Firing statistics of inhibitory neuron with delayed feedback. II: Non-Markovian behavior.

The instantaneous state of a neural network consists of both the degree of excitation of each neuron the network is composed of and positions of impulses in communication lines between the neurons. In neurophysiological experiments, the neuronal firing moments are registered, but not the state of communication lines. But future spiking moments depend essentially on the past positions of impulses in the lines. This suggests, that the sequence of intervals between firing moments (inter-spike intervals, ISIs) in the network could be non-Markovian. In this paper, we address this question for a simplest possible neural "net", namely, a single inhibitory neuron with delayed feedback. The neuron receives excitatory input from the driving Poisson stream and inhibitory impulses from its own output through the feedback line. We obtain analytic expressions for conditional probability density P(tn+1|tn, …, t1, t0), which gives the probability to get an output ISI of duration tn+1 provided the previous (n+1) output ISIs had durations tn, …, t1, t0. It is proven exactly, that P(tn+1|tn, …, t1, t0) does not reduce to P(tn+1|tn, …, t1) for any n≥0. This means that the output ISIs stream cannot be represented as a Markov chain of any finite order.

Firing statistics of inhibitory neuron with delayed feedback. I. Output ISI probability density.

Activity of inhibitory neuron with delayed feedback is considered in the framework of point stochastic processes. The neuron receives excitatory input impulses from a Poisson stream, and inhibitory impulses from the feedback line with a delay. We investigate here, how does the presence of inhibitory feedback affect the output firing statistics. Using binding neuron (BN) as a model, we derive analytically the exact expressions for the output interspike intervals (ISI) probability density, mean output ISI and coefficient of variation as functions of model's parameters for the case of threshold 2. Using the leaky integrate-and-fire (LIF) model, as well as the BN model with higher thresholds, these statistical quantities are found numerically. In contrast to the previously studied situation of no feedback, the ISI probability densities found here both for BN and LIF neuron become bimodal and have discontinuity of jump type. Nevertheless, the presence of inhibitory delayed feedback was not found to affect substantially the output ISI coefficient of variation. The ISI coefficient of variation found ranges between 0.5 and 1. It is concluded that introduction of delayed inhibitory feedback can radically change neuronal output firing statistics. This statistics is as well distinct from what was found previously (Vidybida and Kravchuk, 2009) by a similar method for excitatory neuron with delayed feedback.

Computer simulation of inhibition-dependent binding in a neural network.

Reverberating dynamics of neural network is modeled on PC in order to illustrate possible role of inhibition as binding controller in the network. The network is composed of binding neurons. In the binding neuron model [BioSystems 48 (1998) 263], the degree of temporal coherence between synaptic inputs is decisive for triggering, and slow inhibition is expressed in terms of the degree, which is necessary for triggering. Two learning mechanisms are implemented in the network, namely, adjusting synaptic strength and/or propagation delays. By means of forced playing of external pattern, the network is taught to support dynamics with disconnected and bound patterns of activity. By choosing either high, or low inhibition, one can switch between the disconnected and bound patterns, respectively. This is interpreted as inhibition-controlled binding in the network.

Testing of nonlinear electrofrictiophoresis in agarose gel.

It was theoretically predicted earlier that if a periodic force without constant component is applied to a particle, then the particle can produce a directed drift in some direction. The effect is named nonlinear electrofrictiophoresis, because it is crucial for its appearance that the friction force depends on the particle's velocity in a nonlinear manner. We test a possibility to observe this effect when a mixture of fragments of DNA (the DNA ladder) moves in the agarose gel. For this purpose, we study the nonlinear characteristics of a DNA ladder movement in the gel. The gels with the ladder were run under various electric field strengths. It was found that the friction coefficient for each DNA fragment in the ladder depends on the migration velocity, suggesting that energy dissipation during migration is a nonlinear function of velocity. This nonlinearity makes the system under consideration suitable for observing nonlinear electrofrictiophoresis. A possible velocity of directed drift under periodic electric drive without constant component was estimated numerically for experimentally observed dependencies. The velocity appeared to be comparable with that of migration under a constant field of moderate strength. A possible mechanism of energy dissipation during movement of DNA through the gel is discussed.

Selectivity of chemoreceptor neuron.

Discriminating ability (selectivity) of chemoreceptor neuron is compared with that of its receptor proteins. The process of neuronal triggering is expected to be cooperative and threshold-type in a sense that the neuron can fire if and only if the number of its receptor proteins, which are bound with odor molecules, is above a definite threshold. Both deterministic and stochastic pictures are considered. The stochastic case is treated based on birth and death stochastic process and first passage technique. In both pictures, it is shown that a chemoreceptor neuron can have much a higher selectivity than its individual receptor proteins, provided the chemical stimuli are presented at low concentrations, and the threshold is high enough. This is in agreement with a preliminary estimate based on simplified probabilistic reasoning (Vidybida, A.K., 1999. Cooperative mechanism for improving the discriminating ability in the chemoreceptive neuron. Binomial case. Biol. Cybern. 81, 469-473). The mechanism of selectivity improvement is similar to that described before in cooperative chemical systems. A possibility for this mechanism to be valid at higher stages of processing of chemical signals, as well as in other sensory systems is discussed.

Cooperative mechanism for improving the discriminating ability in the chemoreceptor neuron binomial case.

The discriminating ability (selectivity) of the chemoreceptor neuron is compared with that of its receptor proteins. The process of neuronal triggering is expected to be cooperative and threshold type in a sense that the neuron fires a spike if and only if the number of receptor proteins which are bound with odor molecules is above a definite threshold. The binomial distribution is utilized to estimate the firing probability if a definite odor is applied. It is established that a chemoreceptor neuron can have a much higher selectivity than its individual receptor proteins, provided that the chemical stimuli are presented at low concentrations. A possibility for the above mechanism to be valid in other sensory systems is discussed.

Inhibition as binding controller at the single neuron level.

Natural stimulus for a neuron is a sum of large number of unitary excitatory postsynaptic potentials (EPSP) slightly dispersed in time. We analyze, based on numerical solution of the Hodgkin and Huxley equations, how does the triggering ability of the compound stimulus depend on the relative timing of the EPSPs it comprises. The dependences found suggest that a neuron stimulated from many synaptic inputs can be treated as performing elementary binding function and that inhibition serves as a controller of that kind of binding. The transient process characterized by EPSP operates in this context as a short-term memory mechanism inherent to a single neuron.

Neuron as time coherence discriminator.

Neuronal excitability under stimuli with a complex time course is investigated on the basis of the numerical solution of the Hodgkin-Huxley equations. Each stimulus is composed of 100-1000 unitary excitatory postsynaptic potentials (uEPSP) that start randomly within a definite time window. Probability of initiating a spike [firing probability, FP(W)] as a function of the window width W is calculated by the Monte Carlo method. FP(W) has a step-like shape: it becomes equal to 1 for small W and almost vanishes as W exceeds some value Ws. The role of long-lasting somatic inhibition is analysed. Ws depends on the inhibition potential, but the step-like shape of FP is preserved. It is concluded that the capability of multisynaptic stimulation to cause a spike can be expressed in terms of temporal coherence between the synaptic inputs. Namely, the spike is initiated if the temporal coherence between active inputs is above a definite threshold. The threshold value can be effectively regulated by varying the inhibition potential.

Interaction of energized bacteria cells with particles of colloidal gold: peculiarities and kinetic model of the process.

It is found that the cells of Bacillus cereus B-4368 at energized state can concentrate the colloidal gold particles on their surface. It is shown that the process depends on metabolic reactions proceeding on the plasma membrane. The inhibitory analysis permits to suppose that the metal concentration is due to the functioning of ATP-dependent generator of the transmembrane potential, apparently, of proton ATPase. Kinetic characteristics of the process show the presence of an intermediate state in the formation of biomineral aggregates. A kinetic model of the studied process is suggested which describes the experimental data well.

Selectivity and sensitivity improvement in co-operative systems with a threshold in the presence of noise.

High selectivity (specificity) and sensitivity to natural or artificial stimuli which are normally observed for biological systems can be realized in an ensemble composed of many co-operatively connected primary receptors. The co-operative interaction results in the formation of several stable states and a switching from one state to another is performed in a threshold manner. When any noise is absent the ensemble with a threshold can secure as high a selectivity and sensitivity as is desired. The presence of noise sets limits on the possible informational quality of a system because spontaneous switchings will occur. The question: What advantage as regards selectivity and sensitivity can a co-operative system with a threshold have is considered quantitatively as an example for a bistable chemical system. As a result it is established that a co-operative system may have much higher selectivity and sensitivity than its individual primary receptors.

[Periodic electric field as a possible switch of biopolymer conformation]. / Periodicheskoe élektricheskoe pole kak vozmozhnyi perekliuchatel' konformatsii biopolimerov.

A theoretical model describing the effect of periodic electrical fields (PEF) on the conformation of biopolymers is proposed. The biopolymer is interpreted as a system of classical mechanics consisting of subsystems (molecular groups) connected with each other by potential forces. The existence of PEF manifests itself as a periodic inducing force applied to the molecular group. Dissipation of energy is considered on the basis of liquid (viscous) friction. Arguments are presented in favor of non-Newton rheology of the viscous medium and as a consequence of non-linear dependence of the friction force on velocity. It is found that if the periodic field has more than one harmonics, then due to PEF effect the conformation potential can change to the linear in co-ordinate item.

Periodic electric field as a biopolymer conformation switch: a possible mechanism.

A theoretical model is proposed to describe the influence of a periodic electric field (PEF) upon a biopolymer. The biopolymer is treated as a classical mechanical system consisting of subsystems (molecular groups) which interact with each other through potential forces. The PEF is treated as a periodic driving force applied to a molecular group. The energy dissipation is considered using the model of fluid (viscous) friction. Arguments for the non-linear character of the friction-velocity dependence caused by the non-Newtonian rheology of a viscous medium are formulated. A forced molecular-group motion is investigated for the situation of a small driving-force period, with oscillations overdamped and a driving force consisting of more than one harmonic. As a result, it is established that the motion always gets to a terminal stage when only a small-scale vibration about some point, X*, takes place. The terminal motion is preceded by a transient characterized by the presence of a directional velocity component and so by a drift along a potential profile. The drift goes on until a barrier is met which has a sufficiently large steepness (the barrier height is not important). As a result, the point X* may happen to be remote from the conformation potential local minimum (conformational state). The physical reasons for the drift are described.(ABSTRACT TRUNCATED AT 250 WORDS)