effect of ligand loss on kinetic constant

I run a full 96 plate of samples on a Biacore3000, so 96 cycles all up
My regeneration is ok for ligand no.1 but there is some ligand loss after subsequent cycles.
I know this because i i place a control every 12 cycles and i can see the amount bound decreasing

if we imagine analyte in cycle 1 is the same and analyte in cycle 96 same concentration and its a 1:1 interaction

would the ka, kd bet the same? i understand Rmax will be lower? but are the kinetic constants the same?

the kinetic constants do not vary with the ligand density?

how can i normalize my data based off my control properly?
I currently normalize how much is "bound"1 min after injection stops based on a linear regression for my control, is it ok to do this?
Thanks very much

Even when the Rmax is lower or higher the k_a and k_d will not change. They are independent of the ligand and analyte concentration.
I think your approach is valid to compensate for ligand loss.

As a side note: If you would globally fit data with a decaying ligand concentration or lower Rmax you will notice that the fit is not that well. First try to establish if the lower Rmax is due to ligand activity loss or analyte concentration / activity loss (e.g. due to adsorption to vial wall). Then you can try to fit globally the dissociation first and then globally the association and Rmax with the dissociation fixed. Then globally the association and dissociation with the Rmax locally. Use the values from previous fitting as initial values for the next. In the last fitting the Rmax values should reflect the actual measured (in case of equilibrium) or expected (in case equilibrium is not reached) response levels.

This publication gives an idea how it was done by Ober and Ward
1. Ober, R. J. and Ward, E. S.; Compensation for loss of ligand activity in surface plasmon resonance experiments. Analytical Biochemistry (306) 2: 228-236; 2002.

Kind regards
Arnoud