Computer simulations of stimulus dependent state switching in basic circuits of bursting neurons

Abstract

We investigate the ability of oscillating neural circuits to switch between different states of oscillation in two basic neural circuits. We model two quite distinct small neural circuits. The first circuit is based on invertebrate central pattern generator (CPG) studies [A. I. Selverston and M. Moulins, The Crustacean Stomatogastric System (Springer-Verlag, Berlin, 1987)] and is composed of two neurons coupled via both gap junction and inhibitory synapses. The second consists of coupled pairs of interconnected thalamocortical relay and thalamic reticular neurons with both inhibitory and excitatory synaptic coupling. The latter is an elementary unit of the thalamic networks passing sensory information to the cerebral cortex [M. Steriade, D. A. McCormick, and T. J. Sejnowski, Science 262, 679 (1993)]. Both circuits have contradictory coupling between symmetric parts. The thalamocortical model has excitatory and inhibitory connections and the CPG has reciprocal inhibitory and electrical coupling. We describe the dynamics of the individual neurons in these circuits by conductance based ordinary differential equations of Hodgkin-Huxley type [J. Physiol. (London) 117, 500 (1952)]. Both model circuits exhibit bistability and hysteresis in a wide region of coupling strengths. The two main modes of behavior are in-phase and out-of-phase oscillations of the symmetric parts of the network. We investigate the response of these circuits, while they are operating in bistable regimes, to externally imposed excitatory spike trains with varying interspike timing and small amplitude pulses. These are meant to represent spike trains received by the basic circuits from sensory neurons. Circuits operating in a bistable region are sensitive to the frequency of these excitatory inputs. Frequency variations lead to changes from in-phase to out-of-phase coordination or vice versa. The signaling information contained in a spike train driving the network can place the circuit into one or another state depending on the interspike interval and this happens within a few spikes. These states are maintained by the basic circuit after the input signal is ended. When a new signal of the correct frequency enters the circuit, it can be switched to another state with the same ease.