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Binding Equations for QtiPlot

Ready-to-use formulas for curve fitting and binding analysis

Hyperbolic Binding Equation

Simple Binding
  • Estimates the dissociation constant of a bimolecular interaction
  • Only valid if the ligand concentration is very small

QtiPlot Implementation:

Fraction Bound:
(x)/(Kd+x)
With Signal Calculation:
min+(max-min)*(x)/(Kd+x)

Variables:

  • Kd: Dissociation constant of labeled ligand to the receptor
  • x: Receptor concentration
  • min: Signal of free ligand
  • max: Signal of receptor-bound ligand

Quadratic Binding Equation

Analytical Solution
  • Analytical solution of the bimolecular binding equation
  • Also valid at high ligand concentration

QtiPlot Implementation:

Fraction Bound:
((Atot+x+Kd)-sqrt(((-Atot-x-Kd)*(-Atot-x-Kd))-(4*(Atot*x))))/(2*Atot)
With Signal Calculation:
min+(max-min)*(((Atot+x+Kd)-sqrt(((-Atot-x-Kd)*(-Atot-x-Kd))-(4*(Atot*x))))/(2*Atot))

Variables:

  • Kd: Dissociation constant of labeled ligand to the receptor
  • Atot: Total ligand concentration
  • x: Total receptor concentration
  • min: Signal of free ligand
  • max: Signal of receptor-bound ligand

Competitive Binding Equation

Competition Analysis
  • Analytical solution of the cubic binding equation (equation 17 from Roehrl 2024, Biochemistry)
  • Quantifies the fraction bound of a labeled ligand to a receptor in a system that also contains a competitor molecule that binds to the same site

QtiPlot Implementation:

Fraction Bound:
(((2*(sqrt((Kdir+Kcomp+LST+x-RT)^2-3*((x-RT)*Kdir+(LST-RT)*Kcomp+Kdir*Kcomp)))*cos(acos((-2*(Kdir+Kcomp+LST+x-RT)^3+9*(Kdir+Kcomp+LST+x-RT)*((x-RT)*Kdir+(LST-RT)*Kcomp+Kdir*Kcomp)-27*(-Kdir*Kcomp*RT))/(2*sqrt(((Kdir+Kcomp+LST+x-RT)^2-3*((x-RT)*Kdir+(LST-RT)*Kcomp+Kdir*Kcomp))^3)))/3))-(Kdir+Kcomp+LST+x-RT))/(3*Kdir+(2*(sqrt((Kdir+Kcomp+LST+x-RT)^2-3*((x-RT)*Kdir+(LST-RT)*Kcomp+Kdir*Kcomp)))*cos(acos((-2*(Kdir+Kcomp+LST+x-RT)^3+9*(Kdir+Kcomp+LST+x-RT)*((x-RT)*Kdir+(LST-RT)*Kcomp+Kdir*Kcomp)-27*(-Kdir*Kcomp*RT))/(2*sqrt(((Kdir+Kcomp+LST+x-RT)^2-3*((x-RT)*Kdir+(LST-RT)*Kcomp+Kdir*Kcomp))^3)))/3))-(Kdir+Kcomp+LST+x-RT)))
With Signal Calculation:
min+(max-min)*(((2*(sqrt((Kdir+Kcomp+LST+x-RT)^2-3*((x-RT)*Kdir+(LST-RT)*Kcomp+Kdir*Kcomp)))*cos(acos((-2*(Kdir+Kcomp+LST+x-RT)^3+9*(Kdir+Kcomp+LST+x-RT)*((x-RT)*Kdir+(LST-RT)*Kcomp+Kdir*Kcomp)-27*(-Kdir*Kcomp*RT))/(2*sqrt(((Kdir+Kcomp+LST+x-RT)^2-3*((x-RT)*Kdir+(LST-RT)*Kcomp+Kdir*Kcomp))^3)))/3))-(Kdir+Kcomp+LST+x-RT))/(3*Kdir+(2*(sqrt((Kdir+Kcomp+LST+x-RT)^2-3*((x-RT)*Kdir+(LST-RT)*Kcomp+Kdir*Kcomp)))*cos(acos((-2*(Kdir+Kcomp+LST+x-RT)^3+9*(Kdir+Kcomp+LST+x-RT)*((x-RT)*Kdir+(LST-RT)*Kcomp+Kdir*Kcomp)-27*(-Kdir*Kcomp*RT))/(2*sqrt(((Kdir+Kcomp+LST+x-RT)^2-3*((x-RT)*Kdir+(LST-RT)*Kcomp+Kdir*Kcomp))^3)))/3))-(Kdir+Kcomp+LST+x-RT)))

Variables:

  • Kcomp: Dissociation constant of un-labeled ligand to the receptor
  • Kdir: Dissociation constant of labeled ligand to the receptor
  • LST: Total labeled ligand concentration
  • RT: Total receptor concentration
  • x: Ligand concentration
  • min: Signal of free ligand
  • max: Signal of receptor-bound ligand

💡 How to Use These Formulas in QtiPlot

1. Copy Formula

Click the copy button next to the formula you need

2. Open QtiPlot

Go to Analysis → Fit Wizard or Non-linear Curve Fit

3. Paste Formula

Paste the formula in the expression field

4. Define Parameters

Set initial values for all parameters before fitting