## Fig Percentages of total macromolecule concentration with various numbers of ligands as a function of the fraction of the sites occupied Four identical independent binding sites per macromolecule

The site and ligand conservation equations are:

The four-step algebraic solution (without the math) is:

1. Eliminate [Q] and [R] in Eq (11.26) using Eq (11.27).

2. Solve for the concentrations of occupied sites and eliminate [Ro] and [Qo] using Eq (11.25); solve for the ratios of bound sites to [mmtot]

3. Substitute the result from step 2 into Eq (11.28); with Eq (11.21), arrive at:

[L] K R+ [L] K q + [L] multiplying by KR + [L] and dividing by KR yields:

Which is of the same form as the single-site version Eq (11.22) with an additional term containing the effect of the second (Q) site. In order to permit plotting of the left-hand side of Eq (10.29b) against v, the dependence of [L] on v is needed. This is obtained by cross-multiplying Eq (11.29a) by the product of the three denominators, which yields the quadratic equation:

from which [L] can be calculated as a function of v. Figure 11.13 shows the Scatchard plot for the 2-independent-site model analyzed above. R is the stronger binding of the two sites. The dashed line neglects the presence of the Q sites. The effect of including these is to extend the v/[L] plot to larger values of v. With both sites active, the right hand curve shows the variation of [L] with the binding ratio expressed as a combination of Eqs (11.21) and (11.28):

Because (as in Fig. 11.13) there are 4 sites per macromolecule, this equation shows why the saturation curve ends at v = 4. In addition, to achieve complete saturation, an infinite concentration of ligand in solution is required. This can be seen from Eq (11.26); for the free site concentrations [R] and [Q] to approach zero, [L] must approach «.

## Solar Panel Basics

Global warming is a huge problem which will significantly affect every country in the world. Many people all over the world are trying to do whatever they can to help combat the effects of global warming. One of the ways that people can fight global warming is to reduce their dependence on non-renewable energy sources like oil and petroleum based products.

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