Electronic Neural Models Neuromimes

Neural modeling, or computational neurobiology as it is now called, began in the early 1960s with the creation of real-time, analog, electronic models of single neurons, synapses, and spike generation. Leon Harmon at Bell Labs was one of the first workers to design an analog neural model using PNP bipolar junction transistors (BJTs) that exhibited summation, threshold (for firing), excitation, inhibition, refractoriness, and delay (van Bergeijk and Harmon, 1960). This circuit contained a voltage-controlled astable multivibrator (VCO) that simulated spike generation in response to generator potential. Harmon coined the term neuromime to describe this class of analog neural model. Harmon and co-workers applied their neuromimes to elementary modeling studies of visual and auditory systems, and later to describing the behavior of two reciprocally inhibited neurons (Harmon, 1964).

A seminal paper in the era of analog neuromimes was written by Edwin R. Lewis. Lewis (1963) formalized the concept of synaptic loci, devising simple, RC diode circuits to model the behavior of synapses in generating "ballistic potentials" in the subsynaptic membrane. Circuits were given to model: simple epsps, epsps with antifacilitation, epsps with facilitation (this circuit also contained a PNP BJT, as well as diodes, Rs and Cs), adaptation (the adaptation circuit also contained a PNP BJT), ipsps, and local response loci. A three-PNP transistor, dc excitable, monostable multivibrator (retriggerable) was given for the spike generator locus (SGL) (site of action potential origination). This SGL had an adjustable dc threshold and also exhibited absolute and relative refractoriness.

The author and graduate students J.-M. Wu and E.F. Guignon, inspired by the work of Harmon and Lewis, designed and built their own neuromime computer in 1966. We followed Lewis's designs for synaptic loci, but developed our own SGL circuit using a unijunction transistor (UJT) relaxation oscillator that closely followed the IPFM architecture (Li, 1961). Our SGL circuit is shown in Figure 3.2.1. Note that the SGL is a current-controlled oscillator where the UJT firing frequency is nearly linear with the dc current leaving the input node. The capacitor C1 charges under constant-current conditions from the collector of the PNP BJT, Q1. When VC1 reaches the firing threshold for the 2N489 UJT, its gate conductance abruptly increases, discharging C1. A 6 V negative pulse about 100 s in duration is seen at the UJT B2. This pulse is reshaped by a one-shot (monostable multivibrator) circuit and given a low output impedance at the SGL output. Note that we used negative signals, i.e., a more negative input to Vfa caused the UJT firing frequency to increase. An ipsp was therefore positive going in this system. Figure 3.2-2A illustrates a simple epsp synaptic ballistic filter that we used; an antifacilitating synaptic filter is shown in Figure 3.2-2B.

Relaxation oscillator

Monostable MV

Relaxation oscillator

Monostable MV

(All resistances in kilohms, all Cs in |xF.)

FIGURE 3.2-1 Schematic circuit of an analog SGL circuit developed by the author. Design is based on integral pulse frequency modulation (IPFM) voltage-to-frequency conversion. When a negative voltage (equivalent to depolarization) is applied to the input node, the 2N3905 PNP transistor is turned on and current flows from its collector into Q, charging it so VC1 goes positive. When VC1 exceeds the firing theshold for the 2N489 unijunction transistor, it abruptly conducts, discharging C1 and also producing a negative pulse at its base 1. This negative pulse triggers another UJT connected as a one-shot multivibrator, producing a negative rectangular pulse at the SGL output. The 1N657 diode connected between output and the VC1 node clamps VC1 to the minimum pulse level, preventing C1 from charging over the duration of the output pulse (100 |s), creating an absolute refractory period. A charge put on C1 from a transient input to the circuit slowly leaks off in the absence of further inputs.

(All resistances in kilohms, all Cs in |xF.)

FIGURE 3.2-1 Schematic circuit of an analog SGL circuit developed by the author. Design is based on integral pulse frequency modulation (IPFM) voltage-to-frequency conversion. When a negative voltage (equivalent to depolarization) is applied to the input node, the 2N3905 PNP transistor is turned on and current flows from its collector into Q, charging it so VC1 goes positive. When VC1 exceeds the firing theshold for the 2N489 unijunction transistor, it abruptly conducts, discharging C1 and also producing a negative pulse at its base 1. This negative pulse triggers another UJT connected as a one-shot multivibrator, producing a negative rectangular pulse at the SGL output. The 1N657 diode connected between output and the VC1 node clamps VC1 to the minimum pulse level, preventing C1 from charging over the duration of the output pulse (100 |s), creating an absolute refractory period. A charge put on C1 from a transient input to the circuit slowly leaks off in the absence of further inputs.

Another approach to constructing analog, real-time neuromimes was taken by Hiltz (1962). Instead of using RC diode low-pass filters to model synaptic potentials, Hiltz used linear op amp, low-pass filter circuits and summers to model the generator potential. A retriggerable one-shot multivibrator was used to generate output spikes. The output spikes were fed back to create an absolute and relative refractory period for the SGL.

In 1964, Lewis described an approach to analog electronic neural modeling that used BJT active circuits to model the specific ionic conductances for sodium and potassium ions as described by the nonlinear ODEs in Hodgkin and Huxley's famous 1952 paper. Lewis put his gK and gNa circuits in parallel with a (linear) leakage conductance and a membrane capacitance and found that it did indeed produce realistic action potentials when appropriately "depolarized." By manipulation of certain RC parameters, Lewis's conductance model could exhibit a number of features observed when recording transmembrane potential in real neurons. Clearly, this was a flexible analog neuromime with realistic behavior based on the known transmembrane ionic events at the time. To obtain these effects, however, circuit parameters had to be adjusted, often by trial and error, to obtain the desired emulations.

Unfortunately, the analog circuit approach is subject to the demons of analog electronics, which in a nonlinear regenerative circuit, such as Lewis's, make troubleshooting difficult. Certainly, Lewis's approach was the most biological of the

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