On the role of subthreshold dynamics in neuronal signaling

The role of subthreshold dynamics in neuronal signaling is examined using periodic pulse train stimulation of the Fitzhugh-Nagumo (FN) model of nerve membrane excitability and results from the squid giant axon as an experimental data base. For a broad range of stimulus conditions the first pulse in a pulse train elicited an action potential, whereas all subsequent pulses elicited subthreshold responses, both in the axon and in the FN model. These results are not well described by the Hodgkin and Huxley 1952 model. Various different patterns of subthreshold responses, including chaotic dynamics, can be observed in both systems-the FN model and the axon-depending upon stimulus conditions. For some conditions action potentials are occasionally interspersed among the subthreshold events with randomly occurring interspike intervals. The randomness is directly attributable to the underlying subthreshold chaos-deterministic chaos-rather than to a stochastic noise source. We conclude that this mechanism may contribute to multimodal interspike interval histograms which have been observed from individual neurons throughout the nervous system.     

Changes in impulse activity of neurons of the CA3 area of the hippocampus under the effects of neuromodulator neurotropin]

Neurotropin (Nippon Zoki Co, Ltd) effects on firing patterns of the CA 3 hippocampus neurons in rabbits under a 24-h food deprivation was studied. Neuronal firing was recorded in a state of hunger (40 neurons) and under neurotropin (27 neurons) injected through a catheter implanted into the lateral brain ventricles. Initially, in 20% of neurons histograms had a bimodal interspike interval distribution: 1.5-25 ms and 100-400 ms. Neurotropin (50 microliters) increased the baseline spike rate regularity of hippocampus neurons. Histograms had a monomodal interspike interval distribution. Neurotropin (70 microliters) inhibited firing patterns and histograms, had trimodal interspike interval distribution: 1.5-5 ms; 250-400 ms and 1000 ms. Thus, these data suggested the involvement of neuro-immuno-modulator mechanisms in organization of firing patterns in rabbits.     

Rhythm-induced spike-timing patterns characterized by 1D firing maps

We explore patterns in the spike timing of neurons receiving periodic inputs, with an emphasis on stable characteristics which are realized in both models and in-vitro whole-cell recordings. We report on whole-cell recordings of pyramidal CA1 cells from rat hippocampus and entorhinal cortex and compare this data to model simulations. Cells were injected with a constant current to induce a steady firing rate and then a modest rhythm was added which altered the spike times and their corresponding phases relative to the rhythm. For both experiment and theory the relationship between consecutive spike phases is characterized by a probability distribution with peaks concentrated near a one-dimensional firing map. As is well-known, stable fixed points of this map correspond to the neuron phase-locking to the rhythm. We show that the interaction between noise and sufficiently steep maps can also cause a new kind of spike-time organization, in which consecutive spike time pairs organize into discrete clusters, with transitions between these clusters proceeding in a fixed sequence. This structure is not just a vestige of the noise-free dynamics. This slow dynamics and temporal organization in the relationship between consecutive spike phases is not evident in either the neuron’s voltage traces or single phase or interspike interval histograms. Furthermore, the consecutive spike relationship is also evident in consecutive ISIs, and hence this ordering can be observed without detailed knowledge of the rhythm (e.g. without concurrent LFP recordings).     

A model of the mechanisms of formation of unit activity

Dependence of the temporal structure of the spike discharge of a neuron in a weakly interacting network on the characteristics of excitatory and inhibitory input flows and on cell parameters was analyzed by a mathematical model. The intensity of communication between individual neurons corresponded to the intensity of synaptic communication between real spinal neurons. The temporal course of trace and accommodation processes in the model was similar to that of these processes in real spinal neurons. Connection of inhibitory inputs and an increase in the intensity of their influences were shown to be equivalent to a decrease in the intensity of excitatory input flows. Changes in cell parameters had a significant effect on the spike discharge only in the case of weak input influences (the ratio of the amplitude of the combined ESP evoked by the input spike train to the threshold value of membrane potential at rest was about 1.2:1.0 to 1.4:1.0). An increase in the input flow intensity led to considerable reorganization of the firing pattern: Mean values of interspike intervals and their fluctuations were reduced, histograms of interspike intervals became more symmetrical, and periodic waves appeared on the autocorrelation histograms. It is concluded on the basis of these results and of data in the literature that the main factor determining reorganization of the temporal structure of unit activity in a network of weakly interacting cells is the intensity of the input flow.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 12, No. 2, pp. 199–207, March–April, 1980.     

Interspike interval densities of resonate and fire neurons

The subthreshold dynamics of a neuron can follow one of the two patterns: resonant neurons generate intrinsic subthreshold membrane potential oscillations, whereas in nonresonant neurons these oscillations are not observed. Here, we investigate how these subthreshold behaviors affect the suprathreshold response. Both types of neurons are described by a resonate and fire model, with the stable fixpoint being either a focus or a node. Using analytic expression for a linear oscillator model with threshold and reset, we calculate the multimodal interspike interval densities. We show that a change in model parameters induces qualitative changes in the interspike interval densities.     

Static response of infrared neurons of crotaline snakes—normal distribution of interspike intervals

Background discharges (static responses) of warm fibers in the pit organs (infrared receptive organs) of two species of crotaline snakes were recorded at various temperatures (water, 18-33 degrees C; air, 19-28 degrees C). Mean interspike intervals (means), standard deviations (SD), and coefficients of variation (CV) were calculated, and the goodness of fit of interspike interval histograms to a corresponding normal distribution (i.e., one having the same mean and SD) were tested. Means, SD, and CV were smallest at a certain temperature, which might be the optimum receptor temperature for the species. More than half of the histograms (22/42 for water, 7/10 for air) showed a normal distribution at a significance level of 0.01. This suggests that the spike intervals generated at the spike initiation site are constant, with some random error. Background discharges of three pure infrared secondary neurons from the lateral descending nucleus were analyzed in the same way and compared to the peripheral discharges. There were no histograms with a normal distribution in these central neurons, which might indicate that the constant interspike intervals which appear in the primary afferent fibers are not utilized for information processing at this level but occur only as part of a receptor mechanism which is still unknown. The discharge patterns of primary afferent fibers are also discussed in relation to the known discharge patterns of cold fibers in other animals.     

Bistability and the dynamics of periodically forced sensory neurons

Many neurons at the sensory periphery receive periodic input, and their activity exhibits entrainment to this input in the form of a preferred phase for firing. This article describes a modeling study of neurons which skip a random number of cycles of the stimulus between firings over a large range of input intensities. This behavior was investigated using analog and digital simulations of the motion of a particle in a double-well with noise and sinusoidal forcing. Well residence-time dis tributions were found to exhibit the main features of the interspike interval histograms (ISIH) measured on real sensory neurons. The conditions under which it is useful to view neurons as simple bistable systems subject to noise are examined by identifying the features of the data which are expected to arise for such systems. This approach is complementary to previous studies of such data based, e.g., on nonhomogeneous point processes. Apart from looking at models which form the backbone of excitable model s, our work allows us to speculate on the role that stochastic resonance, which can arise in this context, may play in the transmission of sensory information. Received: 22 March 1993/Accepted in revised form: 8 September 1993     

The effects of influence of electromagnetic irradiation of millimeter wavelength on background impulse activity of supraoptic nucleus' neurons of rats' hypothalamus

In conditions of acute experiment on white rats anaesthetized by Nembutal (40 mg/kg, intraperitoneally), the registration and analysis of background impulse activity of the supraoptic nucleus neurons of rats' hypothalamus in norm and after electromagnetic irradiation of millimeter wavelength on organism, were carried out. Distributions of neurons by the degree of rhythm regularity, the character of types of dynamics of the following impulse flows, the modality of histograms of interspike intervals, the average discharge frequency, the coefficient of interspike intervals variation, were found out. Changes of the background impulse activity which were related mainly to the changes of the inner structure of registered impulse flows, were revealed. Significant shifts were generally observed in the character of dynamics of neuronal current flows and degree of regularity of the impulse activity. Statistically significant changes of the average frequency of discharges of different frequency range neurons' populations were revealed.     

Comparative analysis of spontaneous unit activity of the cerebellum fastigial nucleus' neurons in different periods of vibration influence

In conditions of acute experiment on white rats anaesthetized with Nembutal (40 mg/kg, interperitonially) recording and analysis of spontaneous impulse activity of the fastigial nucleus' neurons in norm and after 5, 10 and 15 days of vibration influence on the organism were carried out. Distribution of the neurons was evaluated by the dynamics of neuronal current flow and the modality of the interspike interval hystograms, as well as the statistical parameters: the average discharge frequency and the coefficient of the interspike interval variation. It is shown that more significant changes in neuronal activity of fastigial nucleus cells are formed during the first 10 days of vibration influence. On the 15th day, there was a tendency towards return to control levels of the parameters under study.     

Global bifurcation structure of a Bonhoeffer-van der Pol oscillator driven by periodic pulse trains

The Bonhoeffer-van der Pol (BVP) oscillator is a valuable dynamical system model of pacemaker neurons. Isochrons, phase transition curves (PTC), and two dimensional bifurcation diagrams served to analyze the neuron's response to periodic pulse stimuli. Responses are described and explained in terms of the nonlinear dynamical system theory. An important issue in the generation of spikes by pacemaker neurons is the existence of both slow and fast dynamics in the state point's trajectory in the phase plane. It is this feature in particular that makes the BVP oscillator a faithful model of living pacemaker neurons. Comparison of the model's responses with those of a living pacemaker was based also on return maps of interspike intervals. Analyzed in detail were the complex discharges called stammering which involve interspike intervals that arise unpredictably and exhibit histograms with several modes separated by the equal intervals.Supported by Trent H. Wells Jr. Inc.     

A New Approach for Determining Phase Response Curves Reveals that Purkinje Cells Can Act as Perfect Integrators

Cerebellar Purkinje cells display complex intrinsic dynamics. They fire spontaneously, exhibit bistability, and via mutual network interactions are involved in the generation of high frequency oscillations and travelling waves of activity. To probe the dynamical properties of Purkinje cells we measured their phase response curves (PRCs). PRCs quantify the change in spike phase caused by a stimulus as a function of its temporal position within the interspike interval, and are widely used to predict neuronal responses to more complex stimulus patterns. Significant variability in the interspike interval during spontaneous firing can lead to PRCs with a low signal-to-noise ratio, requiring averaging over thousands of trials. We show using electrophysiological experiments and simulations that the PRC calculated in the traditional way by sampling the interspike interval with brief current pulses is biased. We introduce a corrected approach for calculating PRCs which eliminates this bias. Using our new approach, we show that Purkinje cell PRCs change qualitatively depending on the firing frequency of the cell. At high firing rates, Purkinje cells exhibit single-peaked, or monophasic PRCs. Surprisingly, at low firing rates, Purkinje cell PRCs are largely independent of phase, resembling PRCs of ideal non-leaky integrate-and-fire neurons. These results indicate that Purkinje cells can act as perfect integrators at low firing rates, and that the integration mode of Purkinje cells depends on their firing rate.     

Modeling neural activity using the generalized inverse Gaussian distribution

Spike trains from neurons are often used to make inferences about the underlying processes that generate the spikes. Random walks or diffusions are commonly used to model these processes; in such models, a spike corresponds to the first passage of the diffusion to a boundary, or firing threshold. An important first step in such a study is to fit families of densities to the trains' interspike interval histograms; the estimated parameters, and the families' goodness of fit can then provide information about the process leading to the spikes. In this paper, we propose the generalized inverse Gaussian family because its members arise as first passage time distributions of certain diffusions to a constant boundary. We provide some theoretical support for the use of these diffusions in neural firing models. We compare this family with the lognormal family, using spike trains from retinal ganglion cells of goldfish, and simulations from an integrate-and-fire and a dynamical model for generating spikes. We show that the generalized inverse Gaussian family is closer to the true model in all these cases. Received: 16 September 1996 / Accepted in revised form: 2 July 1997     

Discharge patterns of chicken cochlear ganglion neurons following kanamycin-induced hair cell loss and regeneration

Hair cells in the basal, high frequency region (>1100 Hz) of the chicken cochlea were destroyed with kanamycin (400 mg/kg/d × 10 d) and allowed to regenerate. Afterwards, single unit recordings were made from cochlear ganglion neurons at various times post-treatment. During the first few weeks post-treatment, only neurons with low characteristic frequencies (<1100 Hz) responded to sound. Despite the fact that the low frequency region of the cochlea was not destroyed, neurons with low characteristic frequencies had elevated thresholds, abnormally broad U-shaped or W-shaped tuning curves and low spontaneous discharge rates. At 2 days post-treatment, the spontaneous discharge rates of some acoustically unresponsive units fluctuated in a rhythmical manner. As recovery time increased, thresholds decreased, tuning curves narrowed and developed a symmetrical V-shape, spontaneous rate increased and neurons with higher characteristic frequencies began to respond to sound. In addition, the proportion of interspike interval histograms with regularly spaced peaks increased. These improvements progressed along a low-to-high characteristic frequency gradient. By 10–20 weeks post-treatment, the thresholds and tuning curves of neurons with characteristic frequencies below 2000 Hz were within normal limits; however, the spontaneous discharge rates of the neurons were still significantly lower than those from normal animals.Abbreviations KM kanamycin - BrdU bromodeoxyuridine - CF characteristic frequency - CAP compound action potential - ISI interspike interval     

On the stationary state of a network of inhibitory spiking neurons

The background activity of a cortical neural network is modeled by a homogeneous integrate-and-fire network with unreliable inhibitory synapses. For the case of fast synapses, numerical and analytical calculations show that the network relaxes into a stationary state of high attention. The majority of the neurons has a membrane potential just below the threshold; as a consequence the network can react immediately – on the time scale of synaptic transmission- on external pulses. The neurons fire with a low rate and with a broad distribution of interspike intervals. Firing events of the total network are correlated over short time periods. The firing rate increases linearly with external stimuli. In the limit of infinitely large networks, the synaptic noise decreases to zero. Nevertheless, the distribution of interspike intervals remains broad. Action Editor: Misha Tsodyks     

Pyramidal unit activity in unanesthetized cats

Pyramidal unit activity in unanesthetized cats at rest and during voluntary movement was recorded by a microelectrode technique from the motor cortex for the forelimb. Some pyramidal neurons were not spontaneously active. The conduction velocity along the axon of these neurons was sometimes high (up to 71.5 m/sec), sometimes low (up to 11.2 m/sec). The remaining pyramidal neurons had spontaneous activity with a mean frequency of 1.29 to 43 spikes/sec. Analysis of interspike interval histograms of spontaneous activity and of autocorrelation histograms showed grouping of the spikes into volleys in most pyramidal neurons (irrespective of the conduction velocity). During voluntary movements the change in the activity of many pyramidal units correlated with changes in the EMG. The firing rate of the pyramidal neurons under these circumstances began to rise at least 50 msec before the increase in amplitude of the EMG and it remained high throughout the movement. The firing rate of most neurons during movement was 40–60/sec. The results are compared with those obtained by other workers who studied pyramidal unit activity of monkeys during voluntary movement.     

Neuron firing in driven nonlinear integrate-and-fire models

Statistical properties of neuron firing are studied in the framework of a nonlinear leaky integrate-and-fire model that is driven by a slow periodic subthreshold signal. The firing events are characterized by first passage time densities. The experimentally better accessible interspike interval density generally depends on the sojourn times in a refractory state of the neuron. This aspect is not part of the integrate-and-fire model and must be modelled additionally. For a large class of refractory dynamics, a general expression for the interspike interval density is given and further evaluated for the two cases with an instantaneous resetting (i.e. no refractory state) and a refractory state possessing a deterministic lifetime. First passage time densities and interspike interval densities following from the proposed theory compare favorably with precise numerical simulations.     

大鼠视上核神经元自发放电节律的确定性机制

利用非线性动力学的方法,在多种生物数据中找到了确定性机制。大鼠下丘脑视上核（ｓｕｐｒａｏｐｔｉｃ ｎｕｃｌｅｕｓ,ＳＯＮ）神经元自发产生不规则的放电。为了研究这些不规则放电是否含有确定性机制,用电流钳对大鼠ＳＯＮ神经元进行全细胞纪录,取动作电位峰峰间期序列（ｉｎｔｅｒｓｐｉｋｅ ｉｎｔｅｒｖａｌ,ＩＳＩ）作为研究对象。采用一种新的检测时间序列非稳定周期轨道的方法分析ＩＳＩ序列,发现ＩＳＩ含有非稳定     

大鼠视上核神经元自发放电节律的确定性机制

利用非线性动力学的方法 ,在多种生物数据中找到了确定性机制。大鼠下丘脑视上核(supraopticnucleus,SON)神经元自发产生不规则的放电。为了研究这些不规则放电是否含有确定性机制 ,用电流钳对大鼠SON神经元进行全细胞纪录,取动作电位峰峰间期序列(interspikeinterval,ISI)作为研究对象。采用一种新的检测时间序列非稳定周期轨道的方法分析ISI序列 ,发现ISI含有非稳定周期轨道族 ,即周期1 ,周期2 ,和周期3存在。结果表明 ,SON神经元的自发放电序列存在确定性的动力学机制。     

Interactions of glutamate and dopamine in a computational model of the striatum

A network model of simplified striatal principal neurons with mutual inhibition was used to investigate possible interactions between cortical glutamatergic and nigral dopaminergic afferents in the neostriatum. Glutamatergic and dopaminergic inputs were represented by an excitatory synaptic conductance and a slow membrane potassium conductance, respectively. Neuronal activity in the model was characterized by episodes of increased action potential firing rates of variable duration and frequency. Autocorrelation histograms constructed from the action potential activity of striatal model neurons showed that reducing peak excitatory conductance had the effect of increasing interspike intervals. On the other hand, the maximum value of the dopamine-sensitive potassium conductance was inversely related to the duration of firing episodes and the maximal firing rates. A smaller potassium conductance restored normal firing rates in the most active neurons at the expense of a larger proportion of neurons showing reduced activity. Thus, a homogeneous network with mutual inhibition can produce equally complex dynamics as have been proposed to occur in a striatal network with two neuron populations that are oppositely regulated by dopamine. Even without mutual inhibition it appears that increased dopamine concentrations could partially compensate for the effects of reduced glutamatergic input in individual neurons.     

Changes in the functional organization of the lateral geniculate body after tetanus toxin injection

Changes in unit activity in the lateral geniculate body during formation of a generator of pathologically enhanced excitation as a result of local injection of tetanus toxin into this nucleus were investigated in unanesthetized cats. To assess changes taking place a classification of geniculate neurons in normal animals obtained by analysis of interspike interval histograms of spontaneous activity and poststimulus histograms of unit activity evoked by photic stimulation was used. As a result of the action of the toxin substantial changes were observed in the quantitative distribution of the neurons by groups. A new group of neurons with a considerably increased duration of the first spike volley also was identified. The appearance of these neurons is connected with disappearance of the inhibitory pause in the overwhelming majority of relay neurons of the nucleus.Institute of General Pathology and Pathological Physiology, Academy of Medical Sciences of the USSR, Moscow. Translated from Neirofiziologiya, Vol. 10, No. 1, pp. 38–43, January–February, 1978.