**3. Discussion**

**− − − − − −** In solution, the bi-molecular association of the heme group to apo-myoglobin is thought to follow a bimodal process. Association of heme to (partially unfolded) apo-myoglobin is fast (k<sup>A</sup> ~10 8 M−<sup>1</sup> ·s −1 ), followed by a slower structural re-arrangement (k ~500 s −1 ) to generate natively-folded holo-myoglobin (at pH 7) in which the iron atom of the heme group is then primarily coordinated by His93 [23]. Accordingly, in-solution affinity of at least partially unfolded apo-myoglobin to the heme prosthetic group has been characterized as rather strong and the complex consisting of both components was assumed to possess a K<sup>D</sup> ~10 <sup>−</sup><sup>11</sup> M, whereas natively-folded holo-myoglobin has been determined to form an even stronger complex (K<sup>D</sup> ~10 <sup>−</sup><sup>13</sup> M to 3 × 10 <sup>−</sup><sup>14</sup> M) [24,25].

In the gas phase, the stability of heme binding to apo-myoglobin has been studied by dissociating holo-myoglobin in the orifice-skimmer region of an electrospray mass spectrometer, i.e., at high pressure, where complex stability was found to correlate with the activation energy of dissociation of the complex in solution [26,27]. In that investigation, heme dissociation kinetics was studied (i) by spraying solutions with pH 5 and (ii) by looking at selected charge state pairs (e.g., 8+ protonated holo-myoglobin and 7+ charged apo-myoglobin). Activation energies ranged from 73 kJ/mol to 106 kJ/mol, depending on myoglobin amino acid sequence mutations. Similar values of activation energies for heme dissociation have been reported for 9+ protonated holo-myoglobin (92 kJ/mol) and for 10+ protonated holo-myoglobin (85 kJ/mol), respectively [19]. Values from our investigations of holo-myoglobin dissociation are somewhat lower but in general stand in good agreement with reported data. The uncertainty of this method has been estimated to be approx. 10% [14]. Hence, myoglobin is considered to be an adequate standard for developing the ESI-MS method by which protein-ligand dissociation reactions may be studied. Interestingly, from ESI-MS ETD studies of multiply charged myoglobin gas phase ions it was concluded that—depending on the complexes´ charge states—the heme group might be coordinated by one of two histidinyl residues, mainly by His93 but also by His64, or by both, suggesting some similarity between in-solution and gas phase complex structures—at least around the heme binding pocket [25]. The existence of relatively defined macromolecular structures during the heme dissociation process (e.g., as transition state) fits our model, so we postulate that dissociation of immune complexes follows in principle a hard spheres model, i.e., entropy contributions at the transition state are small [14]. In fact, in-solution antibody—antigen interactions are enthalpy-driven [28,29]. Non-covalent forces in the gas phase as well as structural properties of other desolvated protein ions [30–32] have demonstrated that higher order protein structures are maintained in the gas phase for a certain period of time [33–35] despite absence of solvation [36]. Hence, similar to myoglobin, the decisive structural properties of antibody-antigen complexes seem preserved in the gas phase, at least to some extent.

The rate limiting factor for irreversible dissociation of immune complexes in the gas phase reaction is the activation barrier that needs to be overcome. With an energy input above a critical threshold, immune complex dissociation proceeds irreversibly but comparatively slowly under CID conditions. At each set energy regime, certain portions of immune complexes reach above threshold conditions which results in mixtures of surviving immune complexes and dissociated products within the timeframe of each single measurement. Thus, despite the de facto irreversible character of the dissociation reaction, apparent equilibrium conditions can be assumed. In contrast to previous work we look at average charge states, to represent a respective protein-ligand complex that has been translated into the gas phase by electrospray, and extrapolate to conditions with no additional external energy contributions, such as multiple charging and acceleration of the complex in the gas phase. Both conditions cannot be realized by experiment, because mass spectrometry experiments are performed with accelerated and (multiply) charged ions. Approximation and extrapolation to "resting and neutral" gas phase complexes is expected to provide a better comparison with in-solution data. As we performed all our work using commercial mass spectrometers, we have no means to change the duration times of the ions in the collision cell. However, by keeping all instrument settings (temperature, pressure, charge states of the complexes, gas identity) constant for the entire duration of the experiments (except of the collision cell voltage difference), we assume that reaction times do not differ too much, when comparing dissociation yields and applying the intensities of all ions for our calculations. Consistent with the literature we observed that at higher collision cell voltage differences the dissociation yields were higher as compared to those which were obtained by applying lower collision cell voltage differences.

As a consequence, from all above considerations it appears well possible to semi-quantitatively compare apparent gas phase binding strengths between complexes and to relate these to in-solution dissociation constants of antibody-antigen complexes, after correcting the energy terms, i.e., by subtracting external energy contributions.
