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Communication between cells Slide 2 R I1I1 Biology Electrical equivalent I2I2 I = I 1 + I 2 I Slide 3 Nernst Equation The Nernst equation relates the potential difference to the concentration difference in equilibrium: C i / C o = exp { - Z e (V i -V o )/kT } or V i - V o = (kT/Ze) ln (C o /C i ) with e = charge electron Z = valence of ion k = Boltzmann constant T = temperature C i (C o ) = concentration inside (outside) membrane Slide 4 Example of Nernst equation t=0 R + 50 N a + 50 Cl - 100 N a + 100 Cl - 100 t >> 0 R + 50 N a + 64 Cl - 114 N a + 86 Cl - 86 V = 0V = - 10 If both N a and Cl, but not R + can migrate through the membrane. Slide 5 Nernst equation for squid axon Slide 6 Problems with Nernst equation considers only a single ion. If multiple ions are involved, it assumes equal permeability for all ions Applies only to passive transport ions migrate independently of each other Slide 7 Goldman/Hodgkin/Katz equation The Nernst equation relates the potential difference to the concentration difference in equilibrium for a single neuron. When several ions are involved, we obtain for equilibrium : P k [K] o +P Na [Na] o +P Cl [Cl] i V = (RT/F) ln --------------------------------- P k [K] i +P Na [Na] i +P Cl [Cl] o with Pi = permeability of ion i [K] i/o = concentration inside/outside F = Faraday constant T = temperature V = potential difference across membrane Slide 8 Current through an ion channel Slide 9 Schematic overview of the active membrane Slide 10 Hodgkin & Huxley: Current through an ion-channel Ohms law Conductance G=1/R Conductance G is a product of maximal conductance g Ca and the fraction of open channels m 3 h R V ion outside inside 0 mV V mV I 0 mV V mV I Slide 11 State: Gating kinetics Slide 12 Open State: Gating kinetics Slide 13 Open Closed mm mm m Probability: State: (1-m) mm mm Gating kinetics Slide 14 V (mV) mm mm Open Closed mm mm m Probability: State: (1-m) mm mm Channel Open Probability: Gating kinetics Slide 15 -150-100-50050100150 0 0.2 0.4 0.6 0.8 1 m (V) -150-100-50050100150 0 2 4 6 8 x 10 -3 m (V) m (s) -150-100-50050100150 0.2 0.4 0.6 0.8 1 1.2 h (V) V clamp (mV) -100-50050100 0 2 4 6 8 10 h (V) V clamp (mV) h (s) Parameter fitting (2) Slide 16 -150-100-50050100150 0 0.2 0.4 0.6 0.8 1 m (V) -150-100-50050100150 0 2 4 6 8 x 10 -3 m (V) m (s) -150-100-50050100150 0.2 0.4 0.6 0.8 1 1.2 h (V) V clamp (mV) -100-50050100 0 2 4 6 8 10 h (V) V clamp (mV) h (s) Parameter fitting (2) Slide 17 V (mV) mm mm Open Closed mm mm m Probability: State: (1-m) mm mm Channel Open Probability: Gating kinetics g m (t) = g m, max (m - m 0 )(1 - e -t/ ) g h (t) = g h, max (h - h 0 )e -t/ m3hm3h time g gmgm ghgh g Na Slide 18 V mV 0 mV V mV 0 mV ICIC I Na Kirchoffs law: Membrane voltage equation I Na = g max, Na m 3 h(V- V Na ) -C m dV/dt = g max, Na m 3 h(V-V na ) + g max, K n 4 (V-V K ) + g leak (V-V na ) Slide 19 Actionpotential