1. Ions and molecules can move through membranes in various ways.

Transport may be passive (simple diffusion), passive transporter-mediated (facilitated diffusion), or active transporter-mediated (active transport) (look here!)

2. Ionic gradients are of central importance in the functioning of cells. Up to 25% of an animal cell's energy is used to create an ionic gradient by active transport of Na+ ions out of the cell, effectively rendering the cell membrane impermeable to Na⁺. The energy put into maintaining the ionic gradient is used for many cellular functions, including transport of materials such as glucose across cell membranes and for communication by nerve impulses (action potentials).

• Of particular importance is the fact that concentrations of Na⁺ and Cl^- are high outside the cell (as they are in sea water!!!!) and concentrations of K⁺ and trapped organic anions are high within cells..

Component	Intracellular Concentration (mM)	Extracellular Concentration (mM)
Na+	10	120
K+	140	2.5
Ca++	<10-3	2
Cl-	3-4	120
Organic ions	high	0

3. Osmotic balance (Eckert, Fig. 4-14) is maintained in animal cells by the Na⁺/K⁺ pump, which counteracts the slight leakage of cells to Na⁺. (Eckert, Fig. 4-24)

Cell membranes are permeable to K⁺ and Cl^- so they diffuse where they need to and don't contribute to the osmotic pressure. And, the osmotic pressure created by the impermeable organic anions within cells is balanced by the "effective" impermeability of the cell membrane to Na⁺. If some Na⁺ gets into the cell by cotransport, then it is just going to be pumped right back out again. Now, imagine that the pump stops working. This will destroy the effective impermeability of the membrane to Na⁺ and the only impermeable ions left will be the organic anions inside the cell. Water will rush into the cell and the cell will burst.

In protozoans and plant cells, other mechanisms are used to control osmotic pressure., including pumping of hydrogen ions.

4. The resting membrane potential is the result of a balance between the chemical potential of diffusion and the electrical potential.

• This balance is given by the Nernst equation: V = (62/Z)*log₁₀(C_out/C_in), where V (in mV) is the membrane potential, Z is the charge on the ion (Z_K = +1, Z_Cl = -1, Z_Ca = +2, etc.), and (C_out and C_in are the external and internal concentrations of a highly permeable ion such as K⁺. Temperature is 37 degrees C.
• Note: The general form of the Nernst equation is V = 2.303(RT/ZF)*log₁₀(C_out/C_in), where R is the gas constant (remember the gas law from Chemistry?), T is temperature in degrees Kelvin (273 + degrees C), and F is Faraday's constant. Can you figure out how the Nernst equation would look for a house cat with a body temperature of 39 degrees C? What happens if YOUR body temperature rises to 105 degrees F? For practice, assume that the potential across a membrane of one of your cells is -60mV at 37 degrees C - What would the potential be at 105 degrees F?
• The Nernst equation accurately predicts the membrane potential if there is a single permeable ion or a group of equally permeable ions. In the case of nerve cell membranes, the cell membrane is almost equally permeable to K⁺ and Cl^- and almost impermeable to other ions. So, the Nernst equation for either of these ions can be used to calculate the resting membrane potential.
• Let's do a little calculation: Suppose that K_out = 10 mM and K_in = 100 mM. (This is close enough to the actual values.) Then The Nernst equation for potassium would give V = -62 mV. If we try chloride, use Cl_out = 100 mM and Cl_in = 10 mM and we also get V = -62 mV.

Here is a table which shows how to calculate Nernst potentials from ion concentrations, at 37 degrees C:

Cout/Cin	log10(Cout/Cin)	Voltage for Chloride (z= -1) in mV	Voltage for Calcium (z= +2) in mV
1000	3	-186	93
100	2	-124	62
10	1	-62	31
1	0	0	0
0.1	-1	62	-31
0.01	-2	124	-62
0.001	-3	186	-93

Next time: Gibbs-Donnan equilibrium, Goldman constant-field equation, membrane permeability and conductance.

All text and images, not attributed to others, including course examinations and sample questions, are Copyright, 2005, Thomas J. Herbert and may not be used for any commercial purpose without the express written permission of Thomas J. Herbert.