Week 2 review What was covered Dissolve and diffuse 2 compartment model thin vs thick membrane measurements in cells Dissolve and diffuse Assume: dissolve is much faster than diffuse k= partition coefficient(dissolve) d= diffusivity( diffuse) O=-kD ao ac 2 compartment model V2 A=cross-sectional areaL Cl() Assume solute through well stirred baths (in baths c(x, t)=c(t)) solute is conserved(nothing is eating it up or producing it baths big compared to membrane thin membrane Steady State(SS)time constant: tss If at SS then /((t)-c2(1)=P(c(t)-ct) Fick's law for membranes P is the membrane permeability d p(x, d--a dt ( n(x, D)(where n is number of solutes) Definition of fiux From Fick's law for membranes, can get the equilibrium time constant, tEQ (see supplement for derivation) Thin vs. thick membranes When does this theory break down? Compare tss to tEQ: If tEQ >Tss then thin membrane However, if tEQ is on the order of tss then not thin membraneWeek 2 Review What was covered: - Dissolve and diffuse - 2 compartment model - thin vs. thick membrane - measurements in cells Dissolve and diffuse: Assume: dissolve is much faster than diffuse k = partition coefficient (dissolve) D = diffusivity (diffuse) f = -kD ¶c - ¶f = ¶c ¶x ¶x ¶t 2 ¶ c ¶ c = kD ¶t ¶x 2 2 compartment model A= cross-sectional area V1 c1(t) V2 d c2(t) Membrane: only lets Assume: solute through - well stirred baths (in baths c(x,t)=c(t)) - solute is conserved (nothing is eating it up or producing it) - baths big compared to membrane - thin membrane d 2 Steady State (SS) time constant: t SS = 2 p D If at SS then: Dk f = (c1 (t) - c2 (t)) = P(c1 (t) - c 2 t)) Fick’s law for membranes d P is the membrane permeability 1 d f (x, t) = - � (n(x, t)) (where n is number of solutes) Definition of flux A dt From Fick’s law for membranes, can get the equilibrium time constant, tEQ: 1 t EQ = (see supplement for derivation) � 1 1 � AP� � Ł V1 + V2 ł � � Thin vs. thick membranes When does this theory break down? Compare tSS to tEQ: If tEQ>>tSS then thin membrane… However, if tEQ is on the order of tSS then not thin membrane: