A. S. French

A Flexible Neural Analog Using Integrated Circuits

An electronic neural analog is described which contains variable absolute and relative refractory periods, two time constants, and separate control of the ``accommodation to sub-threshold voltage changes and the ``adaptation produced by the occurrence of output pulses (spikes). The extensive use of integrated-circuit operational amplifiers permits an accurate description of input-output relationships over a wide range of values for all parameters. This facilitates comparison of the results obtained both with neural data and mathematical or digitally simulated models of neural activity. The effect of white noise on interval histograms and their parameters is described and its effect when added to other inputs. Noise disrupts the phase-locked patterns produced by sinusoidal stimuli and the averaged response may become a smooth sinusoidal function in the presence of added noise. Adaptation may produce a phase lead to sinusoidal stimuli, while accommodation may produce a phase lag. Corresponding overshoots or undershoots are seen with square-wave inputs.

Practical nonlinear system analysis by Wiener kernel estimation in the frequency domain

Nonlinear systems which have finite memories and are time invariant can be completely described by the Wiener functional expansion, in which a series of multidimensional kernels provide a polynomial approximation to the nonlinear behaviour. The kernels give a best fitting estimation to the total system behaviour in the least mean square sense and can therefore be used to describe systems in which the nonlinearities include discontinuous functions. A modification of the Wiener method described by Lee and Schetzen, which uses kernels defined in terms of cross correlation functions, has been used in most practical attempts to analyse nonlinear systems, but we have previously described how the cross correlations may be replaced with complex multiplications in the frequency domain. The speed of domain translation offered by the fast Fourier transform makes this method more efficient than time domain estimation. In this paper the practical implementation of the technique on a medium sized digital computer is described for nonlinear systems whose outputs are continuous or pulsatile signals. This description should be adequate to allow others to implement the analysis scheme. The technique is well suited to the analysis of nonlinear biological systems, particularly those encountered in neurophysiology, because of its generality, ability to deal with hard nonlinearities and ease of use with systems having pulsatile outputs.

Nonlinear analysis of sensory transduction in an insect mechanoreceptor

Tactile sensilla of the trochanteral hair plate in the coxotrochanteral joint of the cockroach leg were stimulated by random (white noise) displacement and the afferent action potentials resulting from the stimulation were observed. From the resulting signals, the first and second order frequency response functions between the stimulus and the response were computed, together with their inverse Fourier transforms, the time domain Wiener kernels. Analysis of these results shows that the behaviour of the receptor may be minimally accounted for by a cascade of two functional elements, where the first is a linear element affected by the past history of the input signal (memory) and the second is a nonlinear element with no memory. The behaviour of the linear element is very close to that of a time differentiator or velocity detector, while the nonlinear element behaves as a rectifier which transmits the velocity signal only during flexion of the limb. The results suggest that the functional description may correspond to a physical system with two parts. The element performing differentiation is probably a fluid cavity in the mechanical connection from the hair to the dendrite, and the element performing rectification is most likely to be found in the cell membrane of the dendrite.

White-noise analysis of nonlinear behavior in an insect sensory neuron: kernel and cascade approaches

A functional expansion was used to model the relationship between a Gaussian white noise stimulus current and the resulting action potential output in the single sensory neuron of the cockroach femoral tactile spine. A new precise procedure was used to measure the kernels of the functional expansion. Very similar kernel estimates were obtained from separate sections of the data produced by the same neuron with the same input noise power level, although some small time-varying effects were detectable in moving through the data. Similar kernel estimates were measured using different input noise power levels for a given cell, or when comparing different cells under similar stimulus conditions. The kernels were used to identify a model for sensory encoding in the neuron, comprising a cascade of dynamic linear, static nonlinear, and dynamic linear elements. Only a single slice of the estimated experimental second-order kernel was used in identifying the cascade model. However, the complete second-order kernel of the cascade model closely resembled the estimated experimental kernel. Moreover, the model could closely predict the experimental action potential train obtained with novel white noise inputs.

The responses of trochanteral hair plate sensilla in the cockroach to periodic and random displacements

Two types of sensillum have previously been described in the trochanteral hair plate of the cockroach with differences in physical size, extracellularly recorded impulse amplitude and response to displacement. We have now examined the dynamic behaviour of the two types of sesillum in response to sinusoidal and random displacements. Type I sensilla have a frequency threshold of about 6 Hz, below which there is no response to sinusoidal displacement. Above the frequency threshold they behave as velocity sensors with a 90° phase lead of response over displacement and increasing response with increasing frequency. Type II sensilla have no detectable frequency threshold and behave as position sensors at low frequencies. With increasing frequency they display a phase lead over the stimulus but it nerver exceeds about 60°. Random stimulation followed by spectral analysis of the input-output relations give similar descriptions to the sinusoidal results except that low frequency position sensitivity is revealed in the Type I sensilla. The coherence function for both types of sensillum is low, indicating that the linear frequency response functions are poor approximations to the total behaviour of the sensilla. Earlier investigations of these receptors in a range of insects suggested that they are primarily involved in the control of joint positions during very slow movements. However, the present results, together with other recent work, indicates that they are also important in the control of rapid movements.

Ouabain selectively affects the slow component of sensory adaptation in an insect mechanoreceptor

Sensory activity in the cockroach tactile spine neuron adapts rapidly to a step deflection. This rapid adaptation is caused by a rise in the threshold for action potential production, which has two components with different time constants and drug sensitivities. The basis of the slow component is unknown but it is insensitive to a wide range of ion channel blockers. In the present experiments the slow component was selectively reduced by ouabain, suggesting that it is due to the activation of an electrogenic sodium pump.

Potassium Channels in Human and Avian Fibroblasts

The cell-attached and excised inside-out patch-clamp techniques were used to study single-channel characteristics of potassium channels in cultured human and avian fibroblasts. Six different potassium channels were distinguished with conductances of 235 ± 25, 190 ± 57, 114 ± 27, 77 ± 14, 40 ± 6 and 21 ± 4 pS in symmetric 140 mM potassium solutions. The channels were separable by their conductances, ion-selectivities, voltage-sensitivities and kinetic properties. All six channels were found in both fully differentiated human skin fibroblasts and primary cultures of 72 h chick sclerotome. The largest channel (235 pS) had a steep bimodal voltage dependence, being open only around the resting membrane potential. It was imperfectly selective for potassium, having a relative sodium : potassium permeability of 0.3. The 190 pS channel was very potassium-selective, had an S-shaped voltage sensitivity and was calcium-dependent. The two intermediate-size channels (114 and 77 pS) had open probabilities of less than 0.5 under all of the conditions we used. They were not completely selective for potassium and were not voltage-sensitive. The two smallest channels (40 and 21 pS) were not well characterized. They both had open probabilities of less than 0.2 and showed no evidence of voltage-sensitivity. The 40 pS channel seemed highly potassium-selective. A suction stimulus was used to test all observed channels for mechanosensitivity but none of the six potassium channels was mechanosensitive. Another small channel, with very clear mechanical sensitivity, was seen on a few occasions; this channel has not yet been characterized.

The effects of temperature on action potential encoding in the cockroach tactile spine

Summary1.The effect of temperature was observed on the encoding of action potentials from membrane current in the sensory neuron of the cockroach tactile spine. Electrical stimulation was employed, with the tip of a current-passing microelectrode adjacent to the axon where it leaves the soma. Action potentials were detected by extracellular electrodes placed further along the axon.2.The dynamic properties of encoding were studied by measuring the frequency response function between randomly varying input current and the resulting train of action potentials.3.Temperature was carefully controlled by mounting the preparation on a thermoelectric servo-controlled stage. The temperature sensor was a fine thermocouple placed against the wall of the tactile spine and within the same pool of saline solution.4.Temperatures in the range 10 to 35 °C were used. Temperatures outside this range caused failure of action potential production or conduction. The sensitivity of the encoder to electric current did not change appreciably with temperature, but there was an increase in the response to higher frequencies as the temperature was raised, representing more rapid adaptation.5.Comparison with earlier work on transduction of mechanical stimuli indicates that generation of the receptor current is the step with the most thermal sensitivity.6.Conduction velocity in the afferent axon increased with temperature by amounts which agree with previous findings and predictions. The mean rate of firing in the receptor increased strongly with temperature, but the reasons for this are not clear.

Octopamine selectively modifies the slow component of sensory adaptation in an insect mechanoreceptor

The effects of octopamine were studied on the dynamic behavior of the sensory neuron in the cockroach femoral tactile spine. The neuron is a rapidly adapting mechanoreceptor in which adaptation occurs by elevation of the threshold for action potential encoding. The threshold follows increases or decreases of membrane potential, with a delay that involves two separate exponential components. Previous evidence has associated the slow component with sodium pumping and the fast component with sodium channel inactivation. Octopamine reversibly raised the resting threshold and increased but slowed the slow component. These data indicate that octopamine has specific effects on membrane-ionic processes in insect sensory neurons.

DYNAMIC PROPERTIES OF ELECTROTONIC COUPLING BETWEEN CELLS OF EARLY XENOPUS EMBRYOS

Frequency response functions were measured between the cells of Xenopus laevis embryos during the first two cleavage stages. Linear systems theory was then used to produce electronic models which account for the electrical behavior of the systems. Coupling between the cells may be explained by models which have simple resistive elements joining each cell to its neighbors. The vitelline, or fertilization, membrane which surrounds the embryos has no detectable resistance to the passage of electric current. The electrical properties of the four-cell embryo can only be explained by the existence of individual junctions linking each pair of cells. This arrangement suggests that electrotonic coupling is important in the development of the embryos, at least until the four-cell stage.