Multi-objective experimental design for 13C-based metabolic flux analysis

Abstract 13 C-based metabolic flux analysis is an excellent technique to resolve fluxes in the central carbon metabolism but costs can be significant when using specialized tracers. This work presents a framework for cost-effective design of 13 C-tracer experiments, illustrated on two different networks. Linear and non-linear optimal input mixtures are computed for networks for Streptomyces lividans and a carcinoma cell line. If only glucose tracers are considered as labeled substrate for a carcinoma cell line or S. lividans , the best parameter estimation accuracy is obtained by mixtures containing high amounts of 1,2- 13 C 2 glucose combined with uniformly labeled glucose. Experimental designs are evaluated based on a linear ( D -criterion) and non-linear approach ( S -criterion). Both approaches generate almost the same input mixture, however, the linear approach is favored due to its low computational effort. The high amount of 1,2- 13 C 2 glucose in the optimal designs coincides with a high experimental cost, which is further enhanced when labeling is introduced in glutamine and aspartate tracers. Multi-objective optimization gives the possibility to assess experimental quality and cost at the same time and can reveal excellent compromise experiments. For example, the combination of 100% 1,2- 13 C 2 glucose with 100% position one labeled glutamine and the combination of 100% 1,2- 13 C 2 glucose with 100% uniformly labeled glutamine perform equally well for the carcinoma cell line, but the first mixture offers a decrease in cost of $ 120 per ml-scale cell culture experiment. We demonstrated the validity of a multi-objective linear approach to perform optimal experimental designs for the non-linear problem of 13 C-metabolic flux analysis. Tools and a workflow are provided to perform multi-objective design. The effortless calculation of the D -criterion can be exploited to perform high-throughput screening of possible 13 C-tracers, while the illustrated benefit of multi-objective design should stimulate its application within the field of 13 C-based metabolic flux analysis.