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 ([math]\displaystyle{ A_0 }[/math] and [math]\displaystyle{ B_0 }[/math], respectively).

Tasks:

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

Approach:

• Write differential equation for change in A:B over time.

[math]\displaystyle{ \frac{d[A:B]}{dt}=-k_{on}*[A]*[B]-k_{off}*[A:B] }[/math]

• Solve equation at steady state (that is, no change in concentration of the A:B complex.

[math]\displaystyle{ 0=-k_{on}*[A]*[B]-k_{off}*[A:B] }[/math]

• Solve for [math]\displaystyle{ K_D }[/math], the dissociation constant.

Equation 1: [math]\displaystyle{ K_D = k_{off}/k_{on} = \frac{[A][B]}{[A:B]} }[/math]

• Note constraints on system due to conservation of mass.

Equation 2: [math]\displaystyle{ [A_0] = [A] + [A:B] }[/math] Equation 3: [math]\displaystyle{ [B_0] = [B] + [A:B] }[/math]

• Note system of three unknowns with three equations (1-3 above)! Solve for unknowns A, B, and A:B (takes you through a quadratic).