# BE.180:SecondOrderBinding

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### 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:

- 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.

*k*

_{on}* [

*A*] * [

*B*] −

*k*

_{off}* [

*A*:

*B*]

- Solve for
*K*_{D}, the dissociation constant.

- Note constraints on system due to conservation of mass.

*A*

_{0}] = [

*A*] + [

*A*:

*B*]

*B*

_{0}] = [

*B*] + [

*A*:

*B*]

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