Hello,
I have a set of data coming from a dissociation experiment
(protein/ligand). Since the data is required to calculate the constant
of dissociation (Kd) of this pair, I am looking for a way to fit a
Hill function to the data.
I have seen that the package `mosaic` (https://rpubs.com/dtkaplan/646) provides
such approach with `fitModel`.
However, I fail to find the proper starting points and get the error:
```
Error in nlsModel(formula, mf, start, wts, scaleOffset = scOff,
nDcentral = nDcntr) : singular gradient matrix at initial parameter
estimates
```
How can I run this package?
How can I estimate the starting values for the function, considering
that the data is decreasing rather than increasing (so it is probably
an inverse Hill function)?
Thank you
```
df = data.frame(Response = c(890.72, 895.46, 895.63,
894.72, 895.49, 893.59,
892.53, 895.06, 897.21, 889.27, 876.05,
857.96, 862.02, 858.36,
890.94, 890.8, 887.22, 888.91, 890.83,
889.92, 891.76, 890.32,
886.35, 878.11, 866.57, 859.04, 863.64,
880.16, 884.15, 879.57,
878.89, 882.27, 881.59, 880.98, 881.45,
876.19, 868.32, 859.16,
850.53, 853.21, 859.34, 859.73, 861.19),
Dose = c(0.0000000015, 0.000000003,
0.000000006, 0.000000012,
0.000000024, 0.000000048, 0.000000095,
0.00000018,
0.00000038, 0.00000078, 0.0000015,
0.000013, 0.000025,
0.00005, 0.0000000015, 0.000000003,
0.000000006,
0.000000012, 0.000000024, 0.000000048,
0.000000095,
0.00000018, 0.00000038, 0.00000078,
0.0000015, 0.000025,
0.00005, 0.0000000015, 0.000000003,
0.000000006,
0.000000012, 0.000000024, 0.000000048,
0.000000095,
0.00000018, 0.00000038, 0.00000078,
0.0000015, 0.000003,
0.000006, 0.000013, 0.000025, 0.00005)
)
plot(Response~log10(Dose), df)
nls(Response ~ ( (exp((a+b*Dose))) / (1+exp(-(a+b*Dose)) )), data=df)
library(mosaic)
fitModel(Response ~ A * Dose^2/(theta^2 + Dose^2), data = df,
start = list(A = 100, theta = -4))
```