Introduction to Hodgkin-Huxley equations and a model of the c. elegans muscle cell.

1. Open Worm Journal Club #2 C. Elegans body wall muscles are simple actuators Boyle & Cohen 2007

2. Equivalent circuit diagram

4. Cell review

9. Using those basics, a general form can derived

10. General form of the Hodgkin-Huxley Equation Capacitance of membrane Voltage across the membrane Reversal potential of the i-th ion channel Conductance of the i-th ion channel Change of voltage across membrane over time

11. Equivalent circuit diagram Capacitance of membrane Voltage across the membrane Reversal potential of the i-th ion channel Conductance of the i-th ion channel Change of voltage across membrane over time

12. Nonlinear, voltage dependant conductances m and n are known as “activation variables”, while h is an “inactivation variable”. All of them are functions of voltage as well

13. Nonlinear, voltage dependant conductances General form Maximal conductance Activation variable (unitless, real-valued from 0-1) Inactivation variable (unitless, real-valued from 0-1) Constant integers

14. Activation variable dynamics First derivative of an activation variable involves a time constant, a steady state value that is a function of voltage, and a function of the activation variable with respect to time. Inactivation variable follows the same form.

15. Activation variable dynamics A different looking, but equivalent form splits the activation variable into an “alpha” and a “beta” function of voltage

16. Equivalent circuit diagram

17. Muscle cell with “arms” Cell Body 5 arms, 10 compartments each, passive currents Cell body, 1 compartment, active currents

18. The connectional currents Cell Body 1 n N Current flowing into body Current leaving the n-th cell Current entering the n-th cell Current leaking through the membrane of the n-th cell

19. The connectional currents Cell Body 1 n N Current flowing into body Current leaving the n-th cell Current entering the n-th cell Current leaking through the membrane of the n-th cell

20. body wall muscle cells (adult worm) cell lineage shown:

21. Cell Body Cell Body Cell Body Cell Body Cell Body Cell Body Cell Body Cell Body Cell Body Cell Body Cell Body Cell Body Quadrant 1 Quadrant 2 Quadrants of muscle cells

22. Their simplified quadrants of muscle cells Cell Body Cell Body Cell Body Cell Body Cell Body Cell Body Inter-muscular, Intra-quadrant gap junction currents. Occurs between cell bodies Inter-quadrant gap junction currents. Occurs between tips of muscle arms. Quadrant 1 Quadrant 2

23. Equivalent circuit diagram