*1.1. ESI Mass Spectrometric Analysis of Non-Covalent Complexes*

Electrospray mass spectrometric methods have gained broad acceptance for investigation of the constituents of supramolecular complexes and determination of binding surfaces, e.g., for identifying the locations of partial surfaces on antigens which are recognized by an antibody of interest [1]. By contrast, up to now there exists no mass spectrometric method which has gained equal acceptance for investigating gas phase binding strengths of distinct protein-ligand complexes. Previous reports have shown that high pressure mass spectrometry and/or black body irradiation can be applied for analyzing small molecule-ion equilibria and to determine kinetic and thermodynamic properties, such as ion-ligand complex constants in the right order of magnitude [2–4] also for small peptides, the protonated glycine dimer being the smallest possible peptide dimer representative [5]. Gas phase dissociation reactions of Leu-enkephaline dimers [6] and of small proteins, such as ubiquitin [7] had been studied as well. Such investigations included the application of the Eyring–Polanyi equation for bimolecular gas phase reactions [8]. Gas phase dissociation profiles under low pressure collision gas conditions have been determined to estimate relative gas phase binding strengths of DNA duplex structures which correlated to the solution phase stabilities [9] and of antibiotic ligand-peptide complexes [10], respectively. Semi-quantitative analysis of glycan ligand-protein binding has been reported as well to estimate binding strengths by ESI-MS [11].

Recently, and still uncommonly, the combination of fast and robust gas-phase epitope mapping methods [12,13] with mass spectrometry-based determination of quasi-thermodynamic information has been published. The latter was obtained based on desolvated and multiply charged and accelerated protein-protein complex ions in the gas phase [14]. These studies, together with reports on collision induced unfolding reactions of protein ions [15], have enabled the development of a method termed ITEM-TWO (Intact Transition Epitope Mapping—Thermodynamic Weak-force Order) [16] that can simultaneously identify epitopes as well as enables to determine gas phase binding strengths of the respective antibody-epitope peptide interactions. Here, in addition to describing all required experimental in-solution handling steps, we introduce the underlying theoretical concept and explain all necessary mathematical calculations in detail through which the apparent dissociation constants and the apparent activation energies of protein-ligand complex dissociation processes in the gas phase are obtained.
