Introduction to cardiac electrophysiology 1. Dr. Tóth ndrás 2018
Topics Transmembran transport Donnan equilibrium Resting potential
1 Transmembran transport
Major types of transmembran transport
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
Time required for diffusion as a square function of distance
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
Osmotic diffusion across a semipermeable membrane
Mechanism of facilitated diffusion
Principle of transport (facilitated diffusion!!!) of ions across ion channels
The principle of active transzport via the Na /K TPase
Secondary active transport processes
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
Q: What are the principal differences between the following iontransporters? 1. Sodium-calcium exchanger 2. Sodium-hidrogen exchanger 3. Calcium pump of the sarcolemma
2 Ionic equilibrium
o RT ln C zf RT ln X X B zf B lectrochemical potential (difference)
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
Q: What does equilibrium potential mean for a given ion?
Let s see, how the Nernst equation can be utilized to analyze ion movements in case of diffusible ions:
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.
B B 0.1 M K 0.01 M K 1 M HCO 3-0.1 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.
B B 0.1 M K 0.01 M K 1 M HCO 3-0.1 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.
Let s see, what happens, if the cell membrane is NOT permeable for at least one ion:
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
B 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 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
P Hydro = 2.99 atm!!! B 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 quilibrium state (There is no equilibrium between pressures!!!) In Gibbs-Donnan equilibrium a huge transmembrane hydrostatic pressure gradient is present
Q: When is Gibbs-Donnan equilibrium present across a living cell membrane?
3 Resting potential
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
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
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?
Let s see, how living cells can be modelled as multi-ion concentration batteries
Intra- and extracellular ionconcentrations and corresponding resting membrane potential determined experimentally
Cl - Na 1) Na IC (mm) 12 C (mm) 145 eq 65 mv cc cc K 160 3,5-100 mv Cl - 3,6 115-90 mv -90 mv Prot - 150 - - 2) 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
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.
6 0 0-70 -90 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 100 100 1 K 1 100 1 Na The chord conductance equation
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
Major factors affecting resting potential C
Q: Which are the primary conditions for establishing and maintaining steady resting potential?
: 1. Separated ion compartments 2. Selective permeability of the membrane 3. Ionic concentration gradients 4. nergy supply and ion transporters
Cardiac cells
lso in cardiac cells the resting potential should show strong [K ] dependency
In cardiac cells the resting potential is, indeed, primarely [K ] dependent (measured: Vm, and calculated: k curves)
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?
Q: What are the major factors determining the actual value of membrane potential?
: 1. Concentration gradients of the monovalent cations 2. Selective permeability of the membrane for cations 3. Concentration of non-permeable intracellular anions
To be continued!