[R] Help with nonlinear regressional

LuriFax luri-fax at hotmail.com
Tue Sep 2 14:06:17 CEST 2008

Dear All,

I am doing experiments in live plant tissue using a laser confocal
microscope. The method is called "fluorescence recovery after
photo-bleaching"  (FRAP) and here follows a short summary:

1. Record/ measure fluorescence intensity in a defined, round region of
interest (ROI, in this case a small spot) to determine the initial intensity
value before the bleaching. This pre-bleach value is also used for
normalising the curve (pre-bleach is then set to 1).

2. Bleach this ROI (with high laser intensity).

3. Record/ measure the recovery of fluorescence over time in the ROI until
it reaches a steady state (a plateau).
n. Fit the measured intensity for each time point and mesure the half time
(the timepoint which the curve has reached half the plateau), and more...

The recovery of fluorescence in the ROI is used as a measurement of protein
diffusion in the time range of the experiment. A steep curve means that the
molecules has diffused rapidly into the observed ROI and vice versa.

When I do a regressional curve fit without any constraints I get a huge
deviation from the measured value and the fitted curve at the first data
point in the curve (se the bottom picture).

My question is simply: can I constrain the fitting so that the first point
used in fitting is equal to the measured first point? Also, is this method
of fitting statistically justified / a correct way of doing it when it comes
to statistical error? 

Since the first point in the curve is critical for the calculation of the
halftime I get a substantial deviation when I compare the halftime from a
"automatically" fitted curve (let software decide) and a fitting with a
constrained first-point (y0).

I assume that all measured values have the same amount of noise and
therefore it seems strange that the first residual deviates that strongly
(the curve fit is even not in the range of the standard deviation of the
first point). 

I will greatly appreciate some feedback. Thank you.

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