Lecture3-RestingPotential

8/12/2019 Lecture3-RestingPotential

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Sim p le Neur al Circ ui t

Sense a stimulusTransmit the information to integration center

Analysis the information

Transmit the information from integration centerMove the appropriate effector

The information is moved by electrical-chemical-electrical signals


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Neuro ns a re B ad Con du ctors o fElectr ic i ty

The electric carriers are ions not electrons. Electronshave a lot more energy.Neurons are not as well isolated as wires and they are inan environment that tends to absorb the energy so thecharge tends to dissipate rapidly with distance.

The maximum measure speed of a neural generatedelectrical pulse is ~250 mph.The maximum speed of an electron in a wire is ~93,000 mph.

There must be a booster system to regenerate the signalas it moves along the axon. This is the action potential.This requires that the neural membrane must be

polarized and depolarized temporally and spatially.


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Rest in g Mem br ane Po ten t ialMembranes that can depolarize upon stimulation are termedexcitable membranes.Cells have the ability to separate charge such that the interiormembrane has a net negative charge in compared to theextracellular environment. This is the resting membrane potential.How is this established? Who are the players? What are the rules?


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A Mod el for Res t ing Potent ial

The intracellular and extracellular compartment are separated by phospholipid bilayer.The extracellular environment contains Na +, K +,and Cl -.The intracellular environment contains Na +, K +, Cl - and A - (in theform of protein molecules).

Intracellular and extracellular solutions must be electrically neutral.The cell must be in osmotic balance.There must be no net movement of any particular ions into or out ofa the cell.


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Part I:Mo d el o f a Cell

IntracellularExtracellular

117 mM Na +

3 mM K + 90 mM K +

120 mM Cl - 4 mM Cl -

0 mM A - 116 mM A -

Neutrality Extracellular = + 120 (117 + 3) - (120) =0Neutrality Intracellular = +(30+ 90) - (4 +116) = 0

30 mM Na +

The membrane is not permeable to any ions


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Wh at i s A pp arent in th e Mod elPotassium ions are more concentrated inside the cellSodium and chloride ions are more is more concentrated in theexterior medium.There is a anionic species in the cell.Each solution is in osmotic and charge balance.

The net charge across the membrane is zero since there is not ionmovement possible.


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Part II: Mo del Cel l w i th p o tass ium leakchannel


117 mM Na +

3 mM K + 90 mM K +

120 mM Cl - 4 mM Cl -

0 mM A - 116 mM A -

30 mM Na +

Permeable only to potassium ions


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Forces m oving the po tas s ium ionsDiffusion fueled by thermal motion tends to move the K + from theinterior of the cell out into the media.

As the K + leaves the cell, an excess of negative charges are left onthe inner leaflet of the membrane which tend to attract positivecharges on the outer leaflet of the membrane. A electrical gradientacross the membrane is formed.The negative interior attracts K + back into the cell countering theforce of diffusion.The K + is at equilibrium and there is no net flux of ion. This is the

potassium equilibrium potential (E k ). It will generate a specificvoltage difference across the membrane.


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Rest ing Potent ial Ac ros s th e Mem brane


117 mM Na +

3 mM K + 90 mM K +

120 mM Cl - 4 mM Cl -

0 mM A - 116 mM A -

30 mM Na +


-

-

-

+

+

+

-87 mV


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Effect of Tem perature and Ion Charge onRest in g Mem b rane Potent ia l

Generalized Nernst Equation is;E ion = 2.303 (8.135 J/mol K T/z 96,485 C/mol log ([K] o/[K]I) =

= .0001985 T/z log ([K] o/[K]I)

If we increase the temperature to 37 oC, the resting potential with K+is 90 mV.Increasing temperature increases thermal motion favoring diffusionand lowering intracellular K+ hence further polarizing the membrane.If we use an ion with a valence of +2 and assume the same ionconcentrations, the resting potential is 43 mV.Increasing the ionic charge, depolarizes the membrane by favoringthe creation of electrical potential at lower flux.


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Charg e Neutral i ty in Polarized CellsThe ion that are partition due to the membrane potential are stored on theplasma membrane and removed from the bulk solutionThe plasma membrane is acting as a capacitor.The concentration of ions on the membrane is very low in comparison to thebulk ion concentration.

Solution for concentration of ions on membrane of a cell with a 25 m radiusSurface area of sphere = 4 r 2 = 4 (3.14)(0.0025 cm) 2= 8 x 10 -5cm 2

Volume of sphere = 4/3 r 3= 4/3(3.14)(0.0025 cm) 3= 6.5 x 10 -8ml =6.5 x 10 -11 L

The total charge on the membrane/unit area is calculated from: Q=CapVQ= total charge/unit areaCap = The ability of a particular membrane to store charge/unit areadepending on the volt. The units are farad(F)/unit area. Farads are C/V.V = resting potential voltage.


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Calcu lat ing th e[ ion s] o n th e inn erm em b rane leaflet Rest in g Po ten t ial

The total charge on the membrane/unit area is calculated from:Q=CapV

Q= total charge/unit areaCap = The ability of a particular membrane to store charge/unit areadepending on the voltage. The units are farad(F)/unit area. A neuralmembrane has a average capacitance value of 1 F/cm 2. Farads are C/V.V = resting potential voltage.

Q = (1 x10 -6 C/V cm 2)(87 x 10 -3 V) = 9 x 10 -8 C/cm 2(6.25 x10 18 ions/C) =6 x 10 11 ions/cm 2 Total Ions on Membrane = (6 x 10 11 ions/cm 2)(8 x 10 -5cm 2) = 5 x 10 7ions[Ions] on Membrane = (5 x 10 7ions/6.02 x 10 23 ions/mol)/6.5 x 10 -11 L =1.1 x 10 -6M = 0.0011 mMThe bulk concentration of anions in the cell is 120 mM. The bound anionsrepresent only 1/120,000 of the free concentration.


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Effect on Membrane Potential of Alteringthe External [K+]


114 mM Na +

3 ->6 mM K + 91 mM K +

120 mM Cl - 7.9 mM Cl -

0 mM A - 112.1 mM A -

29 mM Na +

-

-

-

+

+

+


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Test ing the Model Ut il izing Squid A xo n

Huxley and Hodgkin tested the potassium model utilizing the giantaxon of squid.The axons are so large the internal voltage can be monitoredutilizing the crude electrophysiology technology available at thetime.


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Ion Concent rat ions in Squid A xo nMeasurements


460 mM Na +

10 mM K + 400 mM K +

540 mM Cl - 60 mM Cl -

0 mM A - 510 mM A -

50 mM Na +



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Calculation of Membrane RestingPotential in Axon

EK+ = .0001985 T/z log ([K] o/[K]I)=.0001985(293/1)log (10/400)=-93 mVThe measured membrane potential is between -70 and -75 mVFurther measurement of the measurements potential at differentexternal [K+] demonstrated that at high concentrations the potential

was controlled by K+ but not at lower concentrations.What are the membrane potential if the other ions are allowed freeexchange? Which is positive?


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Mem b rane Potent ia l o f Other Io n s

ENa+ = .0001985 T/z log ([K] o/[K]I)=.0001985(293/1)log (460/50)=+56 mVECl- = .0001985 T/z log ([K] o/[K]I)=.0001985(293/-1)log (540/60)=-56 mVThe free flow of Cl -would cause a depolarization below that found.

Cl- also tends to be a stabilizing ion with little effect on membranepotential at steady state. The free flow of Na + would cause a profound depolarization.What if Na exchange was occurring at a much low value than K+exchange?

The cell could titrate the membrane potential down to the observedvalue. The measured membrane potential is between -65 and -70mV


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Two Ion s Con tro l Res t ing Potent ial


460 mM Na +

10 mM K + 400 mM K +

540 mM Cl - 60 mM Cl -

0 mM A - 510 mM A -

50 mM Na +


4%

100%


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Determ ining Mem brane Potent ial w i thMu lt iple Io nic Species

A equation was generated by Goldman, Hodgkin and Katz that takesinto account the contribution of multiple ionic species and theredegree of permeability.

Vm = 58 log (p K[K]o + p Na [Na] o)/(p K[K]in + p Na [Na+] in)

P = the permeability of that particular ion species in the systemFor squid axon p K = 1.0 and p Na = 0.04

Vm = 58 log [10 + 0.04(460)]/[400 + 0.04(50)] = -67 mV

This is close to the value determined experimentally but not perfect.

Is there another way to generate a membrane potential with Na + andK+ ions?


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Con tr ibu t ion o f the The Na+/K + Pum p toMemb rane Poten t ial

There is a ATP transporter that removes 3 Na+

ions from inside thecell and delivers then to the external environment that is coupled tothe delivery of 2 external K + ions into the cell from the externalenvironment.This maintains the Na+/K+ gradients in the cell and in additioncauses the internal environment to be more polarized since thecharge exchange is not symmetrical.Mullins and Noda expanded the equation to account for the pump byplacing a coupling value r in the equation. For this pump r=3/2=1.5

Vm = 58 log (rp K[K]o + p Na [Na] o)/(rp K[K]in + p Na [Na+] in)

Vm = 58 log [(1.5)10 + 0.04(460)]/[(1.5)400 + 0.04(50)] = -73 mV

The puts us at the correct value for the membrane potential in thesquid axon. The pump contributes about -6 mV in this system.


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Set t ing th e Rest ing Potent ia l

Free exchange of K+ ions is the major determinant in theestablishment of the resting membrane potential.

Partial exchange of Na+ will significantly modulate the restingmembrane potential in some but not all cells.

There are a number of pumps that are responsible for maintainingthe ion gradients in cells that would collapse over time. They cancontribute to the resting membrane potential but usually by less than-11 mV.

Chloride fluxes can change membrane potentials but these arecompensated for at steady state.


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Requ irem ents for Generat ion of Res t ingPotential

Hodgkin and Huxley could demonstrate that removal of all theaxoplasm from the squid axon had no effect on the establishmentthe membrane resting potential.

Therefore, all the required biological elements are present in theaxon membrane.

These are selective ion channels and ion transporters.

Lecture3-RestingPotential

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