BE.180:SecondOrderBinding: Difference between revisions
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Approach: | Approach: | ||
*Write differential equation for change in '''A:B''' over time. | *Write differential equation for change in '''A:B''' over time. | ||
<math>\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. | *Solve equation at steady state (that is, no change in concentration of the A:B complex. | ||
<math>0=-k_{on}*[A]*[B]-k_{off}*[A:B]</math> | |||
*Solve for <math>K_D</math>, the dissociation constant. | *Solve for <math>K_D</math>, the dissociation constant. | ||
Equation 1: <math>K_D = k_{off}/k_{on} = \frac{[A][B]}{[A:B]}</math></center> | |||
*Note constraints on system due to conservation of mass. | *Note constraints on system due to conservation of mass. | ||
Equation 2: <math>[A_0] = [A] + [A:B]</math> | |||
Equation 3: <math>[B_0] = [B] + [A:B]</math> | |||
*Note system of three unknowns with three equations! Solve for unknowns '''A''', '''B''', and '''A:B'''. | *Note system of three unknowns with three equations! Solve for unknowns '''A''', '''B''', and '''A:B'''. |
Revision as of 18:07, 20 March 2006
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! Solve for unknowns A, B, and A:B.