Alternating and Synchronous Rhythms in Reciprocally Inhibitory Model Neurons Xiao-Jing Wang, John Rinzel Neural computation (1992). 4: Ubong Ime Udoekwere and Vanessa Boyce December 16th 2004

Introduction What is a pacemaker? –Network capable of generating oscillatory behavior without peripheral input i.e. spontaneous activity Pacemaker cell qualities: –Cellular properties: threshold, bursting pattern –Synaptic properties: time course, release mechanism –Patterns of Connection: inhibitory, excitatory

Circuitry Reciprocal inhibition or inhibitory feedback loop –Fire out of phase –Exhibit Post Inhibitory Rebound (PIR) Transient increase in excitability of neuron after end of inhibitory input. –E.g. Thalamic neurons: Low threshold T-type I Ca Hyperpolarization --> de- inactivation--> excitation - Cell i Cell j -

Two scenarios Asynchronous oscillation –Post synaptic conductance (s ji ) is instantaneous and depends on presynaptic potential Synchronous oscillation –Post synaptic conductance (s ji ) is not instantaneous, but decays slowly.

Release: Due to presynaptic termination of inhibition –Active Cell i exerts an inhibitory synaptic effect on Cell j. –As the voltage of active Cell i drops below a certain threshold (synaptic threshold [  syn ]) then Cell j is released from Cell i synaptic influence and exhibits PIR –Cell j becomes active and inhibits Cell i Escape: Due to intrinsic membrane properties Slowly developing I pir during inhibition of Cell j >> the hyperpolarizing effect caused by active Cell i Hence the inhibited Cell j spontaneously depolarizes and inhibits Cell i Both process repeat periodically Asynchronous oscillation - Cell i Cell j -

Aim of paper Examine and generate a model of rhythmic activity in non-oscillatory neurons, i.e. where pace-making input is absent.

Their Model Where: = postsynaptic conductance in cell i due to j = sigmoid function Based on rapidly activating, slowly inactivating T-type Ca current (thalamic neurons) –Constant conductance I L and voltage dependant inward I pir.

Where… k syn = 2 g syn = 0.4 mS/cm 2 g L = 0.1 mS/cm 2 V pir = 120 mV V syn = -80 mV V L = -60 mV Reversal potentials  0 = 10 msec  = 3 Variable values Voltage dependant gating functions m ∞ (V) = 1/{1+ exp[-(V + 65)/7.8]} h ∞ (V) = 1/{1+ exp[(V + 81)/11]}  h (V) = h ∞ (V) exp[(V )/17.8]} g pir = 0.3 mS/cm 2  syn = - 44mV g L = Conductance of Leak current g pir = Conductance of PIR current  syn = synaptic threshold

Alternating Oscillation by the release mechanism Period of oscillation linked to synaptic input

Alternating Oscillation by the escape mechanism Period of oscillation DOES NOT depend on presynaptic cell. Can occur with non-phasic input

Release Mechanism Pacemaker Period

Escape Mechanism

Synchronization by a Slowly Decaying synaptic system First order kinetics for s ji synaptic variable Slow decay rate such that inhibition outlast the PIR event

Application: Central Pattern Generators Network of spinal interneurons that generate rhythmic output