Abstract
Post-translational modifications (PTMs) of proteins play a central role in cellular information encoding, but the complexity of PTM state has been challenging to unravel. A single molecule can exhibit a "modform" or combinatorial pattern of co-occurring PTMs across multiple sites, and a molecular population can exhibit a distribution of amounts of different modforms. How can this "modform distribution" be estimated by mass spectrometry (MS)? Bottom-up MS, based on cleavage into peptides, destroys correlations between PTMs on different peptides, but it is conceivable that multiple proteases with appropriate patterns of cleavage could reconstruct the modform distribution. We introduce a mathematical language for describing MS measurements and show, on the contrary, that no matter how many distinct proteases are available, the shortfall in information required for reconstruction worsens exponentially with increasing numbers of sites. Whereas top-down MS on intact proteins can do better, current technology cannot prevent the exponential worsening. However, our analysis also shows that all forms of MS yield linear equations for modform amounts. This permits different MS protocols to be integrated and the modform distribution to be constrained within a high-dimensional "modform region", which may offer a feasible proxy for analyzing information encoding.