Introduction to electrophysiology 1. Dr. Tóth András

Introduction to electrophysiology 1. Dr. Tóth András

Today topics Transmembran transport Donnan equilibrium Resting potential

Level of significance Entry level (even under 6) Student level (for most of you) Gourmand level (only for the pros)

1. Transmembran transport

1 Major types of transmembran transport

2 dc J: net rate (flux) of diffusion J = DA dx A: area dc/dx: concentration gradient J = DA c x D: diffusion coefficient (D: cm 2 /s) J D = dc A dx Fick s first law of diffusion

3 StokesEinstein equation D = 6 kt π r η Einstein relation ( x 2 ) = 2 Dt Diffusion of solutes as a consequence of the random thermal (Brownian) motion of the particles

4 Time required for diffusion as a function of diffusion distance

5 J J K = = Fick s law for membrane = D DA DA β x β c x c x β: partition coefficient K: permeability coefficient Diffusion across a semipermeable membrane

6 Osmotic motion across a semipermeable membrane

7 van t Hoff s Law π= irtm π= irtc π = RTΦic Φic = T f /1.86 Φ: osmotic coefficient Φic: osmotically effective concentration - osmolarity I.e.: 154 mm NaCl solution π = 6.42 atm Φic = 0.286 osmol/l Definition of the osmotic pressure

8 Mechanism of facilitated diffusion

9 Principle of transport of ions across ion channels

10 The principle of function of the Na /K ATPase

11 Secondary active transport processes

12 Michaelis-Menten equation V max : maximal rate of transport K m : concentration of the substrate for which the rate of transport is equal to V max /2 Transport via proteins shows saturation kinetics

2. Ionic equilibrium

13 µ = µ o RT ln C zfe µ = RT ln [ ] X [ ] X A B zf ( E E ) A B Electrochemical potential (difference)

14 Equilibrium 0 E = zf A [ ] X A ln [ ] zf A X B [ ] X ( E ) A EB = RT ln [ X ] RT [ X ] A EB = ln zf [ X ] B RT ( E E ) B A B For monovalent cations Z = 1 [ ] X [ ] X E = 60mV lg X A B Nernst equation

15 A B A B 0.1 M 0.01 M 1 M 0.1 M K K HCO 3 - HCO 3 - E A E B = -60 mv E A E B = 100 mv Is there equilibrium in any of the two cases? Examples of uses of the Nernst equation

16 A B 0.1 M K 0.01 M K A B 1 M 0.1 M HCO - 3 HCO - 3 E A E B = 60 mv At 60 mv the K is in electrochemical equilibrium across the membran No electric force!!! Examples of uses of the Nernst equation

17 A B 0.1 M K 0.01 M K E A E B = 60 mv At 60 mv the K is in electrochemical equilibrium across the membran No electric force A B 1 M HCO 3-0.1 M HCO 3 - E A E B = 100 mv At the given membran potential the HCO 3- is not in electrochemical equilibrium Electric force: 40 mv Examples of uses of the Nernst equation

18 A B A B [K ] = 0.1 M [P - ] = 0.1 M [K ] = 0.1 M [Cl - ] = 0.1 M [K ] = [Cl - ] = [P - ] = 0.1 M [K ] = [Cl - ] = Initial state Equilibrium? 1. The principle of electroneutrality should be preserved!!! 2. The electrochemical potential should be zero for each diffusible ion!!! (Not for the undiffusible ion!!!) Before Donnan equilibrium is established

19 A B A B [K ] = 0.1 M [P - ] = 0.1 M [K ] = 0.1 M [Cl - ] = 0.1 M [K ] = 0.133 M* [Cl - ] = 0.033 M* [P - ] = 0.1 M [K ] = 0.066 M* [Cl - ] = 0.066 M* Initial state Equilibrium state* (!?) 1. The principle of electroneutrality is, indeed, valid!!! 2. The electrochemical potential is zero for K and Cl -!!! 3. * So, is there any problem??? Gibbs-Donnan equilibrium has been attained

20 PH = 2.99 atm!!! A B A B [K ] = 0.1 M [P - ] = 0.1 M [K ] = 0.1 M [Cl - ] = 0.1 M [K ] = 0.133 M [Cl - ] = 0.033 M [P - ] = 0.1 M [K ] = 0.066 M [Cl - ] = 0.066 M Starting state Equilibrium state (There is no equilibrium between pressures!!!) In Gibbs-Donnan equilibrium a transmembrane hydrostatic pressure gradient is present

3. Resting potential

21 A B 0.1 M NaCl 0.01 M NaCl If the membrane is permeable for cations, but unpermeable for anions, cation current is needed to reach equilibrium!!! The concentration battery

22 Na A B 0.1 M NaCl 0.01 M NaCl In case of electrochemical equilibrium E A E B = - 60 mv The concentration battery

23 Measured intra- and extracellular ionconcentrations

24 Cl - Na E E 1) Na IC(mM) 12 EC(mM) 145 E eq 65mV cc cc K 160 3,5-100mV Cl - 3,6 115-90mV -90 mv - Prot 150 - - E 2) P K P 100 Na cc K 3) Prot= 0 4) E m = 90mV A simplified model of the resting membrane potential in the human skeletal muscle

= = = = = K K m K Na Na m Na Cl Cl m Cl g E E I g E E I g E E I R g R U I ) ( ) ( 0 ) ( 1 Conditions for the chord conductance equation Theoretical estimation for the resting potential 1. 25

26 6 0 Na I Na I K = 0 0 ( E E m m E = g K Na g ) g K g Na Na = ( E E K m g E K g K Na g ) g K Na E Na -70-90 E m K g Na = 1 g K = 100 E m 100 = E E Na K 100 1 1 100 1 The chord conductance equation

27 Theoretical estimation for the resting potential 2. E m = RT F ln k k pk pk [ K [ K ] ] o i k k pna pna [ Na [ Na ] ] o i k k pcl pcl [ Cl [ Cl ] ] i o The constant field (Goldman-Hodgkin-Katz) equation

28 C Major factors affecting resting potential

29 Also in cardiac cells the resting potential is supposed to be [K ] dependent

30 In cardiac cells the resting potential is, indeed, primarily [K ] dependent

Q: What are the principal differences between the following iontransporters? 1. Sodium-calcium exchanger 2. Sodium-hidrogen exchanger 3. Calcium pump of the sarcolemma What does equilibrium potential mean for a given ion??? When is Gibbs-Donnan equilibrium present across a living cell membrane? In Fig. 14 how much Na has to pass the membrane to reach equilibrium? Which are the primary conditions for establishing and maintaining steady resting potential? What is the reason, for in one cell type (rbc) the resting potential equals 30 mv, while in an other (cardiac) cell type it equals 90 mv? What are the major factors determining the actual value of membrane potential?