9/19/10!1!IK=gK(Em-EK)!INa=gNa(Em-ENa)!ICl=gCl(Em-ECl)!IK+INa+KCl=0! ∴Em=gkg∑Ek+gNag∑ENa+gClg∑EClWhere ! g∑=gK+gNa+gClAt the steady state (resting membrane) when there !Is not net current:!For K, Na and Cl:!9/19/10!2!9/19/10!3!The “sodium theory” of the action potential!Action potentials exhibit an overshoot. Thus the peak of the action potential!is well above zero. Hodgkin and Katz suggested (in 1949) that this was due to !a rapid and selective increase increase in the permeability towards sodium.Thus !gNa transiently becomes much greater than gk .How can this idea be tested?!9/19/10!4!Depolarization!Increase in gNa!Na flux!Positive Feedback!I=CmdEdt+IiCurrent flowing through the axon !membrane is assumed to consist of !capacity current and Ionic current.!If the voltage is held constant i.e!The membrane is clamped dE/dt=0!and the membrane current =ionic current!i.e I=Ii!9/19/10!5!Voltage Clamp!9/19/10!6!The potential at which the initial (Na current) is neither inward nor outward!is the reversal potential ENa for the Na current i.e about 117 mV.!9/19/10!7!From traces of Na current as a function of time we can obtain!gNa by using the equation INa=gNa(E-ENa). ENa is the potential at !which the current is nulled.!9/19/10!8!9/19/10!9!=CmdV/dt+gk(E-Ek)+gNa (E-ENa)+ gl(E-El)!Im!If we knew the time and voltage dependence of!gNa and gK we could obtain the form the the action!potential by numerical integration of the following !equation.!9/19/10!10!Im=CmdE/dt+Ik+INa+Ii!=CmdV/dt+gk(E-Ek)+gNa (E-ENa)+ gl(E-El)!gKgNagK=!n4!gNa=!m3h!CmdV/dt!+! n4!gNa(E-Ek)+! (E-ENa)+!gl(E-El)!gNam3h!=!n=probability of 4 charged particles being!in the correct configuration for conduction.!n=probability of 3 charged particles being!In the correct configuration.1-h=probability !of inactivation.!n is the potassium activation parameter,m and h are the !Na activation and inactivation parameters. !With the voltage and time dependence of m,n and h the !Above equation can be solved for V by numerical integration!9/19/10!11!9/19/10!12!9/19/10!13!Channel (Gating) Simulations!Action Potential from Different Cells!9/19/10!14!Cardiac Ion Currents!K+!Ca2+!3Na+!3Na+!Na+!2K+!Ca2+!Ion channels! Carrier mediated ion transport!• Passive ion movement!• Driven by concentration and electrostatic gradients!• Na-K and Ca pumps require ATP!• Capable of driving against concentration gradient!Na-K!pump!Na-Ca!exchanger!Ca!pump!Cardiac Action Potential!0!-80!mV!Na+ current!K+ current!Ca+ current!Na threshold!= depolarizing!= hyperpolarizing!9/19/10!15!Cardiac Cell Currents![K!+!]!i![Ca!++!]!o![Na!+!]!i![Na!+!]!o!-!+!-!-!-!-!-!-! -! -! -!-!-!-![Ca!++!]!i![Ca!++!]!o!-!-![K!+!]!o![Ca!++!]!i!+!+!+! +![K!+!]!i![K!+!]!o!-!-!-!-!-!-! -! -! -!-!-!-!-!0!-80!mV!Chemical !Electrostatic!9/19/10!16!Calcium Cycle in Cardiac