Open worm journal club 2
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Introduction to Hodgkin-Huxley equations and a model of the c. elegans muscle cell.

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

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    Open worm journal club 2 Open worm journal club 2 Presentation Transcript

    • Open Worm Journal Club #2 C. Elegans body wall muscles are simple actuators Boyle & Cohen 2007
    • Equivalent circuit diagram
    • Hodgkin Huxley basics
      • 1952 work by two British physiologists
      • Awarded the 1963 Nobel Prize in Physiology / Medicine
      • Describes how action potentials in neurons are initiated and propagated
      • A set of nonlinear ODEs that approximates the electrical characteristics of excitable cells
    • Cell review
    • Hodgkin Huxley foundations
      • Membrane is modeled as a capacitor
      • Voltage-gated ion channels are modeled as nonlinear electrical conductances
    • Hodgkin Huxley foundations
      • Capacitance is the ability of a body to hold an electrical charge
      • Also the measure of the amount of electrical energy stored for a given electric potential
      • Capacitance is measured in units called the farad.
      • Farad is 1 coulomb per volt
      • Coulomb is the unit of electric charge
      • Volt is the unit of electromotive force / electric potential difference
    • Hodgkin Huxley foundations
      • Resistance is the measure of opposition to an electrical current
      • Conductance is the inverse of resistance & measures how easily electricity flows along a certain path
      • Resistance is measured in units of ohms.
      • Conductance is measured in units of Siemens a.k.a. mhos (get it?)
      • Resistance is the ratio of voltage across it to the current through it
    • Hodgkin Huxley foundations
      • Electric current is a stream of charged objects
      • Current is measured in terms of coulombs per second, also known as Amperes (Amps)
    • 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 i-th ion channel Conductance of the i-th ion channel Change of voltage across membrane over time
    • 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
    • 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
    • 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
    • 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.
    • Activation variable dynamics A different looking, but equivalent form splits the activation variable into an “alpha” and a “beta” function of voltage
    • 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-th cell Current leaking through the membrane of the n-th cell
    • 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
    • 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 Quadrant 1 Quadrant 2 Quadrants of muscle cells
    • 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
    • Equivalent circuit diagram