funding: U.S. National Science Foundation

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

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

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

12. − persistent sodium w/ unequal drives − baseline orbit inhibition on baseline extra drive extra drive slow baseline drive inhibition off 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. applications to respiratory model (1) 1 4 1 2 4 3 3 2 inhibition excitation 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, D2 decrease TE , little ΔTI • increase D3 little ΔTI,ΔTE Rubin et al., J. Neurophysiol., 2009

16. predictions: • increase D1, D2 decrease TE, little ΔTI • increase D3 little ΔTI, ΔTE Rubin et al., J. Neurophysiol., 2009

17. 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 ½-max synapses on

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

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. 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 locomotion with feedback – asymmetric phase modulation under variation of drive drive locomotion without feedback – loss of asymmetry Markin et al., SFN, 2009 drive

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? without feedback RG escape controls phase transitions Lucy Spardy

27. 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? drive

28. Conclusions • escapeandreleaseare 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!