BE.180:SecondOrderBinding

Second Order Binding (of two things)
Givens:
 * A physical interaction between molecules A and B.
 * A system that contains some initial concentration of molecules A and B ($$A_0$$ and $$B_0$$, respectively).

Tasks:
 * Compute the steady state concentrations of free A, free B, and the A:B complex.

Approach: $$\frac{d[A:B]}{dt}=+k_{on}*[A]*[B]-k_{off}*[A:B]$$ $$0=+k_{on}*[A]*[B]-k_{off}*[A:B]$$ Equation 1: $$K_D = k_{off}/k_{on} = \frac{[A][B]}{[A:B]}$$ Equation 2: $$[A_0] = [A] + [A:B]$$ Equation 3: $$[B_0] = [B] + [A:B]$$
 * Write differential equation for change in A:B over time.
 * Solve equation at steady state (that is, no change in concentration of the A:B complex.
 * Solve for $$K_D$$, the dissociation constant.
 * Note constraints on system due to conservation of mass.
 * Note system of three unknowns with three equations (1-3 above)! Solve for unknowns A, B, and A:B (takes you through a quadratic).