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1 1 Box S1 ITC versus van t Hoff data and determination of heat capacity changes ΔCp As mentioned, ITC experiments have the important advantage that two thermodynamic properties, enthalpy (ΔH) and the Gibbs free energy of binding (ΔG) result from one experiment, which is performed at one given temperature. Van t Hoff evaluations are frequently performed to obtain access to thermodynamic parameters. In such cases, the binding event is observed, usually via an easily recordable signal (such as photometric absorption, spectroscopic data, nuclear magnetic resonance or surface plasmon resonance) across a temperature range. To evaluate the measured data, it is rather inadequately assumed that thermodynamic properties such as ΔH will be temperature-independent and can be determined by plotting the binding constants that have been measured at different temperatures linearly against the reciprocal of the temperature. If the temperature window is rather small, an approximate linear correlation may be proposed and the slope of this linear correlation is then extrapolated to assign a binding enthalpy. However, the results of biological processes are hardly temperature-independent and, as such, their thermodynamic properties will also be temperature-dependent. Thus, the Van t Hoff equation cannot be integrated simply by assuming ΔH to be temperature-independent over the considered temperature range. Instead, a non-linear fit has to be applied [1-3]. Integrated:!"#$ =!!! +! =!"!!!!!!!!"!!!!"##!"#$%&'( ln!! ln!! =!!!!!(!)!!!!!" Only if the enthalpy!!(!) is temperature independent! can be taken out of the integral, resulting in the well-known linear form of the Van t Hoff equation (ln K vs. 1/T plot): ln!! ln!! =!!!!!"!!!! =!(!!! ) Otherwise, as an approximation, a non-linear series expansion can be applied.!! =! +!!!!! +!!!!!! +!"#$%&!"#$"! Furthermore, the Van t Hoff evaluation assumes that the binding event follows a two-state transition between free and bound states, and that the recorded change in the signal that has been used to determine the binding constant reflects the entire population of free and bound

2 2 molecules [4]. As the validity of the assumption of a two-state transition is difficult to estimate, the Van t Hoff evaluation is even more difficult to justify, particularly if the binding event passes through multiple states. These considerations argue strongly that care must be taken when using Van t Hoff data as a source of thermodynamic binding information, especially when they are taken from a linear extrapolation. After appropriate corrections, ITC appears to be the more reliable basis of information. Another very informative property, from a theoretical point of view, is the change in heat capacity, ΔC p, of a biological system at a constant pressure. It indicates how well a system can absorb or release heat, and thus provides a crude idea of how many degrees of freedom are available in the system to dissipate or store heat. Experimentally, ΔC p can be deduced from ITC titrations performed at different temperatures [4]. However, this evaluation and its subsequent interpretation run into similar complications to that of the Van t Hoff evaluation. The multi-component system modelling the formation of a protein ligand complex is so difficult, that even across a temperature range of K, major structural changes will occur (for instance, in the ubiquitously present bulk water phase) that make ΔC p interpretations extremely challenging. As a consequence, it is usually rather problematic to discuss ΔC p changes of a protein ligand complex system on a molecular level such that the changes can be easily attributable to actual changes in energetic and structural states, although convincing examples have been reported [5]. The accuracy and relevance of ITC data The accuracy of thermodynamic measurements is an important aspect to address [6,7]. Recorded ITC data will above all depend on composition and ionic strength of the buffer used. Control experiments of the same biological system have been performed across different laboratories, and using different devices, to estimate accuracy [8,9]. Ligand purity, protein stability, a constant water content, and an avoidance of protein self-degradation or autoprotolysis have to be maintained in such experiments [10]. Thus, how accurate can we expect ITC experiments to be? First of all, experiments should be repeated and averaged. Error propagation must be regarded against if other parameters are derived from the originally measured data. Thorough control of the concentrations of prepared solutions and the calibration of instruments are important. Proteins are fragile compounds and their activity depends on the way in which they have been prepared, purified and stored before usage. If protein solutions are prepared from solid material, the actual water content of

3 3 the samples may be crucial. To achieve reliable results, it is highly advised to use material from the same batch for all experiments and to always prepare fresh solutions. Proteases, in particular, are vulnerable to decomposition from autoprotolysis in concentrated solutions. Usually, the highly concentrated ligand solution is titrated drop-wise from a syringe into a large volume of the protein solution until the amount of ligand in the reaction cell is well beyond binding stoichiometry. In principle, this experimental setup can be reversed; however, limited protein solubility, availability or stability at high concentrations can impede the dropwise addition of a highly concentrated protein solution to a diluted ligand solution. Therefore, the purity of high-affinity ligands is particularly crucial for the accuracy of determining thermodynamic parameters. This results from the sigmoidal shape of the titration curve. For potent ligands, all of the molecules that are released from the syringe will find unoccupied binding sites on the protein in the beginning. When increasing amounts of the ligand are added to the protein solution and depending on the binding constant, an increasing amount of ligand will be dynamically exchanged from the protein binding pocket and the heat signal will reduce. Past the stoichiometry of this binding, the heat signal finally reduces (within a small number of injections) to the baseline, where only the heat-of-dilution is still recorded. Any uncertainties concerning the concentration of the protein will shift the titration curve and thus lead to deviations in the expected stoichiometry that can usually be corrected (assuming a 1:1 binding model). Thus, only minor deviations in the determined value of the free energy may occur. A much larger error that results from the integration of all the heat signals will, however, affect the determination of ΔH. Ligand impurities can reduce these heat signals markedly and can lead to a smaller value of the integrated heat signal that reveals the measured ΔH. As a result, an overestimation of the enthalpy entropy compensation will be calculated. Weak binders, such as fragments, are barely recordable as sigmoidal titration curves and are therefore error-prone to evaluate [11]. The inflection point and thus the stoichiometry and the dissociation constant are not experimentally accessible from nonsigmoidal titration curves. Stoichiometry has therefore to be adjusted, making the definition of the end point of a titration difficult. As fragment binding, particularly at high concentration, does not necessarily exhibit 1:1 stoichiometry [12], the integration of the heat signals can become very inaccurate and so it is difficult to obtain a reliable thermodynamic signature from such data. Displacement titrations can be used instead to make calorimetric analysis of fragments accessible [11,13]. Displacement titrations are also applicable to very strong-

4 4 binding ligands, where the normally sigmoidal titration curve for the direct titration degenerates to a step-like shape, rendering the assignment of a K d value unreliable [14]. Considering all these factors including the correction for superimposed protonation events properly, an evaluation of relative differences across a series of congeneric compounds will cancel out most of the systematic errors. In favourable cases, the error of accuracy can be minimised to about 1 kj per mol, particularly if relative comparisons of two related ligands are performed. The ITC experiment records all the changes that involve heat effects resulting from the individually solvated protein and ligand forming the protein ligand complex. Besides conformational and configurational changes of the binding partners (the protein and ligand), this process also involves substantial changes in the water structure. Although this is a multistep process, all modifications are finally compressed into the three thermodynamic parameters ΔG, ΔH, and entropy ( TΔS) that represent the entire complex-formation process. We are subsequently tempted to relate the changes in these parameters with the binding event and solely focus rather naively on the newly formed protein ligand interface. However, much more is involved, including changes in the protein structure (for example, the activation or deactivation of conformational, vibrational or rotational degrees of freedom of protein side-chains remote from the binding site) and rearrangements of the water structure across the surface of the involved binding partners, ligand, protein, and the newly formed protein ligand complex. Compensating entropy entropy changes that result from local effects in the activation or attenuation of methyl group side-chains rotational degrees of freedom [15,16] have even been reported [17]. All these alterations will have an impact on the thermodynamic signature of the binding event. As shown through several examples in this Review, the presence or absence of a single water molecule next to the protein ligand interface can easily shift the thermodynamic profile in enthalpy and entropy by 5 10 kj per mol mutually in either direction. Usually, within a series of congeneric ligands, we tend to think of effects of this magnitude as important. A shift in the enthalpic or entropic contributions of this magnitude may lead to another interpretation of the driving forces of the binding event even if, unexpectedly, the difference only stems from the involvement of just one water molecule that yet determines the deviating thermodynamic profile. This fact can easily lead to misinterpretation, particularly if, rather superficially, a particular drug candidate is assessed as superior [18], say, for its more enthalpic profile. The consideration of complementary information is of utmost importance to reduce this danger of misconception.

5 5 As a consequence, interpretation of thermodynamic data, even across a very narrow congeneric-ligand series, will be barely useful unless the structural properties of every formed protein ligand complex are simultaneously monitored. Such information is available from high-resolution crystallography and the concomitant control of the produced complexes by crystal-structure analysis (or/and nuclear magnetic resonance) are inevitably required for the meaningful interpretation of thermodynamic signatures. Even in ideal cases, where the corresponding crystal structures are available, there are some caveats. ITC data are recorded at ambient temperature in a buffered solution. Crystallographic data however, are collected in the crystalline phase, often at liquid-nitrogen temperature. Thus, can any correlation between the data from solution and crystalline states be expected? Recent comparative diffraction studies that were performed at ambient and low temperatures revealed differences in the scatter of side-chain torsion angles [19]. Supposedly, under the flash-cooling protocol that was applied to freeze protein crystals for diffraction experiments, these side-chain degrees of freedom are still soft enough to allow motion and adjustment; they equilibrate with temperature. Other motions involving larger rearrangements are less likely to occur in the crystalline phase: for example, the complete rearrangement of water-surface layers. With respect to the water-surface layers, flash-cooled crystals will likely mirror the situation at ambient temperature. In several of our investigated compound series, we observed a qualitative correlation of the B-factors (which are attributed to the residual thermal motion in a crystal) with entropic effects monitored by ITC in solution [20,21], although special care is needed in the interpretation of B-factors, as they correlate significantly with the occupancy parameters that are assigned to the bound ligands [20]. Therefore, at least qualitatively, ITC and crystal-structure data seem to correlate, thus allowing for a conclusive discussion of structure along with thermodynamics. This estimation matches well with conclusions of Nakasako, who found high consistency when comparing the solvation patterns of water molecules observed in crystal structures under cryo-conditions with other physicochemical measurements [22]. These findings make us confident that crystal structures are indeed relevant when interpreting ITC data.

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