Biophysical Neural Spiking, Bursting, and Excitability Dynamics in Reconfigurable Analog VLSI

Abstract

We study a range of neural dynamics under variations in biophysical parameters underlying extended Morris-Lecar and Hodgkin-Huxley models in three gating variables. The extended models are implemented in NeuroDyn, a four neuron, twelve synapse continuous-time analog VLSI programmable neural emulation platform with generalized channel kinetics and biophysical membrane dynamics. The dynamics exhibit a wide range of time scales extending beyond 100 ms neglected in typical silicon models of tonic spiking neurons. Circuit simulations and measurements show transition from tonic spiking to tonic bursting dynamics through variation of a single conductance parameter governing calcium recovery. We similarly demonstrate transition from graded to all-or-none neural excitability in the onset of spiking dynamics through the variation of channel kinetic parameters governing the speed of potassium activation. Other combinations of variations in conductance and channel kinetic parameters give rise to phasic spiking and spike frequency adaptation dynamics. The NeuroDyn chip consumes 1.29 mW and occupies 3 mm × 3 mm in 0.5 μm CMOS, supporting emerging developments in neuromorphic silicon-neuron interfaces.

Fig. 1

The NeuroDyn analog VLSI programmable neural emulation platform [29]–[31] is used to generate both tonic firing and intrinsic bursting dynamics using extensions on Hodgkin–Huxley and Morris-Lecar paradigms. (a) Hodgkin–Huxley. (b) Morris-Lecar. (c) extended Morris-Lecar and Hodgkin–Huxley.

Fig. 2

Tonic spiking neural dynamics in the ML model with the extension to include slow inactivation dynamics set as a constant parameter showing simulated and measured data for (a), (c) steady-state (in)activation dynamics, (b), (d) τ voltage-dependent dynamics, and (e), (f) membrane voltage and gating variable waveforms.

Fig. 3

Tonic bursting neural dynamics in the ML model with an extension to include slow inactivation dynamics showing simulated and measured data for (a), (c) steady-state (in)activation dynamics, (b), (d) τ voltage-dependent dynamics, and (e), (f) membrane voltage and gating variable waveforms.

Fig. 4

Simulated tonic bursting neuron with variation of a single conductance parameter g_w governing calcium recovery with increasing values from (a) to (c).

Fig. 5

Measured tonic bursting neuron with variation of a single conductance parameter g_w governing calcium recovery with increasing values from (a) to (c).

Fig. 6

Phasic spiking neural dynamics with simulated and measured data for (a), (c) steady-state (in)activation dynamics, (b), (d) τ voltage-dependent dynamics, and (e), (f) membrane voltage and gating variable waveforms.

Fig. 7

Spike frequency adaptation neural dynamics with simulated and measured data for (a), (c) steady-state (in)activation dynamics, (b), (d) τ voltage-dependent dynamics, and (e), (f) membrane voltage and gating variable waveforms.

Fig. 8

Class 1 excitable neural dynamics with simulated and measured data for (a), (c) steady-state (in)activation dynamics, (b), (d) τ voltage-dependent dynamics, and (e), (f) membrane voltage and gating variable waveforms.

Fig. 9

Class 2 excitable neural dynamics with simulated and measured data for (a), (c) steady-state (in)activation dynamics, (b), (d) τ voltage-dependent dynamics, and (e), (f) membrane voltage and gating variable waveforms.

Fig. 10

ISI Histogram of increasing values τ_n for from (a) to (c) governing K⁺ channel dynamics of simulations between class 1 and class 2 excitable neural dynamics.

Fig. 11

ISI Histogram of increasing values for τ_n from (a) to (c) governing K⁺ channel dynamics of measurements between class 1 and class 2 excitable neural dynamics.