Transduction and transmission in ampullary electroreceptors of catfish

• 1.1. Transduction and transmission in catfish ampullary electroreceptors is mediated by sensory cells bearing microvilli, chemically mediating synapses, nerve terminals and one axon. Although some aspects still remain to be clarified, a number of properties have been found.
• 2.2. Spike generation per seand the modulation of spike frequency by electrical stimuli behave differently with respect to a number of experimental factors.
• 3.3. Stimulus current enters presumably through non-voltage-sensitive or non-specific ion channels.
• 4.4. Fluctuations of the spike frequency may be used as a measure for proper functioning of this sense organ.

     

Functional features of electroreceptors (small pit organs) in the catfish

Characteristics of responses of the small pit organs of the catfishIctalurus nebulosus to the action of electrical stimuli of varied polarity, intensity, and duration were studied. Single fibers of the lateral nerve innervating these organs possessed regular spontaneous activity with a frequency of 35–45/sec or grouped activity, coinciding with the rhythm of the animal's swimming movements. Threshold current densities varied from 10⁻¹¹ to 10⁻¹⁰ A/mm². Electrical stimuli evoked a phasic-tonic response of the receptor. The latent period was 10–50 msec for on-responses and 10–200 msec for off-responses. In the presence of strong electric fields the receptor responded to a cathodal stimulus by excitation, whereas under ordinary experimental conditions an anodal stimulus is excitatory. The properties of small pit organs are compared with the characteristics of other electroreceptors.     

Feedback-induced gain control in stochastic spiking networks

The joint influence of recurrent feedback and noise on gain control in a network of globally coupled spiking leaky integrate-and-fire neurons is studied theoretically and numerically. The context of our work is the origin of divisive versus subtractive gain control, as mixtures of these effects are seen in a variety of experimental systems. We focus on changes in the slope of the mean firing frequency-versus-input bias (f –I) curve when the gain control signal to the cells comes from the cells’ output spikes. Feedback spikes are modeled as alpha functions that produce an additive current in the current balance equation. For generality, they occur after a fixed minimum delay. We show that purely divisive gain control, i.e. changes in the slope of the f –I curve, arises naturally with this additive negative or positive feedback, due to a linearizing actions of feedback. Negative feedback alone lowers the gain, accounting in particular for gain changes in weakly electric fish upon pharmacological opening of the feedback loop as reported by Bastian (J Neurosci 6:553–562, 1986). When negative feedback is sufficiently strong it further causes oscillatory firing patterns which produce irregularities in the f –I curve. Small positive feedback alone increases the gain, but larger amounts cause abrupt jumps to higher firing frequencies. On the other hand, noise alone in open loop linearizes the f –I curve around threshold, and produces mixtures of divisive and subtractive gain control. With both noise and feedback, the combined gain control schemes produce a primarily divisive gain control shift, indicating the robustness of feedback gain control in stochastic networks. Similar results are found when the “input” parameter is the contrast of a time-varying signal rather than the bias current. Theoretical results are derived relating the slope of the f –I curve to feedback gain and noise strength. Good agreement with simulation results are found for inhibitory and excitatory feedback. Finally, divisive feedback is also found for conductance-based feedback (shunting or excitatory) with and without noise. This article is part of a special issue on Neuronal Dynamics of Sensory Coding.     

Receptor Ca current and Ca-gated K current in tonic electroreceptors of the marine catfish Plotosus

The tonic electroreceptors of the marine catfish Plotosus consist of a cluster of ampullae of sensory epithelia, each of which is an isolated receptor unit that is attached to the distant skin with only a long duct. The single-cell layered sensory epithelium has pear-shaped receptor cells interspersed with thin processes of supporting cells. The apical border of the receptor cells is joined to the supporting cells with junctional complexes. Single ampullae were excised and electrically isolated by an air gap. Receptor responses were recorded as epithelial current under voltage clamp, and postsynaptic potentials (PSP) were recorded externally from the afferent nerve in the presence of tetrodotoxin. The ampulla showed a DC potential of -19.2 +/- 6.5 mV (mean +/- SD, n = 18), and an input resistance of 697 +/- 263 K omega (n = 21). Positive voltage steps evoked inward currents with two peaks and a positive dip, associated with PSPs. The apical membrane proved to be inactive. The inward current was ascribed to Ca current, and the positive dip to Ca-gated transient K current, bot in the basal membrane of receptor cells. The Ca channels proved to have ionic selectivity in the order of Sr2+ greater than Ca2+ greater than Ba2+, and presumably they also passed outward current nonselectively. Double-pulse experiments further revealed a current-dependent inactivation for a part of the Ca current.     

Statistical-mechanical measure of stochastic spiking coherence in a population of inhibitory subthreshold neurons

By varying the noise intensity, we study stochastic spiking coherence (i.e., collective coherence between noise-induced neural spikings) in an inhibitory population of subthreshold neurons (which cannot fire spontaneously without noise). This stochastic spiking coherence may be well visualized in the raster plot of neural spikes. For a coherent case, partially-occupied "stripes" (composed of spikes and indicating collective coherence) are formed in the raster plot. This partial occupation occurs due to "stochastic spike skipping" which is well shown in the multi-peaked interspike interval histogram. The main purpose of our work is to quantitatively measure the degree of stochastic spiking coherence seen in the raster plot. We introduce a new spike-based coherence measure M ( s ) by considering the occupation pattern and the pacing pattern of spikes in the stripes. In particular, the pacing degree between spikes is determined in a statistical-mechanical way by quantifying the average contribution of (microscopic) individual spikes to the (macroscopic) ensemble-averaged global potential. This "statistical-mechanical" measure M ( s ) is in contrast to the conventional measures such as the "thermodynamic" order parameter (which concerns the time-averaged fluctuations of the macroscopic global potential), the "microscopic" correlation-based measure (based on the cross-correlation between the microscopic individual potentials), and the measures of precise spike timing (based on the peri-stimulus time histogram). In terms of M ( s ), we quantitatively characterize the stochastic spiking coherence, and find that M ( s ) reflects the degree of collective spiking coherence seen in the raster plot very well. Hence, the "statistical-mechanical" spike-based measure M ( s ) may be used usefully to quantify the degree of stochastic spiking coherence in a statistical-mechanical way.     

Neural dynamics as sampling: a model for stochastic computation in recurrent networks of spiking neurons

The organization of computations in networks of spiking neurons in the brain is still largely unknown, in particular in view of the inherently stochastic features of their firing activity and the experimentally observed trial-to-trial variability of neural systems in the brain. In principle there exists a powerful computational framework for stochastic computations, probabilistic inference by sampling, which can explain a large number of macroscopic experimental data in neuroscience and cognitive science. But it has turned out to be surprisingly difficult to create a link between these abstract models for stochastic computations and more detailed models of the dynamics of networks of spiking neurons. Here we create such a link and show that under some conditions the stochastic firing activity of networks of spiking neurons can be interpreted as probabilistic inference via Markov chain Monte Carlo (MCMC) sampling. Since common methods for MCMC sampling in distributed systems, such as Gibbs sampling, are inconsistent with the dynamics of spiking neurons, we introduce a different approach based on non-reversible Markov chains that is able to reflect inherent temporal processes of spiking neuronal activity through a suitable choice of random variables. We propose a neural network model and show by a rigorous theoretical analysis that its neural activity implements MCMC sampling of a given distribution, both for the case of discrete and continuous time. This provides a step towards closing the gap between abstract functional models of cortical computation and more detailed models of networks of spiking neurons.     

Embedding optimization reveals long-lasting history dependence in neural spiking activity

Information processing can leave distinct footprints on the statistics of neural spiking. For example, efficient coding minimizes the statistical dependencies on the spiking history, while temporal integration of information may require the maintenance of information over different timescales. To investigate these footprints, we developed a novel approach to quantify history dependence within the spiking of a single neuron, using the mutual information between the entire past and current spiking. This measure captures how much past information is necessary to predict current spiking. In contrast, classical time-lagged measures of temporal dependence like the autocorrelation capture how long—potentially redundant—past information can still be read out. Strikingly, we find for model neurons that our method disentangles the strength and timescale of history dependence, whereas the two are mixed in classical approaches. When applying the method to experimental data, which are necessarily of limited size, a reliable estimation of mutual information is only possible for a coarse temporal binning of past spiking, a so-called past embedding. To still account for the vastly different spiking statistics and potentially long history dependence of living neurons, we developed an embedding-optimization approach that does not only vary the number and size, but also an exponential stretching of past bins. For extra-cellular spike recordings, we found that the strength and timescale of history dependence indeed can vary independently across experimental preparations. While hippocampus indicated strong and long history dependence, in visual cortex it was weak and short, while in vitro the history dependence was strong but short. This work enables an information-theoretic characterization of history dependence in recorded spike trains, which captures a footprint of information processing that is beyond time-lagged measures of temporal dependence. To facilitate the application of the method, we provide practical guidelines and a toolbox.     

Two Ca current components of the receptor current in the electroreceptors of the marine catfish Plotosus

In the isolated sensory epithelium of the Plotosus electroreceptor, the receptor current has been dissected into inward Ca current, ICa, and superimposed outward transient of Ca-gated K current, IK(Ca). In control saline (170 mM/liter Na), with IK(Ca) abolished by K blockers, ICa declined in two successive exponential phases with voltage-dependent time constants. Double-pulse experiments revealed that the test ICa was partially depressed by prepulses, maximally near voltage levels for the control ICa maximum, which suggests current-dependent inactivation. In low Na saline (80 mM/liter), ICa declined in a single phase with time constants similar to those of the slower phase in control saline. The test ICa was then unaffected by prepulses. The implied presence of two Ca current components, the fast and slow ICa's, were further examined. In control saline, the PSP externally recorded from the afferent nerve showed a fast peak and a slow tonic phase. The double-pulse experiments revealed that IK(Ca) and the peak PSP were similarly depressed, i.e., secondarily to inactivation of the peak current. The steady inward current, however, was unaffected by prolonged prepulses that were stepped to 0 mV, the in situ DC level. Therefore, the fast ICa seems to initiate IK(Ca) and phasic release of transmitter, which serves for phasic receptor responses. The slow ICa may provide persistent active current, which has been shown to maintain tonic receptor operation.     

Learning in spiking neural networks by reinforcement of stochastic synaptic transmission

It is well-known that chemical synaptic transmission is an unreliable process, but the function of such unreliability remains unclear. Here I consider the hypothesis that the randomness of synaptic transmission is harnessed by the brain for learning, in analogy to the way that genetic mutation is utilized by Darwinian evolution. This is possible if synapses are "hedonistic," responding to a global reward signal by increasing their probabilities of vesicle release or failure, depending on which action immediately preceded reward. Hedonistic synapses learn by computing a stochastic approximation to the gradient of the average reward. They are compatible with synaptic dynamics such as short-term facilitation and depression and with the intricacies of dendritic integration and action potential generation. A network of hedonistic synapses can be trained to perform a desired computation by administering reward appropriately, as illustrated here through numerical simulations of integrate-and-fire model neurons.     

Effect of channel block on the spiking activity of excitable membranes in a stochastic Hodgkin-Huxley model

The influence of intrinsic channel noise on the spontaneous spiking activity of poisoned excitable membrane patches is studied by use of a stochastic generalization of the Hodgkin-Huxley model. Internal noise stemming from the stochastic dynamics of individual ion channels is known to affect the collective properties of the whole ion channel cluster. For example, there exists an optimal size of the membrane patch for which the internal noise alone causes a regular spontaneous generation of action potentials. In addition to varying the size of ion channel clusters, living organisms may adapt the densities of ion channels in order to optimally regulate the spontaneous spiking activity. The influence of a channel block on the excitability of a membrane patch of a certain size is twofold: first, a variation of ion channel densities primarily yields a change of the conductance level; second, a down-regulation of working ion channels always increases the channel noise. While the former effect dominates in the case of sodium channel block resulting in a reduced spiking activity, the latter enhances the generation of spontaneous action potentials in the case of a tailored potassium channel blocking. Moreover, by blocking some portion of either potassium or sodium ion channels, it is possible to either increase or decrease the regularity of the spike train.     

Probabilistic inference in general graphical models through sampling in stochastic networks of spiking neurons

An important open problem of computational neuroscience is the generic organization of computations in networks of neurons in the brain. We show here through rigorous theoretical analysis that inherent stochastic features of spiking neurons, in combination with simple nonlinear computational operations in specific network motifs and dendritic arbors, enable networks of spiking neurons to carry out probabilistic inference through sampling in general graphical models. In particular, it enables them to carry out probabilistic inference in Bayesian networks with converging arrows ("explaining away") and with undirected loops, that occur in many real-world tasks. Ubiquitous stochastic features of networks of spiking neurons, such as trial-to-trial variability and spontaneous activity, are necessary ingredients of the underlying computational organization. We demonstrate through computer simulations that this approach can be scaled up to neural emulations of probabilistic inference in fairly large graphical models, yielding some of the most complex computations that have been carried out so far in networks of spiking neurons.     

An alternative stochastic framework for estimating pure measures of fertility

A stochastic fertility model is developed that incorporates a state of "viable pregnancy" within parity i. This model is used as a framework to derive formulas expressing relationships between various central rates and probabilities within parity i. Specifically, formulas are derived to relate the total fertility rate with the parity progression probability, a pregnancy rate with a pregnancy progression probability, and a direct fertility rate with a direct parity progression probability.     

Emergence of stochastic resonance in a two-compartment hippocampal pyramidal neuron model

Journal of Computational Neuroscience - In vitro studies have shown that hippocampal pyramidal neurons employ a mechanism similar to stochastic resonance (SR) to enhance the detection and...     

Phylogeography of the catfish Hatcheria macraei reveals a negligible role of drainage divides in structuring populations

Southern South America provides a set of unusual geographic features that make it particularly interesting for studying phylogeography. The Andes Mountains run along a north-to-south axis and act as a barrier to gene flow for much of the biota of this region, with southern portions experiencing extensive historical glaciation. Geological data reveal a series of drainage reversals, shifting from Pacific Ocean outlets to Atlantic Ocean outlets because of glacier formation that dammed and reversed rivers. Once glaciers melted around 13 000 years ago, drainages returned to the Pacific Ocean. This geologic history predicts that aquatic organisms in Pacific rivers should have their closest relationships to their counterparts in Atlantic rivers immediately to their east. We tested this prediction in the trichomycterid catfish Hatcheria macraei from 38 locations using the mitochondrial cytochrome b gene. Our results show that most populations found in Pacific rivers were closely related to fish found in the adjacent Atlantic draining Río Chubut. Surprisingly, one documented drainage reversal (from Río Deseado into Río Baker) did not result in movement of H. macraei. Overall, we found the lowest levels of genetic structure between most Pacific rivers that are adjacent to the Atlantic draining Río Chubut. We also found low levels of population structuring among three of four contemporary river basins that drain to the Atlantic Ocean. Our findings suggest that drainage basin boundaries have historically not played an important long-term role in structuring between nine of 11 drainages, an unusual finding in freshwater biogeography.     

A stochastic population approach to the problem of stable recruitment hierarchies in spiking neural networks

Synchrony-driven recruitment learning addresses the question of how arbitrary concepts, represented by synchronously active ensembles, may be acquired within a randomly connected static graph of neuron-like elements. Recruitment learning in hierarchies is an inherently unstable process. This paper presents conditions on parameters for a feedforward network to ensure stable recruitment hierarchies. The parameter analysis is conducted by using a stochastic population approach to model a spiking neural network. The resulting network converges to activate a desired number of units at each stage of the hierarchy. The original recruitment method is modified first by increasing feedforward connection density for ensuring sufficient activation, then by incorporating temporally distributed feedforward delays for separating inputs temporally, and finally by limiting excess activation via lateral inhibition. The task of activating a desired number of units from a population is performed similarly to a temporal k-winners-take-all network.     

An extended model for a spiking neuron class

This paper proposes an extension to the model of a spiking neuron for information processing in artificial neural networks, developing a new approach for the dynamic threshold of the integrate-and-fire neuron. This new approach invokes characteristics of biological neurons such as the behavior of chemical synapses and the receptor field. We demonstrate how such a digital model of spiking neurons can solve complex nonlinear classification with a single neuron, performing experiments for the classical XOR problem. Compared with rate-coded networks and the classical integrate-and-fire model, the trained network demonstrated faster information processing, requiring fewer neurons and shorter learning periods. The extended model validates all the logic functions of biological neurons when such functions are necessary for the proper flow of binary codes through a neural network.