*1.2. Theoretical Concept of Dissociation of Protein-Ligand Complex Ions in the Gas Phase*

In a typical Q-ToF instrument, dissociation of protein-ligand complex ions in the gas phase is induced by collisions of multiply charged complex ions with noble gas atoms in a collision chamber at a given collision energy. The ligand dissociation reaction encompasses in its most simple approximation a single transition state, as is indicated by a "one stage" chemical reaction where **k** # is the apparent rate constant of product formation (see supplemental information for details).

$$\text{Prot} \times \text{Lig}^{\text{m}^+} \quad \overset{k\#}{\rightarrow} \quad \text{Prot} \text{[}^{\text{p}^+} + \text{Lig}^+$$

To drive the multiply charged protein-ligand complexes' gas phase dissociation reaction, the apparent Gibbs energy of activation, ∆**G**# **mg** (m: mean of charge states, g: gas phase) is required, as is represented by a "one-stage" energy diagram (Figure 1A). From the transition state (TS), the reaction proceeds irreversibly towards the products. ∆**G**# **mg** is the apparent Gibbs energy of activation of the abundance weighted mean charge state of multiply charged and accelerated protein-ligand complex ions in the gas phase. Yet, after electrospraying there is always an external energy contribution (∆**Gext** > 0) which needs to be considered during dissociation, as the sum of energies affects the experimentally accessible dissociation energy.

To determine the apparent Gibbs energy of activation of protein complex dissociation of "neutral and resting" protein-ligand complexes, the ESI-dependent external energy contributions need to be considered. Thus, the energy diagram of the complex dissociation reaction requires the introduction of ∆**G**# **m**0**g** , which is the apparent Gibbs energy of activation that is needed for the dissociation of a protein-ligand complex in the gas phase without external energy contributions (Figure 1B).

–

Prot × Lig⌉

∆ #

m+ #

→ Prot⌉

represented by a "one stage" energy diagram (Figure 1A). From the transition state (TS), the reaction ∆ #

p +

+ Lig⌉

'

n +

—

"one stage" chemical reaction where

–

#

**Figure 1.** (**A**) Energy diagram showing the apparent Gibbs energy of activation required by charged and accelerated protein-ligand complexes (∆**G**# **mg** ) to reach the transition state (**TS**) before dissociating into products ions. (**B**) Energy diagram showing the apparent Gibbs energy of activation required by charged and accelerated protein-ligand complexes (∆**G**# **mg** + ∆**Gext** ) and by neutral and resting protein-ligand complexes (∆**G**# **m**0**g** ) to reach the transition state (**TS**) before dissociating into products ions. "neutral and resting" #
