麻省理工学院：《电气工程与计算机科学》学习资料_Week2

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 membrane

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) 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:

What does this mean 1. time to get to Ss cannot be ignored 2. concentration in baths will change significantly before reaching SS 3. amount of solute in membrane might not be negligible 4. overall time profiles of concentration/flux are NOT exponentials(can't reduce to Ficks law for membranes so profiles are not solutions to 1 order linear differential equation) Measurements (To measure time constant of exponential curve: extend a line at initial time and intersecting with the asymptote.. see problem set 1) N How to measure tss? On SMall time scale 1. look at plot of concentration profile in membrane(remember: on short time scale, only membrane concentration is changing; bath concentrations are not changing significantly at this point 2. look at plot of o (t) How to mea On large time scale look at plots of concentration. (in bath or membrane) 2. look at plot of o (t) If you aren t comfortable with figuring out time constants and stuff like that from concentration and flux plots review problem 4 and5 on pset #2 and practice with the simulation software..(and if you are still confused, feel free to ask us(the tas) questions!! @) More measurements Be comfortable with the plots Prof. Freeman put up in lecture which kind of look like this See pg. 145 in the text for nicer graph where P is the permeability of a solute and k is the partitioning coefficient M<60 060<M<160 ■M160 What do these show

What does this mean: 1. time to get to SS cannot be ignored 2. concentration in baths will change significantly before reaching SS 3. amount of solute in membrane might not be negligible 4. overall time profiles of concentration/flux are NOT exponentials (can’t reduce to Fick’s law for membranes so profiles are not solutions to 1st order linear differential equation) Measurements: (To measure time constant of exponential curve: extend a line at initial time and intersecting with the asymptote… see problem set 1) c or f t exponential curve t How to measure tSS? On SMALL time scale: 1. look at plot of concentration profile in membrane (remember: on short time scale, only membrane concentration is changing; bath concentrations are not changing significantly at this point.) 2. look at plot of f(t) How to measure tEQ? On LARGE time scale: 1. look at plots of concentration. (in bath or membrane) 2. look at plot of f(t) If you aren’t comfortable with figuring out time constants and stuff like that from concentration and flux plots review problem 4 and5 on pset #2 and practice with the simulation software… (and if you are still confused, feel free to ask us (the Tas) questions!! ☺ ) More measurements: Be comfortable with the plots Prof. Freeman put up in lecture which kind of look like this: See pg. 145 in the text for nicer graph: where P is the permeability of a solute and k P is the partitioning coefficient. k * * * * * M160 What do these show:

1. since linearly P is linearly dependent on partition coefficient(which was ured in oil), membrane is lipid 2. bigger solutes(M larger) diffuse more slowly(plot above assumed D was the for all solute) 3. if there is a solute that is really off from line(even when you take m into account), probably has specialized transport mechanism in the cell

1. since linearly P is linearly dependent on partition coefficient (which was measured in oil), membrane is lipid 2. bigger solutes (M larger) diffuse more slowly (plot above assumed D was the same for all solute) 3. if there is a solute that is really off from line (even when you take M into account), probably has specialized transport mechanism in the cell