Review: CELL MEMBRANE

A membrane is nature’s method for separating two components,e.g., the inside of a cell from the outside.

Cell membranes are composed of a phospholipid bilayer such that, in a basically water-water interface, the outer and inner walls are ionic and, therefore, attracted to water. On the inside of the membrane bilayer, the fatty ends of the molecules face each other.

hydrophilic

hydrophobic

Inside Cell (water)

Outside Cell (water)

1

2

But ‘things’ must pass into and out of cells, i.e., through membranes

This is accomplished by (at least) 3 different methods:

(i) a substance dissolving (ionizing) in the phospholipid and diffusing through

(ii) passing through water-filled pores

(iii) by means of carriers

The last two imply that things are imbedded in the membrane allowing passage of some ions and water (easily).

Forces on Particles

For a substance to be in equilibrium across a membrane, the work required to bring a substance to points just inside or just outside the membrane must be equal.

Definitions:One volt is the work needed to bring a unit positive charge from infinity to a particular point.

(particle of valence #z) WE = z F V where units are F - coulombs/ moleV - joules/coulombWE - Elec. work

Concentration is the work needed to bring a substance from 1 mole/liter to the concentration in the cell.

WC = R T ln[S] where units are R - gas constantT - degrees Kelvin[S] - conc. of SWC - chem. work

Semi-Permeable Membranes

Diffusion

after time

Net Flow No Net Flow

Potential Gradient

Charged particles set up electric fieldE = F / q (Newtons/Coulomb)

High energy particles cross the membrane

Semi-Permeable Membranes

Charge neutral on both sides of membrane

LargeNeg.Ions

LargePos.Ions

LargePos.Ions

LargeNeg.Ions

after time

D + E = D + E+ +--D - diffusion

E - Elec. field

D-

D+

(currents in dynamic equilibrium)

E+

E-

D-

D+

Osmotic Balance

Semi-permeable Membrane

P (solute)

Water

S (solute)

Diffusion will drive water to equalize concentrations inside and outside the cell

Fick’s Law of Diffusion

dS/dt = D (C1 - C2)where S- solute Ci - concentration in ith compartment

D - diffusion constant

For water to reach equilibrium[S]i + [P]i = [S]o Note: [P]o = 0

If [P]i is not zero, water will be driven osmotically into the cell so that it will swellperhaps to the point of membrane failure (burst).

Cell Model (in equilibrium)Assume [K+]o = 5mM, [Na+]o = 120 mM, [Cl-]i = 5mM, [A- ]i = 108mMwhere A- is a membrane-impermeable ion.

For electrical neutrality outside, [Cl-]o = 125mMFrom Donnan equilibrium, [K+]i = 125 mM

Inside12 mM Na+125 mM K+5 mM Cl-108 mM A-

OutsideNa+ 120 mMK+ 5 mMCl- 125 mM

membraneTotal osmolarity=250 mOsm Total osmolarity=250 mOsm

From the Nernst Equation for either Cl- or K+, the membrane potential is

Vm = (R T/zClF) ln{[ Cl-]o/[Cl-]i} = (R T/zKF) ln{[ K+]o/[K+]i}

(for Cl ) = (-58 mV) log{ 125 mM/5mM} = (-58) 1.398 = -81 mV

However, real cells are NOT IN EQUILIBRIUM so they must expend metabolic energy to maintain the status quo, I.e., this model needs modification.

Nernst Equation(for one substance in equilibrium across membrane)

Zs F Vi + R T ln[S]i = Zs F Vo + R T ln[S]o Where subscript i - inside cell o - outside cell

If Vm = Vi - Vo, Vm = (RT)/ (ZsF) ln([S]o/ [S]i) Nernst Equation

If there are two substances, the Nernst Eq’n readily leads to the Gibbs-Donnan Eq’n.

Vm = (RT/Z1F) ln( [S1]o/[S1]i) = (RT/Z2F) ln( [S2]o/[S2]i)

So(see blackboard for equil. of 2 substances across membrane)

We find (under physiological conditions) using the Nernst equation that the

equilibrium potential for K ~ -76mv and for Na ~ +55 mv. The measured

membrane potential is ~ -70 mv so we conclude that in ‘real life’, the Na ion in

particular is not in equilibrium, i.e., the membrane is not completely impermeable

to the Na ion.

The membrane potential is described well by the Goldman Equation which assumes a constant E-field across the membrane and assumes non-equilibrium membrane potential for the three ions Na+, K+, Cl-

The Goldman Equation is

Vm = (R T/F) ln[{a [K]o + b[Na]o + c[Cl] i}/ {a[K]i + b[Na]i + c[Cl]o} ]where a, b, c are the permeabilities of the membrane to K, Na, Cl respectively

Electrolytes and Potentials Across Membranes

Small pores implies NO IONS PASS

External Internal

Na+ 100 mM/l Na+ 10

Cl- 100 mM/l Cl- 10

No diffusion potential

H2O

Large pores implies MODERATE SIZE IONS PASS

External Internal

Na+ 50 mM/l Na+ 100

Cl- 100 mM/l Cl- 100

R+ 50 mM/l

Na+ 64 mM/l Na+ 86

Cl- 114 mM/l Cl- 86

R+ 50 mM/l

Initially electrically neutral

External Internal+ - 10 mV

200 mM/l 200 mM/lOsmotic Concentration

228 mM/l 172 mM/lOsmotic Concentration

E= (RT/F) ln (Na int / Na ext)