Afferent modulation of dopamine neuron firing patterns

In recent studies examining the modulation of dopamine (DA) cell firing patterns, particular emphasis has been placed on excitatory afferents from the prefrontal cortex and the subthalamic nucleus. A number of inconsistencies in recently published reports, however, do not support the contention that tonic activation of NMDA receptors is the sole determinate of DA neuronal firing patterns. The results of work on the basic mechanism of DA firing and the action of apamin suggest that excitatory projections to DA neurons from cholinergic and glutamatergic neurons in the tegmental pedunculopontine nucleus, and/or inhibitory GABAergic projections, are also involved in modulating DA neuron firing behavior.     

Real-time decoding of dopamine concentration changes in the caudate-putamen during tonic and phasic firing

The fundamental process that underlies volume transmission in the brain is the extracellular diffusion of neurotransmitters from release sites to distal target cells. Dopaminergic neurons display a range of activity states, from low-frequency tonic firing to bursts of high-frequency action potentials (phasic firing). However, it is not clear how this activity affects volume transmission on a subsecond time scale. To evaluate this, we developed a finite-difference model that predicts the lifetime and diffusion of dopamine in brain tissue. We first used this model to decode in vivo amperometric measurements of electrically evoked dopamine, and obtained rate constants for release and uptake as well as the extent of diffusion. Accurate predictions were made under a variety of conditions including different regions, different stimulation parameters and with uptake inhibited. Second, we used the decoded rate constants to predict how heterogeneity of dopamine release and uptake sites would affect dopamine concentration fluctuations during different activity states in the absence of an electrode. These simulations show that synchronous phasic firing can produce spatially and temporally heterogeneous concentration profiles whereas asynchronous tonic firing elicits uniform, steady-state dopamine concentrations.     

Nonlinear sequence-dependent structure of nigral dopamine neuron interspike interval firing patterns.

Firing patterns of 15 dopamine neurons in the rat substantia nigra were studied. These cells alternated between two firing modes, single-spike and bursting, which interwove to produce irregular, aperiodic interspike interval (ISI) patterns. When examined by linear autocorrelation analysis, these patterns appeared to reflect a primarily stochastic or random process. However, dynamical analysis revealed that the sequential behavior of a majority of these cells expressed "higher-dimensional" nonlinear deterministic structure. Dimensionality refers to the number of degrees of freedom or complexity of a time series. Bursting was statistically associated with some aspects of nonlinear ISI sequence dependence. Controlling for the effects of nonstationarity substantially increased overall predictability of ISI sequences. We hypothesize that the nonlinear deterministic structure of ISI firing patterns reflects the neuron's response to coordinated synaptic inputs emerging from neural circuit interactions.     

A10 dopamine neurons: role of autoreceptors in determining firing rate and sensitivity to dopamine agonists

The present experiments investigated the relationship between the spontaneous basal firing rate of A10 dopamine (DA) neurons and their sensitivity to the rate-suppressant effects of intravenously administered apomorphine (APO) and d-amphetamine (AMP) as well as microiontophoretically ejected DA. The results indicated highly significant inverse relationships between basal neuronal activity and sensitivity to DA and DA agonists, i.e. the faster the spontaneous rate of an A10 DA neuron, the less sensitive that cell was to agonist-induced suppression. This relationship was not found for the rate suppressant effects of iontophoretic gamma-aminobutyric acid. There were no significant differences between the effects of iontophoretic DA on pre-glutamate and glutamate-driven activity of the same A10 DA neurons indicating that faster firing rates, per se, did not determine the sensitivity of these cells to DA agonists. Rather, these results suggest that both spontaneous activity and sensitivity to DA agonists may be determined by the density (or sensitivity) of DA autoreceptors on A10 DA neurons. This hypothesis was supported by the finding that antidromically identified mesocortical DA neurons, which were significantly less responsive to DA, APO and AMP exhibited significantly faster firing rates than other A10 DA neurons. Thus, this subpopulation of A10 DA neurons is primarily made up of cells with low autoreceptor density (or sensitivity).     

Pacemaker neuron model with plastic firing rate: Entrainment and learning ranges

The model proposed puts forward a hypothesis on how some pacemaker neurons learn to fire at the frequency imposed by the stimulation. It builds on previous developments in two separate research fields: neural modelling and neuronal learning theory, providing an electrophysiological model of neuronal learning. Simulation results are shown to be in qualitative agreement with experimental data reported for Aplysia and crayfish. The analytical study of the PRC reveals that the postulated learning rule tends to favour the emergence of simple entrainment ratios. The model is worth consideration not only because of its autonomous functioning, described in this paper, but also because it constitutes a suitable building-block for a net aimed at reproducing the temporal-pattern learning phenomena shown by some neural structures.     

Regulation of dopaminergic neuron firing by heterogeneous dopamine autoreceptors in the substantia nigra pars compacta

Dopamine (DA) receptors generate many cellular signals and play various roles in locomotion, motivation, hormone production, and drug abuse. According to the location and expression types of the receptors in the brain, DA signals act in either stimulatory or inhibitory manners. Although DA autoreceptors in the substantia nigra pars compacta are known to regulate firing activity, the exact expression patterns and roles of DA autoreceptor types on the firing activity are highly debated. Therefore, we performed individual correlation studies between firing activity and receptor expression patterns using acutely isolated rat substantia nigra pars compacta DA neurons. When we performed single-cell RT-PCR experiments, D(1), D(2)S, D(2)L, D(3), and D(5) receptor mRNA were heterogeneously expressed in the order of D(2)L > D(2)S > D(3) > D(5) > D(1). Stimulation of D(2) receptors with quinpirole suppressed spontaneous firing similarly among all neurons expressing mRNA solely for D(2)S, D(2)L, or D(3) receptors. However, quinpirole most strongly suppressed spontaneous firing in the neurons expressing mRNA for both D(2) and D(3) receptors. These data suggest that D(2) S, D(2)L, and D(3) receptors are able to equally suppress firing activity, but that D(2) and D(3) receptors synergistically suppress firing. This diversity in DA autoreceptors could explain the various actions of DA in the brain.     

A note on the diffusion approximation for single neuron firing problems

Summary This paper presents a well-known stochastic model used to describe the firing or discharge pattern of a single neuron in terms of various input processes, and shows how the potential level of the neuron can be given by means of a diffusion equation approximation. There is a discussion of the adequacy of this approximation, and the paper concludes with a brief discussion of first passage time problems.Supported in part by a grant from the Alfred P. Sloan Foundation to the Committee on Mathematical Biology and by a grant of the Statistical Branch, Office of Naval Research to the Department of Statistics, University of Chicago.     

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.     

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.     

NMDA receptors in dopaminergic neurons are crucial for habit learning

Dopamine is crucial for habit learning. Activities of midbrain dopaminergic neurons are regulated by the cortical and subcortical signals among which glutamatergic afferents provide excitatory inputs. Cognitive implications of glutamatergic afferents in regulating and engaging dopamine signals during habit learning, however, remain unclear. Here, we show that mice with dopaminergic neuron-specific NMDAR1 deletion are impaired in a variety of habit-learning tasks, while normal in some other dopamine-modulated functions such as locomotor activities, goal-directed learning, and spatial reference memories. In vivo neural recording revealed that dopaminergic neurons in these mutant mice could still develop the cue-reward association responses; however, their conditioned response robustness was drastically blunted. Our results suggest that integration of glutamatergic inputs to DA neurons by NMDA receptors, likely by regulating associative activity patterns, is a crucial part of the cellular mechanism underpinning habit learning.     

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.     

Ionic mechanisms underlying tonic and phasic firing behaviors in retinal ganglion cells

In the retina, the firing behaviors that ganglion cells exhibit when exposed to light stimuli are very important due to the significant roles they play in encoding the visual information. However, the detailed mechanisms, especially the intrinsic properties that generate and modulate these firing behaviors is not completely clear yet. In this study, 2 typical firing behaviors—i.e., tonic and phasic activities, which are widely observed in retinal ganglion cells (RGCs)—are investigated. A modified computational model was developed to explore the possible ionic mechanisms that underlie the generation of these 2 firing patterns. Computational results indicate that the generation of tonic and phasic activities may be attributed to the collective actions of 2 kinds of adaptation currents, i.e., an inactivating sodium current and a delayed-rectifier potassium current. The concentration of magnesium ions has crucial but differential effects in the modulation of tonic and phasic firings, when the model neuron is driven by N-methyl-D-aspartate (NMDA) -type synaptic input instead of constant current injections. The proposed model has robust features that account for the ionic mechanisms underlying the tonic and phasic firing behaviors, and it may also be used as a good candidate for modeling some other firing patterns in RGCs.     

Ionic mechanisms underlying tonic and phasic firing behaviors in retinal ganglion cells: A model study

In the retina, the firing behaviors that ganglion cells exhibit when exposed to light stimuli are very important due to the significant roles they play in encoding the visual information. However, the detailed mechanisms, especially the intrinsic properties that generate and modulate these firing behaviors is not completely clear yet. In this study, 2 typical firing behaviors—i.e., tonic and phasic activities, which are widely observed in retinal ganglion cells (RGCs)—are investigated. A modified computational model was developed to explore the possible ionic mechanisms that underlie the generation of these 2 firing patterns. Computational results indicate that the generation of tonic and phasic activities may be attributed to the collective actions of 2 kinds of adaptation currents, i.e., an inactivating sodium current and a delayed-rectifier potassium current. The concentration of magnesium ions has crucial but differential effects in the modulation of tonic and phasic firings, when the model neuron is driven by N-methyl-D-aspartate (NMDA) -type synaptic input instead of constant current injections. The proposed model has robust features that account for the ionic mechanisms underlying the tonic and phasic firing behaviors, and it may also be used as a good candidate for modeling some other firing patterns in RGCs.     

On the evaluation of firing densities for periodically driven neuron models

The leaky integrate-and-fire model for neuronal spiking events driven by a periodic stimulus is studied by using the Fokker-Planck formulation. To this purpose, an essential use is made of the asymptotic behavior of the first-passage-time probability density function of a time homogeneous diffusion process through an asymptotically periodic threshold. Numerical comparisons with some recently published results derived by a different approach are performed. Use of a new asymptotic approximation is then made in order to design a numerical algorithm of predictor-corrector type to solve the integral equation in the unknown first-passage-time probability density function. Such algorithm, characterized by a reduced (linear) computation time, is seen to provide a high computation accuracy. Finally, it is shown that such an approach yields excellent approximations to the firing probability density function for a wide range of parameters, including the case of high stimulus frequencies.     

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.