Leech%20Heart%20Half-Center%20Oscillator:

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Leech Heart Half-Center Oscillator

• Control of Burst Duration by Low-Voltage
  Activated Calcium Current

Olypher A, et al. (2006) Hill J, et al. (2001)
Math 723 Mathematical Neuroscience Khaldoun
Hamade June 7, 2007
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Introduction

• Half-center oscillators, also called central
  pattern generators (CPG), drive rhythmic
  behaviors
• Burst Period Burst Duration Interburst
  Interval
• Burst period varies depending on functional
  demand of activity (ex. Heart rate, breathing
  rate, locomotion speed)
• Bursting is maintained by slowly inactivating
  inward currents

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Leech Heart CPG

• A pair of mutually inhibitory neurons
• Burst duration is controlled by both, the
  bursting neuron itself and the opposite neuron
• Each neuron on its own is capable of producing a
  bursting pattern the inhibitory coupling adds
• the alternating pattern
• control of burst termination by the opposite
  neuron(IN-1s burst ends because IN-2 escapes
  inhibition starts firing)

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Disinhibition
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Modeling of Leech Heart CPG (Hill et al. 2001)

• One compartment model
• Ionic currents
• INa fast Na
• IP persistent Na
• ICaF fast, low-threshold Ca2
• ICaS slow, low-threshold Ca2
• Ih hyperpolarization-activated cation current
• IK1 delayed rectifier K
• IK2 persistent K
• IKA fast, transient K

In
Out
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Burst duration

• The low-voltage-activated (LVA) calcium current
• ICaF (Fast) contributes to burst initiation
• ICaS (Slow) determines burst duration
• The inactivation time constant of ICaS (th,CaS)
  determines the spike frequency decay rate
• The spike frequency determines the amount of
  inhibition the opposite neuron is receiving
• Once the spike frequency (inhibition) falls below
  a certain value (fFinal) the opposite neuron
  escapes inhibition and begins to burst

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Burst duration (Continued)

• Spike frequency is maximum shortly after burst
  initiation, and declines to fFinal at the end of
  burst
• Low th,CaS correspond to fast inactivation, fast
  frequency decay, and shorter bursts
• High th,CaS correspond to slow inactivation, slow
  frequency decay, and longer bursts
• Maximal value of gh can control the length of
  the interburst duration a higher value allows
  the neuron to escape inhibition earlier, when it
  is still higher

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(Olypher et al. 2006)
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gCaS during bursting, with and without mutual
inhibition
Inhibition
No Inhibition

• Note
• Slope/decay of gCaS dependence on ?
• Difference in minimum value of gCaS during a
  burst between inhibition and disinhibition

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Simulations

• th,CaS was varied unilaterally in mHNv (constant
  in mHNc, ?1) by varying the scaling factor ?
  between 0.25 4
• Period, burst duration, fFinal, and decay time
  constants of gCaS and spike frequency were
  recorded

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Results
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Results
?-mHNv ?-mHNv 0.25 0.5 1 2 4

Period (s) Period (s) 6.14 6.6 7.55 12.44 19.26

Burst Duration (s) mHNv 1.67 2.196 3.82 9.83 16.41
Burst Duration (s) mHNc 4.5 3.71 3.87 2.61 2.78

F-final (Hz) mHNv 4.85 6.054 8.35 8.18 7.51
F-final (Hz) mHNc 6.38 7.49 8.01 7.11 6.69
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Results
(Olypher et al. 2006)
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Results

• Decay time constants for ICas, gCaS, hCaS were
  measured for a representative burst (?1)
• Decay time constants for ICas gCaS were found
  to be equal, while that of hCaS was different
  this was attributed to a voltage decline during
  the burst
• Decay time constant of gCaS was chosen as the
  benchmark
• For each simulation the decay time constants for
  gCaS spike frequency were calculated and
  compared

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Results
(Olypher et al. 2006)

• Note
• Time constant of gCaS decay in the varied neuron
  scaled linearly with ?, on the other hand that of
  the constant neuron remained unchanged
• Time constant of frequency decay was strongly
  correlated to that of gCaS in the varied neuron
  (r20.99), whereas in the constant neuron it
  wasnt (r20.21)

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Hybrid system

• The hybrid system was constructed from a model
  neuron running in real time and a chemically
  isolated living heart neuron, with inhibitory
  coupling through a dynamic clamp
• ICas time constant of inactivation was varied
  unilaterally, once in the model neuron and once
  in the living heart neuron
• Results were similar to those obtained in the
  model system

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Conclusion

• Burst duration is controlled by inactivation of
  ICas
• Scaling th,CaS through ?, scales the decay time
  constant of gCaS ICas equally
• Decay of gCaS is correlated with a parallel decay
  in spike frequency
• fFinal does not vary with (?xth,CaS)
• The escape point (from inhibition) of the
  opposite neuron is not affected by th,CaS

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Conclusion (Continued)

• In living systems th,CaS is not usually modulated
• Varying maximal value of gCaS modifies the burst
  duration, but also affect the output signal of
  the premotor CPG (strength and spike frequency)
• Modulation of the maximal value of gh varies the
  period without affecting the signal output
• gh is modulated in living systems
• So why should we care about the affect of th,CaS ?

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Conclusion (Continued)

• th,CaS sets the baseline period of the CPG
• th,CaS sets the dynamic range over which
  modulation of gh max. can regulate the period of
  the heart half-center oscillator
• gh max sets fFinal (the escapable inhibition) and
  thus the period
• th,CaS sets how long it will take for a burst to
  reach fFinal

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References

• Olypher A, Cymbalyuk G, Calabrese RL. Hybrid
  systems analysis of the control of burst duration
  by low-voltage-activated calcium current in leech
  heart interneurons, J Neurophysiol. 2006 Dec
  96(6)2857-67
• Model
• Hill AA, Lu J, Masino MA, Olsen OH, Calabrese RL.
  A model of a segmental oscillator in the leech
  heartbeat neuronal network. J Comput Neurosci.
  2001 May-Jun 10(3)281-302

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Questions?