BME 5742 Biosystems Modeling and Control

Transcription

1 BME 5742 Bsystems Mdeln and Cntrl Cell Electrcal Actvty: In Mvement acrss Cell Membrane and Membrane Ptental Dr. Zv Rth (FAU) 1

2 References Hppensteadt-Peskn, Ch. 3 Dr. Rbert Farley s lecture ntes Inc Equlbra and Restn Membrane Ptentals, Cre Prncples System, HO- Phy-2 (USC Medcal Schl), 8/2003 eener and Sneyd s Mathematcal Physly, Ch. 2. Dr. Zv Rth (FAU) 2

3 Intrductn Mst anmal cells have an electrcal ptental dfference f mv acrss ther plasma membranes, wth the cytplasm at a neatve ptental relatve t the ECF. Ths restn membrane ptental s present bth n exctable and nn-exctable cells. Tme-dependent chanes n the restn ptental f nerve and muscle cells may lead t actn ptentals mechansm f cmmuncatn between exctable cells. Dr. Zv Rth (FAU) 3

4 Dsscatn f Electrlytes n Aqueus Slutn A J AB J BA B - - When salt cncentratn s hher n ne cmpartment than the ther, there s a dffusn f ns frm the cmpartment f hher cncentratn t the cmpartment f lwer cncentratn. Dr. Zv Rth (FAU) 4

5 Ins Dffusn Mtn A J AB J BA B - - J AB s the rate f dffusn f ns frm A t B. J BA s the rate f dffusn f ns frm B t A. These rates are prprtnal t the cncentratn dfference. Dr. Zv Rth (FAU) 5

6 Under Cncentratn Equalty: A J AB J BA B - - J AB = J BA althuh undrectnal fluxes f each n wll ccur n bth drectns between B and A, at equal rates. There s n net mvement. Dr. Zv Rth (FAU) 6

7 Electrcal Frce Influence A J AB J BA B - - Because ns are electrcally chared they wll als experence a frce f a vltae dfference between A and B exsts. Fr example, f V A >V B then ns mve frm A t B, and - ns mve frm B t A, at a velcty prprtnal t the vltae dfference, untl electrchemcal equlbrum s establshed. Dr. Zv Rth (FAU) 7

8 Electrchemcal Equlbrum Cncentratn dfferences and vltae dfferences are tw nterdependent drvn frces. In a typcal electrchemcal equlbrum, there s a steady-state cncentratn dfference, cunter-balanced by a vltae dfference (created by the mvn chared ns themselves). Dr. Zv Rth (FAU) 8

9 Nernst Equlbrum Ptental -1 v v = T zq ln( ) Ths s ne f the mst mprtant equatns n Electrphysly. It descrbes hw a dfference n nc cncentratn between tw cmpartments can result n a ptental dfference between the tw cmpartments. Vltae s v, and stand fr ntracellular and extracellular ( utsde the cell), S s substance s name. Dr. Zv Rth (FAU) 9

10 Nernst Equlbrum Ptental -2 v v = T zq ln( ) Each n carres z elementary (pstve) chares. In s chare s zq, where q s the chare f a prtn. Fr and we have z = 1, and fr - we have z = -1. Dr. Zv Rth (FAU) 10

11 Cell membrane permeable t S but nt t S Insde Outsde [S] = [S ] S S [S] = [S ] Vltae v Vltae v Dr. Zv Rth (FAU) 11

12 Nernst Equlbrum Ptental -3 v v = T zq ln( ) Assume that the slutns n each sde f the membrane are ntally electrcally neutral. Each n S s balanced by anther n S, wth an ppste chare. Nw, let us assume that membrane s permeable t S but nt t S what happens? Dr. Zv Rth (FAU) 12

13 Nernst Equlbrum Ptental -4 v v = T zq ln( ) Nw, let us assume that membrane s permeable t S but nt t S what happens? Say, that S flws (by dffusn) frm nsde t utsde. Because S cannt thruh membrane, there s a chare buldup acrss the membrane. Ths chare mbalance sets an electrc feld that ppses the dffusn mtn. Dr. Zv Rth (FAU) 13

14 Nernst Equlbrum Ptental -5 v v = T zq ln( ) The abve relatnshp can be shwn t satsfy the equatn and bundary cndtns f a mtn equatn that nclude bth effects dffusn and electrcal feld, actn n substance S. Dr. Zv Rth (FAU) 14

15 Nernst Equlbrum Ptental -6 E = v v = S T zq ln( ) Example: (Squd s axn) ICF cncentratns: : 50, : 397, - : 40 mm. ECF cncentratns: : 437, : 20, - : 556 mm. Resultn Nernst ptentals fr each n (at 27 0 C): : 56, : -77, - : -68 mv. Dr. Zv Rth (FAU) 15

16 Nernst Equlbrum Ptental -7 E = v v = S T zq ln( ) Example: (human cells) Resultn rm temperature Nernst ptentals E fr each n : : 62, : -89, - : -81 mv. The verall measured membrane ptental s arund -85mV. It vares n dfferent cell types, and by temperature Dr. Zv Rth (FAU) 16

17 Nernst Equlbrum Ptental -8 E = v v = S T zq ln( ) In realty, vltae dfferences acrss cell membranes arse because ns mve acrss the membrane at dfferent rates. Mblty f ns s nversely prprtnal t ther sze. In addtn, there are varus carrermedated membrane transprt mechansms that strnly affect the speed f mtn f each n. Dr. Zv Rth (FAU) 17

18 Overall Cell Membrane Ptental v = v = v = E E E Fr each n S we have a membrane cnductance S, determned by the transprt prten embedded n the cell membrane. Overall vltae s a wehted sum f the E S ptentals, wehted accrdn t relatve cnductances. Dr. Zv Rth (FAU) 18

19 Recall Vltae Dvsn V ut 1 R = V 2 = V 2 n n R R = V n Dr. Zv Rth (FAU) 19

20 Cell Membrane Ptental Explaned Superpstn E v = 0, E E R = 0, E R R R = 0 R = E Dr. Zv Rth (FAU) 20

21 Cell Membrane Ptental Examples v = v = v = E E E Typcal cnductance rat fr, and - s 0.7: 0.07: Then v cmes ut t be very clse t E. (True n mst mammal cells) If, fr nstance, jumps t 0.9 when mre sdum channels pen up, then v mves mre twards E. Dr. Zv Rth (FAU) 21