funding: U.S. National Science Foundation

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

goal: to understand the mechanisms of rhythm generation, and modulation, in the mammalian brainstem respiratory network and other central pattern generators (CPGs)

• 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

Talk Outline

examples of central pattern generators

crustacean STG – Rabbeh and Nadim, J. Neurophysiol., 2007

leech heart IN network – Cymbalyuk et al., J. Neurosci., 2002

overall, central pattern generators (CPGs)

•  exhibit rhythms featuring ordered, alternating phases of synchronized activity

+

=

group 1

group 2

CPG rhythm

•  rhythms are intrinsically produced by the network •  rhythms can be modulated by external signals (CPG output encodes environmental conditions)

Nat. Rev. Neurosci., 2005

Pace et al., Eur. J. Neurosci., 2007: preBötzinger Complex (mammalian respiratory brainstem)

starting point for modeling CPG rhythms: eliminate spikes!

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

intermediate

adaptation

persistent sodium

post-inhibitory rebound

relative silent phase duration for cell with varied drive

relative silent phase duration for cell with fixed drive

Daun et al., J. Comp. Neurosci., 2009

fixed varied −

−

Why? transition mechanisms: escape vs. release

Wang & Rinzel, Neural Comp., 1992; Skinner et al., Biol. Cyb., 1994

inhibition on

inhibition off

inhibition on inhibition off

fast fast

slow

example: persistent sodium current w/escape

fast

slow

Daun, Rubin, and Rybak, JCNS, 2009 V

short silent phase for cell w/extra drive

baseline drive

inhibition off

extra drive

baseline orbit inhibition on

persistent sodium w/ unequal drives

baseline extra drive

−

−

fast

slow

V

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

applications to respiratory model (1)

Smith et al., J. Neurophysiol., 2007 I-to-E E-to-I

inhibition excitation

1

2 3

4

1 2 4 3

baseline 3-phase rhythm: slow projection

I-to-E transition forced to be by release: cell 2 releases cells 3 & 4

E-to-I transition by escape: cells 1 & 2 escape to start I phase

main predictions (T = duration): •  increase D1, D2 decrease TE , little ΔTI •  increase D3 little ΔTI, ΔTE

(expiratory adaptation)

(inspiratory adaptation)

E

I

4

3 2

1

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

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):

synapses on synapses ½-max

read off m2 values

trajectories live here!

repeat for different input levels

synapses on synapses ½-max

inhibited

excited

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)

Why is the period invariant?

thus, late-E activation has no impact on period! (similar result if pre-I escapes and recruits early-I)

excitation

inhibition

applications (3) – limbed locomotion model

Markin et al., Ann. NY Acad. Sci., 2009

Spardy et al., SFN, 2010

CPG (RGs, INs)

motoneurons

muscles + pendulum

drive

locomotion with feedback – asymmetric phase modulation under variation of drive

does this asymmetry imply asymmetry of CPG?

Markin et al., SFN, 2009

locomotion with feedback – asymmetric phase modulation under variation of drive

locomotion without feedback – loss of asymmetry

drive

drive

no! – model has symmetric CPG yet still gives asymmetry if feedback is present

rhythm with/without feedback: what is the difference?

with feedback

IN escape controls phase transitions

Lucy Spardy

without feedback

RG escape controls phase transitions

Lucy Spardy

rhythm with/without feedback: what is the difference?

drive

drive

idea: drive strength affects timing of INF escape (end of stance), RGE, RGF escape but not timing of INE escape

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

THANK YOU!