Power-law inter-spike interval distributions infer a conditional maximization of entropy in cortical neurons

The brain is considered to use a relatively small amount of energy for its efficient information processing. Under a severe restriction on the energy consumption, the maximization of mutual information (MMI), which is adequate for designing artificial processing machines, may not suit for the brain. The MMI attempts to send information as accurate as possible and this usually requires a sufficient energy supply for establishing clearly discretized communication bands. Here, we derive an alternative hypothesis for neural code from the neuronal activities recorded juxtacellularly in the sensorimotor cortex of behaving rats. Our hypothesis states that in vivo cortical neurons maximize the entropy of neuronal firing under two constraints, one limiting the energy consumption (as assumed previously) and one restricting the uncertainty in output spike sequences at given firing rate. Thus, the conditional maximization of firing-rate entropy (CMFE) solves a tradeoff between the energy cost and noise in neuronal response. In short, the CMFE sends a rich variety of information through broader communication bands (i.e., widely distributed firing rates) at the cost of accuracy. We demonstrate that the CMFE is reflected in the long-tailed, typically power law, distributions of inter-spike intervals obtained for the majority of recorded neurons. In other words, the power-law tails are more consistent with the CMFE rather than the MMI. Thus, we propose the mathematical principle by which cortical neurons may represent information about synaptic input into their output spike trains.     

Determination of conduction times of the peripheral and central parts of the sensory pathway using evoked somatosensory potentials

Determination of conduction times of the peripheral and central parts of the sensory pathway using evoked somatosensory potentials. Acta physiol. pol., 1985, 36 (3): 216-223. Simultaneous recording of the somatosensory evoked potentials (SEP) from Erb's point, neck and scalp allows investigation of the peripheral and central conduction times. The early components of the SEP produced by stimulation of the median nerve at the wrist were recorded using standardized electrode locations in 15 normal subjects. The difference of the latencies between the first peak of the cortical response (N20) and the peak of the neck response (N14) reflects, probably, the conduction time between the dorsal column nuclei and the cortex. Its value was 6 +/- 0.7 msec. The conduction time difference (between peak Erb's point response (N9) and N14) was 5.5 +/- 0.5 msec and it reflected the peripheral conduction time. For diagnostic application the lower limit of the response amplitudes was determined also for every component.     

RF-cell: A model for populations of randomly interconnected neurons

This paper is concerned with a population of neurons with dense random interconnections, in which the stimulations between neurons are independent of their distance apart. This study is conducted from the viewpoint of the General System Theory. Proposed and used for the first time in studies on the above subject is a new concept referred to as the ‘historical report’ of the mentioned population. It will be shown that the population exhibits cyclic modes of behaviour which are dependent on its structure and historical report and which in the phase space correspond to cycles of hysteresis. A simple model in discrete time is developed and demonstrates, by the help of a computer study, the existence of the cycles of hysteresis.     

Elementary polysynaptic potentials of hippocampal neurons

Synaptic connections of 26 pairs of hippocampal neurons were studied in nonanesthetized rabbits by spike-triggered averaging of intracellularly recorded activity. Synchronized activity was detected in 5 pairs and considered to represent common inputs to the neurons recorded. Hyperpolarizing or depolarizing potentials with 3--4 ms latency were revealed in 3 additional pairs. These potentials are considered to be individual postsynaptic potentials (PSPs) evoked in the target neuron by spikes of the adjacent (0.5--2 mm apart) neuron. A quantum analysis of the individual PSPs was performed. The mean quantum content (0.27--0.65) and quantum size (35--200 mkV) were found to be of the same order as those of the excitatory PSPs previously recorded after intracerebral stimulation. It is concluded that most hippocampal synapses are of low efficacy.     

Focal potentials of Clarke's column neurons

In experiments on cats, we investigated focal potentials of Clarke's column neurons and discharges of individual neurons recorded extracellularly. An ultrasonic scalpel was used to remove the part of the spinal cord between Th₁₃ and L₃, and an electrode was inserted into the face of the caudal segment of the spinal cord along the axis of Clarke's column. Orthodromic excitation of Clarke's column neurons was evoked by stimulating cut nerves of the ipsilateral extremity; antidromic excitation was evoked by stimulating the dorsolateral funiculus, which was preliminarily separated from the removed portion of the spinal cord. It was found that the orthodromic potential, antidromic potential, and discharges are distinctly registered when the method of electrode insertion is used, whereas they were not recorded when the microelectrodes were sunk into the dorsal surface in these experiments. It is demonstrated that orthodromic and antidromic focal potentials of Clarke's column neurons are similar to motoneuron focal potentials with respect to time characteristics. Inversion of the charge sign was recorded with the approach of the microelectrode's tip to the soma of Clarke's column neurons. It is hypothesized that the success of recording focal potentials and extracellular discharges of Clarke's column neurons resulted from the fact that the orientation of dendrites of these cells matches the direction of microelectrode movement. The slender portion of the microelectrode penetrates the interdendritic space, where tension of the extracellular field is the greatest; it then moves through this space to reach the soma.I. P. Pavlov Institute of Physiology, Academy of Sciences of the USSR, Leningrad; A. A. Bogomol'ets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 2, No. 5, pp. 528–535, September–October, 1970.     

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.     

Monosynaptic inhibitory postsynaptic potentials of cortical neurons

Monopolar intracortical stimulation of the auditory cortex was carried out in cats immobilized with D-tubocurarine. A macroelectrode (tip diameter 100 µ) or a microelectrode (tip diameter 10–15 µ) was used for stimulation. In both cases, besides excitatory responses, primary IPSPs with latent periods of 0.4–1.2 and 1.4–6.0 msec were recorded in cortical neurons close to the point of stimulation. The first group of IPSPs are considered to be generated in response to direct stimulation of bodies or axons of inhibitory cortical neurons, i.e., monosynaptically. The amplitude of these IPSPs varied in different neurons from 3 to 15 mV, and their duration from 4 to 150 msec. Additional later inhibitory responses were superposed on many of them. Of the IPSPs generated in auditory cortical neurons in response to stimulation of geniculocortical fibers 1.5% had a latency of 0.8–1.3 msec. They also are assumed to be monosynaptic. It is concluded that the duration of synaptic delay of IPSPs in cortical neurons and spinal motoneurons is the same, namely 0.3–0.4 msec. Axons of auditory cortical inhibitory neurons may be 1.5 mm long. The velocity of impulse conduction along these axons is 1.6–2.8 m/sec. The genesis of some special features of IPSPs of cortical neurons is discussed.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 7, No. 5, pp. 458–467, September–October, 1975.     

The relationship between the Gabor elementary function and a stochastic model of the inter-spike interval distribution in the responses of visual cortex neurons

In a previously reported study (Berger et al. 1990) we analyzed distributions of interspike intervals recorded extracellularly from cat visual cortex under four stimulus conditions. Stimuli were gratings differing in orientation and spatial frequency. The probability density function of first passage time for a random walk with drift process, which is defined by its barrier height and drift coefficient, was used to characterize the generating process of axonal discharge under resting and stimulus conditions. Drift coefficient and barrier height were derived from the sample mean and standard deviation of the measured inter-spike intervals. For cells with simple receptive fields, variations in spatial frequency produced changes only in drift coefficient. Variations in barrier height were produced only by changes in orientation of the stimulus. Currently, the method used to analyze these data was implemented in a simulation which displayed the relationship between the interval distribution of impulses, the random walk which represents the time series characteristic of the spike train model and the Gabor filter function which represents the geometry of the receptive field process.     

Stepwise action potentials of the soma membrane of molluscan neurons

Experiments were carried out on neurons of the visceral complex of ganglia ofHelix pomatia. Application of strong hyperpolarizing stimuli ("electro-convulsive shock") throughan intracellular microelectrode led to dissociation of the original action potential into small components. Repetition of the "electro-convulsive shock" intensified these phenomena. Regular hyperpolarizing stimuli led to the formation of action potentials whose amplitude depended on the intensity and duration of the hyperpolarizing stimuli. The possibility that trigger zones are located on the soma membrane of molluscan neurons is discussed on the basis of the results.     

Complex action potentials of secondary neurons of the rat olfactory bulb

Complex action potentials arising spontaneously or evoked by stimulation of the lateral olfactory tract in secondary neurons of the rat olfactory bulb were recorded. The amplitude and duration of the complex potentials varied depending on synchronization of onset of the individual components (of which more than four were distinguished) and their combination. It is suggested that complex potentials were recorded in cases when the electrode was located in the region of the junction between spike-generating zones (the branching node of the dendrite, the junction of the soma with the dendrites and axon). It is concluded that there are numerous generating zones in the dendrites of the secondary olfactory neurons. Evoked action potentials appeared after the following latent periods: first, about 1 msec; second, about 2 msec; and third, about 3 msec. The results of the analysis showed that the antidromic response appeared after the shortest latent period. These results are evidence of the existence of considerable and varied representation of excitatory synapses in secondary neurons (besides the excitatory input in the olfactory glomeruli).M. B. Lomonosov Moscow State University. Translated from Neirofiziologiya, Vol. 8, No. 6, pp. 575–582, November–December, 1976.     

Effects of pineal factors on the action potentials of sympathetic neurons

Neurons from rat superior cervical ganglia were grown in coculture with pineal cells. Action potentials of neurons in cocultures were 25% longer and were 25% greater in amplitude than those recorded from neurons grown in the presence of ganglionic nonneuronal cells alone. Neurons showed an increase in action potential duration with increasing time in culture. This may have been related to the recovery of nonneuronal cell populations after an initial exposure to the antimitotic agent Ara-C. In cultures not initially exposed to Ara-C, a subsequent exposure after 7 days in culture resulted in a shortening of the action-potential duration. Neuronal cultures were exposed to gel slabs containing the pineal indolamines, serotonin, N-acetylserotonin, and melatonin. Serotonin and N-acetylserotonin showed no effect on the neuronal action potentials at the concentrations tested. Melatonin caused an increase in action-potential duration that was associated not with an increase in action-potential amplitude, but with a decrease in action-potential rise rates. The effects of long-term exposure in melatonin appeared to be reversible in some cells but not in all. Short-term effects of melatonin were observed in older cultures and in younger cultures after the cells were stimulated repeatedly. Older cultures also had higher levels of spontaneous activity. The dependence of the short-term effects of melatonin on electrical activity may suggest a role for melatonin as a neuromodulator.     

Synaptic potentials and transfer functions of lamprey spinal neurons

1. Electrotonic and chemical synaptic potentials were measured as a function of frequency of presynaptic action potentials. Over the frequency range from 0.02 to 10 Hz, the electrotonic synaptic potential was constant, while the chemical synaptic potential decreased in magnitude. Above 10 Hz, both synaptic events decreased in magnitude consistent with filtering by the dendritic structures. 2. Electrotonic synaptic transfer functions from 0.5 to 100 Hz were measured for the I1 reticulospinal Müller axon to spinal neuron electrotonic synaptic junction of the lamprey spinal cord using paired recordings from the pre-synaptic terminals and the post-synaptic neurons. In addition to this two-point synaptic transfer function, individual single point impedance functions of both the post-synaptic soma and the pre-synaptic axon terminal were measured. 3. The measured functions were interpreted with a computational model based on a three dimensional reconstruction of a Lucifer yellow filled motoneuron. Simulations of the model for a synaptic location of the I1 synapse were consistent with the measured synaptic transfer functions. 4. Synaptic potentials were simulated for inputs on dendrites near the I1 axon as well as distal dendritic regions. The high frequency filtering increased as the synaptic location was moved from the soma to the periphery, but the potential response on distal dendrites was larger than would have been predicted from the end of the equivalent cylinder of a Rall model that was used to fit soma impedance functions. 5. Electrotonic post-synaptic potentials were enhanced by the activation of a TTX-sensitive negative conductance.(ABSTRACT TRUNCATED AT 250 WORDS)     

Functional role of plateau potentials in vertebrate motor neurons

The expression of plateau potentials in spinal motor neurons is regulated by neuromodulatory substances. Recent experiments have shed new light on this regulation at the cellular level. It is now possible to evaluate the existence of plateau potentials in intact organisms, including humans, and to address the functional role of plateau potentials in motor control, as well as in information transfer in the brain.     

Various forms of potentials recorded from caudate nucleus neurons

Spontaneous and evoked activity of caudate nucleus neurons was recorded extracellularly in acute experiments on cats. Different forms of potentials were found by analysis of the results. The potentials recorded belong to three types: ordinary action potentials; prepotentials or incomplete spikes differing from ordinary action potentials in their lower amplitude and slower decline, and complex discharges in which a spike of somewhat reduced amplitude is followed by a slow positive-negative wave. In the spontaneous activity prepotentials were observed both in complete action potentials and in isolation. The frequency of the complex discharges was 0.5–1 per second. The slow wave of these discharges blocked prepotential and action potential formation. The origin of these forms of potentials in neurons of the caudate nucleus is discussed and they are compared with analogous forms of potentials described for the Purkinje cells of the cerebellum.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukranian SSR, Kiev. Translated from Neirofiziologiya, Vol. 9, No. 2, pp. 149–156, March–April, 1977.     

Regulation of back-propagating action potentials in hippocampal neurons.

Protein kinase C has recently been shown to modulate the slow recovery from inactivation of Na+ channels in apical dendrites of hippocampal CA1 pyramidal neurons. Moreover, dendritic, A-type K+ channels have been found to be modulated by protein kinases A and C and by mitogen-activated protein kinase. The electrical signalling ability of these dendrites is thus highly regulated by a number of neurotransmitters and second-messenger systems.     

Amplitude of miniature potentials of motor neurons in the frog Rana ridibunda

Miniature synaptic potentials have been recorded from motoneurones of the isolated spinal cord of the frog Rana ridibunda. In normal Ringer's solution, their frequency varied from 5 to 50/sec, whereas their amplitude reached 2-5 mV. Only 50-300 microV (rarely 0.5-1.5 mV) potentials persisted when TTX was added to Ringer's solution and/or Ca was replaced by Mn. However, in Ca-free solution, TTX in combination with Mn did not decrease the amplitude of miniature potentials, provided the initial values varied within 50-300 microV. Noise fluctuations did not exceed 40-50 microV, and the ratio of the number of miniature potentials of 50 microV to the number of 50 microV noise potentials was about 10:1. The observed miniature potentials with an amplitude of 50-100 microV coincide with the quantal units calculated by other authors from statistical analysis of the unitary EPSPs evoked by primary afferents or by ventrolateral tract fibers.     

Zinc-dependent action potentials in giant neurons of the snail,Euhadra quaestia

Summary In giant neurons of subesophageal ganglion of the Japanese land snail,Euhadra quaestia Deshayes, permeation of Zn ions through Ca channels were investigated with a conventional current clamp method.All-or-none action potentials of long duration (90 to 120 sec) were evoked in 24mm Zn containing salines. The overshoots were about +10 mV and the maximum rate of rises (MRRs) was about 2.9 V/sec. The amplitudes and the MRRs of the action potentials depended on external Zn ion concentrations.The action potentials were suppressed by specific Ca-channel inhibitors such as Co²⁺, La³⁺ and Verapamil, but they were resistant to Na-channel inhibitor, tetrodotoxin, even at 30 m.It is concluded that these action potentials are generated by Zn ions permeating Ca channels in snail neuronal membrane.On the basis of Hagiwara and Takahashi's (S. Hagiwara & K. Takahashi, 1967,J. Gen. Physiol. 50:583) model of Ca channels, it is inferred that Zn ions are 5 to 10 times stronger in affinity to Ca channels than Ca ions, but 10 to 20 times less permeable.     

Dendritic action potentials of pyramidal tract neurons in the cat sensorimotor cortex

The intracellular activity of pyramidal tract neurons was studied during electrical stimulation of ventrolateral and ventroposterolateral thalamic nuclei in acute experiments on cats immobilized by myorelaxants. Somatic action potentials were observed and spontaneous spikes were also produced by single and rhythmic stimulation of the thalamic nuclei at the rate of 8–14 Hz, by iontophoretic application of strychnine, and by intracellular depolarizing current pulses. These potentials had a relatively low and variable amplitude of 5–60 mV and are presumed to be dendritic action potentials. It is postulated that these variable potentials arise in the dendrites of pyramidal neurons with multiple zones generating such activity. No interaction was observed where somatic and dendritic action potentials occur simultaneously. The possible functional role of dendritic action potentials is discussed.I. S. Beritashvili Institute of Physiology, Academy of Sciences of the Georgian SSR, Tbilisi. Translated from Neirofiziologiya, Vol. 18, No. 4, pp. 435–443, July–August, 1986.