Introduction to electrophysiology Dr. Tóth András
Topics Transmembran transport Donnan equilibrium Resting potential Ion channels Local and action potentials Intra- and extracellular propagation of the stimulus
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 Stokes Einstein 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 = DA DA D 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 - osmolality 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 EA EB = RT ln [ X ] RT [ X ] A EB = ln zf [ X ] B RT ( E E ) B A B For monovalent cations Z = 1 = 60mV lg [ ] X [ ] X E 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 1.
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 2.
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 3.
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 Gibbs-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 elektroneutrality 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 0 Na I Na ( E E m m I E = g K K Na = 0 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 E m K m 100 = E E Na K 100 1 g Na = 1 g K = 100 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
4. Ion channels
4.1 Experimental techniques
31 Major configurations of the patch clamp technique
32 Single channel current
33 Determination of the mean open time
34 Current-voltage relationship of the inward and outward rectifying channels
4.2 Principles of regulation
35 State diagram of a simple, dual-state ion channel
36 State diagram of a multiple-state ion channel
37 Basic regulatory mechanisms of ion channels
37 a Background channels spontaneously oscillate between open and closed states
37 b Voltage-gated channels also oscillate between the two states, but voltage shifts the equilibrium
37 c The open state of neurotransmitter-gated channels is altered by the binding of a neurotransmitter to the channel (e.g. nicotinic receptor)
37 d The open state of G-protein gated channels is altered by binding of activated G-protein subunits to the channel (following receptor activation e.g. muscarinic receptor)
37 e Modulated channels may be voltage-gated, but the ability of voltage to open the channel may be influenced by covalent modification (e.g. phosphorilation)
4.3 Structure
38 Ion channel superfamilies
39 2D model of the Na channel 1.
40 2D model of the Na channel 2.
4.4 Structure-function relation
41 S 4 helices are the voltage-sensors of voltage-gated channels amino acid homology is extensive
42 Model of the function of the S 4 helix as voltage sensor A total of 6 charges should relocare in the membrane to open the channel
43 Top view of the Na channel showing how the central ion channel is proposed to be lined by one of the helices from each domain
44 Functional model of a K channel
45 Cardiac ion channels
5. Local and action potentials
5.1 Local response
46 Local (subthreshold) response
47 Temporal summation
48 Spatial summation
5.2 Action potential
49 Responses in the membrane potential to increasing pulses of depolarizing current
50 Action potentials from three vertebrate cell types
5.3 Action potentials in the heart
51 Ion concentrations in mammalian heart
52 Fast and slow response in the heart
53 Regional variations in the shape of the action potential of the heart cells
54 Ion currents! Fast sodium Funny Delayed rectifier Calcium I L TL 0 0 Tranzient outward Background Sodium Inward rectifier Explanation of the kinetic differences
55 The effect of tetrodotoxin on the fast response
6. Propagation of the stimulus
6.1 Basic principles of propagation
56 Potential changes recorded by an extracellular electrode located at different distances from the current electrode
57 Maximum change in recorded membrane potential plotted versus distance from the point of current passage
58 Potencial changes in a model RC-circuit
59 Electric model of the axon membrane
60 R m R i C Time constant determined in a membrane
61 Model of decremental propagation (voltage divider - resistance ratio)
62 R R m i Length constant determined in the membrane
63 Model of conduction of the local (subthreshold) response
64 Electric model for the propagation of potential changes
65 Model of conduction of the AP in nonmyelinated fibers
66 Saltatory conduction of the action potential in myelinated fibers
67 Conduction velocity of the action potential determined in unmyelinated and myelinated fibers
6.2 AP propagation in heart
68 MW < 1500 Ca 2 ph E m Structure of the electric synapse (gap junction)
69 Electric model of the cardiac cells
70 Computer simulation of impulse propagation at the microscopic level
The significance of gap junctions in normal stimulus propagation in the heart
71 Subcellular stimulus propagation
72 Differences in delays of intra- and intercellular activation single cell wide network
73 Differences in delays of intra- and intercellular activation multi-cell wide network
74 Impulse propagation (isochron lines) in case of normal gap junction coupling (homogenious AP-population)
75 Impulse propagation (isochron lines) in severe gap junction uncoupling (heterogenous AP-population)
76 In severe gap junction uncoupling propagation velocity may decrease TWO orders of magnitude (!!!) (from 36.7 cm/s to only 0.31 cm/s)
77 In case of normal gap junction coupling isochron lines are relatively regularly placed, AP-population is homogenous
78 In case of critical gap junction uncoupling action potentials form clusters with significant delays
79 Distribution of the cells forming the different clusters in case of critical uncoupling turn back behaviour of the stimulus easily leading to reentry can be observed
Questions What are the principal differences between the following iontransporters? Sodium-calcium exchanger Sodium-hidrogen exchanger Calcium pump of the sarcolemma What does equilibrium potential mean for a given ion? How the Nernst equation can be used to analyze ion movements in case of diffusible ions? What will happen, if the membrane is not permeable for at least one ion? When is Gibbs-Donnan equilibrium present across a living cell membrane? In Fig. 22 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 the membrane potential?
Questions What is the difference between a membrane receptor and an ion channel? Are there membrane receptors, which are also ion channels? How is possible, that Na ions can pass an ion channel, but K ions don t? How is possible, that K ions can pass an ion channel, but Na ions don t? Which are the most important properties of the ion channels? What is the difference between electrochemical potential and membrane potential? Which are the most important features of the local response? Special forms of local response? What are the major differences between local response and action potential? What is the reason for the very different kinetic properties of the action potentials recorded in different cell types? How could you change the shape of the action potential? What is the effect of tetrodotoxin on fast response? Why is good for us to maintain a resting potential in the cells of our body, if it costs such a substantial amount of energy (ATP)?
Questions What is the explanation for the fact, that postsynaptic action potentials are generated at the axon hillock? Which factors determine action potential conduction velocity in myelinated fibers? And in unmyelinated fibers? Why is conduction velocity significantly higher in myelinated than in unmyelinated fibers? How would you explain the expression that cardiac muscle is functional syncytium? Where are electric synapses (i.e. gap junctions) located in the mammalian body? Which are the major functional differences between electric and chemical synapses? What is the prime factor determining direction of impulse propagation in the three dimensional cardiac muscle? Why is the transmission of stimulus through AV node dramatically slower than in other parts of the heart? Is there fast and slow action potential propagation? What may be the reason?
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