Ligand Binding and the Saturation Fraction, Ya

Ligand Binding and Saturation Fraction, Ya (lig)

The life of any organism is largely shaped by its dynamic capabilities. Does the organism move and, if so, how and how fast? How does it find and ingest nutrients? How does it interact with its environment and potentially reshape that environment, and so forth? By the same token, a biological process is shaped by its dynamics. How fast does the process occur? How is it regulated and by what? How does the dynamics of a process implement or shape the dynamic capacities of the organism itself?While it might seem hopeless to learn anything about the dynamic processes of a organism, which by its very nature represents a multitude of complex, interacting processes, it is still possible to gain considerable insight concerning individual processes, particularly those involving reversible ligand binding events. In fact many key protein-medicated biological processes have been shown to be regulated by specific and reversible ligand binding events.

For example, hemoglobin's capacity to bind oxygen is regulated by the local concentration of several factors in the blood. An elevated oxygen concentration enhances the binding of oxygen to hemoglobin whereas elevated concentrations of other factors -- such as protons, carbon dioxide, 2,3-diphosphoglycerate, and chloride -- diminish hemoglobin's capacity to bind oxygen. The opposing effects of these factors account for hemoglobin's dynamic transport of oxygen from the lungs, where the oxygen concentration is high, to the capillaries where the concentration of oxygen is lower while the concentrations of these other factors are all relatively high as a result of metabolic respiration. In likewise fashion, the activities of numerous enzymes are fine-tuned or regulated by the environmental concentrations of ligands that serve to augment or diminsh an enzyme's activity in accordance with the cell's metabolic needs at any given point in time.

If the efficiency by which a protein mediates a process is modulated by bound regulatory ligands, the dynamics of the process may be understood, at some level at least, by measuring ligand binding under different conditions. One measurement of ligand binding is called the "saturation fraction" or the "association fraction," Ya. This parameter is simply the fraction of all ligand binding sites that are occupied by ligand in a given set of conditions. In some cases, a protein will only bind one ligand of given kind whereas other proteins, especially multi-subunited proteins, may bind several subunits of a given kind. In many cases, a protein may also bind different kinds of ligands, each being characterized by its own saturation fraction under specified conditions. By convention, the saturation fraction varies in value from zero to one (0% to 100%). For example, when a protein with two binding sites for the same ligand is "50% saturated," only 1 out of the 2 sites -- on average -- will be occupied by ligand in the entire protein population; in other words, only half the sites will be occupied.

In a biological system the saturation fraction can be a dynamic parameter, changing as the organism responds to chemical changes in the environment. For example, the saturation fraction of hemoglobin in terms of bound oxygen changes as the molecules course through the blood moving from areas of high oxygen concentration (lungs) to areas of low oxygen concentration (capillaries). The changes in hemoglobin saturation fraction account for the delivery of oxygen to tissues that are respiring aerobically. A couple of ways to think about the saturation fraction is that this parameter is akin to a sponge continuously being squeezed and soaked, or a glass continuously being filled and emptied. The dyanmics of the saturation fraction are animated in a cartoon of wine glass being filled and emptied.

With precise quantitative measurements it is fairly straightforward to relate the dynamics of a protein-mediated process ti temporal changes in the saturation fraction for regulatory ligand binding. Essentially three requirments must be met:

A protein's activity must be quantitatively related to the saturation fraction for a given regulatory ligand.
The biological range of ligand concentration variation in the cell or in the organism must be established.
The temporal fluctuation of the ligand concentration must also be established.

To develop a more detailed understanding of these relationships, a series of ligand binding situations is examined in detail, progressing in complexity as follows:

monovalent ligand binding
bivalent, noninteractive ligand binding
trivalent, semi-interactive ligand binding
bivalent, interactive ligand binding
multivalent, interactive ligand binding

These ligand binding systems are all interconnected by the same types of mathematical relationships that can be rearranged to produce the following types of graphical displays of ligand binding as measured against the ligand concentration, [L]:

Rectangular Hyperbolic Plot: Ya, the associated fraction, plotted against [L];
pH Saturation Plot: Ya plotted against pL ( i.e., -log [L] );
Log Saturation Plot: Ya plotted against plotted against [L] on a log axis;
Henderson-Hasselbalch Plot: log (Yd / Ya ) plotted against against pL
Hill Plot: log (Ya / Yd ) plotted against against log [L];
Scatchard Plot: (n * Ya ) / [L] plotted against log n * Ya where n * Ya = r, the number of ligands bound to a molecule with n ligand binding sites.
Michaelis-Menton Plot: Vo / Vmax* plotted against [S] where Vo/ Vmax, the initial reaction velocity over the maximal reaction velocity behaves as Ya and [S] is the initial concentration of substrate in the reaction.

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