Transcript Alternating and Synchronous Rhythms in Reciprocally

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
Circuitry
Cell i
• 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.
Cell j
– E.g. Thalamic neurons:
• Low threshold T-type ICa
• Hyperpolarization --> deinactivation--> excitation
Two scenarios
• 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.
Asynchronous oscillation
•
Cell i
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 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
• Based on rapidly activating, slowly inactivating T-type Ca
current (thalamic neurons)
– Constant conductance IL and voltage dependant inward Ipir.
Where:
= postsynaptic conductance in cell i due to j
= sigmoid function
Variable values
Where…
Voltage dependant gating functions
ksyn= 2
gsyn= 0.4 mS/cm2
m∞(V) = 1/{1+ exp[-(V + 65)/7.8]}
gL= 0.1 mS/cm2
h∞(V) = 1/{1+ exp[(V + 81)/11]}
t0 = 10 msec
f=3
gpir= 0.3 mS/cm2
qsyn = - 44mV
Reversal potentials
Vpir= 120 mV
Vsyn= -80 mV
VL= -60 mV
th(V) = h∞(V) exp[(V + 162.3)/17.8]}
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