Optimal Transitions for Targeted Protein Quantification: Best Conditioned Submatrix Selection

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Multiple reaction monitoring (MRM) is a mass spectrometric method to quantify a specified set of proteins. In this paper, we identify a problem at the core of MRM peptide quantification accuracy. In mathematical terms, the problem is to find for a given matrix a submatrix with best condition number. We show this problem to be NP-hard, and we propose a greedy heuristic. Our numerical experiments show this heuristic to be orders of magnitude better than currently used methods.