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The simplest thermodynamic equation for transport is

G = RTln(C2/C1)

Upon first examination, we might think that transport has taken place if there exists a concentration difference (gradient) across the membrane. There are three conditions when C2 (concentration on one side of the membrane) is not equal to C1 on the other side of the membrane. However, only one of these conditions results directly from active transport.

a. sequestration:

In a case of sequestration, the following conditions exist:

C2-total is not equal to C1-total but C2-free is equal to C1-free

An example of this condition is the red blood cells and oxygen. Total oxygen concentrations inside the cell are much higher than outside, but at equilibrium, free oxygen levels are the same on both sides of the membrane. This is because the hemoglobin inside the cell holds (sequesters) lots of bound oxygen.

b. electrical potential:

In a case where an electrical potential exists across a membrane, at equilibrium C2 will not be equal to C1 because of the charge imbalance across the membrane. Two forces, chemical potential (from concentration difference), and electrical potential (derived from differences in charge distribution) are both unequal, but are balancing each other. Conduction down nerve axons is an example of this phenomenon.

c. active transport:

Active transport is driven by a reaction or process that has a negativeG value (e.g. hydrolysis of ATP). This free energy permits transport against a concentration gradient and results in a transmembrane condition where C2 is not equal to C1.

Membrane transport:

Membrane transport can be classified into one of three categories (not all transport across the membrane is active).

a. passive diffusion: transport occurs through the membrane at non-specific sites; the rate depends on the solubility in the hydrocarbon phase of membrane of the molecule being transported.

J = Dm (C2-C1)/l

where J is the flux of the transported molecule across the membrane, Dm is the effective diffusion coefficient (incorporates solubility) and l is thickness of the membrane. Perhaps surprisingly, water passes easily.

b. facilitated transport:

In facilitated transport some specific membrane structure is involved such as:

a. a protein, such as the anion exchange protein in the erythrocyte
b. a gap junction, which is a gated pore
c. an ionophore, which can form a transmembrane pore or act as a shuttle for ions

Facilitated transport can be distinguished from passive diffusion

c. active transport:

We will examine three examples of active transport systems:

a. sodium-potassium pump (in the older literature it is called NaK-ATPase)
b. sodium-glucose cotransport system (symport in older texts)
c. phosphotransferase system (E. coli)

Examples of active transport systems:

a. sodium-potassium pump:

The sodium-potassium pump is a a2b2 tetramer.

The alpha subunits, 95 kDa in molecular weight, are transmembrane proteins and act to hydolyze ATP.

The beta subunits, 40 kDa in molecular weight, are integral membrane glycoproteins located on the outside of the membrane.

The stoichiometry of the transport reaction cycle is 2 K+ pumped in and 3 Na+ The catalytic cycle is regulated by ion binding and release. The alpha subunit becomes phosphorylated upon the binding of 3 Na++
b. sodium-glucose cotransport system:

The sodium-glucose cotransport system establishes a sodium ion gradient based on the hydrolysis of ATP (see above). The transport protein binds both glucose and Na+; glucose moves up its concentration gradient as sodium moves down its.

c. phosphotransferase system:

The phosphotransferase system accomplishes active transport by converting glucose to glucose-6-phosphate. This reaction is carried out through the agency of several proteins and is driven energetically by phosphoenolpyruvate (PEP). The sequence of reactions is as follows:

PEP transfers a phosphate to Enzyme-I to form E-I -P, which in turn transfers it to Hpr (a small heat-stable protein) to form Hpr-P, which transfers it to Enzyme-III to form E-III -P.

E-III -P associates with Enzyme-II, a transmembrane protein which undergoes a conformation change, opening a glucose binding site on the outside of the cell.

E-II changes conformation upon binding glucose and releases the glucose to the inside of the cell, where E-III- P transfers the phosphate group to the glucose.

Since there is no transmembrane protein capable of binding glucose-6-phosphate, it is now "locked" inside the cell.

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