leech heart half- center oscillator: control of burst duration by low- voltage activated calcium...

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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CaCaSCaSCaSCaS

CaCaFCaFCaFCaF

NaPPP

NaNaNaNaNa

EVgI

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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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(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