Robust Selection of Gene Modifications

In recent years, increasingly sophisticated computational methods have been developed to identify optimal genetic modifications to achieve a desired metabolic engineering objective. Notable examples include OptReg [1], OptKnock [2], and GDLS [3]. The problem of identifying optimal genetic modifications can be formulated in terms of either operating state variables such as reaction flux or control variables such as gene expression. The optimal design “tunes” these variables such that the solution meets the engineering objective while satisfying several different constraints reflecting physicochemical considerations, experimental observations and assumptions about the physiology of the cell or organism. Typically, the number of optimization model variables far exceeds the number of constraints, resulting in an underdetermined system with a large number of degrees of freedom. Previously, this type of model uncertainty was addressed by estimating the possible ranges of the flux or gene expression variables. For example, flux balance analysis was used to characterize the maximal and minimal flux through each reaction in a metabolic network.

Our work addresses another type of uncertainty, which arises from the imprecision of engineering interventions, which rely on statistical events such as cellular transformation (or transfection) and stochastic steps in gene expression. Generally, an optimal solution may be sensitive to perturbations in the parameters of the problem, such that small deviations in the parameters render the solution suboptimal or even infeasible. In this paper, we describe a robust formulation of a computational metabolic engineering optimization problem. Specifically, we investigate a robust optimization problem with the objective of maximizing a desired metabolite product through gene up-regulation operations. The uncertain parameters in this formulation are the flux capacities, which are set by the expression levels of the corresponding genes. Our formulation introduces a probabilistic constraint on the flux resulting from a corresponding gene up-regulation operation: Prob{v<y.Cap}≥α. Here, v is the flux, y is the binary decision variable for the up-regulation operation, and Cap is the uncertain flux capacity.  The problem of optimizing the decision variables y (whether to up-regulate a gene or not) can then be re-formulated as a mixed-integer linear program (MILP) in a chance-constrained framework [4].

To evaluate the robust formulation, we performed a series of comparisons with a deterministic formulation, where the flux capacities were treated as known constants, rather than distributions. As the test system, we used a previously developed metabolic model of the fat cell, for which detailed metabolic flux data were at hand. The test metabolic engineering objective was to maximize the lipid storage of the fat cell subject to physiologically meaningful uptake of glucose, amino acids and fatty acids. The distributions of flux capacities were estimated by computing the maximal fluxes resulting from changes in enzyme activities using enzyme control flux (ECF) analysis [5]. Our results suggest that the gene up-regulation operations identified by the robust formulation yield a higher expected increase in lipid storage compared to the operations identified by the deterministic formulation.

[1] P. Pharkya and C. D. Maranas, "An optimization framework for identifying reaction activation/inhibition or elimination candidates for overproduction in microbial systems," Metab. Eng., vol. 8, pp. 1-13, 1, 2006.

[2] A. P. Burgard, P. Pharkya and C. D. Maranas, "Optknock: A bilevel programming framework for identifying gene knockout strategies for microbial strain optimization," Biotechnol. Bioeng., vol. 84, pp. 647-657, 2003.

[3] D. S. Lun, G. Rockwell, N. J. Guido, M. Baym, J. A. Kelner, B. Berger, J. E. Galagan and G. M. Church, "Large-scale identification of genetic design strategies using local search," Mol Syst Biol, vol. 5, 08/18/print, 2009.

[4] F. S. Hillier, "Chance-Constrained Programming with 0-1 or Bounded Continuous Decision Variables," Management Science, vol. 14, pp. pp. 34-57, Sep., 1967.

[5] H. Kurata, Q. Zhao, R. Okuda and K. Shimizu, "Integration of enzyme activities into metabolic flux distributions by elementary mode analysis," BMC Systems Biology, vol. 1, pp. 31, 2007.