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

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

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

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

Nat. Rev. Neurosci., 2005

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

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

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

− 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

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

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

− 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

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

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

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

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

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

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

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

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

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)

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

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?

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

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

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

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?

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

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