Single inward rectifier channels in horizontal cells

Resolving molecular contributions of ion channel noise to interspike interval variability through stochastic shielding

Molecular fluctuations can lead to macroscopically observable effects. The random gating of ion channels in the membrane of a nerve cell provides an important example. The contributions of independent noise sources to the variability of action potential timing have not previously been studied at the level of molecular transitions within a conductance-based model ion-state graph. Here we study a stochastic Langevin model for the Hodgkin-Huxley (HH) system based on a detailed representation of the underlying channel state Markov process, the "[Formula: see text]D model" introduced in (Pu and Thomas in Neural Computation 32(10):1775-1835, 2020). We show how to resolve the individual contributions that each transition in the ion channel graph makes to the variance of the interspike interval (ISI). We extend the mean return time (MRT) phase reduction developed in (Cao et al. in SIAM J Appl Math 80(1):422-447, 2020) to the second moment of the return time from an MRT isochron to itself. Because fixed-voltage spike detection triggers do not correspond to MRT isochrons, the inter-phase interval (IPI) variance only approximates the ISI variance. We find the IPI variance and ISI variance agree to within a few percent when both can be computed. Moreover, we prove rigorously, and show numerically, that our expression for the IPI variance is accurate in the small noise (large system size) regime; our theory is exact in the limit of small noise. By selectively including the noise associated with only those few transitions responsible for most of the ISI variance, our analysis extends the stochastic shielding (SS) paradigm (Schmandt and Galán in Phys Rev Lett 109(11):118101, 2012) from the stationary voltage clamp case to the current clamp case. We show numerically that the SS approximation has a high degree of accuracy even for larger, physiologically relevant noise levels. Finally, we demonstrate that the ISI variance is not an unambiguously defined quantity, but depends on the choice of voltage level set as the spike detection threshold. We find a small but significant increase in ISI variance, the higher the spike detection voltage, both for simulated stochastic HH data and for voltage traces recorded in in vitro experiments. In contrast, the IPI variance is invariant with respect to the choice of isochron used as a trigger for counting "spikes."

Voltage- and calcium-gated ion channels of neurons in the vertebrate retina

In this review, we summarize studies investigating the types and distribution of voltage- and calcium-gated ion channels in the different classes of retinal neurons: rods, cones, horizontal cells, bipolar cells, amacrine cells, interplexiform cells, and ganglion cells. We discuss differences among cell subtypes within these major cell classes, as well as differences among species, and consider how different ion channels shape the responses of different neurons. For example, even though second-order bipolar and horizontal cells do not typically generate fast sodium-dependent action potentials, many of these cells nevertheless possess fast sodium currents that can enhance their kinetic response capabilities. Ca2+ channel activity can also shape response kinetics as well as regulating synaptic release. The L-type Ca2+ channel subtype, CaV1.4, expressed in photoreceptor cells exhibits specific properties matching the particular needs of these cells such as limited inactivation which allows sustained channel activity and maintained synaptic release in darkness. The particular properties of K+ and Cl- channels in different retinal neurons shape resting membrane potentials, response kinetics and spiking behavior. A remaining challenge is to characterize the specific distributions of ion channels in the more than 100 individual cell types that have been identified in the retina and to describe how these particular ion channels sculpt neuronal responses to assist in the processing of visual information by the retina.

Stochastic representations of ion channel kinetics and exact stochastic simulation of neuronal dynamics

In this paper we provide two representations for stochastic ion channel kinetics, and compare the performance of exact simulation with a commonly used numerical approximation strategy. The first representation we present is a random time change representation, popularized by Thomas Kurtz, with the second being analogous to a "Gillespie" representation. Exact stochastic algorithms are provided for the different representations, which are preferable to either (a) fixed time step or (b) piecewise constant propensity algorithms, which still appear in the literature. As examples, we provide versions of the exact algorithms for the Morris-Lecar conductance based model, and detail the error induced, both in a weak and a strong sense, by the use of approximate algorithms on this model. We include ready-to-use implementations of the random time change algorithm in both XPP and Matlab. Finally, through the consideration of parametric sensitivity analysis, we show how the representations presented here are useful in the development of further computational methods. The general representations and simulation strategies provided here are known in other parts of the sciences, but less so in the present setting.

Permeation properties and differential expression across the auditory receptor epithelium of an inward rectifier K+ channel cloned from the chick inner ear

The auditory receptor epithelium is an excellent model system for studying the differential expression of ion channel genes. An inward rectifier potassium current is among those which have been measured in only subsets of chick cochlear hair cells. We have cloned and characterized an inward rectifier potassium channel (cIRK1) from the chick cochlear sensory epithelium. cIRK1 functional properties are similar to those of the native channel, and the transcript encoding cIRK1 is limited to the low frequency half of the epithelium. This localization is in agreement with the distribution of the native hair cell current, suggesting that the differential current expression is transcriptionally regulated. The primary structure of cIRK1 is highly homologous to the mouse inward rectifier IRK1. However, we found that cIRK1 exhibited reduced single-channel conductance (17 picosiemens) and lower sensitivity to Ba2+ block (K1/2 = 12 microM). We identified Gln-125 near the putative pore region as being responsible for these differences. Site-directed mutagenesis was used to change Gln-125 to Glu (the residue in IRK1), resulting in a channel with a single-channel conductance of 28 picosiemens and a Ba2+ block of K1/2 = 2 microM. We propose that Gln-125 may form part of the external vestibule of the pore.

Push-pull model of the primate photopic electroretinogram: a role for hyperpolarizing neurons in shaping the b-wave

Existing models of the primate photopic electroretinogram (ERG) attribute the light-adapted b-wave to activity of depolarizing bipolar cells (DBCs), mediated through a release of potassium that is monitored by Müller cells. However, possible ERG contributions from OFF-bipolar cells (HBCs) and horizontal cells (HzCs) have not been explored. We examined the contribution of these hyperpolarizing second-order retinal cells to the photopic ERG of monkey by applying glutamate analogs to suppress photoreceptor transmission selectively to HBC/HzCs vs. DBCs. ERGs of Macaca monkeys were recorded at the cornea before and after intravitreal injection of drugs. Photopic responses were elicited by bright 200-220 ms flashes on a steady background of 3.3 log scotopic troland to suppress rod ERG components. 2-amino-4-phosphonobutyric acid (APB), which blocks DBC light responses, abolished the photopic b-wave and indicated that DBC activity is requisite for photopic b-wave production. However, applying cis-2,3-piperidine dicarboxylic acid (PDA) and kynurenic acid (KYN), to suppress HBCs/HzCs and third-order neurons, revealed a novel ERG response that was entirely positive and was sustained for the duration of the flash. The normally phasic b-wave was subsumed into this new response. Applying n-methyl-dl-aspartate (NMA) did not replicate the PDA+KYN effect, indicating that third-order retinal cells are not involved. This suggests that HBC/HzC activity is critical for shaping the phasic b-wave. Components attributable to depolarizing vs. hyperpolarizing cells were separated by subtracting waveforms after each drug from responses immediately before. This analysis indicated that DBCs and HBC/HzCs each can produce large but opposing field potentials that nearly cancel and that normally leave only the residual phasic b-wave response in the photopic ERG. Latency of the DBC component was 5-9 ms slower than the HBC/HzC component. However, once activated, the DBC component had a steeper slope. This resembles properties known for the two types of cone synapses in lower species, in which the sign-preserving HBC/HzC synapse has faster kinetics but probably lower gain than the slower sign-inverting G-protein coupled DBC synapse. A human patient with "unilateral cone dystrophy" was found to have a positive and sustained ERG that mimicked the monkey ERG after PDA+KYN, indicating that these novel positive photopic responses can occur naturally even without drug application. These results demonstrate that hyperpolarizing second-order neurons are important for the primate photopic ERG.(ABSTRACT TRUNCATED AT 400 WORDS)

Inwardly rectifying whole-cell and single-channel K currents in the murine macrophage cell line J774.1

Inward currents in the murine macrophage-like cell line J774.1 were studied using the whole-cell and cell-attached variations of the patch-clamp technique. When cells were bathed in Na Hanks' (KCl = 4.5 mM, NaCl = 145 mM), and the electrode contained Na-free K Hanks' (KCl = 145 mM) single-channel currents were observed at potentials below -40 mV which showed inward rectification, were K-selective, and were blocked by 2.5 mM Ba in the pipette. Single-channel conductance was 29 pS, and was proportional to the square root of [K]o. Channels manifested complex kinetics, with multiple open and closed states. The steady-state open probability of the channel was voltage dependent, and declined from 0.9 to 0.45 between -40 and -140 mV. When hyperpolarizing voltage pulses were repetitively applied in the cell-attached patch mode, averaged single-channel currents showed inactivation. Inactivation of inwardly rectifying whole-cell current was measured in Na Hanks' and in two types of Na-free Hanks': one with a normal K concentration (4.5 mM) and the other containing 145 mM K. Inactivation was shown to have Na-dependent and Na-independent components. Properties of single-channel current were found to be sufficient to account for the behavior of the macroscopic current, except that single-channel current showed a greater degree of Na-independent inactivation than whole-cell current.

Ion channel expression by white matter glia: I. Type 2 astrocytes and oligodendrocytes

White matter is a compact structure consisting primarily of neuronal axons and glial cells. As in other parts of the nervous system, the function of glial cells in white matter is poorly understood. We have explored the electrophysiological properties of two types of glial cells found predominantly in white matter: type 2 astrocytes and oligodendrocytes. Whole-cells and single-channel patch-clamp techniques were used to study these cell types in postnatal rat optic nerve cultures prepared according to the procedures of Raff et al. (Nature, 303:390-396, 1983b). Type 2 astrocytes in culture exhibit a "neuronal" channel phenotype, expressing at least six distinct ion channel types. With whole-cell recording we observed three inward currents: a voltage-sensitive sodium current qualitatively similar to that found in neurons and both transient and sustained calcium currents. In addition, type 2 astrocytes had two components of outward current: a delayed potassium current which activated at 0 mV and an inactivating calcium-dependent potassium current which activated at -30 mV. Type 2 astrocytes in culture could be induced to fire single regenerative potentials in response to injections of depolarizing current. Single-channel recording demonstrated the presence of an outwardly rectifying chloride channel in both type 2 astrocytes and oligodendrocytes, but this channel could only be observed in excised patches. Oligodendrocytes expressed only one other current: an inwardly rectifying potassium current that is mediated by 30- and 120-pS channels. Because these channels preferentially conduct potassium from outside to inside the cell, and because they are open at the resting potential of the cell, they would be appropriate for removing potassium from the extracellular space; thus it is proposed that oligodendrocytes, besides myelinating axons, play an important role in potassium regulation in white matter. The conductances present in oligodendrocytes suggest a "modulated Boyle and Conway mechanism" of potassium accumulation.