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Alternating and Synchronous Rhythms in Reciprocally Inhibitory Model Neurons. Xiao-Jing Wang, John Rinzel Neural computation (1992). 4: 84-97. Ubong Ime Udoekwere and Vanessa Boyce December 16th 2004. Introduction. What is a pacemaker?
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Alternating and Synchronous Rhythms in Reciprocally Inhibitory Model Neurons Xiao-Jing Wang, John Rinzel Neural computation (1992). 4: 84-97 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
Cell i - - Cell j 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 ICa • Hyperpolarization --> de-inactivation--> excitation
Asynchronous oscillation Post synaptic conductance (sji) is instantaneous and depends on presynaptic potential Synchronous oscillation Post synaptic conductance (sji) is not instantaneous, but decays slowly. Two scenarios
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 [Qsyn]) 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 Ipir 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 Cell i - - Cell j Asynchronous oscillation
Aim of paper • Examine and generate a model of rhythmic activity in non-oscillatory neurons, i.e. where pace-making input is absent.
= postsynaptic conductance in cell i due to j = sigmoid function Their Model • Based on rapidly activating, slowly inactivating T-type Ca current (thalamic neurons) • Constant conductance IL and voltage dependant inward Ipir. Where:
Reversal potentials Vpir= 120 mV Vsyn= -80 mV VL= -60 mV Where… Variable values Voltage dependant gating functions ksyn= 2 m∞(V) = 1/{1+ exp[-(V + 65)/7.8]} gsyn= 0.4 mS/cm2 gL= 0.1 mS/cm2 h∞(V) = 1/{1+ exp[(V + 81)/11]} t0 = 10 msec th(V) = h∞(V) exp[(V + 162.3)/17.8]} f = 3 gpir= 0.3 mS/cm2 qsyn = - 44mV gL = Conductance of Leak current gpir = Conductance of PIR current qsyn = 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
Pacemaker Period Release Mechanism
Pacemaker Period Escape Mechanism
Synchronization by a Slowly Decaying synaptic system • First order kinetics for sji synaptic variable • Slow decay rate such that inhibition outlast the PIR event
Application: Central Pattern Generators • Network of spinal interneurons that generate rhythmic output