networks

This paper presents a sequential configuration model to represent the coordinated firing patterns of memory traces in groups of neurons in local networks. Computer simulations are used to study the dynamic properties of memory traces selectively retrieved from networks in which multiple memory traces have been embedded according to the sequential configuration model. Distinct memory traces which utilize the same neurons, but differ only in temporal sequencing are selectively retrievable. Firing patterns of constituent neurons of retrieved memory traces exhibit the main properties of neurons observed in multi microelectrode recordings. The paper shows how to adjust relative synaptic weightings so as to control the disruptive influences of cross-talk in multipy-embedded networks. The theoretical distinction between (primarily anatomical) beds and (primarily physiological) realizations underlines the fundamentally stochastic nature of network firing patterns, and allows the definition of 4 degrees of clarity of retrieved memory traces.     

Switching mechanisms and bout times in a pair of reciprocally inhibitory neurons

Within the appropriate parameter regime, a deterministic model of a pair of mutually inhibitory neurons receiving excitatory driving currents exhibits bistability—each of the two stable states corresponds to one neuron being active and the other being quiescent. The presence of noise in the driving currents results in a system that randomly switches back and forth between these two states, causing alternating bouts of spiking activity. In this work, we examine the random bout durations of the two neurons and dependence on system parameters. We find that bout durations of each neuron are exponentially distributed, with changes in system parameters altering only the mean of the distribution. Synaptic inhibition independently controls the bout durations of the two neurons—the mean bout time of a neuron is a function of efferent (or outgoing) inhibition, and is independent of afferent (or incoming) inhibition. Furthermore, we find that the mean bout time of a neuron exhibits a critical dependence on the time course (rather than amplitude) of efferent inhibition—mean bout time of a neuron grows exponentially with the time course of efferent inhibition, and the growth rate of this exponential function depends only on the excitatory driving current to that neuron (and not on any other system parameters). We discuss the relevance of our results to the regulation of sleep-wake cycling by medullary and pontine structures within the brain.     

Functional model of biological neural networks

A functional model of biological neural networks, called temporal hierarchical probabilistic associative memory (THPAM), is proposed in this paper. THPAM comprises functional models of dendritic trees for encoding inputs to neurons, a first type of neuron for generating spike trains, a second type of neuron for generating graded signals to modulate neurons of the first type, supervised and unsupervised Hebbian learning mechanisms for easy learning and retrieving, an arrangement of dendritic trees for maximizing generalization, hardwiring for rotation-translation-scaling invariance, and feedback connections with different delay durations for neurons to make full use of present and past informations generated by neurons in the same and higher layers. These functional models and their processing operations have many functions of biological neural networks that have not been achieved by other models in the open literature and provide logically coherent answers to many long-standing neuroscientific questions. However, biological justifications of these functional models and their processing operations are required for THPAM to qualify as a macroscopic model (or low-order approximate) of biological neural networks.     

Information coding and oscillatory activity in synfire neural networks with and without inhibitory coupling

When a population spike (pulse-packet) propagates through a feedforward network with random excitatory connections, it either evolves to a sustained stable level of synchronous activity or fades away (Diesmann et al. in Nature 402:529-533 1999; Cateau and Fukai Neur Netw 14:675-685 2001). Here I demonstrate that in the presence of noise, the probability of the survival of the pulse-packet (or, equivalently, the firing rate of output neurons) reflects the intensity of the input. Furthermore, inhibitory coupling between layers can result in quasi- periodic alternation between several levels of firing activity. These results are obtained by analyzing the evolution of pulse-packet activity as a Markov chain. For the Markov chain analysis, the output of the chain is a linear mapping of the input into a lower-dimensional space, and the eigenvalues and eigenvectors of the transition matrix determine the dynamics of the evolution. Synchronous propagation of firing activity in successive pools of neurons are simulated in networks of integrate-and-fire and compartmental model neurons, and, consistent with the discrete Markov process, the activation of each pool is observed to be predominantly dependent upon the number of cells that fired in the previous pool. Simulation results agree with the numerical solutions of the Markov model. When inhibitory coupling between layers are included in the Markov model, some eigenvalues become complex numbers, implying oscillatory dynamics. The quasiperiodic dynamics is validated with simulation with leaky integrate-and-fire neurons. The networks demonstrate different modes of quasiperiodic activity as the inhibition or excitation parameters of the network are varied.     

A new regime for highly robust gamma oscillation with co-exist of accurate and weak synchronization in excitatory–inhibitory networks

A great number of biological experiments show that gamma oscillation occurs in many brain areas after the presentation of stimulus. The neural systems in these brain areas are highly heterogeneous. Specifically, the neurons and synapses in these neural systems are diversified; the external inputs and parameters of these neurons and synapses are heterogeneous. How the gamma oscillation generated in such highly heterogeneous networks remains a challenging problem. Aiming at this problem, a highly heterogeneous complex network model that takes account of many aspects of real neural circuits was constructed. The network model consists of excitatory neurons and fast spiking interneurons, has three types of synapses (GABA_A, AMPA, and NMDA), and has highly heterogeneous external drive currents. We found a new regime for robust gamma oscillation, i.e. the oscillation in inhibitory neurons is rather accurate but the oscillation in excitatory neurons is weak, in such highly heterogeneous neural networks. We also found that the mechanism of the oscillation is a mixture of interneuron gamma (ING) and pyramidal-interneuron gamma (PING). We explained the mixture ING and PING mechanism in a consistent-way by a compound post-synaptic current, which has a slowly rising-excitatory stage and a sharp decreasing-inhibitory stage.     

Bioprocess model building using artificial neural networks

Artificial neural networks are made upon of highly interconnected layers of simple neuron-like nodes. The neurons act as non-linear processing elements within the network. An attractive property of artificial neural networks is that given the appropriate network topology, they are capable of learning and characterising non-linear functional relationships. Furthermore, the structure of the resulting neural network based process model may be considered generic, in the sense that little prior process knowledge is required in its determination. The methodology therefore provides a cost efficient and reliable process modelling technique. One area where such a technique could be useful is biotechnological systems. Here, for example, the use of a process model within an estimation scheme has long been considered an effective means of overcoming inherent on-line measurement problems. However, the development of an accurate process model is extremely time consuming and often results in a model of limited applicability. Artificial neural networks could therefore prove to be a useful model building tool when striving to improve bioprocess operability. Two large scale industrial fermentation systems have been considered as test cases; a fed-batch penicillin fermentation and a continuous mycelial fermentation. Both systems serve to demonstrate the utility, flexibility and potential of the artificial neural network approach to process modelling.     

A computer based model for realistic simulations of neural networks

The use of computer simulations as a neurophysiological tool creates new possibilities to understand complex systems and to test whether a given model can explain experimental findings. Simulations, however, require a detailed specification of the model, including the nerve cell action potential and synaptic transmission. We describe a neuron model of intermediate complexity, with a small number of compartments representing the soma and the dendritic tree, and equipped with Na⁺, K⁺, Ca²⁺, and Ca²⁺ dependent K⁺ channels. Conductance changes in the different compartments are used to model conventional excitatory and inhibitory synaptic interactions. Voltage dependent NMDA-receptor channels are also included, and influence both the electrical conductance and the inflow of Ca²⁺ ions. This neuron model has been designed for the analysis of neural networks and specifically for the simulation of the network generating locomotion in a simple vertebrate, the lamprey. By assigning experimentally established properties to the simulated cells and their synapses, it has been possible to verify the sufficiency of these properties to account for a number of experimental findings of the network in operation. The model is, however, sufficiently general to be useful for realistic simulation also of other neural systems.     

Neutral impulsive shunting inhibitory cellular neural networks with time-varying coefficients and leakage delays

In this article, we consider a class of neutral impulsive shunting inhibitory cellular neural networks with time varying coefficients and leakage delays. We study the existence and the exponential stability of the piecewise differentiable pseudo almost-periodic solutions and establish sufficient conditions for the existence and exponential stability of such solutions. An example is provided to illustrate the theory developed in this work.     

Stability and structural constraints of random brain networks with excitatory and inhibitory neural populations

The stability of brain networks with randomly connected excitatory and inhibitory neural populations is investigated using a simplified physiological model of brain electrical activity. Neural populations are randomly assigned to be excitatory or inhibitory and the stability of a brain network is determined by the spectrum of the network’s matrix of connection strengths. The probability that a network is stable is determined from its spectral density which is numerically determined and is approximated by a spectral distribution recently derived by Rajan and Abbott. The probability that a brain network is stable is maximum when the total connection strength into a population is approximately zero and is shown to depend on the arrangement of the excitatory and inhibitory connections and the parameters of the network. The maximum excitatory and inhibitory input into a structure allowed by stability occurs when the net input equals zero and, in contrast to networks with randomly distributed excitatory and inhibitory connections, substantially increases as the number of connections increases. Networks with the largest excitatory and inhibitory input allowed by stability have multiple marginally stable modes, are highly responsive and adaptable to external stimuli, have the same total input into each structure with minimal variance in the excitatory and inhibitory connection strengths, and have a wide range of flexible, adaptable, and complex behavior.     

Mechanically induced pendelluft flow in a model airway bifurcation during high frequency oscillation

A single bifurcation with adjustable branch compliances, resistances and inertances was used to study the generation of pendelluft flows during ventilation at tidal volumes of 5-15 ml and frequencies of 6-26 Hz, corresponding to parent branch Reynolds numbers of 400-8000 and Womersley parameter values of 12-25. Pendelluft was quantified by the ratio of tidal volume sum in sibling branches to tidal volume in the parent branch. This tidal volume fraction being greater than one in all experiments where an asymmetry in branch mechanics was imposed, indicated that some degree of pendelluft was always present. Asymmetries in compliance and in inertance produced much greater pendelluft than an asymmetry in resistance. The largest tidal volume fraction, equal to 2.75, was recorded when inertance in both sibling branches was high, resistance was low, and compliances differed by a factor of five. Tidal volume fraction always peaked at an optimal frequency between 12-24 Hz, similar to the frequencies at which physiologic transport optima have previously been observed.