*1.3. ESI Mass Spectral Information Extraction*

ESI-MS of large biomolecules and macromolecular non-covalent complexes in positive ion mode records series of multiply protonated ions which represent a Gaussian ion intensity distribution of individual charge states for a given molecular/supra-molecular species (complex) [17,18]. For semi-quantitative analyses of ESI mass spectra we postulate that the overall ion characteristics, such as gas phase reactivity of complex dissociation, is well represented by the mean charge state (**m**+) of the recorded ion series of a molecular/supra-molecular species (Figure 2). <sup>+</sup>

 m<sup>+</sup> n <sup>+</sup> p + **Figure 2.** NanoESI mass spectrum of gas phase dissociation of protein complex (e.g., holo-myoglobin; apo-myoglobin—heme complex). Gaussian fits of ion intensities of the related charge state series for each molecular or supra-molecular species (complex) are shown (dashed charge state envelope curves). The arrows point to apices which are determined as maxima of fitted curves. The vertical dashed lines provide heights of charge structure envelopes which represent relative intensities of holo-protein complex ions (h, educts; red), ligand ions (i, product; green), and apo-protein ions (j, product; blue). Locations on the *m*/*z* axis match with mean charge states of holo-protein complex ions (m+, educts), ligand ions (n <sup>+</sup>, product) as well as apo-protein ions (p <sup>+</sup>, product).

Mean charge states of each ion species, e.g., holo-protein ions (educts) and of apo-protein as well as of ligand ions (products) can be separately determined from the mass spectrum. Normalization of ion intensities is achieved by summation of all apex values and setting the sum to 100% (equations and calculations are shown in the supplemental information).

### *1.4. Data Analysis Procedure* The "steep part" of the dissociation reaction depend the "energy

A series of mass spectra in which the collision cell voltage difference is increased stepwise records ion signals with varying intensities of all ion species, i.e., educts and products, as they emerge from the collision induced complex dissociation reaction. Plotting the normalized intensities of the educts of the complex dissociation reaction in the gas phase as a function of collision cell voltage difference (∆**CV**) provides a sigmoidal shaped curve with Boltzmann characteristics (Figure 3A). The "steep part" of the dissociation reaction dependence (interval 2dx), i.e., the "energy regime" with greatest dependence between educt ion intensities and ∆**CV**, as well as the determination of ∆**CV**<sup>50</sup> from the Boltzmann fit to the data points is inferred by mathematical procedures which lead to the equation of the tangent line (see supplemental information for calculations). regime" with greatest dependence between educt ion intensities and –

 () function. The tangent line equation is taken from the Boltzmann fit. " " desc between the lowest and highest data points on the sigmoidal fit. " " is the x # **Figure 3.** (**A**) Course of normalized ion intensities of complex ions (*norm* (*educts*)) as a function of collision cell voltage differences (∆**CV**). Each data point is the mean of several independent measurements. Vertical bars give standard deviations. The curve was fitted using a Boltzmann function. The tangent line equation is taken from the Boltzmann fit. "**a**" describes the difference between the lowest and highest data points on the sigmoidal fit. "**2dx**" is the x-axis interval within which the steepest decline of educts is observed; the center of the **2dx** interval is ∆**CV50**. (**B**) Arrhenius plot for the course of protein-ligand complex dissociation in the gas phase. The value for **lnk** # **m**0**g** is taken from the point of the line at 1 **Tamb** .

– # # # ∆ # – ∆ # Since, in the gas phase of a Q-ToF mass spectrometer, the collision of multiply charged and accelerated complex ions takes place upon reaching elevated energies, the collision temperature (**Tcoll** ) that is attained by the complex during collision induced dissociation needs to be considered as well. As proposed by a model for collisional activation [19], **Tcoll** can be expressed as the sum of ambient temperature, **Tamb**, plus external temperature contribution, **Text** (see supplemental information for definitions, energy conversion factors [19–21], and equations).

 # − # = = = # the apparent rate constant of dissociation of "neutral and resting" = # of "neutral and resting" = # which is termed "Intact Transition Epitope Mapping— TWO)" According to the Eyring–Polanyi equation [22], **k** # is directly proportional to an apparent thermodynamic quasi equilibrium dissociation constant, **K**# **D** . The apparent gas phase thermodynamic quasi equilibrium dissociation constant, **K**# **D mg** , is also given by the relative ion intensities (cf. Figures 1 and 3). Accordingly, for each experimentally set ∆**CV** value, a corresponding **k** # **mg** value can be calculated (see supplemental information for equations). From the Arrhenius equation, the apparent energy of activation of protein–ligand complex dissociation ∆**G**# **mg** can be determined. Plotting **lnk** # **mg** as a function of 1 **Tcoll** provides the intercept with the y-axis, which is ln **A** (pre-exponential factor), and the slope of the line, which is − ∆**G**# **mg R** (Figure 3B). Note, at **Tcoll** = **Tamb** = **298 K** it can be concluded that ∆**CV** = 0. Hence, from the Arrhenius plot a value for **k** # **m**0**g** is obtained, i.e., the apparent rate constant of dissociation of "neutral and resting" protein-ligand complexes. Similarly, at ∆**CV** = 0 the value for **K**# **D m**0**g** , is calculated, i.e., the apparent gas phase thermodynamic equilibrium dissociation constants of protein-ligand complex dissociation, corrected for external energy

contributions; i.e., of "neutral and resting" protein-ligand complexes. Therefore, at ∆**CV** = 0 the value for ∆**G**# **m**0**g** is calculated as well, i.e., the apparent Gibbs energy of activation of neutral and resting protein-ligand complexes (see Supplement for equations).

The entire procedure, which is termed "Intact Transition Epitope Mapping—Thermodynamic Weak-force Order (ITEM-TWO)", starts with either generating the protein-ligand complex by mixing the two components in solution or by simply maintaining the natively obtained protein-ligand complex in an electrospray-compatible solution. No further in-solution sample handling steps are needed. A few microliters of complex-containing solution are loaded into a nano-electrospray capillary and all solubilized components including the protein-ligand complex are simultaneously transferred into the gas phase by electrospray. Mass spectrometric data acquisition involves collision induced dissociation of the complex in the gas phase at various applied collision cell voltage differences (∆**CV**). Subsequent in-depth data analysis of intensities of both, resulting product ions and remaining educt ions (survivors) at each of the applied collision energies enables the apparent non-covalent complex stability to be characterized. In this reports supplement, the entire data analysis procedure is described in all detail. In contrast to previous reports the complex dissociation reaction is monitored by investigating the mean charge states and the normalized average intensities of each ion species.
