Introduction to cardiac electrophysiology 1. Dr. Tóth András 2018

Transcription

1 Introduction to cardiac electrophysiology 1. Dr. Tóth ndrás 2018

2 Topics Transmembran transport Donnan equilibrium Resting potential

3 1 Transmembran transport

4 Major types of transmembran transport

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

6 Time required for diffusion as a square function of distance

7 J J K Fick s law for membrane D D D x c x c x : partition coefficient K: permeability coefficient Diffusion kinetics across a semipermeable membrane

8 Osmotic diffusion across a semipermeable membrane

9 Mechanism of facilitated diffusion

10 Principle of transport (facilitated diffusion!!!) of ions across ion channels

11 The principle of active transzport via the Na /K TPase

12 Secondary active transport processes

13 Michaelis-Menten equation V max : maximal rate of transport K m : concentration of substrate at a transport rate equal to V max /2 Protein-mediated transport shows saturation kinetics

14 Q: What are the principal differences between the following iontransporters? 1. Sodium-calcium exchanger 2. Sodium-hidrogen exchanger 3. Calcium pump of the sarcolemma

15 2 Ionic equilibrium

16 o RT ln C zf RT ln X X B zf B lectrochemical potential (difference)

17 quilibriu m 0 RT ln X X B zf B zf X B RT ln X RT X B ln zf X B B For monovalent cations Z = 1 X 60mV lg X X B Deduction of the Nernst equation

18 Q: What does equilibrium potential mean for a given ion?

19 Let s see, how the Nernst equation can be utilized to analyze ion movements in case of diffusible ions:

20 B B 0.1 M 0.01 M 1 M 0.1 M K K HCO 3 - HCO 3 - B = -60 mv B = 100 mv Is there equilibrium in any of the two cases? xamples of use of the Nernst equation 1.

21 B B 0.1 M K 0.01 M K 1 M HCO M HCO 3 - B = 60 mv t 60 mv the K is in electrochemical equilibrium across the membran No electric force!!! xamples of use of the Nernst equation 2.

22 B B 0.1 M K 0.01 M K 1 M HCO M HCO 3 - B = 60 mv t -60 mv the K is in electrochemical equilibrium across the membran No electric force B = 100 mv t the given membran potential the HCO 3- ion is not in electrochemical equilibrium lectric force: 40 mv xamples of uses of the Nernst equation 3.

23 Let s see, what happens, if the cell membrane is NOT permeable for at least one ion:

24 B 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 quilibrium? 1. The principle of electroneutrality should be preserved!!! 2. The electrochemical potential should be zero for each diffusible ion!!! (But not for the undiffusible ion!!!) Before Gibbs-Donnan equilibrium is established 1

25 B B [K ] = 0.1 M [P - ] = 0.1 M [K ] = 0.1 M [Cl - ] = 0.1 M [K ] = M* [Cl - ] = M* [P - ] = 0.1 M [K ] = M* [Cl - ] = M* Initial state quilibrium state* (!?) 1. The principle of elektroneutrality is, indeed, valid!!! 2. The electrochemical potential is zero for both K and Cl -!!! 3. * So, is there any problem??? Gibbs-Donnan equilibrium has been attained

26 P Hydro = 2.99 atm!!! B B [K ] = 0.1 M [P - ] = 0.1 M [K ] = 0.1 M [Cl - ] = 0.1 M [K ] = M [Cl - ] = M [P - ] = 0.1 M [K ] = M [Cl - ] = M Starting state quilibrium state (There is no equilibrium between pressures!!!) In Gibbs-Donnan equilibrium a huge transmembrane hydrostatic pressure gradient is present

27 Q: When is Gibbs-Donnan equilibrium present across a living cell membrane?

28 3 Resting potential

29 B 0.1 M NaCl 0.01 M NaCl If the membrane is permeable for cations, but not for anions, a cation current is needed to reach equilibrium!!! The principle of the concentration battery 1

30 Na B 0.1 M NaCl 0.01 M NaCl In case of electrochemical equilibrium: B = - 60 mv The principle of the concentration battery 2

31 Q: How many Na ions should pass the membrane to reach equilibrium?. Very-very little? Very little? Rather little? Medium? Rather much? Very much? Very-very much?

32 Let s see, how living cells can be modelled as multi-ion concentration batteries

33 Intra- and extracellular ionconcentrations and corresponding resting membrane potential determined experimentally

34 Cl - Na 1) Na IC (mm) 12 C (mm) 145 eq 65 mv cc cc K 160 3,5-100 mv Cl - 3, mv -90 mv Prot ) P K 100 P Na cc K 3) Prot 0 4) m 90 mv simplified model of the resting membrane potential in the human skeletal muscle

35 K K m K Na Na m Na Cl Cl m Cl g I g I g I R g R U I ) ( ) ( 0 ) ( 1 quilibrium conditions for the chord conductance equation Theoretical estimation for the resting potential 1.

36 Na m K I Na ( m m I g K K Na g 0 ) g K g Na Na ( K m g K g K Na ) g In case of: g Na = 1 & g K = 100 g Na K Na m K Na The chord conductance equation

37 Theoretical estimation for the resting potential 2. 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

38 Major factors affecting resting potential C

39 Q: Which are the primary conditions for establishing and maintaining steady resting potential?

40 : 1. Separated ion compartments 2. Selective permeability of the membrane 3. Ionic concentration gradients 4. nergy supply and ion transporters

41 Cardiac cells

42 lso in cardiac cells the resting potential should show strong [K ] dependency

43 In cardiac cells the resting potential is, indeed, primarely [K ] dependent (measured: Vm, and calculated: k curves)

44 Q: What may be the reason why in a given cell type (e.g. RBC) the resting potential is 30 mv, while in another (e.g. cardiac) cell type it is 90 mv?

45 Q: What are the major factors determining the actual value of membrane potential?

46 : 1. Concentration gradients of the monovalent cations 2. Selective permeability of the membrane for cations 3. Concentration of non-permeable intracellular anions

47 To be continued!