Membrane voltage changes in a compartmental chain model of a neurone

A mathematical model of the neurone has been developed using the method of subdivision of the neurone into a number of equivalent circuit compartments. Compartmental characteristics have been investigated by calculating the shape indices of the output produced in response to a given somatic input conductance change. A generalised form of compartmental chain has been chosen to allow calculation of the shape indices produced by a variety of geometrical configurations including the straight and tapering chain forms. Equations have been deduced from the computations made on a CDC 6600 computer relating the peak amplitude of the output response to the compartmental diameter for both the straight and tapering chain forms. The effect of variation in the location of the input conductance injection site has also been related to the peak amplitude of the somatic response. The optimum characteristics of the input conductance pulse shape have been computed initially using a rectangular pulse and later the more physiologically relevant double exponential shape. The effect of alteration in the end compartmental terminal impedances over the range from open to short circuit conditions was also calculated. The establishment of optimum single compartmental chain criteria allows the future investigation of multiple chain and pyramidal cell configurations.     

在脉冲污染环境中具有阶段结构的捕食食饵Gompertz模型的动力学性质

研究了在脉冲污染环境中,捕食者具有阶段结构的捕食食饵Gompertz模型的动力学性质,获得了捕食者灭绝周期解全局吸引和系统持续生存的条件.     

The effect of dendritic voltage-gated conductances on the neuronal impedance: a quantitative model

Neuronal impedance characterizes the magnitude and timing of the subthreshold response of a neuron to oscillatory input at a given frequency. It is known to be influenced by both the morphology of the neuron and the presence of voltage-gated conductances in the cell membrane. Most existing theoretical accounts of neuronal impedance considered the effects of voltage-gated conductances but neglected the spatial extent of the cell, while others examined spatially extended dendrites with a passive or spatially uniform quasi-active membrane. We derived an explicit mathematical expression for the somatic input impedance of a model neuron consisting of a somatic compartment coupled to an infinite dendritic cable which contained voltage-gated conductances, in the more general case of non-uniform dendritic membrane potential. The validity and generality of this model was verified through computer simulations of various model neurons. The analytical model was then applied to the analysis of experimental data from real CA1 pyramidal neurons. The model confirmed that the biophysical properties and predominantly dendritic localization of the hyperpolarization-activated cation current I (h) were important determinants of the impedance profile, but also predicted a significant contribution from a depolarization-activated fast inward current. Our calculations also implicated the interaction of I (h) with amplifying currents as the main factor governing the shape of the impedance-frequency profile in two types of hippocampal interneuron. Our results provide not only a theoretical advance in our understanding of the frequency-dependent behavior of nerve cells, but also a practical tool for the identification of candidate mechanisms that determine neuronal response properties.     

Identification of the cable parameters in the somatic shunt model

 We show that the first five moments of the soma potential and soma current uniquely and stably determine the soma conductance and capacitance and the dendritic electrotonic length, conductance, and capacitance in the so-called somatic shunt model of the passive behavior of a neuron. We test our resulting input admittance algorithm on synthetic data and demonstrate the regularizing effect of knowledge of the ratio of soma to dendrite surface areas. Received: 9 June 1999 / Accepted in revised form: 24 January 2000     

Response of a pacemaker neuron model to stochastic pulse trains

 We investigated the response of a pacemaker neuron model to trains of inhibitory stochastic impulsive perturbations. The model captures the essential aspect of the dynamics of pacemaker neurons. Especially, the model reproduces linearization by stochastic pulse trains, that is, the disappearance of the paradoxical segments in which the output firing rate of pacemaker neurons increases with inhibition rate, as the coefficient of variation of the input pulse train increases. To study the response of the model to stochastic pulse trains, we use a Markov operator governing the phase transition. We show how linearization occurs based on the spectral analysis of the Markov operator. Moreover, using Lyapunov exponents, we show that variable inputs evoke reliable firing, even in situations where periodic stimulation with the same mean rate does not. Received: 30 April 2001 / Accepted in revised form: 19 September 2001     

Transient response in a somatic shunt cable model for synaptic input activated at the terminal

Rall's neuron model is extended by including a non-uniform time constant together with synaptic input modeled as a square step of conductance. An analytic solution (in series form) for the electrotonic potential is obtained. The major conclusion reached is that a lower somatic time constant attenuates the amplitude of the potential at the soma, brought about by the activation of a synapse located at the distal end of the dendritic cable in an initially polarized neuron.     

Voltage clamping with a single microelectrode.

A technique is described which allows neurons to be voltage clamped with a single microelectrode, and the advantages of this circuit with respect to conventional bridge techniques are discussed. In this circuit, the single microelectrode is rapidly switched from a current passing to a recording mode. The circuitry consists of: (1) an electronic switch; (2) a high impedance, ultralow input capacity amplifier; (3) a sample-and-hold module; (4) conventional voltage clamping circuitry. The closed electronic switch allows current to flow through the electrode. The switch then opens, and the electrode is in a recording mode. The low input capacity of the preamplifier allows the artifact from the current pulse to rapidly abate, after which time the circuit samples the membrane potential. This cycle is repeated at rates up to 10 kHz. The voltage clamping amplifier senses the output of the sample-and-hold module and adjusts the current pulse amplitude to maintain the desired membrane potential. The system was evaluated in Aplysia neurons by inserting two microelectrodes into a cell. One electrode was used to clamp the cell and the other to independently monitor membrane potential at a remote location in the soma.     

Voltage clamping with a single microelectrode

A technique is described which allows neurons to be voltage clamped with a single microelectrode, and the advantages of this circuit with respect to conventional bridge techniques are discussed. In this circuit, the single micro electrode is rapidly switched from a current passing to a recording mode. The circuitry consists of: (1) an electronic switch; (2) a high impedance, ultralow input capacity amplifier; (3) a sample-and-hold module; (4) conventional voltage clamping circuitry. The closed electronic switch allows current to flow through the electrode. The switch then opens, and the electrode is in a recording mode. The low input capacity of the preamplifier allows the artifact from the current pulse to rapidly abate, after which time the circuit samples the membrane potential. This cycle is repeated at rates up to 10 kHz. The voltage clamping amplifier senses the output of the sample-and-hold module and adjusts the current pulse amplitude to maintain the desired membrane potential. The system was evaluated in Aplysia neurons by inserting two microelectrodes into a cell. One electrode was used to clamp the cell and the other to independently monitor membrane potential at a remote location in the soma.     

How to record a million synaptic weights in a hippocampal slice

A key step toward understanding the function of a brain circuit is to find its wiring diagram. New methods for optical stimulation and optical recording of neurons make it possible to map circuit connectivity on a very large scale. However, single synapses produce small responses that are difficult to measure on a large scale. Here I analyze how single synaptic responses may be detectable using relatively coarse readouts such as optical recording of somatic calcium. I model a network consisting of 10,000 input axons and 100 CA1 pyramidal neurons, each represented using 19 compartments with voltage-gated channels and calcium dynamics. As single synaptic inputs cannot produce a measurable somatic calcium response, I stimulate many inputs as a baseline to elicit somatic action potentials leading to a strong calcium signal. I compare statistics of responses with or without a single axonal input riding on this baseline. Through simulations I show that a single additional input shifts the distribution of the number of output action potentials. Stochastic resonance due to probabilistic synaptic release makes this shift easier to detect. With ~80 stimulus repetitions this approach can resolve up to 35% of individual activated synapses even in the presence of 20% recording noise. While the technique is applicable using conventional electrical stimulation and extracellular recording, optical methods promise much greater scaling, since the number of synapses scales as the product of the number of inputs and outputs. I extrapolate from current high-speed optical stimulation and recording methods, and show that this approach may scale up to the order of a million synapses in a single two-hour slice-recording experiment.     

Noninvasive cardiac output estimation: a preliminary study

 The availability of a simple-to-use, automatic measurement system for noninvasive flow estimation is imperative, given the clinical demand for an acceptable noninvasive procedure rather than the standard invasive procedure of thermodilution. A method for calculating cardiac output from noninvasively derived pressure pulses has been developed, and the results of a preliminary evaluation study on post-cardiac surgery patients for whom invasive flow measures were readily available for comparison are provided in this report. The proposed method relies on fast Fourier transform (FFT) analysis of pulses measured externally at the carotid and femoral pressure points. A transfer function of the aorta is computed from digitally filtered pulse measurements, and a tapered model of the aorta is parametrically adapted using a simplex optimization algorithm so that its transfer function matches that derived experimentally. An aortic input impedance term is obtained from the optimized model and utilized along with the carotid pulse (analogous to input voltage) to compute aortic flow. In addition to its automation, attractive features of this method include the requirement for relatively few pulses for analysis as well as considerable resistance to noise artifact. For 59 data records collected from 54 post-cardiac surgery patients, the average flow measurements computed over several pulses compare well with the standard, invasive method of thermodilution. Preliminary results also indicate a strong potential for tracking changes in cardiac output over time, and invite further use of the method in monitoring hemodynamically unstable patients. Received: 18 February 1997 / Accepted in revised form: 12 May 1997     

Synaptic depression increases the selectivity of a neuron to its preferred pattern and binarizes the neural code

The preferred pattern of a neuron is defined here by the set of features detected by its excitatory inputs. It is shown that the Leaky integrate-and-fire (LIF) model of a neuron has a poor selectivity to its preferred pattern. Its response is determined by the total current injected by input spike trains. Thus, a few inputs with a high activity (an incomplete pattern) can elicit the same response as many inputs (a complete pattern) with a weak activity. A theoretical model of depressing synapse with linear recovery is proposed which eliminates this problem. Using this model, the time-averaged current injected in the soma by a spike train becomes independent on its frequency. The neural code thus becomes binary, and the response strength of the target neuron depends only on the number of active inputs. Simulations show that a biological model of strong synaptic depression has effects similar to those of the ideal linear model. The best selectivity is obtained with long somatic decay time constants (>50 ms) and with depression recovery time constants larger or equal to the somatic decay time constant. Thus, by eliminating information carried in the input firing rate, a neuron can improve its pattern recognition performance.     

The biophysical properties of spines as a basis for their electrical function: a comment on Kawato & Tsukahara (1983)

In a theoretical study of the passive cable properties of dendritic spines Kawato & Tsukahara (1983) claim to have proved that "the dendritic spine has no significant electrical function" (from their discussion). However, Kawato & Tsukahara restrict their analysis to current inputs to spines. Since the dimensions of spines are very small, their input resistance is expected to be very large and the synaptic input to spines has to be modeled as conductance change. Under this assumption, spines show interesting (non-linear) electrical properties: i) the somatic potential induced by an excitatory synapse on a spine may depend strongly on the shape of the spine and ii) the effect of inhibition might be confined to the spine.     

Transient Response in a Dendritic Neuron Model for Current Injected at One Branch

Mathematical expressions are obtained for the response function corresponding to an instantaneous pulse of current injected to a single dendritic branch in a branched dendritic neuron model. The theoretical model assumes passive membrane properties and the equivalent cylinder constraint on branch diameters. The response function when used in a convolution formula enables one to compute the voltage transient at any specified point in the dendritic tree for an arbitrary current injection at a given input location. A particular numerical example, for a brief current injection at a branch terminal, illustrates the attenuation and delay characteristics of the depolarization peak as it spreads throughout the neuron model. In contrast to the severe attenuation of voltage transients from branch input sites to the soma, the fraction of total input charge actually delivered to the soma and other trees is calculated to be about one-half. This fraction is independent of the input time course. Other numerical examples, which compare a branch terminal input site with a soma input site, demonstrate that, for a given transient current injection, the peak depolarization is not proportional to the input resistance at the injection site and, for a given synaptic conductance transient, the effective synaptic driving potential can be significantly reduced, resulting in less synaptic current flow and charge, for a branch input site. Also, for the synaptic case, the two inputs are compared on the basis of the excitatory post-synaptic potential (EPSP) seen at the soma and the total charge delivered to the soma.     

The Subcellular Distribution of T-Type Ca2+ Channels in Interneurons of the Lateral Geniculate Nucleus

Inhibitory interneurons (INs) in the lateral geniculate nucleus (LGN) provide both axonal and dendritic GABA output to thalamocortical relay cells (TCs). Distal parts of the IN dendrites often enter into complex arrangements known as triadic synapses, where the IN dendrite plays a dual role as postsynaptic to retinal input and presynaptic to TC dendrites. Dendritic GABA release can be triggered by retinal input, in a highly localized process that is functionally isolated from the soma, but can also be triggered by somatically elicited Ca²⁺-spikes and possibly by backpropagating action potentials. Ca²⁺-spikes in INs are predominantly mediated by T-type Ca²⁺-channels (T-channels). Due to the complex nature of the dendritic signalling, the function of the IN is likely to depend critically on how T-channels are distributed over the somatodendritic membrane (T-distribution). To study the relationship between the T-distribution and several IN response properties, we here run a series of simulations where we vary the T-distribution in a multicompartmental IN model with a realistic morphology. We find that the somatic response to somatic current injection is facilitated by a high T-channel density in the soma-region. Conversely, a high T-channel density in the distal dendritic region is found to facilitate dendritic signalling in both the outward direction (increases the response in distal dendrites to somatic input) and the inward direction (the soma responds stronger to distal synaptic input). The real T-distribution is likely to reflect a compromise between several neural functions, involving somatic response patterns and dendritic signalling.     

Setting the pace: new insights into central pattern generator interactions in box jellyfish swimming

Central Pattern Generators (CPGs) produce rhythmic behaviour across all animal phyla. Cnidarians, which have a radially symmetric nervous system and pacemaker centres in multiples of four, provide an interesting comparison to bilaterian animals for studying the coordination between CPGs. The box jellyfish Tripedalia cystophora is remarkable among cnidarians due to its most elaborate visual system. Together with their ability to actively swim and steer, they use their visual system for multiple types of behaviour. The four swim CPGs are directly regulated by visual input. In this study, we addressed the question of how the four pacemaker centres of this radial symmetric cnidarian interact. We based our investigation on high speed camera observations of the timing of swim pulses of tethered animals (Tripedalia cystophora) with one or four rhopalia, under different simple light regimes. Additionally, we developed a numerical model of pacemaker interactions based on the inter pulse interval distribution of animals with one rhopalium. We showed that the model with fully resetting coupling and hyperpolarization of the pacemaker potential below baseline fitted the experimental data best. Moreover, the model of four swim pacemakers alone underscored the proportion of long inter pulse intervals (IPIs) considerably. Both in terms of the long IPIs as well as the overall swim pulse distribution, the simulation of two CPGs provided a better fit than that of four. We therefore suggest additional sources of pacemaker control than just visual input. We provide guidelines for future research on the physiological linkage of the cubozoan CPGs and show the insight from bilaterian CPG research, which show that pacemakers have to be studied in their bodily and nervous environment to capture all their functional features, are also manifest in cnidarians.     

A Statistical Model for In Vivo Neuronal Dynamics

Single neuron models have a long tradition in computational neuroscience. Detailed biophysical models such as the Hodgkin-Huxley model as well as simplified neuron models such as the class of integrate-and-fire models relate the input current to the membrane potential of the neuron. Those types of models have been extensively fitted to in vitro data where the input current is controlled. Those models are however of little use when it comes to characterize intracellular in vivo recordings since the input to the neuron is not known. Here we propose a novel single neuron model that characterizes the statistical properties of in vivo recordings. More specifically, we propose a stochastic process where the subthreshold membrane potential follows a Gaussian process and the spike emission intensity depends nonlinearly on the membrane potential as well as the spiking history. We first show that the model has a rich dynamical repertoire since it can capture arbitrary subthreshold autocovariance functions, firing-rate adaptations as well as arbitrary shapes of the action potential. We then show that this model can be efficiently fitted to data without overfitting. We finally show that this model can be used to characterize and therefore precisely compare various intracellular in vivo recordings from different animals and experimental conditions.     

Syntheses of spinal cord field potentials in the terrapin

A compartmental model of a terrapin motoneuron has been set up to compute membrane potential variations associated with synaptic input at different locations or with antidromic invasion. Membrane potential distributions obtained in that way were used to compute field potentials by means of a volume conduction formalism. The model was used to simulated field potentials measured in the spinal cord in response to stimulation of a muscle nerve with the intention to discriminate between different activation hypothesis for the generation of the spinal cord potential. Extracellular potentials calculated with an excitatory input distributed over the whole dorsal dendritic tree were found to give better reconstruction when compared with excitation restricted to the distal part of the dorsal dendrites, or with somatic inhibition.     

Electrochemical protoplast fusion in citrus

We report here the development of a novel protoplast fusion method for citrus somatic hybridization. This new procedure, which we have named electrochemical protoplast fusion, is based on chemically induced protoplast aggregation, using a low concentration of polyethylene glycol, and DC pulse-promoted membrane fusion. Based on the results of nucleus and mitochondria molecular analyses, we were successful in using this method to regenerate both symmetric somatic hybrids and cybrids. Various parameters, including pulse intensity, pulse length, and composition of the fusion media, were tested, and the optimum fusion condition selected consisted of two 100-s pulses of 1,500 V cm^–1. Our conclusion is that electrochemical fusion is a reliable and reproducible method that combines the best features of both the chemical and electrical methods, thereby promoting cell division and high embryogenesis rates of the fused cells. It represents a new approach to citrus somatic hybridization. Various interesting features of this new approach are presented and discussed.     

Voltage transients in neuronal dendritic trees.

An analytical method is outlined for calculating the passive voltage transient at each point in an extensively branched neuron model for arbitrary current injection at a single branch. The method is based on a convolution formula that employs the transient response function, the voltage response to an instantaneous pulse of current. For branching that satisfies Rall's equivalent cylinder constraint, the response function is determined explicitly. Voltage transients, for a brief current injected at a branch terminal, are evaluated at several locations to illustrate the attenuation and delay characteristics of passive spread. A comparison with the same transient input terminal input, the fraction of input charge dissipated by various branches in the neuron model is illustrated. These fractions are independent of the input time course. For transient synaptic conductance change at a single branch terminal, a numerical example demonstrates the nonlinear effect of reduced synaptic driving potential. The branch terminal synaptic input is compared with the same synaptic conductance input applied to the soma on the basis of excitatory postsynaptic potential amplitude at the soma and charge delivered to the soma.