32.1.26 Boltzmann

Function

\[y=\frac{A_1-A_2}{1+e^{(x-x_0)/dx}}+A_2\]

Brief Description

Boltzmann Function - produce a sigmoidal curve.

Sample Curve

Parameters

Number: 4

Names: A1, A2, x0, dx

Meanings: A1 = initial value, A2 = final value, x0 = center, dx = time constant

Lower Bounds: none

Upper Bounds: none

Derived Parameters

The span: span=abs(A1-A2)

The concentration at half response: EC50=exp(x0)

The concentration at 10% response: EC10=exp(x0 - dx*ln(9))

The concentration at 20% response: EC20=exp(x0 - dx*ln(4))

The concentration at 80% response: EC80=exp(x0 + dx*ln(4))

The concentration at 90% response: EC90=exp(x0 + dx*ln(9))

Constraints

dx ! = 0

Script Access

nlf_boltzman(x,A1,A2,x0,dx)

Function File

FITFUNC\BOLTZMAN.FDF

Category

Origin Basic Functions, Growth/Sigmoidal