[R] saturation binding in nlme

[David Airey]

To estimate saturation binding parameters Bmax and Kd in a receptor  
saturation binding experiment, I use the following nonlinear equation  
and the nls() function:

bmax*X*dummy
------------  + ns*X + background = total binding
kd+X

where X is concentration, and dummy is an indicator to allow shared  
estimation of the nonspecific binding parameter ns. This equation  
describes two fitted lines, a linear fit for observed nonspecific  
binding, and a nonlinear fit for observed total binding. The linear  
component ns*X + background is shared.

In our experiments we don't actually observe data for the Michaelis- 
Menten component of the equation. It is inferred by subtraction of  
observed total and observed nonspecific data, or estimated in the  
combined data by sharing the ns parameter by adding a 1-0 indicator  
variable to the equation (1 for total, 0 for nonspecific).

I now need to do the same kind of estimation but in the context of  
nlme(), because we have multiple isogenic animals measured per  
genetically different strain, and we are interested in whether Bmax  
and Kd differ by strain. Easy enough to save out the Bmax and Kd from  
multiple uses of nls() and use a ttest or anova, but I'd like to try  
nlme().

Sharing parameters as above seems incompatible with using nlme(). Is  
it? I am planning on simply subtracting observed total and predicted  
nonspecific data to get me specific data per animal to estimate using  
nlme(), but I am curious if I can't estimate the data with nlme using  
the equation above.

Cheers,

-Dave