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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) – PowerPoint PPT presentation

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


1
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
2
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3
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

4
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)

5
Disinhibition
6
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
7
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

8
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

9
(Olypher et al. 2006)
10
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

11
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

12
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13
Results
14
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
15
Results
(Olypher et al. 2006)
16
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

17
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)

18
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

19
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

20
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 ?

21
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

22
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

23
Questions?
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