Transcript Leech Heart Half Center Oscillator

Leech Heart HalfCenter Oscillator:
Control of Burst Duration by LowVoltage Activated Calcium Current
Olypher A, et al. (2006); Hill J, et al. (2001)
Math 723: Mathematical Neuroscience
Khaldoun Hamade
June 7, 2007
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
dV
Ionic currents:
C
 (I
 INa : fast Na+
 IP : persistent Na+
In

Out
fast, low-threshold Ca2+
slow, low-threshold Ca2+
Ih : hyperpolarization-activated
cation current
 ICaF :
 ICaS :
delayed rectifier K+
persistent K+
IKA : fast, transient K+
 IK1 :
 IK2 :

dt
Na
 I P  I CaF  I CaS  I h
 I K 1  I K 2  I KA  I L  I SynS )
3
I Na  g Na m Na
hNa (V  E Na )
I P  g P mP (V  E Na )
2
I CaF  g CaF mCaF
hCaF (V  ECa )
2
I CaS  g CaS mCaS
hCaS (V  ECa )
I h  g h mh2 (V  Eh )
I K 1  g K 1mK2 1hK 1 (V  E K )
I K 2  g K 2 mK2 2 (V  E K )
2
I KA  g KA mKA
hKA (V  E K )
I L  g L (V  E L )
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
2
I CaS  g CaS mCaS
hCaS (V  ECa )
dhCaS h ,CaS (V )  hCaS

dt
 h ,CaS (V )
 h ,CaS (V )  0.2 
5.25
1  e  250 (V  0.043)
(Olypher et al. 2006)
gCaS during bursting, with and without mutual inhibition
Inhibition
No Inhibition
Note:
• Slope/decay of gCaS dependence on η
• Difference in minimum value of gCaS during a burst between inhibition and
disinhibition
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
Results
Burst Duration
Period
20
18
18
Burst Duration (s)
20
14
12
mHNv
10
mHNc
8
6
4
2
16
14
12
mHNv
10
mHNc
8
6
4
2
0
0
0.25
0.5
1
2
4
0.25
0.5
η
1
η
Final Frequency
14
12
F-final (Hz)
Period (s)
16
10
8
mHNv
6
mHNc
4
2
0
0.25
0.5
1
η
2
4
2
4
Results
η-mHNv
0.25
0.5
1
2
4
Period (s)
6.14
6.6
7.55
12.44
19.26
mHNv
1.67
2.196
3.82
9.83
16.41
mHNc
4.5
3.71
3.87
2.61
2.78
mHNv
4.85
6.054
8.35
8.18
7.51
mHNc
6.38
7.49
8.01
7.11
6.69
Burst
Duration (s)
F-final (Hz)
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 lowvoltage-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