Supratim Ray

Transcription

1 Supratim Ray

2 Biophysics of Action Potentials Passive Properties neuron as an electrical circuit Passive Signaling cable theory Active properties generation of action potential Techniques Random Variables, Poisson and Renewal Processes Correlations various techniques Journal Session Kohn and Smith, 2005, JNS 2

3 Kandel, Schwartz and Jessell, Principles of Neural Science, Chapters 7-9 Johnston and Wu, Foundation of Cellular Neurophysiology, Chapter 4 The Passive Axon Tutorial in Neurons in Action 3

4 Individual neurons are the elementary signaling elements of the nervous system - Ramon y Cajal Nervous tissue was thought to function like a gland. Using staining techniques developed by Camillo Golgi, Cajal was able to stain individual cells, thus showing that nervous tissue is not one continuous web but a network of discrete cells. 4

5 Four morphologically defined regions Dendrites Cell body (Soma) Axon Pre-synaptic terminal Figure 2-2, Kandel, Schwartz and Jessell 5

6 Four functional regions - Figure 2-8, Kandel, Schwartz and Jessell Input, Integrative, Conductile and Output 6

7 Figure 27-11, Kandel, Schwartz and Jessell 7

8 Figure 1.2, Johnston and Wu 8

9 Dynamic polarization Flow of information is unidirectional, from the dendrites to the soma to the axons Connectional specificity Nerve cells do not connect indiscriminately to form random networks; each cell makes specific connections with only certain postsynaptic target cells but not others - Ramon y Cajal 9

10 10 Neuron as a electrical circuit

11 Figure 2-9, Kandel, Schwartz and Jessell Plasma membrane is 6-8 nm thick, made of lipid bilayer. Due to the hydrophobic lipids, it is difficult for ions to pass through the plasma membrane. All cells (not just neurons), at rest, maintain a difference in electrical potential on either side of the plasma membrane, which arises due to an unequal distribution of electrically charged ions such as positively charged Na + and K +, and negatively charged amino acids and proteins. 11

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13 Transport of solutes occurs from regions of higher electrochemical potential to regions of lower electrochemical potential (can be derived from the second law of Thermodynamics). µ i = µ i0 + RTln(C i )+ z i FV Subscript i refers to the particular ion RTln(C i ) is the contribution of the ion s concentration (C i ). R = Gas constant (8.315 Joule/ºmole), T = Temperature. z i FV is the contribution of electric potential. Here z i is the charge of the ion (+1 for Na +, -1 for Cl -, +2 for Ca 2+ etc). F = number of Coulombs of charge in a mole of unit charges (9.65x10 4 coul/mole), and V is the electrical potential. This whole term is the work required to bring a mole of ions with charge z i from 0 potential to potential V. µ i 0 is the electrochemical potential of the ion at unity concentration and zero potential. It contains the contribution of all factors other than concentration and potential, such as the interaction between the ion and solvent, effects of pressure etc. 13

14 Equilibrium potential is the membrane potential at which there is no net flux of the ion species across the cell membrane µ inside = µ outside µ 0 + RTln(C inside )+ zfv inside = µ 0 + RTln(C outside )+ zfv outside V inside -V outside = (RT/zF)ln(C out /C in ) (Nerst s Equation) 14

15 When only potassium ions are permeable, membrane potential will be equal to the equilibrium potential of potassium. Figure 7-3, Kandel, Schwartz and Jessell 15

16 Figure 7-4, Kandel, Schwartz and Jessell Overall potential depends on the relative number of ion channels 16

17 Each ion channel channel can be represented as a conductor and a battery Figure 7-8, Kandel, Schwartz and Jessell 17

18 INa+IK+ICl=0 Iion = gion x(vm-eion) Figure 7-9 and 7-13, Kandel, Schwartz and Jessell 18

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21 See this video: how_the_sodium_potassium_pump_works.html 21

22 See this video: how_the_sodium_potassium_pump_works.html 22

23 23 Cable Theory

24 Three passive electrical properties important to electrical signaling 1. Resting membrane resistance 2. Membrane capacitance 3. Intracellular axial resistance along axons and dendrites 24

25 Figure 8-1, Kandel, Schwartz and Jessell Membrane resistance, rin, depends on the total number of resting ion channels, and hence both on the density of resting ion channels in the membrane and the size of the cell. Often we use the Specific Membrane Resistivity, Rm (units of Ohm.cm 2 ), which only on the density of resting ion channels and their conductance. For a spherical cell, rin = Rm/4πa 2 where a is the radius of the cell 25

26 Figure 8-2 and 8-3, Kandel, Schwartz and Jessell Membrane capacitance causes a gradual change in membrane potential Specific capacitance per unit area (Cm) is about 1 µf/cm 2. Input Capacitance (cin) is directly proportional to the area of the membrane. For a spherical cell, cin = Cm*(4πa 2 ) where a is the radius of the cell For a spherical cell (Isopotential), Vm = ImRm(1-exp(-t/tm)), where tm = RmCm is the membrane constant of the cell. 26

27 Figure 4-6, Johnston and Wu Cylinder geometry dependent terms Terms independent of cylinder geometry 27

28 Figure 4-6, Johnston and Wu = Membrane current per unit length of cylinder. Total current through a membrane patch = x. 28

29 Figure 4-6, Johnston and Wu Space constant increases with the square root of the fibre diameter 29

30 Infinite cable, injected with a current step Figure 4-7, Johnston and Wu 30

31 Error function: erf(x) Complimentary Error function: erfc(x) 31

32 Figure 4-8, Johnston and Wu 32

33 Figure 4-9, Johnston and Wu Using 33

34 Figure 4-10, Johnston and Wu Propagation Speed: Figure 4-11 and 4-12, Johnston and Wu 34

35 Passive propagation in an infinitely long cable if a constant current is injected: The steady state voltage decays exponentially with distance with a space constant that is proportional to the square root of fibre diameter. At the point of injection, the voltage rise is proportional to the error function (erf), faster than an exponential. The voltage rises fastest at the point of injection and more slowly as we move further away. The propagation speed is determined by the time it takes to reach half the steady state value at any distance. This time increases linearly with distance. The propagation speed is therefore proportional to the space constant and increases as the square root of the fibre diameter. 35

36 36 Generation of action potential

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38 Ionic currents must be measured as a function of membrane potential. Difficult to achieve in practice because of a strong interdependence of the membrane potential and the gating of sodium/potassium channels. Depolarization Inward Sodium Opening of Sodium channels Need to measure the ionic currents while keeping the membrane potential fixed: A Voltage clamp 38

39 Developed by Kenneth Cole in Used by Alan Hodgkin and Andrew Huxley in early 1950s to study the ionic mechanisms underlying the action potential Squid axon recording movies 39

40 Controls part of the water jet propulsion system Squid use this system primarily for making brief but very fast movements through the water Extremely large (up to 1 mm, typically 0.5 mm) 40

41 Leak Capacitive Voltage-clamp allows total membrane current to be separated into ionic and capacitive components, because the second term is zero when Vm is not changing Small depolarization produces a transient capacitive current and a steady leak current because of the resting channels (mostly potassium) that are always open and are responsible for the resting membrane potential Higher level of depolarization produces a transient inward current followed by a pronounced outward current Figure 9-3, Kandel, Schwartz and Jessell 41

42 Tetrodotoxin (TTX) is a sodium channel blocker. TTX binds to sodium channels with high affinity. Produced by puffer fish. Figure 9-3, Kandel, Schwartz and Jessell Tetraethylammonium (TEA) is a cation that blocks certain voltage gated potassium channels with a relatively low affinity 42

43 Figure 9-5, Kandel, Schwartz and Jessell Figure 9-6, Kandel, Schwartz and Jessell 43

44 Single ion channels are binary 44

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47 Figure 9-9, Kandel, Schwartz and Jessell 47

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51 No attenuation of an action potential magnitude - only the time gets delayed with distance 51

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53 Myelination decreases the flow of current across the membrane, enhancing propagation. Unmyelinated regions between myelin sheaths are rich in sodium channels, which regenerate the action potentials Myelin effectively decreases the membrane capacitance. Conduction velocity increases linearly with the diameter of the fiber (including the myelin) Called Saltatory motion. Saltare means jump in Latin 53

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