1Physiology 472/572 - 2011 - Quantitative modeling of biological systems Lecture 6: Nernst potential, membrane potential Which way will K+ move across the membrane: • high to low electric potential? • high to low concentration? Electrochemical potential of a substance X • FEzaln RTμ~xXX+= • aX is the activity of X, equal to [X] at low concentration • in general, aX < [X] due to non-ideal behavior of solution • R = gas constant = 8.32 J/mol-K • T = temperature = 310 K at 37 C • zX = charge (e.g. -1) • F = Faraday constant = 96500 coulomb/mol • E = electric potential At equilibrium, electrochemical potentials are equal on both sides • inxinXoutxoutXFEzaln RTFEzaln RT +=+ • outXinXxoutXinXxoutinXaalogFzRT 2.303-aalnFzRT-E-EE ===, the Nernst potential for X • 2.303 RT/F = 0.0615 V = 61.5 mV For the above example • assuming aK = [K] gives EK = -61.5 mV • using activity values gives smaller value (~ 55 mV) [K+]out = 1 mM [K+]in = 10 mM Eout = 0 Ein = -85 mV2• actual membrane potential Em = Ein - Eout = -85 mV • K+ moves from out to in, against the concentration gradient • current is gK(Em - EK) where gK is the membrane conductance for K+ • conductance is mainly due to ion channels Membrane resting potential • under resting (steady-state) conditions, cell membranes are polarized • membrane potential (inside - outside) is generally 70 - 100 mV • for each ion X, with membrane conductance gX, the current iX = gX(Em - EX) • consider multiple ionic species, total current must be zero • gNa(Em - ENa) + gK(Em - EK) + gCl(Em - ECl) = 0 • ClKNaClClKKNaNamgggEgEgEgE++++= • ENa = 62 mV, EK = -95 mV, ECl = -87 mV • if gNa = 0.15 mS/cm2, gK = 2.1 mS/cm2, gCl = 0.3 mS/cm2, then Em = -85 mV • resting membrane potential is highly dependent on the values of the conductances Membrane potential - the Goldman-Hodgkin-Katz equation • also called constant field equation • inCloutKoutNaoutClinKinNam[Cl]g[K]g[Na]g[Cl]g[K]g[Na]glnFRT-E++++= • widely used, although it is based on assumptions that do not apply to ion channels • see http://www.nernstgoldman.physiology.arizona.edu/ for simulator [Na+]out = 142 mM [Na+]in = 14 mM [K+]out = 4 mM [K+]in = 140 mM [Cl-]out = 103 mM [Cl-]in = 4 mM Eout = 0 Ein = -85
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