Determination of Protein–Ligand Binding Affinities by Thermal Shift Assay

Abstract

Quantification of protein–ligand interactions is crucial for understanding the protein’s biological function and for drug discovery. In this study, we employed three distinct approaches for determination of protein–ligand binding affinities by a thermal shift assay using a single ligand concentration. We present the results of the comparison of the performance of the conventional curve fitting (CF) method and two newly introduced methods - assuming zero heat capacity change across small temperature ranges (ZHC) and utilizing the unfolding equilibrium constant (UEC); the latter has the advantage of reducing calculations by obtaining the unfolding equilibrium constant directly from the experimental data. Our results highlight superior performance of the ZHC and UEC methods over the conventional CF method in estimating the binding affinity, irrespective of the ligand concentration. In addition, we evaluated how the new methods can be applied to high-throughput screening for potential binders, when the enthalpy (ΔH_L) and molar heat capacity change (ΔC_PL) of ligand binding are unknown. Our results suggest that, in this scenario, using the −300 cal K^–1 mol^–1 assumption for ΔC_pL and either −5 kcal mol^–1 or the average enthalpy efficiency-based estimation for ΔH_L(T) can still provide reasonable estimates of the binding affinity. Incorporating the new methods into the workflow for screening of small drug-like molecules, typically conducted using single-concentration libraries, could greatly simplify and streamline the drug discovery process.

Proteins rarely function in isolation: virtually all biological processes mediated by proteins, from signal transduction to cellular regulation and immune responses, involve direct interactions with other molecules.^1,2 Therefore, the development of robust methods to accurately determine protein–ligand binding affinities is crucial for advancing drug discovery and therapeutic development.³ Traditional techniques such as isothermal titration calorimetry (ITC) or surface plasmon resonance (SPR), while accurate, are resource-intensive and not suitable for high-throughput screening. Therefore, there is a high demand for methods that can accurately determine binding affinities in a high-throughput screening manner.

Among experimental techniques employed to study protein–ligand interactions, a thermal shift assay (TSA), also known as differential scanning fluorimetry (DSF) or ThermoFluor, is emerging as a cost-effective, rapid, high-throughput screening technique for identifying protein ligands.^4,5 The method is based on the phenomenon of ligand-mediated protein stabilization against thermal denaturation, that arises from the energetic coupling of ligand binding and protein unfolding.^4,6 TSA has been widely used for buffer optimization to increase protein stability (important for crystallization, or design of vaccine- or antibody-based therapies), including identification of small molecules that increase protein stability by specifically binding to it (used in drug discovery).^7,8 It is now increasingly recognized that TSA can also be used to determine the binding affinity (K_d) of a protein–ligand interaction.⁹⁻¹¹ The energetic relationship between ligand binding and protein unfolding leads to ligand-dependent changes in the unfolding transition temperature (ΔT_m) of a protein, and this dependency can be used to determine the binding affinity of the ligand.^4,6

Determination of protein–ligand binding affinities by TSA offers many advantages over other methods, particularly where high affinity interactions are concerned.^11,12 ITC, SPR, and stopped-flow assay of inhibition of enzymatic activity (SFA) have inherent limitations in measuring high-affinity binding.¹¹ In the case of ITC, for example, tight binding with an affinity in the picomolar range can only be quantified by performing competitive displacement experiments.¹³ Other significant advantages of TSA over ITC include the ability to measure protein–ligand interactions that are driven by entropy, or when the ligand has a high heat of dilution. Although NMR is another attractive technique for characterizing protein–ligand interactions, it is cost-intensive, limited to relatively weak affinities (above the low micromolar range), requires large protein concentrations, and lacks the throughput of TSA.¹⁴ Fluorescence polarization/anisotropy technique requires a significant mass difference between the protein and ligand, along with the covalent attachment of a fluorescent label to the ligand, which also limits experimental throughput.^15,16

Although the potential of TSA for determining binding affinities is well recognized, the existing methods described in the literature require a set of measurements for a range of different ligand concentrations.⁹⁻¹¹ The requirement for a greater amount of ligand and increased experimental time means the existing methods cannot be easily translated into high-throughput drug screening applications. In this study, we addressed this problem and developed an approach that can use data for a single ligand concentration, significantly simplifying the determination of binding affinity from TSA.

Here, we compared three distinct approaches for TSA-based protein–ligand affinity measurements, 1) curve fitting (CF), 2) assuming zero heat capacity change across small temperature ranges (ZHC), and 3) utilizing knowledge of the unfolding equilibrium constant (UEC). We evaluated these approaches for several different receptor–ligand pairs by comparing the TSA-derived binding affinities, calculated over a range of ligand concentrations, with the values obtained using ITC - a technique that is often considered a golden standard for measuring K_d. The receptors used in this study were bacterial proteins dipeptide permease protein A (DppA) from Helicobacter pylori and sensing domains of chemoreceptors transducer-like protein 3 (Tlp3) from Campylobacter jejuni, chemotactic transducer of amino acids type A (CtaA) from Pseudomonas fluorescens and transducer-like protein C (TlpC) from H. pylori.¹⁷⁻²¹

Our results revealed that the CF approach, that, up to date, has been widely used to estimate K_d from TSA data,^4,6,22 yields values that not only significantly deviate from the values determined using ITC, but are also strongly dependent on ligand concentration, the latter finding being consistent with the previous reports.⁴ In contrast, both the ZHC and UEC methods introduced in this work demonstrated good agreement with ITC irrespective of the ligand concentration used in the TSA. The novel approaches described herein enable accurate determination of binding affinity from TSA data collected for a single ligand concentration. Implementation of these methods for screening of small drug-like molecules, that is typically performed using libraries of molecules at one fixed concentration, would significantly enhance and streamline the drug discovery workflow. It is important to recognize that the methods developed here were tested on a set of ligands with limited chemical diversity. Therefore, to fully validate and extend the applicability of our approach, further experimental studies with ligands of varying chemical properties are necessary.

Materials and Methods

Protein Purification and Thermal Shift Assays

The proteins were overexpressed in Escherichia coli and isolated to >98% purity as described previously.^21,23−25 Stock solutions of ligands were prepared in the same buffers as the corresponding proteins. The thermal shift assays (TSAs) were performed in triplicates, in a 25 μL final volume of mixture containing 5 μM or 10 μM of protein in the appropriate buffer, 10× SYPRO Orange and varying concentrations of ligand. The samples were heated from 35 to 85 °C with a ramp rate of 0.5 °C min^–1, and protein unfolding was monitored by following the SYPRO Orange fluorescence (excitation/emission 530 nm/555 nm) using a Rotor-Gene Q real-time PCR cycler (Qiagen). All the measurements were performed in triplicate and the values are presented as mean ± SD.

TSAs of the sensing domain of C. jejuni Tlp3 (10 μM) were carried out in a buffer containing 100 mM Tris-HCl pH 8.0 and 150 mM NaCl. Ligands were added at 3 mM (L-isoleucine, L-leucine, L-norvaline (Nva)), or 10 mM (L-valine) concentration. To assess the ligand-concentration-dependent variability of the calculated binding affinities, the assay with Ile was repeated at nine different concentrations ranging from 0.1 mM (∼1 K_d (determined previously using ITC)¹⁸) to 20 mM (receptor-saturating concentration).

TSAs of the sensing domain of P. fluorescens CtaA (5 μM) were carried out in a buffer containing 100 mM sodium citrate pH 5.5 and 200 mM NaCl. Ligands (L-valine, L-alanine, L-serine or L-leucine) were added at 20 μM concentration. To assess the ligand-concentration-dependent variability of the calculated binding affinities, the assay with Ser was repeated at seven different concentrations ranging from 10 μM to 70 μM (∼1 K_d (determined previously using ITC)¹⁹ to ∼7.5 K_d (receptor-saturating concentration)).

TSA of the sensing domain of H. pylori TlpC (20 μM) was carried out with or without 7.5 mM L-lactate in a buffer containing 100 mM HEPES pH 7.0 and 250 mM NaCl. TSA of H. pylori DppA (10 μM) was performed with or without its ligand, tetrapeptide Ser-Thr-Ser-Ala (STSA) (200 μM), in a buffer solution containing 100 mM Tris pH 8.0 and 150 mM NaCl.

Thermal Shift Assay Data Analysis Approaches

In the methods that follow, it is assumed that protein unfolding occurs as a two-state transition state, and the ligand only binds the folded form and stabilizes it.

Curve Fitting (CF) Method

In TSA, as a protein starts to unfold upon heating, interaction between the SYPRO Orange dye and exposed hydrophobic residues leads to a sigmoidal increase in the fluorescence intensity. As the temperature rises, the fluorescence intensity eventually reaches the plateau and then decreases due to aggregation of the denatured protein-dye complexes.⁴ Data points collected after the plateau were excluded, and the sigmoidal part of the unfolding curve was fit (using GraphPad Prism 7.02) to the following equation to determine ΔH_u(T_o), ΔC_pu(T_o) and T_o by nonlinear regression:^4,6

1

where F(T) is the fluorescence intensity at temperature T, T_o is the temperature at the midpoint of the protein unfolding transition in the absence of ligand (also known as the protein’s melting temperature), F_min and F_max are the pre- and post-transitional fluorescence intensities, respectively, R is the molar gas constant (1.987 cal K^–1 mol^–1), ΔH_u(T_o) is the enthalpy of protein unfolding in the absence of ligand, and ΔC_pu(T_o) is the molar heat capacity change on protein unfolding in the absence of ligand.

Since the melting temperature of the protein in the presence of a ligand (T_m) cannot be accurately and reliably estimated using eq 1(4,6) due to the presence of multiple unknowns, we calculated T_m by fitting the sigmoidal portion of the fluorescence intensity data to the Boltzmann sigmoid equation:

2

where δ is the slope of the fluorescence intensity data.

The calculated values of H_u(T_o), ΔC_pu(T_o), T_o and T_m were then used to calculate the ligand binding affinity in terms of dissociation constant at T_m (K_d(T_m)) using the following equation:¹²

3

where [L]_Tm is free ligand concentration at T_m. The following approximations can be made: [L]_Tm=[L]_total/2 when [L]_total<[P]_total; [L]_Tm=[L]_total–[P]_total/2 when [L]_total ≥ [P]_total;¹² and [L]_Tm ≈ [L]_total when [L]_total ≫ [P]_total.⁶

Zero Heat Capacity Change (ZHC) Method

In this method, the enthalpy of unfolding (ΔH_u(T_o)) in the absence of ligand was calculated by following the method described by Wright et al. 2017.²⁶ The F_min and F_max were obtained from the nonlinear least-squares fitting of the fluorescence data using eq 2. The fraction of protein unfolded (Q_u), folded (Q_f) and the equilibrium constant of unfolding (K_u) in the absence of ligand were calculated at each temperature (T) using eqs 4, (5) and (6), respectively.

4

5

6

The Gibbs free energy of unfolding (ΔG_u(T)) for each temperature was then calculated using the equation:

7

where K_u(T) is the unfolding equilibrium constant at temperature T.

A linear equation of best fit of ΔG_u(T) versus temperature corresponding to 10–50% of unfolding enables the calculation of free energy (ΔG_u(T_o)), entropy (ΔS_u(T_o)), and enthalpy (ΔH_u(T_o)) of unfolding in the absence of ligand.²⁶ The values of the regression coefficient (R²) should be greater than 0.9 to indicate reliable values of these thermodynamic parameters. It should be noted that this linear fit implicitely assumes ΔC_pu(T_o) is zero (i.e., ΔH_u(T_o) is independent of temperature); this assumption holds when the temperature range is small.

The midpoint transition temperatures in the absence (T_o) and presence of ligand (T_m) were then calculated using eq 2. Finally, the values of ΔH_u(T_o), ΔC_pu(T_o)=0, T_o and T_m were used to calculate the dissociation constant (K_d(T_m)) at T_m using eq 3.

Unfolding Equilibrium Constant (UEC) Method

The advantage of this method over the previous two is that it does not require calculation of the thermodynamic parameters ΔH_u(T_o) and ΔC_pu(T_o) to determine the dissociation constant at the protein’s melting temperature K_d(T_o). The equation can be derived by modifying the equation presented by Brandts and Lin, 1990 as follows (Figure 1).¹²

Figure 1.

Determination of the unfolding equilibrium constant in the presence of ligand K_eq(T_o) from the sigmoidal unfolding curves. T_o is the temperature at the midpoint of the protein unfolding transition in the absence of ligand. Q_u and Q_f are the fractions of unfolded and folded protein.

Let P represent the folded and P′ represent the unfolded form of the protein. For the reaction P⇌P′, the expression for the unfolding constant, K(T) = [P′]/[P], can be rearranged to give

8

Assuming that ligand L binds only to the folded form of the protein,¹² the expression for the binding constant can be written as

K_L(T) = [PL]/[P][L], which can be rearranged to give

9

The unfolding constant in the presence of ligand, K_(eq)(T) can be written as

10

Since at the protein’s melting temperature T_o, K(T_o) = 1, we can write

11

which can be rearranged to give an expression for the dissociation constant K_d at T_o

12

The K_eq(T_o) can be determined directly from the experimental data as shown in Figure 1, with Q_u and Q_f calculated using eqs 4 and (5). Again, the following approximations can be made: [L]_To = [L]_total/2 when [L]_total < [P]_total, [L]_To = [L]_total – [P]_total/2 when [L]_total ≥ [P]_total¹² and [L]_To ≈ [L]_total when [L]_total ≫ [P]_total.⁶ Substituting the values of K_eq(T_o) and [L]_To in eq 12 enables the calculation of the binding affinity at T_o, K_d(T_o).

Calculation of Dissociation Constant at Other Temperatures (T)

The dissociation constant at temperature T (K_d(T)) can be obtained from the dissociation constant at T_m (K_d(T_m)) using the following equation:¹²

13

where ΔH_L(T) is the enthalpy of ligand binding (also known as van’t Hoff enthalpy of binding) at temperature T and ΔC_pL is the molar heat capacity change due to ligand binding. The binding enthalpy can be measured using ITC, but when unknown, previous studies suggested to use values ranging from −5.0 to −15.0 kcal mol^–1.^6,27,28 Here, we compared calculations using the values of −15.0 kcal mol^–1, −5.0 kcal mol^–1, the enthalpy obtained from ITC, or the enthalpy estimated using the average enthalpy efficiencies of ligand atoms.

If ΔC_pL is not known, the approximate K_d(T) can be calculated using the following simplified equation:⁶

14

Calculation of Molar Heat Capacity Change of Ligand Binding (ΔC_pL)

The molar heat capacity change due to ligand binding (ΔC_pL) was calculated based on the crystal structures of free and/or ligand-bound proteins (PDB IDs: 4XMR, 6W3S, 6W3T, 6W3X, 6Q0F, 6PXY, 6PY5, 6PY4, 5WBF, and 6OFQ)^18−21,29 by following the method described in Baker and Murphy 1998.³⁰ Any missing residues were modeled using the MODELER comparative modeling software.³¹ The accessible surface areas (ASA) were calculated using the NACCESS program.³² For each structure, 20 models were generated, and the average ASA was used to compute the ΔC_pL.

The molar heat capacity change due to ligand binding (ΔC_pL) was calculated from the difference in apolar (ΔASA_ap) and polar (ΔASA_pol) accessible surface areas upon ligand binding (ΔASA = ASA(ligand-bound) – ASA(ligand-free) – ASA(ligand)) using the following equation:³⁰

15

with the empirical parameters Δc_p,ap and Δc_p,pol set at 1.82 and −1.09, respectively.

It should be noted that in cases where there is evidence of coupling of multiple equilibria, connecting multiple protein conformations, the observed apparent association constant is the population weighted average of the intrinsic association constants for each reaction.^33,34 Among the four proteins studied here, the TSA of Tlp3 showed the presence of multiple conformations, which became less pronounced upon the addition of ligand (Supplementary Figure 1), indicating that binding of the ligand is only weakly coupled to the conformational equilibrium or conformational changes. In such instances, it is reasonable to assume a ΔC_pL of −300 cal mol^–1 K^–1 at room temperature.³⁴

Enthalpy of Ligand Binding (ΔH_L(T))

The enthalpy of ligand binding (ΔH_L(T)) was determined using the average enthalpy efficiencies of −0.66, −0.33, and −0.13 kcal mol^–1 per heavy (non-hydrogen) atom for heavy atom counts of 0–19, 20–39, and 40–77, respectively, as described in Reynolds and Holloway 2011.³⁵ The calculated ΔH_L(T) values for the ligands used in this study are provided in Table 1.

Table 1. Enthalpies of Ligand Binding (ΔH_L(T)) Estimated from Average Enthalpy Efficiencies.

Ligand	Number of Heavy Atoms	ΔHL(T) (kcal mol–1)
l-Isoleucine	9	–5.94
l-Leucine	9	–5.94
l-Valine	8	–5.28
l-Norvaline	8	–5.28
l-Alanine	6	–3.96
l-Serine	7	–4.62
l-Lactate	6	–3.96
Ser-Thr-Ser-Ala (STSA)	25	–8.25

Effect of Approximation of Free Ligand Concentration on the Accuracy of Binding Affinity

The concentration of free ligand at the protein’s melting temperature ([L]_To) was approximated to the total ligand concentration ([L]_total) when [L]_total ≥ [P]_total. To evaluate the impact of this approximation on the binding affinities of Tlp3-Ile and CtaA-Ser interactions, we calculated the free ligand concentration at the protein’s melting temperature using the following equation:¹²

16

The binding affinities of Tlp3-Ile (over a ligand concentration range of 0.1 mM to 20 mM) and CtaA-Ser interactions (over a ligand concentration range of 10 μM to 70 μM) at the protein’s melting temperature (K_d(T_o)) were calculated using the binding affinity (K_d(25 °C) and enthalpy of binding (ΔH_L(25 °C)) obtained from ITC (as shown in Table 1 for K_d(T_o) and Table 2 for ΔH_L(25 °C)). The UEC method was employed to calculate K_d(T_o), assuming that ΔH_L(25 °C) remains invariant over the small temperature range.

Table 2. Midpoint Transition Temperatures in the Presence of Ligand (T_m) and Dissociation Constants at T_m (K_d(T_m)) and/or T_o (K_d(T_o)).

			Dissociation Constant at Tm, Kd(Tm) (μM)			Dissociation Constant at To, Kd(To) (μM)
Ligand	Protein	Midpoint Transition Temperature in Presence of Ligand, Tm (K)	CF	ZHC	Using Data from ITCa,b	UEC	Using Data from ITCa,b
l-Isoleucine	Tlp3	337.6 ± 0.3	1728 ± 384	711 ± 147	630 ± 62	705 ± 205	530 ± 62
l-Leucine	Tlp3	337.3 ± 0.2	2164 ± 411	875 ± 152	799 ± 38	949 ± 182	676 ± 32
l-Norvaline	Tlp3	336.8 ± 0.3	3805 ± 1495	1424 ± 470	1762 ± 47	1584 ± 671	1532 ± 82
l-Valine	Tlp3	337.7 ± 0.3	5099 ± 1291	2116 ± 505	3055 ± 267	2291 ± 534	2495 ± 166
l-Valine	CtaA	330.7 ± 0.2	0.5 ± 0.1	4.0 ± 0.4	4 ± 1	2.5 ± 0.4	4 ± 1
l-Alanine	CtaA	329.2 ± 0.1	2.0 ± 0.2	8.9 ± 0.6	7.4 ± 0.4	5 ± 1	7.1 ± 0.4
l-Serine	CtaA	328.2 ± 0.3	4.9 ± 1.3	18 ± 4	13 ± 1	6 ± 3	12 ± 1
l-Leucine	CtaA	327.8 ± 0.3	7.4 ± 1.9	26 ± 7	10 ± 2	11 ± 3	10 ± 2
l-Lactate	TlpC	320.4 ± 0.2	213 ± 28	581 ± 54	2062 ± 11	250 ± 87	1081 ± 8
STSA	DppA	344.5 ± 0.4	10 ± 2	34 ± 5	140 ± 12	29 ± 2	89 ± 9

^aUsing enthalpy of binding (ΔH_L) from ITC (Table 3)

^bUsing molar heat capacity change of binding (ΔC_pL) from Table 3.

Results

We employed three distinct approaches to determine protein–ligand binding affinities by a thermal shift assay: curve fitting (CF), zero heat capacity change assumption (ZHC), and unfolding equilibrium constant (UEC) method. All three methods are applicable to single-transition protein unfolding data. The traditional CF method enables the calculation of the protein unfolding enthalpy (ΔH_u(T_o)), molar heat capacity change (ΔC_pu(T_o)), and melting temperature in the absence of ligand (T_o) by fitting the experimental data to equation 1. The ZHC method assumes that the molar heat capacity change due to unfolding (ΔC_pu(T_o)) is zero, and estimates ΔH_u(T_o) using the unfolding equilibrium constant. In both methods, the melting temperature in the presence of ligand (T_m) is then obtained by fitting the fluorescence intensity data to the Boltzmann sigmoid equation 2, and the binding affinity at the melting temperature in the presence of ligand (K_d(T_m)) is determined by substituting the calculated parameters into equation 3. In contrast, the third method, UEC, has an advantage in that these thermodynamic parameters are not required for calculating the binding affinity at the protein’s melting temperature (K_d(T_o)). Instead, the UEC method utilizes the unfolding equilibrium constant in the presence of ligand to directly calculate K_d(T_o).

The dissociation constants at the melting temperature obtained using the CF, ZHC and UEC methods were then converted into the dissociation constants at 25 °C (K_d(T)). For CtaA, TlpC and DppA, the molar heat capacity change due to ligand binding (ΔC_pL) was calculated from the crystal structures of the respective complexes. In the case of Tlp3, which exists in multiple conformational states in solution, and where ligand binding only weakly impacts on the conformational equilibrium, an assumed ΔC_pL value of −300 cal mol^–1 K^–1 was used.³⁴ To assess the quantitative agreement with the binding affinities obtained from ITC, we calculated the mean relative deviation (MRD) as the mean of (|(K_d determined using TSA) – (K_d determined from ITC)|/(K_d determined from ITC)) for each method.

Dissociation Constant Calculations Using the Curve Fitting (CF) Approach

Determination of the thermal unfolding parameters (T_o, ΔH_u(T_o), ΔC_pu(T_o)) for the proteins in the absence of ligands using the CF method yielded the following values: (T_o = 321.2 ± 0.6 K, ΔH_u(T_o) = −95 ± 3 kcal mol^–1, ΔC_pu(T_o) = 13.5 ± 0.9 kcal mol^–1 K^–1) for Tlp3; (T_o = 311.0 ± 2.2 K, ΔH_u(T_o) = −116 ± 15 kcal mol^–1, ΔC_pu(T_o) = 15.9 ± 1.5 kcal mol^–1 K^–1) for CtaA; (T_o = 300.0 ± 1.9 K, ΔH_u(T_o) = −62 ± 12 kcal mol^–1, ΔC_pu(T_o) = 9.6 ± 0.5 kcal mol^–1 K^–1) for TlpC; and (T_o = 319.6 ± 7.6 K, ΔH_u(T_o) = −26 ± 33 kcal mol^–1, ΔC_pu(T_o) = 4.4 ± 0.5 kcal mol^–1 K^–1) for DppA. The midpoint transition temperatures in the presence of ligand T_m and the dissociation constants at T_m (K_d(T_m)) calculated using the CF method (equation 3) are presented in Table 2.

It is clear from above that the T_o for CtaA and TlpC are very low (near or below to the experimental temperature range), this is a limitation of the curve fitting method in accurately and reliably estimating T_o (and potentially ΔH_u and ΔC_pu) while attempting to fit experimental data to equation 1 without bias. In this method, there are three unknown variables (T_o, ΔH_u(T_o), and ΔC_pu(T_o)) that must be calculated by fitting the experimental data to equation 1. Due to the presence of multiple unknowns in the equation, there exist numerous combinations of these variables if biases, such as imposing restrictions on T_o or ΔH_u(T_o) or ΔC_pu(T_o) to be greater than or less than or equal to certain values, are introduced during the calculation process. This is a common challenge encountered when dealing with equations containing multiple unknowns. Researchers often perform the fitting process while keeping certain variables fixed at assumed values, thereby introducing bias into the calculations (even though the exact values of these variables are unknown)^5,36 or obtain those values by performing DSC experiments.²² Therefore, the calculation of unfolding energies using the CF method may be flawed due to these inherent challenges.

The dissociation constants at T_m (K_d(T_m)) were converted to dissociation constants at 25 °C (K_d(T)) shown in Table 3. Table 3 also illustrates that the enthalpy of ligand binding (ΔH_L(T)), required for this conversion, can be measured experimentally (e.g., using ITC), calculated from the average enthalpy efficiencies of non-hydrogen atoms of the ligand, or given an assumed value (−15 kcal mol^–1 or −5 kcal mol^–1). For each method to obtain ΔH_L(T), we assessed the agreement with the binding affinities K_d(T) obtained from ITC by calculating the MRDs of K_d. The MRD values were 0.83 for ΔH_L(T) = −15 kcal mol^–1, 0.97 for ΔH_L(T) = −5 kcal mol^–1, 0.87 for ΔH_L(T) calculated from the average enthalpy efficiencies, and 0.97 for the ΔH_L(T) obtained from ITC.

Table 3. Dissociation Constants at 25 °C (K_d(T)) Calculated by the Curve Fitting (CF) Method Using Assumed, Calculated, or Measured Values for Enthalpies of Binding ΔH_L(T).

			Curve Fitting (CF) Method (Kd(T) μM)
					ΔHL(T) Calculated from the Average Enthalpy Efficiencies		ΔHL(T) from ITC
Protein–Ligand Complex	Ligand Concentration	Molar Heat Capacity Change due to Ligand Binding (ΔCpL, cal K–1 mol–1)	ΔHL(T) = −15 kcal mol–1	ΔHL(T) = −5 kcal mol–1	kcal mol–1	Kd(T) (μM)	kcal mol–1	Kd(T) (μM)	Kd(T) from ITC (μM)
Tlp3-Ile	3 mM	–300	29 ± 7	209 ± 50	–5.94	174 ± 42	–4.40	235 ± 57	86 ± 1018
Tlp3-Leu	3 mM	–300	37 ± 9	267 ± 59	–5.94	222 ± 49	–4.60	288 ± 64	105 ± 629
Tlp3-Nva	3 mM	–300	70 ± 30	489 ± 204	–5.28	463 ± 194	–6.50	365 ± 153	168 ± 929
Tlp3-Val	10 mM	–300	84 ± 24	611 ± 167	–5.28	578 ± 158	–4.40	688 ± 188	405 ± 2729
CtaA-Val	20 μM	–44	0.03 ± 0.01	0.18 ± 0.04	–5.28	0.2 ± 0	1.70	0.6 ± 0.1	4.7 ± 1.219
CtaA-Ala	20 μM	–17	0.17 ± 0.02	0.8 ± 0.1	–3.96	1.0 ± 0.1	–1.91	1.4 ± 0.1	5.2 ± 0.319
CtaA-Ser	20 μM	2	0.5 ± 0.1	2.3 ± 0.6	–4.62	2.4 ± 0.7	–1.85	4 ± 1	9.5 ± 1.119
CtaA-Leu	20 μM	–60	0.7 ± 0.2	3.0 ± 0.8	–5.94	2.6 ± 0.7	1.90	9 ± 2	11.9 ± 1.819
TlpC-lactate	7.5 mM	–54	34 ± 5	110 ± 15	–3.96	124 ± 17	–21.32	16 ± 2	155 ± 520
DppA-STSA	200 μM	–95	0.20 ± 0.04	1.9 ± 0.3	–8.25	0.9 ± 0.2	–11.80	0.4 ± 0.1	5.9 ± 0.621

Dissociation Constant Calculations Using the Zero Heat Capacity Change (ZHC) Approach

The enthalpies of unfolding (ΔH_u(T_o)) of free Tlp3, CtaA, TlpC, and DppA were determined using the ZHC method. Figure 2 illustrates fitting data to a linear equation representing the relationship between the Gibbs free energy of unfolding ΔG_u and temperature T in the range corresponding to 10–50% unfolding. The high values of the regression coefficient R² (greater than 0.9) indicate the methodology is suitable for estimating the thermodynamic parameters for these proteins.²⁶

Figure 2.

Line of best fit representing the relationship between the Gibbs free energy of unfolding ΔG_u and temperature in the range corresponding to 10–50% of unfolding for (A) 10 μM Tlp3, (B) 5 μM CtaA, (C) 20 μM TlpC, and (D) 10 μM DppA in the absence of ligand.

Determination of the thermal unfolding parameters for the proteins in the absence of ligands using the ZHC method yielded the following values: (T_o = 335.0 ± 0.3 K, ΔH_u(T_o) = 148 ± 7 kcal mol^–1, ΔC_pu(T_o) = 0 kcal K^–1 mol^–1)) for Tlp3; (T_o = 326.4 ± 0.4 K, ΔH_u(T_o) = 84 ± 17 kcal mol^–1, ΔC_pu(T_o) = 0 cal K^–1 mol^–1) for CtaA; (T_o = 314.6 ± 0.4 K, ΔH_u(T_o) = 91 ± 3 kcal mol^–1, ΔC_pu(T_o) = 0 kcal K^–1 mol^–1) for TlpC; and (T_o = 337.9 ± 0.4 K, ΔH_u(T_o) = 68 ± 4 kcal mol^–1, ΔC_pu(T_o) = 0 kcal K^–1 mol^–1) for DppA.

The dissociation constants at T_m (K_d(T_m)) calculated using the ZHC method are presented in Table 2. These values were converted to dissociation constants at 25 °C (K_d(T)) shown in Table 4. Table 4 allows direct comparison of the dissociation constants measured by ITC and derived by the ZHC method using different assumptions for the enthalpy of ligand binding (ΔH_L(T)). To quantify the agreement between the ITC- and ZHC method-derived values for each assumption about enthalpy, we calculated the MRDs of K_d. The MRD values were 0.82 for ΔH_L(T) = −15 kcal mol^–1, 0.28 for ΔH_L(T) = −5 kcal mol^–1, 0.36 for ΔH_L(T) calculated from the average enthalpy efficiencies, and 0.44 for the ΔH_L(T) obtained from ITC.

Table 4. Dissociation Constants at 25 °C (K_d(T)) Calculated by the Zero Heat Capacity Change (ZHC) Method Using Assumed, Calculated, or Measured Values for Enthalpies of Binding ΔH_L(T).

			Zero Heat Capacity Change (ZHC) Method (Kd(T), μM)
					ΔHL(T) Calculated from the Average Enthalpy Efficiencies		ΔHL(T) from ITC
Protein–Ligand Complex	Ligand Concentration	Molar Heat Capacity Change due to Ligand Binding (ΔCpL, cal K–1 mol–1)	ΔHL(T) = −15 kcal mol–1	ΔHL(T) = −5 kcal mol–1	kcal mol–1	Kd(T) (μM)	kcal mol–1	Kd(T) (μM)	Kd(T) from ITC (μM)
Tlp3-Ile	3 mM	–300	12 ± 3	86 ± 19	–5.94	71 ± 16	–4.40	97 ± 22	86 ± 1018
Tlp3-Leu	3 mM	–300	15 ± 3	108 ± 22	–5.94	90 ± 18	–4.60	117 ± 24	105 ± 629
Tlp3-Nva	3 mM	–300	26 ± 10	183 ± 65	–5.28	173 ± 62	–6.50	137 ± 49	168 ± 929
Tlp3-Val	10 mM	–300	35 ± 10	253 ± 66	–5.28	240 ± 62	–4.40	285 ± 74	405 ± 2729
CtaA-Val	20 μM	–44	0.29 ± 0.03	1.5 ± 0.2	–5.28	1.5 ± 0.2	1.70	4.7 ± 0.5	4.7 ± 1.219
CtaA-Ala	20 μM	–17	0.8 ± 0.1	3.9 ± 0.3	–3.96	4.6 ± 0.3	–1.91	6.3 ± 0.4	5.2 ± 0.319
CtaA-Ser	20 μM	2	1.7 ± 0.4	8 ± 2	–4.62	9 ± 2	–1.85	13 ± 3	9.5 ± 1.119
CtaA-Leu	20 μM	–60	2.3 ± 0.6	11 ± 3	–5.94	9 ± 2	1.90	30 ± 8	11.9 ± 1.819
TlpC-lactate	7.5 mM	–54	92 ± 10	301 ± 30	–3.96	340 ± 33	–21.32	44 ± 5	155 ± 520
DppA-STSA	200 μM	–95	0.7 ± 0.1	6.8 ± 1.1	–8.25	3.2 ± 0.6	–11.80	1.4 ± 0.3	5.9 ± 0.621

Dissociation Constant Calculations Using the Unfolding Equilibrium Constant (UEC) Approach

In the UEC method, the thermal unfolding parameters ΔH_u(T_o) and ΔC_pu(T_o) are not required. Instead, the dissociation constant at the protein’s melting temperature (K_d(T_o)) is calculated from the value of the unfolding equilibrium constant in the presence of ligand at T_o (K_(eq)(T_o)), determined directly from the unfolding curves as shown in Figure 1. The K_d(T_o) values calculated for all analyzed protein–ligand pairs using the UEC method are shown in Table 2. The dissociation constant values calculated at 25 °C (K_d(T)) are shown in Table 5. This table allows a direct, side-by-side comparison of the dissociation constants measured by ITC and derived by the UEC method using different assumptions for the enthalpy of ligand binding (ΔH_L(T)). The calculated MRD values of ITC- and UEC method-derived K_d values were 0.84 for ΔH_L(T) = −15 kcal mol^–1, 0.40 for ΔH_L(T) = −5 kcal mol^–1, 0.34 for ΔH_L(T) calculated from the average enthalpy efficiencies, and 0.37 for the ΔH_L(T) obtained from ITC.

Table 5. Dissociation Constants at 25 °C (K_d(T)) Calculated by Unfolding Equilibrium Constant (UEC) Method Using Assumed, Calculated, or Measured Values for Enthalpies of Binding ΔH_L(T).

			Unfolding Equilibrium Constant (UEC) Method (Kd(T) μM)
					ΔHL(T) Calculated from the Average Enthalpy Efficiencies		ΔHL(T) from ITC
Protein–Ligand Complex	Ligand Concentration	Molar Heat Capacity Change due to Ligand Binding (ΔCpL, cal K–1 mol–1)	ΔHL(T) = −15 kcal mol–1	ΔHL(T) = −5 kcal mol–1	kcal mol–1	Kd(T) (μM)	kcal mol–1	Kd(T) (μM)	Kd(T) from ITC (μM)
Tlp3-Ile	3 mM	–300	16 ± 5	102 ± 30	–5.94	86 ± 25	–4.40	115 ± 33	86 ± 1018
Tlp3-Leu	3 mM	–300	21 ± 4	138 ± 27	–5.94	116 ± 23	–4.60	148 ± 29	105 ± 629
Tlp3-Nva	3 mM	–300	36 ± 15	230 ± 97	–5.28	218 ± 92	–6.50	174 ± 74	168 ± 929
Tlp3-Val	10 mM	–300	51 ± 12	333 ± 78	–5.28	316 ± 74	–4.40	372 ± 87	405 ± 2729
CtaA-Val	20 μM	–44	0.25 ± 0.04	1.1 ± 0.2	–5.28	1.2 ± 0.2	1.70	3.0 ± 0.5	4.7 ± 1.219
CtaA-Ala	20 μM	–17	0.6 ± 0.1	2.4 ± 0.5	–3.96	3.2 ± 0.6	–1.91	3.8 ± 0.7	5.2 ± 0.319
CtaA-Ser	20 μM	2	0.7 ± 0.3	3 ± 1	–4.62	4 ± 2	–1.85	5 ± 2	9.5 ± 1.119
CtaA-Leu	20 μM	–60	1.1 ± 0.3	5 ± 1	–5.94	5 ± 1	1.90	13 ± 3	11.9 ± 1.819
TlpC-lactate	7.5 mM	–54	63 ± 22	154 ± 53	–3.96	169 ± 59	–21.32	36 ± 12	155 ± 520
DppA-STSA	200 μM	–95	1.0 ± 0.1	7.4 ± 0.6	–8.25	3.9 ± 0.3	–11.80	1.9 ± 0.1	5.9 ± 0.621

Analysis and Comparison of the Accuracy of the Three Methods Using a Single Ligand Concentration

To compare the accuracy of determination of the binding affinity at the melting temperature by the three methods, we calculated the MRDs between TSA- and ITC-derived K_d using data presented in Table 2. The MRD values for the ZHC and UEC methods (0.43 and 0.35, respectively) were markedly lower than that for the CF method (0.96), indicating that the ZHC and UEC methods introduced in this study provide significantly more accurate estimates of the binding affinities at the protein’s melting temperature compared to the CF method. Since all three methods use the same temperature conversion equation for K_d (equation 13), the accuracy of the K_d values calculated by the ZHC and UEC methods at 25 °C was also significantly higher than for the CF method, as demonstrated by the lower listed MRD values at 25 °C.

To analyze how different assumptions for the enthalpy of ligand binding (ΔH_L) affect the accuracy of conversion of dissociation constants at the melting temperature to dissociation constants at 25 °C, we compared the MRDs of K_d at 25 °C for each assumption. We observed that both the ZHC and UEC methods produce more reliable affinity values when the enthalpy of binding (ΔH_L) is obtained from ITC, calculated from the average enthalpy efficiencies, or when an assumed ΔH_L value happens to closely match that obtained from ITC experiments.

We note, however, that even when the experimentally determined ΔH_L values are used (ITC), the use of the CF method resulted in substantial deviations from the experimentally determined K_d for certain protein–ligand pairs (Tlp3-Ile, CtaA-Val, CtaA-Ala, TlpC-lactate, and DppA-STSA), with the calculated K_d ranging from 3 times higher or 4 to 14 times lower than the ITC-derived values (Table 3). These deviations indicate that the CF method does not consistently provide reliable estimates of the binding affinity for all protein–ligand interactions. In contrast, as seen in Tables 4 and 5, the ZHC- and UEC-method-derived K_d values do not deviate from the ITC values by more than 2–3 fold when the ΔH_L is obtained from ITC or calculated from the average enthalpy efficiencies. Given that the K_d measurements of the same interaction obtained using different experimental techniques (including differential scanning calorimetry (DSC), ITC or SPR) show some deviation and typically fall within a 2- to 3-fold range,^11,37−40 we conclude that both the ZHC and UEC methods produce reliable estimates of the binding affinities, and exhibit a much improved performance compared to the CF method.

Analysis of Ligand Concentration-Dependent Variations in the Calculated Binding Constants

Previously reported methods of estimation of binding affinity using TSA produced results that were strongly biased by the concentration of the ligand in the experimental setup.⁴ Consequently, in our investigation, we determined the dissociation constants for the Tlp3-Ile and CtaA-Ser interactions using a range of ligand concentrations and assessed concentration-dependent variability in K_d for the CF, ZHC and UEC methods. The K_d(T) values were calculated using the ΔH_L(T) obtained from ITC and the ΔC_PL using the crystal structures of the respective complexes. Figure 3 depicts the impact of Ile and Ser concentration on the calculated dissociation constants for Tlp3 and CtaA at 25 °C. For the Tlp3-Ile interaction, the MRDs of K_d determined using the ZHC and UEC methods (0.38 and 0.30, respectively), were significantly lower than that for the CF method (0.73). Similarly, for the CtaA-Ser interaction, the MRDs of K_d calculated using the ZHC and UEC methods (0.24 and 0.41, respectively), were considerably lower than that for the CF method (0.79). The MRD values and the data presented in Figure 3 indicate that the CF method demonstrated substantial ligand concentration-dependent variations in the calculated binding affinity, in agreement with previous literature reports.⁴ In comparison to the CF method, the K_d(T) values determined using the ZHC and UEC methods deviated less from the ITC-derived K_d(T) over the tested range of ligand concentrations, suggesting that the ZHC and UEC methods can produce reliable and consistent calculations of K_d over a broad range of ligand concentrations relative to the respective dissociation constants.

Figure 3.

Ligand concentration-dependent variations in the binding constants K_d(T) derived using the three TSA-based methods described in this study and comparison with the K_d(T) value determined using ITC for the (A) Tlp3-Ile interaction and (B) CtaA-Ser interaction.

Effect of Approximation of Free Ligand Concentration on the Accuracy of Binding Affinity

The comparison of K_d(T) values calculated using [L]_To and [L]_total for Tlp3-Ile and CtaA-Ser interactions is presented in Figure 4. The mean deviation, defined as the average of the absolute differences between K_d(T) values determined using [L]_To and those determined using [L]_total, was 0.23 μM for Tlp3-Ile and 0.32 μM for CtaA-Ser. The low mean deviation values indicate that the approximation of the free ligand concentration ([L]_To) has no substantial impact on the accuracy of the calculated binding affinities.

Figure 4.

Effect of approximation of free ligand concentration on the accuracy of binding affinity derived using the UEC method and comparison with the K_d(T) value for (A) the Tlp3-Ile interaction and (B) the CtaA-Ser interaction.

Conversion of Binding Affinities Determined at Melting Temperature to Room Temperature Values when ΔH_L(T) and ΔC_PL Are Unknown

As the final step of our analysis, we considered how our new method can be applied to high-throughput screening for potential binders. To model this scenario, we assumed that neither the crystal structures nor ITC measurements for enthalpy of binding (ΔH_L(T)) were available. With regards to the molar heat capacity change value (ΔC_pL), we tested and compared two assumptions; first, we used the simplified equation 14, assuming that the equation 13 term containing ΔC_pL is negligibly small, as proposed by Pantoliano et al., 2001.⁶ Second, we assumed that ΔC_pL is −300 cal mol^–1 K^–1 at room temperature.³⁴ With regards to the enthalpy of binding (ΔH_L(T)), we compared calculations using either the presumed ΔH_L values of −5 kcal mol^–1 or −15 kcal mol^–1,^4,6,22,36 or values calculated from the average enthalpy efficiencies of non-hydrogen atoms of the ligand.³⁵

We employed the UEC method and these assumptions to calculate K_d(T) from the values determined at melting temperature (Table 2) using the full equation 13, or its simplified version (14). Analysis of the results presented in Figure 5 showed that, in many cases, using equation 13 with ΔC_pL = −300 cal K^–1 mol^–1 and either ΔH_L(T) = −5 kcal mol^–1 or ΔH_L(T) calculated from average enthalpy efficiencies provided more reliable K_d(T) estimates compared to the simplified equation 14. Therefore, in the context of high-throughput drug screening, when ΔH_L and ΔC_PL are unknown, and calculation of ΔH_L from average enthalpy efficiencies for hundreds or thousands of library compounds may be not practical, we recommend employing the full equation (equation 13), assuming ΔC_pL = −300 cal K^–1 mol^–1 and ΔH_L(T) = −5 kcal mol^–1.

Figure 5.

Comparison of the binding affinities at 25 °C calculated using the unfolding equilibrium constant (UEC) method when the enthalpy and molar heat capacity change of binding are unknown and are assigned assumed values. The experimentally determined value (ITC) is also shown as a reference point.

Discussion

The thermal shift assay (TSA) has emerged as a cost-effective, parallelizable, simple, and fast technique for assessing protein stability and ligand binding affinity. In contrast to circular dichroism spectroscopy, DSC, SPR, NMR and ITC, TSA can be easily conducted using standard real-time PCR instruments or fluorescence plate readers. Furthermore, the assay requires relatively small amounts of protein, and is therefore compatible with high-throughput screening and suitable for large-scale studies.

TSA has been widely employed in diverse research areas, including lead compound screening for target proteins^6,8 and protein buffer optimization.^7,8 Recent studies have brought into the spotlight its potential as a method for determination of protein–ligand binding affinities.⁹⁻¹¹ However, many of the previously reported methods require measurements over a range of ligand concentrations to accurately estimate binding affinity.⁹⁻¹¹ Here, we introduced two novel approaches that allow reliable determination of binding affinity from TSA data collected for a single ligand concentration. The simplification of the process should allow implementation of these methods for screening of drug-like molecules, that is typically performed using libraries of molecules at one fixed concentration. This would significantly reduce resource requirements and enhance the efficiency of the drug discovery workflow.

Our results demonstrate that the CF approach, extensively employed thus far for estimating K_d from TSA data,^4,6,22 yielded values that significantly deviate from the values determined through ITC. In contrast, the newly introduced ZHC and UEC methods of K_d determination introduced in this work demonstrated close agreement with the values obtained from ITC. This is reflected in the mean relative deviation (MRD) from the ITC-derived K_d for the CF method (0.96) being significantly higher than those for the ZHC and UEC methods (0.43 and 0.35). Furthermore, our analysis demonstrates that while the K_d calculations using the CF method produced significant ligand concentration-dependent variations, the calculations based on the ZHC and UEC methods were stable over the tested range of ligand concentrations. This suggests that the ZHC and UEC methods can generate reliable estimations of K_d regardless of the specific ligand concentration used.

The ZHC approach uses the same equation and thermal unfolding parameters (T_o, ΔH_u(T_o) and ΔC_pu(T_o)) for the calculation of the binding affinity as the CF method. However, the calculation of ΔH_u(T_o) is improved by employing a recently reported technique,²⁶ where we assume that the molar heat capacity change due to unfolding, ΔC_pu(T_o), is zero. On the other hand, the UEC approach offers an advantage over the previous two methods in that it does not require the calculation of the thermal unfolding parameters ΔH_u(T_o) and ΔC_pu(T_o) to determine the binding affinity. Instead, the UEC method calculates the binding affinity using the unfolding equilibrium constant derived directly from the fluorescence intensity data. This simplifies the process by reducing the number of calculations.

It needs to be noted that the analysis of the TSA data allows the calculation of K_d at the protein’s melting temperature, and this value then needs to be converted to K_d at the physiologically relevant temperature. In this study, we evaluated different ways of conversion to 25 °C, because the referenced ITC experiments were performed at that temperature. However, the same approach can be applied to convert to any temperature that reflects the native protein environment (to gauge the strength of protein–ligand interactions in vivo), or that was used to measure K_d using a different method (to compare results for consistency).

To accurately convert the binding affinity to other temperatures using equation 13, one requires the knowledge of the thermodynamic parameters such as enthalpy (ΔH_L(T)) and molar heat capacity change of ligand binding (ΔC_pL). Although the enthalpy of binding can be experimentally measured using ITC or DSC, (for example Lo et al. 2004;⁴ Matulis et al. 2005;³⁶ Linkuvienė et al. 2022¹¹), the challenges associated with these methods, including lack of high-throughput, are well recognized. To circumvent this limitation, various studies proposed to use different assumed values for ΔH_L(T), ranging from −5.0 to −15.0 kcal mol^–1. This variation in the suggested values highlights the lack of consensus in the field and the need for an accessible method to estimate this value. To address this need, our methodology integrated a straightforward estimation of the enthalpy using the average enthalpy efficiencies of ligand atoms. Our analysis demonstrated that both the ZHC and UEC methods generate more accurate affinity values when the enthalpy of binding is derived from ITC, calculated from the average enthalpy efficiencies, or when an assumed ΔH_L value is close to that obtained from ITC experiments. In addition, we observed that when one cannot estimate the molar heat capacity change of ligand binding (ΔC_pL) (from e.g. a crystal structure of the complex), using an assumed value of −300 cal K^–1 mol^–1 for the ΔC_pL provides better binding affinity estimates compared to the approximated equation that negates the ΔC_pL term altogether (equation 14). Based on our findings, if no specific information about ΔH_L(T) and ΔC_pL is available, assuming a value of −300 cal K^–1 mol^–1 for ΔC_pL, and either −5 kcal mol^–1 or the average enthalpy efficiencies-based estimation for ΔH_L(T) can still provide reasonable estimates of the binding affinity.

When considering TSA for high-throughput screening, one needs to note that the technique is not suitable for hydrophobic proteins or fluorescent ligands due to potential high background fluorescence. Additionally, buffers with high heat capacity should be avoided.^4,7 The temperature range should be chosen based on the transition temperature (T_m) of the protein under investigation; in this study, a range of 35 to 85 °C was used because all tested proteins had T_m values exceeding 50 °C.

The ligand concentration in high-throughput TSA screening for potential binders is an important parameter to consider and optimize. By using a ligand concentration of at least 1–2 times the estimated dissociation constant (K_d), one would ensure that there is sufficient binding to detect and measure. At the same time, one would want to avoid using a concentration that is so high that it exceeds solubility limits, resulting in aggregation that can interfere with the assay. Additionally, some small molecules, when used as high concentrations, quench the fluorescence of the dye used in the assay.⁶ It has been suggested that it may be optimal to use high-throughput screening libraries with the ligand concentration of 25 μM or less.⁶ Using this concentration for screening would mean that hits with K_d greater than ∼25 μM may not be detected, but these weaker binders are typically disregarded anyway in favor of more potent ones.⁶

Conclusion

The thermal shift assay (TSA) has emerged as a powerful tool for determination of the binding affinity (K_d) of protein–ligand interactions. Its broad applicability, simplicity, speed, cost-effectiveness and high-throughput capability make it a favored choice for drug discovery. Implementation of the new approaches described in our study would significantly enhance the efficiency of TSA by providing accurate binding affinity measurements from data collected for a single ligand concentration, reducing experimental complexity, and enabling streamlined drug discovery efforts. However, it is important to note that our developed method was applied to a set of ligands with limited chemical diversity. Therefore, further experimental studies with ligands of varying chemical nature are necessary to validate and extend the applicability of our approach.

Data Availability Statement

All data are included in the article and in the Supporting Information.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsptsci.4c00293.

• Fluorescence intensity data of proteins undergoing thermal unfolding in the presence or absence of ligands (PDF)

Author Contributions

M.F.K.: Designed and performed research, contributed new analytic tools, analyzed data, Writing–original draft. M.M.R.: Performed research. Y.X.: Performed research. A.M.: Analyzed data. B.J.S.: Funding acquisition, analyzed data, Writing–review and editing. K.M.O.: Funding acquisition, Writing–review and editing. A.R.: Designed research, Funding acquisition, Analyzed data, Supervision, Writing–review and editing.

The authors declare no competing financial interest.