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.
Equation 1: 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.
Equation 2: 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]}
Equation 3: 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).