Multiple rhythmic states in a model respiratory CPG

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Multiple rhythmic states in a model respiratory
CPG
SIAM Conference on Applications of Dynamical
Systems May 19, 2009
Contributors Ilya Rybak, Natalia Shevtsova
Drexel Univ. College of Medicine Jeffrey Smith
NIH Silvia Daun, Bard Ermentrout, Jonathan
Rubin Univ. of Pittsburgh
Silvia Gruhn Univ. Köln
funding NIH, U.S. National Science Foundation
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Goal to understand the mechanisms of rhythm
generation, and modulation, in the mammalian
respiratory pacemaker network and other central
pattern generators (CPGs)

• Outline
• Brief introduction to CPGs
• Transition mechanisms in inhibitory networks
• -- review
• -- changes in drives to CPG components
• Respiratory network dynamics

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three examples of central pattern generators
(CPGs)
1) half-center oscillator (Brown, 1911)
components not intrinsically rhythmic generates
repetitive activity without time-dependent drive
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2) locomotor CPG (model) Rybak et al., J.
Physiol., 2006
see also Golubitsky, Stewart, et al.
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3) cortex (Yuste et al., Nat. Rev. Neurosci.,
2005)
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• idea
• CPGs feature alternation of 2 synch. cell
  groups
• similar rhythms may arise from different
  mechanisms
• mechanisms determine responses to changes in
  drive to 1 or more groups

• strategy compare 3 half-center relaxation
  oscillator CPG models, featuring 3 different
  rhythmic mechanisms
• analyze change in period with change in drive to
  both cells and independent phase modulation with
  change in drive to one cell (asymmetric drive)

Daun, Rubin, and Rybak, JCNS, 2009 also see
Curtu et al., SIADS, 2008
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time courses for half-center oscillations from 3
mechanisms persistent sodium, post-inhibitory
rebound (T-current), adaptation (Ca/K-Ca)
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asymmetric drive simulation results
intermediate
adaptation
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asymmetric drive results (cont.)
highly tunable
robust
high phase independence
Daun, Rubin, and Rybak, JCNS, 2009
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Iinh s(vpre)(v-vinh)
for vinh lt v lt vexc
Iexc s(vpre)(v-vexc)
where

idea n oscillators n trajectories in
shared 2-d phase plane, not 3n-dimensional phase
space
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analysis I. escape vs. release
inhibition off
inhibition off
inhibition on
inhibition on
Skinner et al., Biol. Cybernetics, 1994
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1) persistent sodium current escape
Daun, Rubin, and Rybak, JCNS, 2009
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2) postinhibitory rebound release
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3) adaptation escape release
synaptic threshold
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analysis II. asymmetric drive
baseline orbit
inhibition on
baseline
extra drive
extra drive

• persistent sodium
• current escape

baseline drive
inhibition off
short silent phase for cell w/extra drive
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2) post-inhibitory rebound release
inhibition on
similar durations despite very different drives
baseline drive
baseline orbit
inhibition off
extra drive
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3) adaptation escape release
zero inhibition critical point
max inhibition critical point
increasing drive
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3) adaptation escape release (cont.)
synaptic threshold
shortened slightly due to stronger drive, which
promotes escape
prolonged due to delayed adaptation
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back to respiratory networks (Smith talk, MS57,
10 AM Rubin talk, MS88, Wed., 10 AM)
excitatory preBötC kernel is embedded within
3-component inhibitory ring network
Smith et al., J. Neurophysiol., 2007
Rybak et al., Prog. Brain Res., 2007
Rubin et al., J. Neurophysiol., 2009
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large network simulations capture multiple rhythms
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activity-based computational model 4 cells, 4
slow variables, voltage-dependent coupling
FAST
excitatory kernel
i 2,3,4 inhibitory cells
SLOW
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three-phase rhythm
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only features two fast jumps
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projection to two-parameter (i.e., slow variable)
plane shows role of escape
release
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can explain frequency effects of changes in
drives to different cells by effects on
escape/release
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multiple rhythms (see MS88, Wed., 10 AM)
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summary

• CPGs can exhibit complex rhythmic activity
  patterns
• Different network components can yield similar
  rhythms
• Transition mechanisms shape responses to drives
• Transitions by escape, as with persistent sodium
  current, are optimal for independent phase
  modulation
• Fast-slow decomposition and parametrization of
  slow dynamics yield transition mechanisms and
  effects of drives in multi-cell, multi-phase
  rhythms