1. Linking neural dynamics and coding
Rhythms in central pattern generators – implications of escape and release
Jonathan Rubin
Department of Mathematics
University of Pittsburgh
Linking neural dynamics and coding
BIRS – October 5, 2010
funding: U.S. National Science Foundation

2. goal: to understand the mechanisms of rhythm generation, and modulation, in the mammalian brainstem respiratory network and other central pattern generators (CPGs)
Talk Outline
Brief introduction to CPGs
Transition mechanisms in pairs with reciprocal inhibition
-- escape/release
-- changes in drives to single component
Applications of ideas to larger networks

3. examples of central pattern generators
crustacean STG – Rabbeh and Nadim, J. Neurophysiol., 2007
leech heart IN network – Cymbalyuk et al., J. Neurosci., 2002

4. rhythms are intrinsically produced by the network
overall, central pattern generators (CPGs)
exhibit rhythms featuring ordered, alternating phases of synchronized activity
rhythms are intrinsically produced by the network
rhythms can be modulated by external signals (CPG output encodes environmental conditions) + =
group 1
group 2
CPG rhythm

5. Nat. Rev. Neurosci., 2005

6. starting point for modeling CPG rhythms: eliminate spikes!
Pace et al., Eur. J. Neurosci., 2007:
preBötzinger Complex (mammalian respiratory brainstem)

7. half-center oscillator (Brown, 1911): components not intrinsically rhythmic; generates rhythmic activity without rhythmic drive −
reciprocal inhibition

8. time courses for half-center oscillations from 3 mechanisms: persistent sodium, post-inhibitory rebound (T-current), adaptation (Ca/K-Ca)

9. − simulation results: unequal constant drives fixed varied
persistent sodium
post-inhibitory rebound
relative silent phase duration for cell with varied drive
relative silent phase duration for cell with fixed drive
intermediate
adaptation
Daun et al., J. Comp. Neurosci., 2009

10. Why? transition mechanisms: escape vs. release
slow
inhibition off
inhibition off
inhibition on
inhibition on
fast
fast
Wang & Rinzel, Neural Comp., 1992; Skinner et al., Biol. Cyb., 1994

11. V example: persistent sodium current w/escape slow fast
Daun, Rubin, and Rybak, JCNS, 2009

12. − V persistent sodium w/ unequal drives slow fast baseline extra drive
baseline drive
inhibition off
extra drive
baseline orbit
inhibition on
slow
fast V
short silent phase for cell w/extra drive
Daun, Rubin, and Rybak, JCNS, 2009

13. Summary
escape: independent phase modulation (e.g., persistent sodium current)
release: poor phase modulation (e.g., post-inhibitory rebound)
adaptation = mix of release and escape: phase modulation by NOT independent (e.g., Ca/K-Ca currents)
Daun et al., JCNS, 2009

14. 3 4 1 4 2 1 3 2 applications to respiratory model (1) I-to-E E-to-I
inhibition
excitation 1 2 3 4 4 2 1
Smith et al., J. Neurophysiol., 2007
I-to-E
E-to-I

15. baseline 3-phase rhythm: slow projection
(expiratory adaptation) E
E-to-I transition by escape: cells 1 & 2 escape to start I phase I 1 4
(inspiratory adaptation)
I-to-E transition forced to be by release: cell 2 releases cells 3 & 4 3 2
main predictions (T = duration):
increase D1, D decrease TE , little ΔTI
increase D little ΔTI, ΔTE
Rubin et al., J. Neurophysiol., 2009

16. predictions: increase D1, D2 decrease TE, little ΔTI
increase D little ΔTI, ΔTE
Rubin et al., J. Neurophysiol., 2009

17. basic rhythm lacks late-E (RTN/pFRG) activity
applications to respiratory model (2): include RTN/pFRG, possible source of active expiration
basic rhythm lacks late-E (RTN/pFRG) activity
Rubin et al., J. Comp. Neurosci., 2010

18. hypercapnia (high CO2 ):
model as increase in drive to late-E neuron
late-E oscillations emerge quantally
I period does not change

19. Why is the period invariant? Phase plane for early-I (cell 2):
trajectories live here!
read off m2 values
synapses on
synapses ½-max

20. repeat for different input levels
excited
inhibited
synapses on
synapses ½-max

21. Why is the period invariant?
even with late-E activation, early-I activates by escape -
starts inhibiting expiratory cells while they are fully active (full inhibition to early-I and late-E)
inhibition
excitation
thus, late-E activation has no impact on period!
(similar result if pre-I escapes and recruits early-I)

22. applications (3) – limbed locomotion model
CPG
(RGs, INs)
motoneurons
Markin et al., Ann. NY Acad. Sci., 2009
muscles + pendulum
Spardy et al., SFN, 2010

23. does this asymmetry imply asymmetry of CPG?
locomotion with feedback – asymmetric phase modulation under variation of drive
drive
does this asymmetry imply asymmetry of CPG?

24. no! – model has symmetric CPG yet still gives asymmetry if feedback is present
drive
locomotion with feedback – asymmetric phase modulation under variation of drive
locomotion without feedback – loss of asymmetry
Markin et al., SFN, 2009

25. rhythm with/without feedback: what is the difference?
with feedback
IN escape controls phase transitions
Lucy Spardy

26. rhythm with/without feedback: what is the difference?
RG escape controls phase transitions
Lucy Spardy

27. OP : how does feedback shelter INE from drive?
idea: drive strength affects timing of INF escape (end of stance), RGE, RGF escape but not timing of INE escape
drive
OP : how does feedback shelter INE from drive?

28. Conclusions
escape and release are different transition mechanisms that can yield similar rhythms in synaptically coupled networks
in respiration, different mechanisms are predicted to be involved in different transitions
transition mechanisms within one network may change with changes in state
transition mechanisms determine responses to changes in drives to particular neurons – could be key for feedback control

29. THANK YOU!