HillEquationCurve Class

public class HillEquationCurve : NonlinearCurve

Public Class HillEquationCurve
	Inherits NonlinearCurve

public ref class HillEquationCurve : public NonlinearCurve

type HillEquationCurve = 
    class
        inherit NonlinearCurve
    end

Inheritance

Object  →  Curve  →  NonlinearCurve  →  HillEquationCurve

Use the HillEquationCurve class to represent a three-parameter Hill curve, also known as the Hill equation, commonly used in pharmacology and biochemistry to describe cooperative binding phenomena.

The Hill equation extends the Michaelis-Menten model by adding a Hill coefficient (n) that accounts for cooperative binding. When n = 1, it reduces to the Michaelis-Menten equation. When n > 1, it indicates positive cooperativity; when n < 1, negative cooperativity.

The equation is:

Parameters:

• V_max – Maximum response (asymptotic value as x → ∞). See VMax.
• K – Half-maximal concentration (x value at which y = V_max/2). See K.
• n – Hill coefficient (cooperativity parameter). See HillCoefficient.

Applications:

• Pharmacological dose-response curves
• Receptor-ligand binding with cooperativity
• Oxygen binding to hemoglobin
• Allosteric enzyme regulation
• Gene expression modeling

For details on how to fit a curve of this type, see the NonlinearCurveFitter class.

Reference