1

Neurobiophysics

“Animal Electricity”

2

Concepts

The intracellular and extracellular fluids have unequal concentrations of specific ions.

Na+ K+ Cl- H+ HCO3-

The differences in concentrations are maintained

by the expenditure of energy (work).

3

Nernst Potential

VEq = RT/ZF ln(Cout /Cin)

Naout /Nain = 12/1 VNa = + 66 mV Kout /Kin = 1/40 VK = - 97 Clout /Clin = 30/1 VCl = - 90

Measured Membrane Potential Vm = - 90 mV

4

Goldman

Theory:

Movement of ions across (through) the membrane is due to a Driving Force.

Driving Force = Diffusion Gradient + Electric Field

5

Goldman

Assumptions:

Permeability - Velocity of ionic movement across the membrane is proportional to ion solubility in the membrane ion mobility in the electric field reciprocal of the membrane thickness

Constant Electric Field - Potential varies linearly with the thickness of the membrane

6

Goldman

Equation:

VEq = RT/ZF ln PKKout + PNaNaout + PClClin PKKin + PNaNain + PClClout

Pi = Permeability Coefficient

7

Goldman

If permeability of Cl- is either very small (nerve cells) or very large (skeletal muscle) Cl- ions can be ignored.

Let = PNa / PK

VEq = - RT/ZF ln Kin + Nain

Kout + Naout

8

Permeability

VEq = - RT/ZF ln Kin + Nain

Kout + Naout

Presume permeability is due to macromolecules (channels / pores) through the membrane that are selective to specific ions (Na+ K+ Cl- H+ HCO3

-).

What happens if the permeability changes? What happens if the pores open/close

completely?

9

Ionic Currents

Electric current is the movement of charge per time.

Ions are charged particles.

How many ions per second = 1 ampere ?

Ionic Charge = 1.60 x 10-19 coulomb Faraday’s Constant = 9.65 x 104 coulomb per

mol Avogadro’s Number = 6.02 x 1023 ions per mol

10

Ionic Current Net Driving Force = Vm - VEq

Vm = Membrane Potential VEq = Nernst Potential I Vm - VEq Let Proportionality Factor = Conductance g Note: The transmembrane conductance is

probabilistic and represents a population characteristic, NOT the value of a single pore.

If Vm - VEq < 0 implies positive ion enters the cell. If Vm - VEq > 0 implies positive ion leaves the cell.

11

Ionic Currents

Vm = - 60 mV

Inject Na or K into the cell, Vm increases (less negative).Eject Na or K from the cell, Vm decreases (more negative).Therefore the flow of ions results in changes to the membrane potential.

Na+

K+

12

Ionic Currents

Change in Conductance

Ionic Current Flow

Change in Membrane Potential

When a single ionic species flows, the effect is to drive the membrane potential TOWARDS the equilibrium (Nernst) potential for that ion.

13

Changes in Membrane Potential

Channel SodiumPotassium

Permeability

Conductance

Ionic/Current Flow

Vm

Inward Outward