Open Worm Journal Club #2 C. Elegans body wall muscles are simple actuators Boyle & Cohen 2007
Equivalent circuit diagram
Hodgkin Huxley basics <ul><li>1952 work by two British physiologists </li></ul><ul><li>Awarded the 1963 Nobel Prize in Phy...
Cell review
Hodgkin Huxley foundations <ul><li>Membrane is modeled as a  capacitor </li></ul><ul><li>Voltage-gated ion channels are mo...
Hodgkin Huxley foundations <ul><li>Capacitance is the ability of a body to hold an electrical charge </li></ul><ul><li>Als...
Hodgkin Huxley foundations <ul><li>Resistance is the measure of opposition to an electrical current </li></ul><ul><li>Cond...
Hodgkin Huxley foundations <ul><li>Electric current is a stream of charged objects </li></ul><ul><li>Current is measured i...
Using those basics,  a general form can derived
General form of the Hodgkin-Huxley Equation Capacitance of membrane Voltage across the membrane Reversal potential of the ...
Equivalent circuit diagram Capacitance of membrane Voltage across the membrane Reversal potential of the i-th ion channel ...
Nonlinear, voltage dependant conductances m and n are known as “activation variables”, while h is an “inactivation variabl...
Nonlinear, voltage dependant conductances General form Maximal conductance Activation variable (unitless, real-valued from...
Activation variable dynamics First derivative of an activation variable involves a time constant, a steady state value tha...
Activation variable dynamics A different looking, but equivalent form splits the activation variable into an “alpha” and a...
Equivalent circuit diagram
Muscle cell with “arms” Cell Body 5 arms,  10 compartments each, passive currents Cell body, 1 compartment, active currents
The connectional currents Cell Body 1 n N Current flowing into body Current leaving the n-th cell Current entering the n-t...
The connectional currents Cell Body 1 n N Current flowing into body Current leaving the n-th cell Current entering the n-t...
body wall muscle cells (adult worm) cell lineage shown:
Cell Body Cell Body Cell Body Cell Body Cell Body Cell Body Cell Body Cell Body Cell Body Cell Body Cell Body Cell Body Qu...
Their simplified quadrants of muscle cells Cell Body Cell Body Cell Body Cell Body Cell Body Cell Body Inter-muscular, Int...
Equivalent circuit diagram
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Open worm journal club 2

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

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Open worm journal club 2

  1. 1. Open Worm Journal Club #2 C. Elegans body wall muscles are simple actuators Boyle & Cohen 2007
  2. 2. Equivalent circuit diagram
  3. 3. Hodgkin Huxley basics <ul><li>1952 work by two British physiologists </li></ul><ul><li>Awarded the 1963 Nobel Prize in Physiology / Medicine </li></ul><ul><li>Describes how action potentials in neurons are initiated and propagated </li></ul><ul><li>A set of nonlinear ODEs that approximates the electrical characteristics of excitable cells </li></ul>
  4. 4. Cell review
  5. 5. Hodgkin Huxley foundations <ul><li>Membrane is modeled as a capacitor </li></ul><ul><li>Voltage-gated ion channels are modeled as nonlinear electrical conductances </li></ul>
  6. 6. Hodgkin Huxley foundations <ul><li>Capacitance is the ability of a body to hold an electrical charge </li></ul><ul><li>Also the measure of the amount of electrical energy stored for a given electric potential </li></ul><ul><li>Capacitance is measured in units called the farad. </li></ul><ul><li>Farad is 1 coulomb per volt </li></ul><ul><li>Coulomb is the unit of electric charge </li></ul><ul><li>Volt is the unit of electromotive force / electric potential difference </li></ul>
  7. 7. Hodgkin Huxley foundations <ul><li>Resistance is the measure of opposition to an electrical current </li></ul><ul><li>Conductance is the inverse of resistance & measures how easily electricity flows along a certain path </li></ul><ul><li>Resistance is measured in units of ohms. </li></ul><ul><li>Conductance is measured in units of Siemens a.k.a. mhos (get it?) </li></ul><ul><li>Resistance is the ratio of voltage across it to the current through it </li></ul>
  8. 8. Hodgkin Huxley foundations <ul><li>Electric current is a stream of charged objects </li></ul><ul><li>Current is measured in terms of coulombs per second, also known as Amperes (Amps) </li></ul>
  9. 9. Using those basics, a general form can derived
  10. 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. 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. 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. 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. 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. 15. Activation variable dynamics A different looking, but equivalent form splits the activation variable into an “alpha” and a “beta” function of voltage
  16. 16. Equivalent circuit diagram
  17. 17. Muscle cell with “arms” Cell Body 5 arms, 10 compartments each, passive currents Cell body, 1 compartment, active currents
  18. 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. 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. 20. body wall muscle cells (adult worm) cell lineage shown:
  21. 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. 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. 23. Equivalent circuit diagram

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