The response of a model neurone to a white noise input

We consider a simple model of a neurone in which the input voltage is integrated to form the somatic potential, and a pulse is emitted when this reaches a threshold; the somatic potential is then reset to its resting value. We subject this model to a white-noise input, and evaluate the cross correlation between input white noise and the output pulse train; this is proportional to the small-signal impulse response of the model. Some numerical estimations are presented.     

Hidden oscillations in generalized linear mammaillary compartmental models

Oscillations due to complex eigenvalues, known to exist but difficult to detect, are sometimes totally hidden in the output of compartmental models, i.e., none of their modes appear in the output. An example is constructed of a class of linear compartmental models with complex eigenvalues, which have oscillating modes appearing in the output for some single-pool-input/single-pool-output (SpISpO) configurations, while for other such configurations all oscillations are totally hidden in the output. To generate the example, generalized mammillary compartmental models are defined in which a central pool exchanges with peripheral submodels called clusters, through individual connector pools, and their transfer functions are calculated corresponding to all SpISpO configurations. When such a model is repetitive, i.e., when it has identical peripheral clusters, and the input or the output is in the central pool, then it is zero-state equivalent, up to a multiplicative constant, with a reduced model having one peripheral cluster only. We analyze the visibility of an eigenvalue, i.e., whether or not the modes associated with it appear in the output, for repetitive generalized mammillary models. Sufficient conditions are given for such models to have oscillating modes appearing in the impulse response for some input/output configurations, while for other such configurations all oscillations are totally hidden, i.e., none appear in the output. A particularly interesting example is presented of a class of linear models with complex eigenvalues satisfying these conditions. This class has the structure of nonlinear models used to describe the process of protein synthesis and turnover.     

Electrical consequences of spine dimensions in a model of a cortical spiny stellate cell completely reconstructed from serial thin sections

We built a passive compartmental model of a cortical spiny stellate cell from the barrel cortex of the mouse that had been reconstructed in its entirety from electron microscopic analysis of serial thin sections (White and Rock, 1980). Morphological data included dimensions of soma and all five dendrites, neck lengths and head diameters of all 380 spines (a uniform neck diameter of 0.1 m was assumed), locations of all symmetrical and asymmetrical (axo-spinous) synapses, and locations of all 43 thalamocortical (TC) synapses (as identified from the consequences of a prior thalamic lesion). In the model, unitary excitatory synaptic inputs had a peak conductance change of 0.5 nS at 0.2 msec; conclusions were robust over a wide range of assumed passive-membrane parameters. When recorded at the soma, all unitary EPSPs, which were initiated at the spine heads, were relatively iso-efficient; each produced about 1 mV somatic depolarization regardless of spine location or geometry. However, in the spine heads there was a twentyfold variation in EPSP amplitudes, largely reflecting the variation in spine neck lengths. Synchronous activation of the TC synapses produced a somatic depolarization probably sufficient to fire the neuron; doubling or halving the TC spine neck diameters had only minimal effect on the amplitude of the composite TC-EPSP. As have others, we also conclude that from a somato-centric viewpoint, changes in spine geometry would have relatively little direct influence on amplitudes of EPSPs recorded at the soma, especially for a distributed, synchronously activated input such as the TC pathway. However, consideration of the detailed morphology of an entire neuron indicates that, from a dendro-centric point of view, changes in spine dimension can have a very significant electrical impact on local processing near the sites of input.     

Coding with spike shapes and graded potentials in cortical networks

In cortical neurones, analogue dendritic potentials are thought to be encoded into patterns of digital spikes. According to this view, neuronal codes and computations are based on the temporal patterns of spikes: spike times, bursts or spike rates. Recently, we proposed an 'action potential waveform code' for cortical pyramidal neurones in which the spike shape carries information. Broader somatic action potentials are reliably produced in response to higher conductance input, allowing for four times more information transfer than spike times alone. This information is preserved during synaptic integration in a single neurone, as back-propagating action potentials of diverse shapes differentially shunt incoming postsynaptic potentials and so participate in the next round of spike generation. An open question has been whether the information in action potential waveforms can also survive axonal conduction and directly influence synaptic transmission to neighbouring neurones. Several new findings have now brought new light to this subject, showing cortical information processing that transcends the classical models.     

Solutions for transients in arbitrarily branching cables: I. Voltage recording with a somatic shunt.

An analytical solution is derived for voltage transients in an arbitrarily branching passive cable neurone model with a soma and somatic shunt. The response to injected currents can be represented as an infinite series of exponentially decaying components with different time constants and amplitudes. The time constants of a given model, obtained from the roots of a recursive transcendental equation, are independent of the stimulating and recording positions. Each amplitude is the product of three factors dependent on the corresponding root: one constant over the cell, one varying with the input site, and one with the recording site. The amplitudes are not altered by interchanging these sites. The solution reveals explicitly some of the parameter dependencies of the responses. An efficient recursive root-finding algorithm is described. Certain regular geometries lead to "lost" roots; difficulties associated with these can be avoided by making small changes to the lengths of affected segments. Complicated cells, such as a CA1 pyramid, produce many closely spaced time constants in the range of interest. Models with large somatic shunts and dendrites of unequal electrotonic lengths can produce large amplitude waveform components with surprisingly slow time constants. This analytic solution should complement existing passive neurone modeling techniques.     

Conductance transients onto dendritic spines in a segmental cable model of hippocampal neurons.

Dendritic shaft (Zd) and spine (Zsp) input impedances were computed numerically for sites on hippocampal neurons, using a segmental format of cable calculations. The Zsp values for a typical spine appended onto a dendritic shaft averaged less than 2% higher than the Zd values for the adjacent dendritic shaft. Spine synaptic inputs were simulated by a brief conductance transient, which possessed a time integral of 12 X 10(-10)S X ms. This input resulted in an average peak spine response of 20 mV for both dentate granule neurons and CA1 pyramidal cells. The average spine transient was attenuated less than 2% in conduction across the spine neck, considering peak voltage, waveform parameters, and charge transfer. The spine conductance transient resulted in an average somatic response of 100 microV in the dentate granule neurons, because of passive electrotonic propagation. The same input transient was also applied to proximal and distal sites on CA1 pyramidal cells. The predicted responses at the soma demonstrated a clear difference between the proximal and distal inputs, in terms of both peak voltage and waveform parameters. Thus, the main determinant of the passive propagation of transient electrical signals in these neurons appears to be dendritic branching rather than signal attenuation through the spine neck.     

Deterrence coding by a larval Manduca chemosensory neurone mediating rejection of a non-host plant, Canna generalis L.

Abstract. The physiological basis of phagodeterrence was studied electrophy-siologically and behaviourally in the phytophagous caterpillars Manduca sexta and Manduca quinquemaculata. The model unacceptable non-host plant was the canna lily, Canna generalis. A strongly deterrent extract was obtained from fresh leaves of canna by extraction with hot ethanol or ethyl acetate in a blender. Behavioural rejection of these extracts was similar to that of fresh leaves, although less intense. In contrast, blender extracts using other solvents, as well as leaf surface rinses, were phagostimulant or neutral. Chromatographic fractionation of the deterrent ethanolic extract showed the active principles to be moderately polar and separable into two fractions. Previous ablation experiments had shown that the medial maxillary styloconica and epipharyngeal sensilla are the two most important chemosensory organs in mediating behavioural rejection of canna leaves; if only one of these organs is spared, the animal completely rejects canna. We investigated the neural responses of the medial styloconica and their contribution to the sensory coding responsible for this phagodeterrence. The active fractions of the deterrent ethanolic extract elicited a vigorous response from one chemosensory neurone in the medial styloconica. This neurone is distinguishable from others in the medial styloconica by its unique temporal response parameters and the characteristic shape changes of its action potentials. The response frequency of this neurone correlates with the degree of phagodeterrence in a dose-dependent manner. Threshold deterrence occurs at a concentration of extract (1%) that elicits firing in this neurone at a rate of c. 50 spikes/s peak instantaneous frequency and 30 total spikes in the first Is. We conclude that this is a ’deterrent neurone’ in the sense that vigorous response from this neurone is a sufficient sensory code for behavioural rejection of canna. Thus input from a single sensory neurone is capable of blocking feeding, since only one (unilateral) medial styloconicum is needed to mediate this rejection.     

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.     

Local changes in the transmembrane ion currents in plastic reorganization of electrogenesis in isolated neurons of the pond snail

Transmembrane ion currents were studied on limited (pore diameter 6-15 mcm) areas of isolated neurone's soma membrane. The significant differences of the amplitude and correlation of input and output currents of various areas of the cell membrane were observed. The different directions of transmembrane ion currents' local changes were recorded only in the site of action stimulus during the formation of plastic changes of neurone responses. Natural heterogeneity of total ion current of cell membrane, rapid changes of current components values at local influences probably testify to the possibility of selective plasticity of separate neurone areas.     

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.     

Back-Propagation Operation for Analog Neural Network Hardware with Synapse Components Having Hysteresis Characteristics

To realize an analog artificial neural network hardware, the circuit element for synapse function is important because the number of synapse elements is much larger than that of neuron elements. One of the candidates for this synapse element is a ferroelectric memristor. This device functions as a voltage controllable variable resistor, which can be applied to a synapse weight. However, its conductance shows hysteresis characteristics and dispersion to the input voltage. Therefore, the conductance values vary according to the history of the height and the width of the applied pulse voltage. Due to the difficulty of controlling the accurate conductance, it is not easy to apply the back-propagation learning algorithm to the neural network hardware having memristor synapses. To solve this problem, we proposed and simulated a learning operation procedure as follows. Employing a weight perturbation technique, we derived the error change. When the error reduced, the next pulse voltage was updated according to the back-propagation learning algorithm. If the error increased the amplitude of the next voltage pulse was set in such way as to cause similar memristor conductance but in the opposite voltage scanning direction. By this operation, we could eliminate the hysteresis and confirmed that the simulation of the learning operation converged. We also adopted conductance dispersion numerically in the simulation. We examined the probability that the error decreased to a designated value within a predetermined loop number. The ferroelectric has the characteristics that the magnitude of polarization does not become smaller when voltages having the same polarity are applied. These characteristics greatly improved the probability even if the learning rate was small, if the magnitude of the dispersion is adequate. Because the dispersion of analog circuit elements is inevitable, this learning operation procedure is useful for analog neural network hardware.     

Physiological characteristics of the synaptic response of an identified sensory nonspiking interneuron in the crayfish Procambarus clarkii girard

Voltage-dependent variability in the shape of synaptic responses of the LDS interneuron, an identified nonspiking cell of crayfish, to mechanosensory stimulation was studied using intracellular recording and current injection techniques. Stimulation of the sensory root ipsilateral to the interneuron soma evoked a large depolarizing synaptic response. Its peak amplitude was decreased and the time course was shortened when the LDS interneuron was depolarized by current injection. When the cell was hyperpolarized, the peak amplitude was increased and the time course was prolonged. Upon large hyperpolarization, however, the amplitude did not increase further while the time course showed a slight decrease. The dendritic membrane of the LDS interneuron was found to show an outward rectification upon depolarization and an inward rectification upon large hyperpolarization. Current injection experiments at varying membrane potentials revealed that the voltage-dependent changes in the shape of the synaptic response were based on an increase in membrane conductance due to the rectifying properties of the LDS interneuron. Stimulation of the contralateral root evoked a small depolarizing potential comprising an early excitatory response and a later inhibitory component. Its shape also varied depending on the membrane potential in a manner similar to that of the synaptic response evoked ipsilaterally.     

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.     

Decomposition-based qualitative experiment design algorithms for a class of compartmental models.

Qualitative experiment design, to determine experimental input/output configurations that provide identifiability for specific parameters of interest, can be extremely difficult if the number of unknown parameters and the number of compartments are relatively large. However, the problem can be considerably simplified if the parameters can be divided into several groups for separate identification and the model can be decomposed into smaller submodels for separate experiment design. Model decomposition-based experiment design algorithms are proposed for a practical class of large-scale compartmental models representative of biosystems characterized by multiple input sources and unidirectional interconnectivity among subsystems. The model parameters are divided into three types, each of which is identified consecutively, in three stages, using simpler submodel experiment designs. Several practical examples are presented. Necessary and sufficient conditions for identifiability using the algorithm are also discussed.     

High quality photoplethysmograph signals from a laser Doppler flowmeter: preliminary studies of two simultaneous outputs from the finger

An improvement in the quality of a photoplethysmograph signal derived from a laser Doppler flowmeter probe has been achieved by incorporating an auxiliary fibre in the probe head. This fibre is positioned at an optimum distance from the laser light transmitting fibre and overcomes the problem of high frequency signals which mask the detailed features of the photoplethysmograph pulse when a small fibre separation is used. These two signals may be recorded simultaneously from the same site and a correlation between the Doppler output and the photoplethysmograph amplitude has been demonstrated in the finger. The amplitude is shown to be affected by the relative position of the point of measurement with respect to the heart, a factor which does not appear to influence significantly the Doppler output.     

A hybrid computer model of stochastic activity of the neurone

The authors describe a hybrid computer neurone model intended for the investigation of stochastic transformations effected by neurones in correlation to some of their physiological parameters. The model is designed so as to give the best possible characterization of the internal dynamics of a neurone with minimum limiting conditions. It allows the generation of suitable input stochastic processes or operates with input processes obtained experimentally in the living neurone and it carries out basic statistical tests of the output stochastic process.     

Vestibular integrator neurons have quadratic functions due to voltage dependent conductances

The nonlinear properties of the dendrites of the prepositus hypoglossi nucleus (PHN) neurons are essential for the operation of the vestibular neural integrator that converts a head velocity signal to one that controls eye position. A novel system of frequency probing, namely quadratic sinusoidal analysis (QSA), was used to decode the intrinsic nonlinear behavior of these neurons under voltage clamp conditions. Voltage clamp currents were measured at harmonic and interactive frequencies using specific nonoverlapping stimulation frequencies. Eigenanalysis of the QSA matrix reduces it to a remarkably compact processing unit, composed of just one or two dominant components (eigenvalues). The QSA matrix of rat PHN neurons provides signatures of the voltage dependent conductances for their particular dendritic and somatic distributions. An important part of the nonlinear response is due to the persistent sodium conductance (g_NaP), which is likely to be essential for sustained effects needed for a neural integrator. It was found that responses in the range of 10 mV peak to peak could be well described by quadratic nonlinearities suggesting that effects of higher degree nonlinearities would add only marginal improvement. Therefore, the quadratic response is likely to sufficiently capture most of the nonlinear behavior of neuronal systems except for extremely large synaptic inputs. Thus, neurons have two distinct linear and quadratic functions, which shows that piecewise linear?+?quadratic analysis is much more complete than just piecewise linear analysis; in addition quadratic analysis can be done at a single holding potential. Furthermore, the nonlinear neuronal responses contain more frequencies over a wider frequency band than the input signal. As a consequence, they convert limited amplitude and bandwidth input signals to wider bandwidth and more complex output responses. Finally, simulations at subthreshold membrane potentials with realistic PHN neuron models suggest that the quadratic functions are fundamentally dominated by active dendritic structures and persistent sodium conductances.     

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.