Quantitative analysis of protease recognition by inhibitors in plasma using microscale thermophoresis

High abundance proteins like protease inhibitors of plasma display a multitude of interactions in natural environments. Quantitative analysis of such interactions in vivo is essential to study diseases, but have not been forthcoming, as most methods cannot be directly applied in a complex biological environment. Here, we report a quantitative microscale thermophoresis assay capable of deciphering functional deviations from in vitro inhibition data by combining concentration and affinity measurements. We obtained stable measurement signals for the substrate-like interaction of the disease relevant inhibitor α-1-antitrypsin (AAT) Z-variant with catalytically inactive elastase. The signal differentiates between healthy and sick AAT-deficient individuals suggesting that affinity between AAT and elastase is strongly modulated by so-far overlooked additional binding partners from the plasma.


Supplement Supplementary Information 1: Theoretical background
We defined the thermophoretic amplitude as the difference between minimal and maximal depletion signals in the low and high end range of I 2 concentrations, respectively (Fig.1b). To better illustrate how the thermophoretic amplitude behaves in these two concentration ranges, we have analyzed the theoretical equilibrium for both situations separately in more detail.
In the low end range of I 2 concentrations, interactions between I 2 and E are almost non-existent.
Therefore, the proportion of bound E depends solely on its interaction with I 1 (Fig. 1b, dark grey box). The proportion of bound E at this point is a function of both, the concentration of I 1 as well as the dissociation constant between E and I 1 (K D (EI 1 )) in plasma. Higher concentrations of I 1 shift the equilibrium towards EI 1 complexes, while a higher K D (EI 1 ) results in a decrease of EI 1 complexes (Fig 1a, dark grey box). The thermophoretic depletion of I 1 -bound E is considerably larger than that of the free E. Hence, the measured thermophoretic depletion reflects the proportion of E bound to I 1 in the mixture, which varies between the plasma samples.
At maximal concentration of I 2 , all E is bound to I 2 independent of the other parameters due to the high affinity between E and I 2 (Fig. 1b, light grey box). The thermophoretic depletion is the depletion of EI 2 complexes and is the same for all the plasma samples and only depends on the amount of labeled probe E spiked into a sample. Thermophoretic depletion of I 2 -bound E is also considerably larger than that of the free E.
Taken together, the thermophoretic amplitude depends on the proportion of I 1 -bound E in the sample at I 2 concentrations approaching zero. We obtain the largest amplitude when all E is free at lowest I 2 concentration in equilibrium. Accordingly, the thermophoretic amplitude decreases with decreasing K D (EI 1 ) values and increasing I 1 concentrations (Fig. 1c, d, smaller insertion graphs).

Supplementary Information 2: Mathematical analysis of the system Defining the system
Let us consider the chemical binding equilibrium between ligands ! and ! and fluorescently labeled binder , where ! is AAT in plasma, ! is elafin, and is labeled elastase in the system studied in this paper.
The binding is recorded as the difference in the thermophoretic depletion between molecule in the free state and in the bound states ! and ! . Thermophoretic depletion of a molecule is described by its Soret coefficient ! !"#$%&#$ . We assume that Soret coefficients of free and bound species of molecule in the sample are different:

Detected fluorescence
Steady-state concentration of molecule , ! , at the position where the temperature is increased by small ∆ (5-10 K) can be found as: where ! ! is concentration of molecule when ∆ = 0 1 . (Notice, that subscript "0" in the concentration term will always denote the cold concentration at ∆ = 0).
Similarly for ! and ! : Fluorescence detected from a sample of , ! , and ! mixture can be expressed as sum of fluorescence detected from molecule in free and bound states: Detected fluorescence can be further expressed as a product of quantum efficiency of the dye attached to the molecule !"#$%&#$ and concentration of a particular species: We focus on a likely case that quantum efficiencies of bound and unbound species are equal:

Thermophoretic depletion
Depletion by definition is the fraction of fluorescence detected in the heated state over the fluorescence detected in the cold state: From . 8 and then . 6 − (7) after algebraic transformations follows that is given by:

Amplitude
We defined Amplitude in the paper as the difference between the thermophoretic depletion at negligible concentration of ! in the reaction and after adding the maximal concentration of ! : From . (9) follows: