Passive Electrical Properties of the Neuron

1. Passive Electrical Properties of the Neuron Reference: Eric R. Kandel: Essentials of neural Science and Behavior. P149 - 159

2. I. Equivalent Circuit of the Membrane andPassive Electrical Properties

3. Equivalent Circuit of the Membrane andPassive Electrical Properties • Equivalent Circuit of the Membrane • What Gives Rise to C, R, and V? • Model of the Resting Membrane • Passive Electrical Properties • Time Constant and Length Constant • Effects on Synaptic Integration

4. Ions Cannot Diffuse Across the Hydrophobic Barrier of the Lipid Bilayer

5. The Lipid Bilayer Acts Like a Capacitor The voltage (Vm)across a capacitor is proportional to the charge (Q) stored on the capacitor: + + + + Vm = Q/C - - - - ∆Vm = ∆Q/C ∆Qmust change before ∆Vm can change

6. Capacitance is Proportional to Membrane Area + - + + - - + + + - - - - + + + + - - Vm = Q/C - - + + - + - + + + - - - - - - - + + + + - - - + + + - +

7. The Bulk Solution Remains Electroneutral

8. + + + + Electrical Signaling in the Nervous System isCaused by theOpening or Closing of Ion Channels - + - - + + - + - + - + + - - + - The Resultant Flow of Charge into the Cell Drives the Membrane Potential Away From its Resting Value

9. Each K+ Channel Acts as a Conductor (Resistance) γ conductance; r resistance

10. Ion Channel Selectivity and Ionic Concentration Gradient Result in an Electromotive Force

11. An Ion Channel Acts Both as a Conductor and as a Battery γk , conductance of one k+ channel RT [K+]o EK= •ln zF [K+]i

12. All the K+ Channels Can be Lumped into One Equivalent Structure

13. An Ionic Battery Contributes to VM in Proportion to the Membrane Conductance for That Ion

14. When gK is Very High, gK•EK Predominates

15. The K+ Battery Predominates at Resting Potential ≈ gK

16. The K+ Battery Predominates at Resting Potential ≈ gK

17. [K+]o = 4 mmol.l-1

18. Equivalent Circuit of the Membrane andPassive Electrical Properties • Equivalent Circuit of the Membrane • What Gives Rise to C, R, and V? • Model of the Resting Membrane • Passive Electrical Properties • Time Constant and Length Constant • Effects on Synaptic Integration

19. Passive Properties Affect Synaptic Integration

20. Experimental Set-up forInjecting Current into a Neuron

21. Equivalent Circuit for Injecting Current into Cell Im total membrane current Ii Ionic membrane current Ic Capacitive membrane current

22. If the Cell Had Only Resistive Properties

23. If the Cell Had Only Resistive Properties ∆Vm = I x Rin

24. If the Cell Had Only Capacitive Properties PNS, Fig 8-2

25. If the Cell Had Only Capacitive Properties ∆Vm = ∆Q/C

26. The rate of change in the membrane potential is slowed by the membrane capacitance t =Rin x Cin t

27. Time constant (τ): The time taken to reach 63% of the final voltage . The time constants of different neurons typically range from 1 to 20 ms

28. The Vm Across C is Always Equal toVm Across the R Out ∆Vm = IxRin ∆Vm = ∆Q/C In

29. Synaptic potentials that originate in dendrites are conducted along the dendrite toward the cell body and the trigger zone. The cytoplastic core of a dendrite offers significant resistance to the longitudinal flow of current because it has a relatively small cross-sectional area and ions flowing down the dendrite collide with other molecules. The greater the length of the cytoplastic core, the greater the resistance since the ions experience more collisions the further they travel. The larger the diameter of the cytoplasmic core, the lower the resistance will be in a given length due to the greater number of charges carriers at any point.

30. Spread of Injected Current is Affected by ra and rm A neuronal process, either an axon or dendrite, can be divided into unit lengths, which can be represented in an electrical equivalent circuit. Each unit length of the process is a circuit with its own membrane resistance (rm) and capacitance(cm). All the circuits are connected by resistors(ra), which represent the axial resistance of segments of cytoplasm.

31. ra and rm ra: The axial resistance of a unit length (1 cm) of the cytoplasmic core, expressed in Ω /cm. Axial resistance depends on both the specific resistivity of the cytoplasm, p, measured in Ω.cm, and the cross-sectional area of a dendrite with radius a: ra = p/(πa2) rm, the membrane resistance per unit length of cylinder is expressed in Ω.cm. Membrane resistance depends on both the specific resistance of a unit area of membrane, Rm, measured in Ω cm2, and the circumference of the dendrite rm = Rm/2πa For a dendrite of a uniform diameter, rm is the same for equal lengths of membrane cylinder.

32. The current that is injected flows out through several pathways across successive membrane cylinders along the length of the process. Each of these current pathways is made up of two resistive components in series: the total axial resistance rx, and the membrane resistance rm, of the unit membrane cylinder. rx = rax The membrane component, rm, has the same value at each outflow pathway along the cell process. Length Constant

33. More current flows across a membrane cylinder near the site of injection than at more distant regions because current always follows the path of least resistance, and the total axial resistance, rx, increase with distance form the site of injection Because ΔVm = Imrm, the change in membrane potential, ΔVm (x), produced by the current across a membrane cylinder becomes smaller as one moves down the dendrite away from the current electrode. This decay with distance has an exponential shape, expressed by the equation: Δvm (x) = ΔVoe-x/λ λ is the membrane length constant, x is the distance from the site of current injection, and V0 is the change in membrane potential produced by the current flow at the site of the current electrode (x=0)

34. The length constant is the distance along the dendrite form the site of current injection to the site where Vm has decayed to 1/e, or 37% of its initial value, and is determined as follows: Length Constant l = √rm/ra ra = p/(πa2) rm = Rm/2πa l = √Rma/2p Large-diameter axon will have a longer length constant than narrower axons. Typical values of the length constant fall in the range 0.1 to 1.0 mm.

35. Such passive spread of voltage changes along the neuron is called electrotonic conduction. The efficiency of this process, which is measured by the length constant, has two important effects on neuronal function. First, it influences spatial summation, the process by which synaptic potentials generated in different regions of the neuron are added together at the trigger zone, the decision-making component of the neuron.

36. A second important feature of electrotonic conduction is its role in the propagation of the action potential. Once the membrane at any point along an axon has been depolarized beyond threshold, an axon has been depolarized beyond threshold, an action potential potential is generated in that region in response to the opening of voltage-gated Na+ channels. This local depolarization then spreads electronically along the axon, causing the threshold for generating an action potential.

37. II. Propagation of the action potential. Why does action potential, once initiated, run the length of the axon?

38. Passive electrical properties of a plasma membrane can be thought of as a simple electrical circuit.

39. Cable properties of an axon. The change in Vm passively spreads in both directions along the axon Amplitude of the change decays exponentially as it moves away from its source

40. Length constant: • - distance over which the potential falls by 1-(1/e) or 63% from its original value. • depends on the rm (resistance of the membrane) and the ra (longitudinal resistance).

41. Unlike the passive local current, action potentials travel down the length of the axon without decrement

42. How is an action potential propagated along the length of the axon without any decline in amplitude? Hodgkin's undergraduate research project Hypothesis: The inactive membrane ahead of the action potential becomes depolarized by the electronically conducted local current.

43. Hodgkin's undergraduate research project Conclusion: the passive cable properties of the axon permit the electronic spread of local currents from areas undergoing an action potential to inactive membrane areas ahead of the action potential.

44. How does the passive local current bring about an action potential in membrane areas that are inactive?

46. Summary Propagation of an action potential depends on: • Passive cable properties of the axons • - Local currents spread electrotonically. • Distance conducted depends on the resistance of the membrane and the cytosol. • Presence of voltage-sensitive Na+ channels that respond to the passive depolarization due to the electrotonically spreading local current. • - this is what is meant by an excitable membrane • - the opening of the Na+ channels with positive feedback regulation regeneratesthe action potential in the inactive membrane area.

47. Passive Membrane Properties and Axon Diameter Affect the Velocity of Action Potential Propagation • According to Ohm’s law, I =V/R, the larger the axoplasmic resistance, the smaller the current flow around the loop, and thus the longer it takes to changes the charge on the membrane of the adjacent segment. • Since ΔV = Q/C, the larger the membrane capacitance, the more charge must be deposited on the membrane to change the potential across the membrane, so the current must flow for a longer time to produce a given depolarization.

48. Therefore, the time takes for depolarization to spread along the axon is determined by both the axial resistance and the capacitance per unit length of the axon (ra and cm). The rate of passive spread varies inversely with the produce racm. If this product is reduced, the rate of passive spread of a given depolarization will increase and the action potential will propagate faster

49. Rapid propagation of the action potential is functionally important, and two distinct mechanisms have evolved to increase it. One adaptive strategy is to increase conduction velocity by increasing the diameter of the axon core. ra decrease in proportional to the square of axon diameter.

50. The second mechanism for increasing conduction velocity by reducing racm is myelination, the wrapping of glial cell membrane around an axon. This process is functional equivalent to increasing the thickness of the axonal membrane by as much as 100 times. Because the capacitane of a parallel-plate capacitor such as the membrane is inversely proportional to the thickness of the insulatin, myelination decrease cm and thus racm.