Analytic Expressions for Rate and CV of a Type I Neuron Driven by White Gaussian Noise

We study the one-dimensional normal form of a saddle-node system under the influence of additive gaussian white noise and a static “bias current” input parameter, a model that can be looked upon as the simplest version of a type I neuron with stochastic input. This is in contrast with the numerous studies devoted to the noise-driven leaky integrate-and-fire neuron. We focus on the firing rate and coefficient of variation (CV) of the interspike interval density, for which scaling relations with respect to the input parameter and noise intensity are derived. Quadrature formulas for rate and CV are numerically evaluated and compared to numerical simulations of the system and to various approximation formulas obtained in different limiting cases of the model. We also show that caution must be used to extend these results to the neuron model with multiplicative gaussian white noise. The correspondence between the first passage time statistics for the saddle-node model and the neuron model is obtained only in the Stratonovich interpretation of the stochastic neuron model, while previous results have focused only on the Ito interpretation. The correct Stratonovich interpretation yields CVs that are still relatively high, although smaller than in the Ito interpretation; it also produces certain qualitative differences, especially at larger noise intensities. Our analysis provides useful relations for assessing the distance to threshold and the level of synaptic noise in real type I neurons from their firing statistics. We also briefly discuss the effect of finite boundaries (finite values of threshold and reset) on the firing statistics.

Inwardly Rectifying and Ca2+-Permeable AMPA-Type Glutamate Receptor Channels in Rat Neocortical Neurons

Itazawa, Shun-Ichi, Tadashi Isa, and Seiji Ozawa. Inwardly rectifying and Ca2+-permeable AMPA-type glutamate receptor channels in rat neocortical neurons. J. Neurophysiol. 78: 2592–2605, 1997. Current-voltage ( I-V) relations and Ca2+ permeability of α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA)type glutamate receptor channels were investigated in neurons of rat neocortex by using the whole cell patch-clamp technique in brain slices. To activate AMPA receptor channels, kainate was used as a nondesensitizing agonist. A patch pipette was filled with solution containing 100 μM spermine to maintain the inward rectification of Ca2+-permeable AMPA receptor channels. Three types of responses to kainate were observed: type I response with outwardly rectifying I-V relation, type II response with I-V relation of marked inward rectification, and intermediate response with I-V relation of weaker inward rectification. Neurons with type I, type II and intermediate I-V relations were referred to as type I, type II, and intermediate neurons, respectively. Of a total of 223 recorded cells, 90 (40.4%) were type I, 129 (57.8%) intermediate, and 4 (1.8%) type II neurons. Properties of AMPA receptor channels were examined in the former two types of neurons. The value of PCa:PCs, the ratio of the permeability coefficients of Ca2+ and Cs+, was estimated from the reversal potentials of kainate responses in the outside-out patches bathed in Na+-free solution containing 100 mM Ca2+ according to the constant-field equation. They ranged from 0.05 to 0.10 (0.08 ± 0.02, mean ± SD, n = 8) for type I neurons and from 0.14 to 1.29 (0.60 ± 0.37, n = 11) for the intermediate neurons. There was a close correlation between the inward rectification and the Ca2+ permeability in AMPA receptor channels in these neurons. Intermediate neurons stained with biocytin were nonpyramidal cells with ellipsoidal-shaped somata. Type I neurons had either triangular- or ellipsoidal-shaped somata. Excitatory postsynaptic currents (EPSCs) recorded in both type I and intermediate neurons had 6-cyano-7-nitroquinoxaline-2,3-dione-sensitive fast and d−2-amino-5-phosphonovalerate-sensitiveslow components. The I-V relation of the fast component exhibited inward rectification in the intermediate neuron, whereas that in the type I neuron showed slight outward rectification. The fast component of EPSCs in the intermediate neuron was suppressed more prominently (to 56 ± 15% of the control, n = 12) than that in the type I neuron (to 78 ± 6% of the control, n = 6) by bath application of 1 mM spermine. These results indicate that inwardly rectifying and Ca2+-permeable AMPA receptor channels are expressed in a population of neurons of rat neocortex and are involved in excitatory synaptic transmission.

Cellular studies of peripheral neurons in siphon skin of Aplysia californica

1. To account for the similarity in the kinetics of habituation between the central and peripheral components of siphon withdrawal, we have tested the idea (52) that each centrally located mechanoreceptor sensory neuron sends two branches to siphon motor neurons; one to centrally located siphon motor neurons and a collateral branch that remains in the periphery and innervates the peripheral siphon motor neurons. 2. We have found a group of peripheral siphon motor neurons and tested the connection onto these cells by central mechanoreceptors. In addition, we have defined by various electrophysiological and morphological criteria two general classes of peripheral neurons that lie along the course of the siphon nerve. 3. One class (type I) consists of only a single cell in each animal. This peripheral neuron typically has the largest cell body found lying along the siphon nerve and is the only peripheral nerve cell that appears white when viewed under epi-illumination. The type I neuron often has a highly regular firing pattern, which occurs in the absence of spontaneous synaptic input. The three-dimensional morphology of this neuron suggests a paucity of fine processes, most of which do not arborize and may terminate in the connective tissue sheath. Fine structural observations of the peripheral white cell have revealed the presence of large densecore granules. The peripheral type I neuron is similar in most of its electrophysiological and morphological properties to central neurons postulated to be neurosecretory. The peripheral white cell is, at present, the only peripheral neuron we can identify with certainty as a unique individual. 4. The second class (type II) of peripheral neurons are siphon motor neurons for the peripheral component of the siphon-withdrawal reflex. In contrast to the type I neurons, members of the second class of peripheral neurons possess smaller, more spherical cell bodies that have varying amounts of orange pigmentation and which give rise to a relatively well-developed and arborized dendritic tree. Type II neurons feature an irregular spontaneous firing pattern that is occasionally modulated by a rich spontaneous synaptic input. Peripheral siphon motor neurons have restricted motor fields that produce contraction of the mantle floor and the base of the siphon. Most of the type II neurons were found to be electrically coupled to one another. 5. The peripheral siphon motor neurons resemble the central siphon motor neurons in that they receive a collateral synapse from centrally located mechanoreceptor sensory neurons. This peripheral sensory-to-motor synapse exhibits the same kinetics of decrement as its central counterpart, both of which parallel behavioral habituation. 6. The rich mechanoreceptor input onto the relatively isolated dendritic trees of the peripheral siphon motor neurons provide a uniquely restricted neuropil to study the sensory-to-motor synapse. The peripheral motor neurons may, therefore, be a useful simple preparation for the cellular study of behavioral plasticity.