Presynaptic learning and memory with a persistent firing neuron and a habituating synapse: a model of short term persistent habituation

Our paper explores the interaction of persistent firing axonal and presynaptic processes in the generation of short term memory for habituation. We first propose a model of a sensory neuron whose axon is able to switch between passive conduction and persistent firing states, thereby triggering short term retention to the stimulus. Then we propose a model of a habituating synapse and explore all nine of the behavioral characteristics of short term habituation in a two neuron circuit. We couple the persistent firing neuron to the habituation synapse and investigate the behavior of short term retention of habituating response. Simulations show that, depending on the amount of synaptic resources, persistent firing either results in continued habituation or maintains the response, both leading to longer recovery times. The effectiveness of the model as an element in a bio-inspired memory system is discussed.     

A role for phasic dopamine neuron firing in habit learning

In this issue of Neuron, Wang et?al. (2011) show that mice with dopamine neuron-specific NMDAR1 deletion have attenuated phasic dopamine neuron firing and a deficit in habit learning. These findings indicate that brain regions sensitive to phasic dopamine signals may underlie habit learning.     

Empirical examination of the threshold model of neuron firing

An elementary model of neuronal activity involves temporal and spatial summation of postsynaptic currents that are elicited by presynaptic spikes and that, in turn, elicit postsynaptic potentials at a trigger zone; when the potential at the trigger zone exceeds a threshold level, a postsynaptic spike is generated. This paper describes three methods of estimating the summation function, that is, the function of time that converts the synaptic current into potential at the trigger zone: namely, maximum likelihood, cross-correlation analysis and cross-spectral analysis. All three methods, when applied to input-output data collected on various neurons of Aplysia californica, give comparable results. As estimated, the summation function involved in the explored cells has an early positive-going swing that is large and brief. In the cell L5, but not in R2, there was also a late negative-going swing of longer duration.Prepared with the partial support of the National Science Foundation Grant MCS 77-22986 to DRB and NSF and NIH grants to JPS     

A hidden Markov model approach to neuron firing patterns.

Analysis and characterization of neuronal discharge patterns are of interest to neurophysiologists and neuropharmacologists. In this paper we present a hidden Markov model approach to modeling single neuron electrical activity. Basically the model assumes that each interspike interval corresponds to one of several possible states of the neuron. Fitting the model to experimental series of interspike intervals by maximum likelihood allows estimation of the number of possible underlying neuron states, the probability density functions of interspike intervals corresponding to each state, and the transition probabilities between states. We present an application to the analysis of recordings of a locus coeruleus neuron under three pharmacological conditions. The model distinguishes two states during halothane anesthesia and during recovery from halothane anesthesia, and four states after administration of clonidine. The transition probabilities yield additional insights into the mechanisms of neuron firing.     

Millimeter waves thermally alter the firing rate of the Lymnaea pacemaker neuron

The effects of millimeter waves (mm-waves, 75 GHz) and temperature elevation on the firing rate of the BP-4 pacemaker neuron of the pond snail Lymnaea stagnalis were studied by using microelectrode techniques. The open end of a rectangular waveguide covered with a thin Teflon film served as a radiator. Specific absorption rates (SARs), measured in physiological solution at the radiator outlet, ranged from 600 to 4200 W/kg, causing temperature rises from 0.3 to 2.2 °C, respectively. Irradiation at an SAR of 4200 W/kg caused a biphasic change in the firing rate, i.e., a transient decrease in the firing rate (69 ± 22% below control) followed by a gradual increase to a new level that was 68 ± 21% above control. The biphasic changes in the firing rate were reproduced by heating under the condition that the magnitude (2 °C) and the rate of temperature rise (0.96 °C/s) were equal to those produced by the irradiation (for an SAR of 4030 W/kg). The addition of 0.05 mM of ouabain caused the disappearance of transient responses of the neuron to the irradiation. It was shown that the rate of temperature rise played an important role in the development of a transient neuronal response. The threshold stimulus for a transient response of the BP-4 neuron found in warming experiments was a temperature rise of 0.0025 °C/s. Bioelectromagnetics 18:89–98, 1997. © 1997 Wiley-Liss, Inc.     

On a stochastic model for the firing sequence of a neuron

A stochastic model of a neuron with excitatories and inhibitories incident on it is studied. The excitatory and the inhibitory sequences are independent renewal processes. The effect of an excitatory is to increase the membrane potential by random amounts that are independently and identically distributed, while an inhibitory causes a reset of the potential to the rest level so that the accumulation must start anew. When the potential crosses a threshold level K, the neuron fires. Immediately after this, the membrane potential returns to the rest level. An expression for the probability density function of the interval between two successive firings is derived, and special cases worked out. Graphs of the mean and the mean − √variance versus the threshold level are presented and discussed.     

Channel density regulation of firing patterns in a cortical neuron model

Modifying the density and distribution of ion channels in a neuron (by natural up- and downregulation or by pharmacological intervention or by spontaneous mutations) changes its activity pattern. In this investigation we analyzed how the impulse patterns are regulated by the density of voltage-gated channels in a neuron model based on voltage-clamp measurements of hippocampal interneurons. At least three distinct oscillatory patterns, associated with three distinct regions in the Na-K channel density plane, were found. A stability analysis showed that the different regions are characterized by saddle-node, double-orbit, and Hopf-bifurcation threshold dynamics, respectively. Single, strongly graded action potentials occur in an area outside the oscillatory regions, but less graded action potentials occur together with repetitive firing over a considerable range of channel densities. The relationship found here between channel densities and oscillatory behavior may partly explain the difference between the principal spiking patterns previously described for crab axons (class 1 and 2) and cortical neurons (regular firing and fast spiking).     

A neuron model with learning capability and its relation to mechanisms of association

A neuron model with the ability of learning has been examined by means of mathematical and statistical methods. By use of the established anatomical concepts the main features of the model can be described as follows.The synapses are randomly distributed on the dendrites in a way that can be described by poisson processes. The afferent connections to the synapses are also random.The input signals are divided into excitatory, inhibitory and unspecified signals. The latter, whose detailed action is not specified, may involve excitatory as well as inhibitory action on the cell. Signals are described in terms of impulse frequencies.Learning takes place through facilitation of excitatory synapses. The condition for facilitation is the occurrence of simultaneous presynaptic and postsynaptic activity. The synaptical changes occurring during repeated learning are superimposed. Inhibitory synapses are capable of influencing learning by blocking the dendritic transmission.It is shown that, under certain conditions, a collection of model cells is able to work as an associative memory. This means that a pattern of output signals that once occurred through the combined action of the excitatory, the inhibitory, and the unspecified signals may later be recalled by applying just the two former signal patterns. It is shown that excitatory and inhibitory signals are similar in their ability to evoke associations.However there is also a difference between excitation and inhibition due to the fact that the pattern of inhibitory signals is subject to a non-linear transformation. This implies that great similarity is required between the inhibitory pattern once present during learning and the inhibitory pattern that is fed in later in order to obtain an associative recall. This phenomenon is called pattern separation and is supposed to be of importance when discriminating between patterns.     

Ion channel density and threshold dynamics of repetitive firing in a cortical neuron model

Modifying the density and distribution of ion channels in a neuron (by natural up- and down-regulation, by pharmacological intervention or by spontaneous mutations) changes its activity pattern. In the present investigation, we analyze how the impulse patterns are regulated by the density of voltage-gated channels in a model neuron, based on voltage clamp measurements of hippocampal interneurons. At least three distinct oscillatory patterns, associated with three distinct regions in the Na-K channel density plane, were found. A stability analysis showed that the different regions are characterized by saddle-node, double-orbit, and Hopf bifurcation threshold dynamics, respectively. Single strongly graded action potentials occur in an area outside the oscillatory regions, but less graded action potentials occur together with repetitive firing over a considerable range of channel densities. The presently found relationship between channel densities and oscillatory behavior may be relevance for understanding principal spiking patterns of cortical neurons (regular firing and fast spiking). It may also be of relevance for understanding the action of pharmacological compounds on brain oscillatory activity.     

An interaction model of a poisson and a renewal process related to neuron firing

This paper discusses a neuronal model based on a model of Coleman and Gastwirth (1969). It is assumed that the excitatory input forms a Poisson process while the inhibitory input forms a stationary renewal process. The proposed interaction scheme is as follows: an inhibitor deletes at most N consecutive excitatory inputs and a response only occurs after the cummalative storage of M excitatory inputs. The Laplace transform of the probability density function (p.d.f.) of the inter-response intervals is derived together with results of the numerical inversions.     

Diffusion models for firing of a neuron with varying threshold

A stochastic model for the firing of a neuron with refractory properties is treated analytically. Refractory behavior is modeled by a threshold function θ(t) which is infinite immediately after the neuron fires, as well as during the absolute refractory period, and then decreases monotonically to the quiescent threshold level, θ_∞, during the relative refractory period. Using Wald's identity, input-output relations are derived analytically for the exponential threshold which has a time constant equal to the membrane time constant. A method for computing these relations for a general threshold is presented and is explicitly used for the general exponential threshold and the Hagiwara threshold, θ(t) = θ_∞e^α/t, where a is a constant.     

A model for neuron firing with exponential decay of potential resulting in diffusion equations for probability density

A neuron is assumed to receive synaptic input of both excitatory and inhibitory natures from a large number of neighboring neurons; it is also assumed that a large number of such impulses are required to raise the neuron’s transmembrane potential to its threshold potential, at which it “fires” or “spikes”. The model is similar to one of Gerstein and Mandelbrot, except that in the absence of input an exponential decay of potential toward a resting level is introduced. Computational methods of determining the spike timeinterval distribution are discussed, along with the inverse problem of estimating the parameters of the system from observed spike time-interval data.     

Attentional modulation of firing rate and synchrony in a model cortical network

The response of a neuron in the visual cortex to stimuli of different contrast placed in its receptive field is commonly characterized using the contrast response curve. When attention is directed into the receptive field of a V4 neuron, its contrast response curve is shifted to lower contrast values (Reynolds et al., 2000). The neuron will thus be able to respond to weaker stimuli than it responded to without attention. Attention also increases the coherence between neurons responding to the same stimulus (Fries et al., 2001). We studied how the firing rate and synchrony of a densely interconnected cortical network varied with contrast and how they were modulated by attention. The changes in contrast and attention were modeled as changes in driving current to the network neurons. We found that an increased driving current to the excitatory neurons increased the overall firing rate of the network, whereas variation of the driving current to inhibitory neurons modulated the synchrony of the network. We explain the synchrony modulation in terms of a locking phenomenon during which the ratio of excitatory to inhibitory firing rates is approximately constant for a range of driving current values. We explored the hypothesis that contrast is represented primarily as a drive to the excitatory neurons, whereas attention corresponds to a reduction in driving current to the inhibitory neurons. Using this hypothesis, the model reproduces the following experimental observations: (1) the firing rate of the excitatory neurons increases with contrast; (2) for high contrast stimuli, the firing rate saturates and the network synchronizes; (3) attention shifts the contrast response curve to lower contrast values; (4) attention leads to stronger synchronization that starts at a lower value of the contrast compared with the attend-away condition. In addition, it predicts that attention increases the delay between the inhibitory and excitatory synchronous volleys produced by the network, allowing the stimulus to recruit more downstream neurons. Action Editor: David Golomb     

Lead and copper contamination of soil from industrial activities and firing ranges

Lead still remains one of the most thoroughly investigated heavy metals in the environment. Although the identification of lead in soil is a routine matter, its environmental consequence is still much debated because of its potential mobility. We have investigated leadand copper-contaminated soil from two different areas. One was in an urban area, which formerly had a lead smelter within the city. The other a firing range, in which hundreds of thousands of rounds were fired into a very large mound known as a berm. Homogeneity tests, depth profiles, and Pb-Cu correlations are discussed.     

Analysis of motor unit firing characteristics in patients with motor neuron diseases

This study was designed to evaluate firing rate variability in patients with upper/lower motor neuron disorders. Twenty healthy subjects and 19 patients with motor neuron disorders participated in the study. Consecutive motor unit action potential pairs from extensor digitorum communis (EDC) muscle were recorded from each subject with trigger-delay line mode. Patients with motor neuron disorders (17.7?±?10.8?ms) showed significantly higher mean time variability of interpotential interval value than healthy volunteers (10.3?±?0.1?ms) (p?相似文献   

A model for the variability of interspike intervals during sustained firing of a retinal neuron.

The statistics of the variability of interspike intervals of ganglion cells in the retina of goldfish are modeled by assuming the noise in an integrate-and-fire mechanism is proportional to the reciprocal of a normally distributed variable. This model meets the constraint that the coefficient of variation of the interspike. This does not change when the mean firing rate of the neuron changes. Alternative sources of variability of interspike intervals are discussed.     

The retrograde frequency response of passive dendritic trees constrains the nonlinear firing behaviour of a reduced neuron model

Our goal was to investigate how the propagation of alternating signals (i.e. AC), like action potentials, into the dendrites influenced nonlinear firing behaviour of motor neurons using a systematically reduced neuron model. A recently developed reduced modeling approach using only steady-current (i.e. DC) signaling was analytically expanded to retain features of the frequency-response analysis carried out in multicompartment anatomically reconstructed models. Bifurcation analysis of the extended model showed that the typically overlooked parameter of AC amplitude attenuation was positively correlated with the current threshold for the activation of a plateau potential in the dendrite. Within the multiparameter space map of the reduced model the region demonstrating "fully-bistable" firing was bounded by directional DC attenuation values that were negatively correlated to AC attenuation. Based on these results we conclude that analytically derived reduced models of dendritic trees should be fit on DC and AC signaling, as both are important biophysical parameters governing the nonlinear firing behaviour of motor neurons.