1 / 15

Action Potential - Review

Action Potential - Review. V m = V Na G Na + V K G K + V Cl G Cl G Na + G K + G Cl. Current Paths. Response to an injected step current charge Capacitor (I Rm = 0) Transmembrane Ionic Flux (I Rm ) Along Axoplasm ( D V). Current Flow - Initial.

dava
Download Presentation

Action Potential - Review

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Action Potential - Review • Vm = VNa GNa + VK GK + VCl GCl • GNa + GK + GCl

  2. Current Paths • Response to an injected step current charge • Capacitor (IRm = 0) • Transmembrane Ionic Flux (IRm) • Along Axoplasm (DV)

  3. Current Flow - Initial • All current flows thru the capacitor • (low resistant path to injected step current) • Redistributed charges change Vm • Current begins to flow thru Rm and spreads laterally, • affecting adjacent membrane capacitance. • At injection point, dv/dt 0, Ic = 0 • Transmembrane current carried only by Rm, • remainder of current spread laterally along axon. • (Rm relatively high resistance, axon relatively low)

  4. Current Flow - Sequential • The process is repeated at adjacent membrane • due to influence of the lateral current along axon. • As the capacitor initially accumulates charge, • Vm changes, current flows thru Rm, dv/dt 0, Ic = 0. • Transmembrane current carried only by Rm, • remainder of current spreads laterally along axon. • etc, etc, etc, etc.

  5. Passive Membrane - Analytical • Note: T = RmC and VIN = RmIIN • Response to step current for • C DV/dt + V/R = IIN (0 < t < Dt) • Vm(t) = Vr + VIN(1 - e-t/T) • Response to removal of step current for • C DV/dt + V/R = 0 (t > 0) • Vm(t’) = Vr + VIN(1 - e-Dt / T) e-t’/ T

  6. Cable Equation Passive Membrane • Propagating Voltage V’ = Vm - VResting • Current Im = -dIin/dX = dIout/dX • General Cable Equation d2V’/dX2 = (Rout + Rin) Im • Passive Membrane Im = V’/Rm + C(dV’/dt) • V’ = Vq e-X/l where l = [ Rm / (Rout + Rin) ]1/2

  7. Cable Equation (Passive) - continued • General Cable Equation d2V’/dX2 = (Rout + Rin) Im • Passive Membrane Im = V’/Rm + C(dV’/dt) • Action Potential Equation (by substituting from above) • (Rout + Rin)-1 d2V’/dX2 = V’/Rm + C(dV’/dt)

  8. Cable Equation Active Membrane • d2V’/dX2 = (Rout + Rin) Im • since Rout >> Rin d2V’/dX2 = Rout Im • Assumption • Action potential travels at constant velocity q • so X = q t • d2V’/dX2 = d2V’/d(q t)2 = (1/d2)d2V’/dt2

  9. Cable Equation (Active) - continued • From • (Rout + Rin)-1 d2V’/dX2 = V’/Rm + C(dV’/dt) • d2V’/dX2 = Rout Im • d2V’/dX2 = d2V’/d(q t)2 = (1/d2)d2V’/dt2 • Substituting and rearranging • (Rinq2)-1(d2V’/dt2) - C(dV’/dt) - V’/Rm = 0 • Im - IC - IRm = 0 • Note: Differential Potential V’ = Vm - VResting • is the propagating potential.

  10. Cable Equation (Active) - continued • (Rinq2)-1(d2V’)/dt2 - C(dV’/dt) - V’/Rm = 0 • d2V’/dt2 - (Rinq2) C(dV’/dt) - (Rinq2)/Rm V’ = 0 • Solving the differential equation and using typical values for C=10-13 F, Rin=109W and Rm = 1010 W • and q = 100 m/s (1 m/s < q < 100 m/s) • and boundary conditions (t=¥,V’=0) and (t=0, V’=Va) • V’ = Vae-.916t

  11. Propagating Action Potential

  12. Action Potential • If a stimulus exceeds threshold voltage, then • a characteristic non-linear response occurs. • An voltage waveform the so called electrogenic • “Action Potential” is generated due to a change in the membrane permeability to sodium and potassium ions. • The action potential is propagated undiminished and with constant velocity along the nerve axon.

  13. Hodgkin-Huxley Equation • Unit Membrane Model • Longitudinal resistance of axoplasm per unit length • Resistance = Resistivity / Cross Sectional Area • Membrane Current Density (Flux) • Currents (Capacitive, Sodium, Potassium, Others) • Uses Conductances rather than Resistances • Variable Permeabilities as a function of Vm’(t) • Sodium GNa = GNa M3H • Potassium GK = GK N4

  14. H & H - continued • Conductances Gna and GK are variable and are defined by their respective permeabilities. • Sodium Gna = GNa M3H • Potassium GK = GK N4 • M is the hypothetical process that activates GNa • H is the hypothetical process that deactivates GNa • N is is the hypothetical process that activates GK • M, H, N are membrane potential and time dependent • G = G Max

  15. H & H - Concluding Remark • The Hodgkin-Huxley Model was first developed in the 1940’s and published in the 1950’s. • It does not explain how or why the membrane permeabilities change, but it does model the shape and speed of the action potential quite faithfully. • Empirical values were developed for the GNa, GK, GL • as well as the hypothetical permeability relationships for M, H, N using the giant squid axon.

More Related