leech heart half- center oscillator: control of burst duration by low- voltage activated calcium...
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Leech Heart Half-Center Oscillator:Control of Burst Duration by Low-Voltage Activated Calcium Current
Math 723: Mathematical NeuroscienceKhaldoun Hamade
June 7, 2007
Olypher A, et al. (2006); Hill J, et al. (2001)
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
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-1’s burst ends because IN-2 escapes inhibition & starts firing)
Disinhibition
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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IIII(Idt
dVC
SynSLKAKK
hCaSCaFPNa
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12
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KKAKAKAKA
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CaCaSCaSCaSCaS
CaCaFCaFCaFCaF
NaPPP
NaNaNaNaNa
EVgI
EVhmgI
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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 (τh,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
Burst duration (Continued)
Spike frequency is maximum shortly after burst initiation, and declines to fFinal at the end of burst
Low τh,CaS correspond to fast inactivation, fast
frequency decay, and shorter bursts
High τh,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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hVh
dt
dh
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(Olypher et al. 2006)
gCaS during bursting, with and without mutual inhibition
Note:
• Slope/decay of gCaS dependence on η
• Difference in minimum value of gCaS during a burst between inhibition and disinhibition
Inhibition No Inhibition
Simulations
τh,CaS was varied unilaterally in mHNv (constant
in mHNc, η=1) by varying the scaling factor η between 0.25 & 4
Period, burst duration, fFinal, and decay time constants of gCaS and spike frequency were recorded
ResultsPeriod
0
2
4
6
8
10
12
14
16
18
20
0.25 0.5 1 2 4
η
Pe
rio
d (
s)
mHNv
mHNc
Burst Duration
0
2
4
6
8
10
12
14
16
18
20
0.25 0.5 1 2 4
η
Bu
rst
Du
rati
on
(s
)
mHNv
mHNc
Final Frequency
0
2
4
6
8
10
12
14
0.25 0.5 1 2 4
η
F-f
ina
l (H
z)
mHNv
mHNc
Results
η-mHNv 0.25 0.5 1 2 4
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
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
mHNc 6.38 7.49 8.01 7.11 6.69
Results
(Olypher et al. 2006)
Results Decay time constants for ICas, gCaS, & hCaS were
measured for a representative burst (η=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
Results(Olypher et al. 2006)
Note:
• Time constant of gCaS decay in the varied neuron scaled linearly with η, 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 (r2=0.99), whereas in the constant neuron it wasn’t (r2=0.21)
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
Conclusion
Burst duration is controlled by inactivation of ICas
Scaling τh,CaS through η, 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 (ηxτh,CaS)
The escape point (from inhibition) of the opposite neuron is not affected by τh,CaS
Conclusion (Continued)
In living systems τh,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 τh,CaS ?
Conclusion (Continued)
τh,CaS sets the baseline period of the CPG
τh,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
τh,CaS sets how long it will take for a burst to reach fFinal
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
