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
