Ligand Binding and the Saturation Fraction, Ya

The life of any organism is 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.

Hemoglobin's capacity to bind oxygen, for example, 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 diminish 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 which simply equals the fraction of all ligand binding sites 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 Ya 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 and Ya = 0.5, or 50%.

In a biological system the saturation fraction is 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. One way to think about biological molecules is that they are like sponges for other molecules and the saturation fraction is measure of how much the sponge takes up. Because the processes are dynamic, the sponge is continuously being squeezed and soaked. Like a sponge, there is also a limit to the binding capacity of any biological molecule. Another analogy one can make for biological molecules is they are like drinking vessels being continuously filled and emptied. In this case, the saturation fraction provides a quantitative measure for just how full the vessel is (e.g., 1/4, 1/2, etc.) at any one instant.

Through precise quantitative measurements, it is reasonably straightforward to relate the dynamics of a protein-mediated process to temporal changes in the saturation fraction for a ligand that regulates the protein's activity . Essentially three requirements 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 known.
The temporal fluctuation of the ligand concentration must also be known.

With increasing complexity, different types of ligand binding systems are examined in detail in a series of weekly exercises devoted to:

monovalent ligand binding systems
bivalent, non-interactive ligand binding systems
trivalent, semi-interactive ligand binding systems
bivalent, interactive ligand binding systems
multivalent, interactive ligand binding systems
Michaelis-Menten enzyme kinetics
Ligand-regulated enzyme kinetics

These ligand binding systems are all interrelated by the similar mathematical equations. Depending on how the equations are rearranged, one can analyze the ligand binding system using the following graphical formats where Yd is dissociation fraction (equal to 1-Ya), [L] is the equilibrium ligand concentration, and [S] is the initial substrate concentration.

Graphical Plot	Y-Axis vs. X-Axis
Rectangular hyperbolic:	Ya vs. [L]
pH saturation:	Ya vs. pL ( i.e., -log [L] )
Log saturation:	Ya vs. [L] plotted on a log axis
Henderson-Hasselbalch:	log (Yd / Ya ) vs. pL
Hill:	log (Ya / Yd ) vs. log [L]
Scatchard:	r / [L] vs. r r = n * Ya = the average number of ligand molecules bound to a receptor with n ligand binding sites
Michaelis-Menten:	Vo / Vmax vs. [S] Vo/ Vmax (the initial reaction velocity over the maximal reaction velocity) is mathematically equivalent to Ya.

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©	Duane W. Sears Revised: October 07, 2010