MODEL OF PASSIVE MEMBRANE AND CABLE THEORY

1. MODEL OF PASSIVE MEMBRANEANDCABLE THEORY Dr. Ayça BİLGİNOĞLU

2. History of cabletheory • In the 1850s it was developed by William Thomson, later known as Lord Kelvin. • Mathematical models of signal decay in submarine telegraphic cables.

3. Later, Hermann and Cremer independently developed the cable theory for neuronal fibers during the early 20thcentury. • Further mathematical theories of nerve fiber conduction based on cable theory were developed by Kenneth Stewart Cole, Sir Alan Lloyd Hodgkin, and Rushton during the 30s,40s and 50s.

4. Cable theory, • is developedtoexplainthe mechanism forpropogation of theAPsandexcitabilityfromonepart of a neuronormuscleto a distalpart.

5. It is imperative that the body be able to transmit a signal from one point to another very rapidly. • The only way that this can be accomplished by an electrical mechanism.

6. Because, blood flows, diffusion and signaling molecules are much too slow to allow rapid signaling. • In contrast, electricity flows very quickly, at the speed of light (3x108 m/sec) in a copper wire.

7. Therefore, the body makesuse of electricityforrapidsignaling in thenervoussystem, skeletalmuscle, heartandsmoothmuscle.

8. In cable theory membrane is expressed as passive. • Passive; the membrane properties (e.g., resistance, capacitance, …) are not changed by membrane potential.

9. On cellmembrane, therearetwocurrents. Iiis ioniccurrent Im (flux of ionsthroughpassive protein channels.) Icis capacitivecurrent. (thiscurrentoccursbetweenparallelplates of capacitorwhilethecapacitorchargedanddischarged.)

10. I = dQ / dt = C (dV / dt) (capacitive current) • Q: charges • C: capacitance • V: voltage • Capacitive current passes on conductors while the potential passes between two parallel plaque of conductors.

11. Outside of cell constant current source Inside of cell

12. Time Constant of Cell Membrane • Time constant of cell membrane is changed by the capacitance of the cell membrane (Cm) and the membrane potential (Em) • τm = Rm.Cm

13. The membrane time constant is important to define the conduction velocity of axon.

14. The time constant can be measured on the buildup of the pulse (time to reach 63% of the final voltage) or on the decay (time to reach 37% of the initial voltage).

15. Vm(t) = Im.Rm [-e-t/τ]

16. ri ri ri Space (length) Constant of Cell Membrane rd rd rd The membrane resistance (rm) is same along the axon but cytoplasmic resistance (ri) is not same and it changes along the axon. Since currents prefer the place in which the resistance is lower, the current will be lower from the distance of injection point. Also, the potential will decay along the distance from injection point. [Vm(x) = Im(x) rm].

17. Therefore, the potential decay is expressed as an exponential and it is • Vm = V0 e-x/λ . • V0 : the potential at the current injection point. • λ : space or length constant. (the distance at which the voltage decays to 37% of the initial value or the changes potential proportion to ‘e’ (= 2,718).)

18. λ = √(rm / ri + rd) • The greater the membrane resistance and the smaller the internal longitudinal resistance (larger cell diameter), the greater the λ value is required.

19. Distance,x

20. AllorNoneProperty • A slightly stronger stimulus initiates an AP. • But insufficient stimulus cannot bring the membrane potential of a large enough membrane area to the threshold potential. • Thereby this term can be explained with all or none property of AP.

21. Voltage-gatedchannelsand AP • If the membrane is depolarized, the conductivity of Na+ (gNa) will be increased. (by activation of Na+ channels) • Thus, the INa will be increased.

22. It expressedthat, thebiggerdepolarization can causethebiggerconductivity. • Finally, a positivefeedbackmechanismwill be arisedbetweengNaand Em .

24. Somefactorseffect onpropagation (conduction)velocity • If the Ca2+ concentration in the outside of the cell decrease, some sinusoidal waves are observed on cell membrane potential. • If the conductivity of sodium is higher, the conduction velocity will be higher.

25. If the capacitance of membrane in an unit surface is decrease, the conduction velocity will be higher. • If the conductivity of axoplasma is higher, the conduction velocity will be higher.

26. The conduction velocity depends on the temperature. • If the radius of axon is higher, the conduction velocity will be higher. • Myelin is increased the conduction velocity.

27. Equivalentcircuitforactivecellmembrane For an active cell membrane, a cell membrane contains active resistance. (changeable by potential) gNa = 1/RNa and (it is proportional to the account of Na+ open channel at the same time.) gK = 1/RK (it is proportional to the account of open K+ channel at the same time.)

28. (gKEK + gNaENa + gClECl) Em = (gK + gNa+ gCl)

29. Patch-ClampTechnique • In Patch-clamp experiments, the various ion currents (such as Na+, Ca2+, or K+ currents) can be isolated from the total ionic current and analyzed individually. • With this experiment, whole cell membrane holds same voltage (potential).

35. The types of Patch-Clamp

36. REFERENCES • Pehlivan F. (5. Baskı). Biyofizik. Pelikan Kitabevi. • Sperelakis N. (1995). Cell Physiology. Academic Press. Inc. • Hille B. (2001). Ionic Channels of Excitable Membranes. Sinauer Associates. Inc.