1. Leech Heart Half- Center Oscillator: Control of Burst Duration by Low- Voltage Activated Calcium Current Math 723: Mathematical Neuroscience Khaldoun Hamade June 7, 2007 Olypher A, et al. (2006); Hill J, et al. (2001)

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-1’s 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:  I Na : fast Na +  I P : persistent Na +  I CaF : fast, low-threshold Ca 2+  I CaS : slow, low-threshold Ca 2+  I h : hyperpolarization-activated cation current  I K1 : delayed rectifier K +  I K2 : persistent K +  I KA : fast, transient K + In Out

7. Burst duration The low-voltage-activated (LVA) calcium current:  I CaF (Fast): contributes to burst initiation  I CaS (Slow): determines burst duration The inactivation time constant of I CaS (τ h,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 ( f Final ) the opposite neuron escapes inhibition and begins to burst

8. Burst duration (Continued) Spike frequency is maximum shortly after burst initiation, and declines to f Final at the end of burst  Low τ h,CaS correspond to fast inactivation, fast frequency decay, and shorter bursts  High τ h,CaS correspond to slow inactivation, slow frequency decay, and longer bursts *** Maximal value of g h 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. g CaS during bursting, with and without mutual inhibition Note: Slope/decay of g CaS dependence on η Difference in minimum value of g CaS during a burst between inhibition and disinhibition InhibitionNo Inhibition

11. Simulations τ h,CaS was varied unilaterally in mHNv (constant in mHNc, η=1) by varying the scaling factor η between 0.25 & 4 Period, burst duration, f Final, and decay time constants of g CaS and spike frequency were recorded

13. Results

14. η-mHNv0.250.5124 Period (s)6.146.67.5512.4419.26 Burst Duration (s) mHNv 1.672.1963.829.8316.41 mHNc 4.53.713.872.612.78 F-final (Hz) mHNv 4.856.0548.358.187.51 mHNc 6.387.498.017.116.69

15. Results (Olypher et al. 2006)

16. Results Decay time constants for I Cas, g CaS, & h CaS were measured for a representative burst (η=1) Decay time constants for I Cas & g CaS were found to be equal, while that of h CaS was different; this was attributed to a voltage decline during the burst Decay time constant of g CaS was chosen as the benchmark For each simulation the decay time constants for g CaS & spike frequency were calculated and compared

17. Results (Olypher et al. 2006) Note: Time constant of g CaS 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 (r 2 =0.99), whereas in the constant neuron it wasn’t (r 2 =0.21)

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 I Cas 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 I Cas Scaling τ h,CaS through η, scales the decay time constant of g CaS & I Cas equally Decay of g CaS is correlated with a parallel decay in spike frequency f Final does not vary with (ηx τ h,CaS ) The escape point (from inhibition) of the opposite neuron is not affected by τ h,CaS

20. Conclusion (Continued) In living systems τ h,CaS is not usually modulated Varying maximal value of g CaS modifies the burst duration, but also affect the output signal of the premotor CPG (strength and spike frequency) Modulation of the maximal value of g h varies the period without affecting the signal output g h is modulated in living systems So why should we care about the affect of τ h,CaS ?

21. Conclusion (Continued) τ h,CaS sets the baseline period of the CPG τ h,CaS sets the dynamic range over which modulation of g h max. can regulate the period of the heart half-center oscillator g h max sets f Final (the escapable inhibition) and thus the period τ h,CaS sets how long it will take for a burst to reach f Final

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