Bio-Rad Microplate Manager Software - Manual (Page 45)

Analyzing Data Using a Standard Curve
37
Log/Logit and 4-Parameter Fit
Both the Log/Logit and the 4-Parameter curve fit methods are based on the same
equation:
A - D
y = ______________ + D
1 + ( conc / C ) B
which can be expressed in the equivalent form:
logit y = a + b * log
10
(conc)
where
logit y = ln (y'/1-y'), B = -b/ln
10
= slope at inflection point of curve
y' = (y-D)/(A-D) C = EXP(a/B) = concentration at midpoint between A & D
The difference between the Log/Logit and the 4-parameter curve fit options is in how
the parameters A and D (the asymptotes for conc -> 0 and conc -> ∞, respectively)
are calculated.
In the Log/Logit method, the parameters A and D are fixed to the response of the
lowest and highest standards, respectively, and only the B and C values are fitted.
The Log/Logit method requires that at least one standard lies within the intermediate
range between the two asymptote portions of the S-shaped standard curve.
In the 4-parameter method, all 4 parameters A, B, C, D are fitted. The algorithm
used by the program fits the parameters A, B, C, D iteratively with non-linear
regression (Levenberg-Marquardt method) as described in Ref 2. The starting
values for the A, B, C, D parameters are taken from an initial Log/Logit fit. In
Microplate Manager 6.0 the 4-parameter logistic curve uses 2000 iterations. If the fit
does not converge in this number of iterations, the program will report fitting failed
and not display a curve.
In both methods, the B value is the slope at the inflection point or half maximum of
the curve. The 50% Value is the Mean Y Axis Value of the A & D asymptotes. The
C value is the concentration (X value) for the 50% Y value which corresponds to the
midpoint between A and D.