MichaelisMentenCurve Class

Represents a Michaelis-Menten curve used for modeling enzyme kinetics and saturation processes.

Definition

Namespace: Numerics.NET.Curves.Nonlinear
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 10.0.0
C#
public class MichaelisMentenCurve : NonlinearCurve
Inheritance
Object  →  Curve  →  NonlinearCurve  →  MichaelisMentenCurve

Remarks

Use the MichaelisMentenCurve class to represent a two-parameter Michaelis-Menten curve commonly used in enzyme kinetics and other saturation processes.

The Michaelis-Menten equation describes the rate of enzymatic reactions by relating reaction rate to substrate concentration. It is characterized by two parameters: Vmax (maximum rate) and Km (Michaelis constant, the substrate concentration at which the reaction rate is half of Vmax).

The equation is:

y(x) = \frac{V_{max} \cdot x}{K_m + x}

Parameters:

  • Vmax – Maximum reaction rate (asymptotic value as x → ∞). See VMax.
  • Km – Michaelis constant (substrate concentration at half-maximum rate). See Km.

Applications:

  • Enzyme kinetics
  • Receptor-ligand binding
  • Saturation phenomena in chemistry and biology
  • Nutrient uptake in ecology

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

Constructors

MichaelisMentenCurve Constructs a new Michaelis-Menten curve.

Properties

Km Gets or sets the Michaelis constant (Km).
Parameters Gets the collection of parameters that determine the shape of this Curve.
(Inherited from Curve)
VMax Gets or sets the maximum reaction rate (Vmax).

Methods

Clone Constructs an exact copy of this instance.
(Inherited from Curve)
EqualsDetermines whether the specified object is equal to the current object.
(Inherited from Object)
FillNumericalPartialDerivatives Fills a dense vector with the partial derivatives of the curve with respect to each of the curve parameters computed using numerical differentiation.
(Inherited from NonlinearCurve)
FillPartialDerivatives Fills a dense vector with the partial derivatives of the curve with respect to each of the curve parameters.
(Overrides NonlinearCurve.FillPartialDerivatives(Double, DenseVector<Double>))
FinalizeAllows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object)
FindRoots Gets the set of X-coordinates where the curve crosses the X-axis.
(Inherited from Curve)
GetCurveFitter Returns a CurveFitter object that can be used to fit the curve to data.
(Inherited from NonlinearCurve)
GetDerivative Returns a Curve that represents the derivative of this Curve.
(Inherited from Curve)
GetHashCodeServes as the default hash function.
(Inherited from Object)
GetInitialFitParameters Returns a vector containing initial values for the parameters for a curve fit through the specified data.
(Overrides NonlinearCurve.GetInitialFitParameters(Vector<Double>, Vector<Double>))
GetPartialDerivatives Returns a vector with the partial derivatives of the curve with respect to each of the curve parameters.
(Inherited from NonlinearCurve)
GetTypeGets the Type of the current instance.
(Inherited from Object)
Integral Gets the definite integral of the curve between the specified X-coordinates.
(Inherited from Curve)
MemberwiseCloneCreates a shallow copy of the current Object.
(Inherited from Object)
OnParameterChanged Called after a Curve parameter has been changed.
(Inherited from Curve)
OnParameterChanging Called before the value of a curve parameter is changed.
(Inherited from Curve)
SetParameter Sets a curve parameter to the specified value.
(Inherited from Curve)
SlopeAt(Double[]) Gets the slopes of the curve at the specified X-coordinates.
(Inherited from Curve)
SlopeAt(Double) Gets the slope of the curve at the specified X-coordinate.
(Overrides Curve.SlopeAt(Double))
SlopeAt(ReadOnlySpan<Double>) Gets the slopes of the curve at the specified X-coordinates.
(Inherited from Curve)
SlopeAt(Vector<Double>) Gets the slopes of the curve at the specified X-coordinates.
(Inherited from Curve)
SlopeAt(ReadOnlySpan<Double>, Span<Double>) Gets the slopes of the curve at the specified X-coordinates.
(Inherited from Curve)
Solve Finds the x value where the curve reaches the specified y value.
(Inherited from Curve)
TangentAt Gets the tangent line to the curve at the specified X-coordinate.
(Inherited from Curve)
ToStringReturns a string that represents the current object.
(Inherited from Object)
ValueAt(Double[]) Gets the Y-values of the curve at the specified X-coordinates.
(Inherited from Curve)
ValueAt(Double) Gets the Y-value of the curve at the specified X-coordinate.
(Overrides Curve.ValueAt(Double))
ValueAt(ReadOnlySpan<Double>) Gets the Y-values of the curve at the specified X-coordinates.
(Inherited from Curve)
ValueAt(Vector<Double>) Gets the Y-values of the curve at the specified X-coordinates.
(Inherited from Curve)
ValueAt(ReadOnlySpan<Double>, Span<Double>) Gets the Y-values of the curve at the specified X-coordinates.
(Inherited from Curve)

See Also