The F_norm is calculated by dividing fluorescence values from the TRIC trace at 670nm after the laser is turned on (hot region, F_hot) by values that are obtained before the laser is turned on (the initial fluorescence, IF, or cold region, F_cold ). Ratio is determined isothermally by dividing the initial fluorescence at 670nm by the fluorescence at 650nm.

A binding-specific Ligand-Induced Fluorescence Change (LIFC) can influence both the measured ratio and F_norm-values of the dose response curve that is used to fit the K_d or the EC50. A strong change in initial fluorescence not only causes a difference in amplitude, but also a shift of the dose-response curve along the X-axis.

Imagine an extreme case where binding quenches fluorescence completely for TRIC data analysis. The initial fluorescence would begin at 100%, drop to 50% at the K_d, and reach 0% at full saturation. In contrast, the TRIC/Spectral Shift traces would only reflect signal from unbound targets, as bound targets would not contribute to any fluorescence (completely quenched at high ligand concentration/bound state). Due to normalization, all TRIC traces would be identical across all concentrations, until the IF signal disappears entirely due to lack of fluorescence.

Now consider a more realistic scenario where fluorescence drops by 50% upon binding. At the K_d, half the targets are unbound (100% fluorescence) and half are bound (50% fluorescence). The normalized TRIC/ Spectral Shift signal is influenced by both, but it disproportionately reflects the higher signal from the unbound state. This results in an overestimation of the unbound fraction, shifting the curve closer to the unbound side.

 

Simulation of a binding affinity experiment with LIFC on TRIC data

The simulation below illustrates the impact of varying initial fluorescence on TRIC data. The parameter IF₆₇₀unbound is adjusted across five values: 500 (representing no fluorescence change), 625, 750, 875, and 1000 raw fluorescence counts (indicating 50% quenching in the bound state). These changes are visually represented by the increasing blue shading in the accompanying image.

Additional simulation parameters:

• Target concentration: 5 nM
• Assumed Kd: 30 nM
• Ligand concentration: 16-point 1:1 dilution range [0.125 nM – 4096 nM]
• F_670(hot)unbound: 425 counts
• F_670(hot)bound: 450 counts
• IF₆₇₀bound: 500 counts
   

Calculation of Fnorm using the formula above results in variations not only in amplitude but also in an X-axis shift, most evident in the normalized Fnorm values. Therefore, any initial fluorescence change must be accounted for when fitting Fnorm data to determine Kd values.
 

Therefore, the impact of ligand-induced fluorescence changes must be considered when fitting the ratio and F_norm dose-response curves. The same considerations apply to Spectral Shift, only here for changes to IF₆₅₀ instead of F_cold.  F_norm and Ratio will hereafter be collectively referred to as normalized response. In both cases, a correction factor must be applied to the denominator of the formula underlying F_norm or the ratio if the reason for the ligand-induced fluorescence changes is determined to be binding specific (see Ligand-induced-fluorescence-changes-LIFC).
 

K_d – model with ligand induced initial fluorescence change

With the help of mass-action kinetics we are able to derive a formula for the fraction bound in case of a binding event. The fraction bound is defined by the binding affinity K_d and the concentration of the target molecule and depends on the ligand concentration.

where
f(c) is the fraction bound at a given ligand concentration c
K_d is the dissociation constant or binding affinity and
cT is the final concentration of target in the assay.

The measured fluorescence F of the F₁ and the F₀ region is defined by the fraction bound and the fluorescence of the unbound and bound state of the binding event.

Assuming that the target concentration is much lower than the K_d, the K_d is typically identical to the inflection point (half maximal effective concentration) of the normalized response. This changes when the ligand induces a change in initial fluorescence. In these cases, the normalized response used for the calculation of the K_d is influenced by the change in initial fluorescence. Hence, this influence on the normalized response needs to be accounted for. The K_d no longer aligns with the inflection point of the dose-response curve of the normalized response.

To ensure accurate Kd determination, changes in initial fluorescence must be incorporated into the calculation. Using the formulas above, a model is derived that accounts for ligand-induced fluorescence changes associated with binding, enabling accurate fitting of both normalized response and ratio data.

with

For the K_d fit, we calculate r from the measured initial fluorescence and use it as a constant in the formula fitted to the F_norm data. The factor r is also called initial fluorescence ratio and is also displayed to the user in MO.Control 2.

If there is no variation in the initial fluorescence, then r = 1. Inserting this in the formula of the F_norm reduces the formula to the following.

Hill fit with initial fluorescence change

MO.Control 2 also compensates for initial fluorescence changes when the Hill model is fitted. The Hill model without compensation for an initial fluorescence is as follows.

Introducing the same correction factor r, as described for the K_d-fit results in the following equation.

with