Motivation: Recent advances in cell-free protein expression systems allow specific labeling of proteins with amino acids containing stable isotopes (¹⁵N, ¹³C and ²H), an important feature for protein structure determination by nuclear magnetic resonance (NMR) spectroscopy. Given this labeling ability, we present a mathematical optimization framework for designing a set of protein isotopomers, or labeling schedules, to reduce the congestion in the NMR spectra. The labeling schedules, which are derived by the optimization of a cost function, are tailored to a specific protein and NMR experiment.
Results: For 2D ¹⁵N-¹H HSQC experiments, we can produce an exact solution using a dynamic programming algorithm in under 2 h on a standard desktop machine. Applying the method to a standard benchmark protein, calmodulin, we are able to reduce the number of overlaps in the 500 MHZ HSQC spectrum from 10 to 1 using four samples with a true cost function, and 10 to 4 if the cost function is derived from statistical estimates. On a set of 448 curated proteins from the BMRB database, we are able to reduce the relative percent congestion by 84.9% in their HSQC spectra using only four samples. Our method can be applied in a high-throughput manner on a proteomic scale using the server we developed. On a 100-node cluster, optimal schedules can be computed for every protein coded for in the human genome in less than a month.
Availability: A server for creating labeling schedules for ¹⁵N-¹H HSQC experiments as well as results for each of the individual 448 proteins used in the test set is available at http://nmr.proteomics.ics.uci.edu
