# 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**(**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle A_0}**and**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle 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.

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \frac{d[A:B]}{dt}=+k_{on}*[A]*[B]-k_{off}*[A:B]}**

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

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle 0=+k_{on}*[A]*[B]-k_{off}*[A:B]}**

- Solve for
**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle K_D}**, the dissociation constant.

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle K_D = k_{off}/k_{on} = \frac{[A][B]}{[A:B]}}**

- Note constraints on system due to conservation of mass.

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle [A_0] = [A] + [A:B]}**

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle [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).