Michaelis Menten Curve 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#
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 10.0.0
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
| Michaelis | 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) |
| Equals | Determines whether the specified object is equal to the current object. (Inherited from Object) |
| Fill |
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) |
| Fill |
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>)) |
| Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object) |
| Find |
Gets the set of X-coordinates where the curve crosses
the X-axis.
(Inherited from Curve) |
| Get |
Returns a CurveFitter object that can be used to fit the curve to data.
(Inherited from NonlinearCurve) |
| Get |
Returns a Curve that represents the derivative
of this Curve.
(Inherited from Curve) |
| Get | Serves as the default hash function. (Inherited from Object) |
| Get |
Returns a vector containing initial values for the parameters for a curve fit
through the specified data.
(Overrides NonlinearCurve.GetInitialFitParameters(Vector<Double>, Vector<Double>)) |
| Get |
Returns a vector with the partial derivatives
of the curve with respect to each of the curve parameters.
(Inherited from NonlinearCurve) |
| Get | Gets 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) |
| Memberwise | Creates a shallow copy of the current Object. (Inherited from Object) |
| OnParameter |
Called after a Curve parameter has been changed.
(Inherited from Curve) |
| OnParameter |
Called before the value of a curve parameter is changed.
(Inherited from Curve) |
| Set |
Sets a curve parameter to the specified value.
(Inherited from Curve) |
| Slope |
Gets the slopes of the curve at the specified X-coordinates.
(Inherited from Curve) |
| Slope |
Gets the slope of the curve at the specified X-coordinate.
(Overrides Curve.SlopeAt(Double)) |
| Slope |
Gets the slopes of the curve at the specified X-coordinates.
(Inherited from Curve) |
| Slope |
Gets the slopes of the curve at the specified X-coordinates.
(Inherited from Curve) |
| Slope |
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) |
| Tangent |
Gets the tangent line to the curve at the
specified X-coordinate.
(Inherited from Curve) |
| ToString | Returns a string that represents the current object. (Inherited from Object) |
| Value |
Gets the Y-values of the curve at the specified X-coordinates.
(Inherited from Curve) |
| Value |
Gets the Y-value of the curve at the specified X-coordinate.
(Overrides Curve.ValueAt(Double)) |
| Value |
Gets the Y-values of the curve at the specified X-coordinates.
(Inherited from Curve) |
| Value |
Gets the Y-values of the curve at the specified X-coordinates.
(Inherited from Curve) |
| Value |
Gets the Y-values of the curve at the specified X-coordinates.
(Inherited from Curve) |