Page 441 - Excel for Scientists and Engineers: Numerical Methods

418 EXCEL: NUMERICAL METHODS

In the dose-response form of the equation, the y-axis (the response) is
normalized to 100% and the x-axis (usually logarithmic) is normalized so that the
midpoint (the half-maximum response or ECSo) occurs at x = 0.

Logistic Curve with Variable Slope. In equation A4-11, the coefficient a
determines the slope of the rising part of the curve; in biochemistry a is referred
to as the Hill slope. Figure A4-14 illustrates the effect of varying Hill slope. At
the midpoint the slope is a/4.

-10 -5 0 5 10
X

Figure A4-14. Variable slopes of logistic curve.
The three curves have a = 0.5, 1 and 2, respectively.

Logistic Curve with Additional Parameters. Equation A4-12 is the
logistic equation with addition parameters that determine the height of the
"plateau" and the offset of the mid-point from x = 0.
b
Y= (A4- 12)
c + e-ax
The height of the plateau is equal to b/c.