Modeling and optimization of a multi-product biosynthesis factory for multiple objectives
Introduction
Increasingly sophisticated mathematical models for multi-product biosynthesis factories are now available for Escherichia coli (Chassagnole et al., 2002; Dengering et al., 2004), Corynebacterium glutamicum (Wendisch et al., 2006), Saccharomyces cerevisiae (Rizzi et al., 1997; Teusink et al., 2000) and Penicillium chrysogenum (Zangirolami et al., 1997), thus enabling experts to extend the reach of their competencies in systems area such as modeling and optimization to knowledge-based biologics and fermentation industry (Lee et al., 2009). In addition, validation and optimization of the kinetic parameters in central carbon metabolism are feasible through modern microbial metabolomics. Numerical difficulties associated with such a highly nonlinear central carbon metabolism model is circumvented through model reduction (Gerdtzen et al., 2004), piecewise optimization (Schmid et al., 2004), linlog approximation (Visser et al., 2004) and Lagrange linearization (Vital-Lopez et al., 2006). A computational framework termed OptReg (Pharkya and Maranas, 2006) is available, and it is a versatile tool for strain design which allows a broad array of genetic manipulations given the highly complex linear metabolic model of an organism such as E. coli. A common feature in these works is the pseudo-stationary assumption. By setting the time derivatives of the metabolite concentration to zero in a system of differential mass balances, stationary fluxes and metabolite concentrations can be calculated when engineering interventions in the form of gene knockouts and/or manipulations are introduced. In all cases, desirable interventions result in the partitioning of carbon sources to maximize the production of a targeted end-product.
Optimization involves the search for one or more feasible solutions that correspond to the maxima or minima of one or more objectives. Almost all works on optimization of a multi-product biosynthesis factory focussed on a single objective (e.g., Schmid et al., 2004; Visser et al., 2004; Vital-Lopez et al., 2006). However, conflicting objectives are commonly encountered in bioprocesses (Halsall-Whitney and Thibault, 2006; Lee et al., 2007; Oh et al., 2009; Sendin et al., 2006). When there are conflicting objectives, it is not possible to obtain a single solution which is simultaneously optimal for all the objectives (i.e., utopia point). Therefore, it is highly desirable to consider multi-objective optimization (MOO) involving the search for tradeoffs (or Pareto-optimal front or equally good solutions).
There have been a few MOO studies of metabolic processes. Based on the S-system representation of the S. cerevisiae kinetics, Sendin et al. (2006) have compared the MOO of ethanol production using weighted sum method, goal attainment method, normal boundary intersection (NBI), multi-objective indirect optimization method (MIOM) and multi-objective evolutionary algorithm (MOEA). Among them, the MIOM approach is workable when a nonlinear model is converted into an equivalent S-system (synergistic systems) by aggregating all reactions contributing to generation or consumption of a given metabolite as a product of power functions. The power functions of the generation (influx term) or consumption (efflux term) of a given metabolite are formed by multiplying the rate constant and each contributing metabolite concentration raised to a real exponent. The power-law approximation in the form of S-system and generalized mass action (GMA) provide the modeling framework under biochemical systems theory (BST). The S-system is converted into a system of linear equations at steady-state by logarithmic transformation of influxes and effluxes. Applying multi-objective linear programming (MOLP) to S-system is numerically less daunting than applying other MOO methods to the original highly nonlinear model. To our knowledge, BST model is not available for the central carbon metabolism of E. coli.
Data for tryptophan biosynthesis modeling in E. coli are mostly drawn from well-developed experimental approaches of microbiology and genomics. The tryptophan biosynthesis models constructed using microbiology and genomics data focus on operon regulation and stability with hardly any consideration of the central carbon metabolism as being capable of carbon flux control through its enzymatic activities. This motivated us to develop an augmented model (Section 2) by linking the central carbon metabolism of E. coli to the tryptophan biosynthesis. The developed augmented model serves as a platform for the mixed-integer, nonlinear MOO study that involves concurrent gene knockouts and manipulations for strain improvement. Linking an operon-based model for tryptophan synthesis that accounts for the well-studied macromolecular synthesis and regulatory effects of operon repression, transcriptional attenuation and enzyme inhibition, to the central carbon metabolism of E. coli, allows us to formulate metabolic pathway recipe, possibly for the first time, for engineering a wild strain targeted for industrial production of desired amino acids via mixed-integer, nonlinear MOO.
The two objectives selected for MOO in this study, are maximization of l-tryptophan and l-serine production in one organism. l-serine is mainly used in the production of antibiotics. l-tryptophan is an active ingredient of anti-depressants and sleeping tablets, and it is one of the eight essential amino acids in pre- and post-surgery infusion fluid. There are conflicting economic demands for producing tryptophan and serine in a single organism. Producing tryptophan and serine in one organism rather than two different organisms is a case for flexible multi-product biosynthesis factory. The flexibility is scalable through engineering interventions of the metabolic pathways to respond to changes in types of products and their quantities demanded in a highly competitive market. On a broader perspective, manufacturers will be able to shorten the research and development time using a multi-product biosynthesis factory serving as a re-configurable biocatalytic template to produce novel and useful products in the future.
Organisms such as E. coli and C. glutamicum have similar central carbon metabolism and branched pathways such as those leading to aromatic amino acids and serine biosynthesis. Therefore, single-product technologies accumulated through the studies of an individual organism can be channeled towards the singular purpose of studying a multi-product biosynthesis factory. Our current research is the first step in exploring the challenges of designing a multi-product factory via E. coli from the metabolic engineering viewpoint. We choose E. coli motivated primarily by the availability of detailed models and extensive literature. Results presented later in this paper show that some serine is produced even when the tryptophan production is optimized and vice versa. In general, MOO can provide a range of optimal solutions including those for optimizing each objective individually. Advances in post-fermentation separations will be less of an issue when costs and substrate availability for fermentation are relatively more important.
l-serine and l-tryptophan have a symbiotic relationship in E. coli (see Fig. 1, Fig. 2). In the final step of the terminal tryptophan biosynthesis pathway, the conversion of l-serine and indole into l-tryptophan and water is catalyzed by the β2 subunit of tryptophan synthase. The manufacturer may determine the relative amounts of serine and tryptophan to be produced simultaneously using a single fermenter since the same organism can be re-configured in response to market needs. Serine is soluble in the aqueous fermentation broth. Tryptophan is sparingly soluble in the aqueous solution and appears as solid crystals towards the end of fermentation. Post-fermentation steps for tryptophan include filtration and crystallization. Ion-exclusion chromatography can be used to extract serine from the same post-fermentation solution. Using two fermenters rather than one fermenter potentially increases the post-fermentation separation steps needed to achieve products of desired quality, and, in general, production costs.
The earlier study by us (Lee et al., 2009) considered the enzymatic sub-systems DAHPS and PEPCxylase at the start of the three branched pathways, and SerSynth together with the central carbon metabolism. In the current research, the aromatic amino acids pathway beginning with DAHPS is expanded by considering additional key metabolites, flux balances and trp operon model at the DNA macromolecular level. The resulting augmented model developed in Section 2.3 is more detailed than that employed by us in Lee et al. (2009). Hence, it is a more realistic platform to ferret the challenges of creating a multi-product biosynthesis factory based on known metabolic engineering principles.
In summary, the objectives of this study are: development of an augmented model for E. coli, and MOO for maximizing l-typtophan and l-serine production in one organism. Section 2 describes the aromatic amino acid pathways leading to tryptophan and serine biosynthesis, tryptophan operon model, augmented model and its parameters estimation. 3 Optimization problem and solution, 4 Results and discussion present MOO, optimal results obtained and discussion. Closing remarks are given in Section 5.
Section snippets
Aromatic amino acids pathways
DAHPS is the starting point of the common pathway of the aromatic amino acids biosynthesis (Fig. 1) leading to chorismate biosynthesis. Starting from chorismate, there are three separate terminal branches (Fig. 2) leading to the final production of l-tyrosine, l-phenylalanine and l-tryptophan. Of interest to the present study are the common aromatic amino acid and tryptophan terminal pathways. Details are given in Appendix A.
Tryptophan operon model
The original central carbon metabolism (Chassagnole et al., 2002)
Problem formulation
Gene repression and overexpression (i.e. gene manipulation) as well as gene knockouts help to redistribute the various metabolic fluxes in the central carbon metabolism. The challenge lies in identifying target genes to be manipulated or knocked out so as to simultaneously optimize the desired fluxes leading to the enhanced production of useful amino acids as end-products. Concurrent gene knockout and manipulation will naturally amplify the targeted fluxes to a greater extent than using either
Two-gene identification
Pareto-optimal results obtained (Fig. 4a) using the gene multiplier range of 0.8–1.25 reveal the existence of two separate segments and two isolated chromosomes C1 and C2. Discontinuity between the two separate Pareto segments indicates an on–off switching mechanism with forward and backward paths favouring tryptophan and serine biosynthesis respectively. The sharp on–off pattern is a result of switching between two sets of genes (Fig. 4b) responsible for enhancing tryptophan and serine
Closing remarks
The central carbon metabolism model was used successfully in MOO in an earlier study by the authors (Lee et al., 2009). What is lacking in that study is the integration of the central carbon metabolism and the dynamic trp operon model, and its effect on optimization. This provides the prime motivation for developing the augmented model presented. The ability of the augmented model to channel carbon fluxes through the common aromatic amino acid and terminal tryptophan biosynthesis pathways is
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