Conceived and designed the experiments: SR CDM. Performed the experiments: SR. Analyzed the data: SR CDM. Contributed reagents/materials/analysis tools: SR PFS CDM. Wrote the paper: SR CDM.
The authors have declared that no competing interests exist.
Computational procedures for predicting metabolic interventions leading to the overproduction of biochemicals in microbial strains are widely in use. However, these methods rely on surrogate biological objectives (e.g., maximize growth rate or minimize metabolic adjustments) and do not make use of flux measurements often available for the wild-type strain. In this work, we introduce the OptForce procedure that identifies all possible engineering interventions by classifying reactions in the metabolic model depending upon whether their flux values must increase, decrease or become equal to zero to meet a pre-specified overproduction target. We hierarchically apply this classification rule for pairs, triples, quadruples, etc. of reactions. This leads to the identification of a sufficient and non-redundant set of fluxes that
Over the past few years, there has been an unprecedented increase in the use of microorganisms for the production of biofuels, industrial chemicals and pharmaceutical precursors. In this regard, biotechnologists are confronted with the challenge to efficiently convert biomass and other renewable resources into useful biochemicals. With the advent of organism-specific mathematical models of metabolism, scientists have used computations to identify genetic modifications that maximize the yield of a desired product. In this paper, we introduce OptForce, an algorithm that identifies all possible metabolic interventions that lead to the overproduction of a biochemical of interest. Unlike existing techniques, OptForce does not rely on the maximization of a fitness function to predict metabolic fluxes. Instead, OptForce contrasts the metabolic flux patterns observed in an initial strain and a strain overproducing the chemical at the target yield. The essence of this procedure is the identification of all coordinated reaction modifications that force the network towards the overproduction target. We used OptForce to predict metabolic interventions for succinate overproduction in
An overarching challenge for metabolic engineers is to optimize the conversion of biomass and other renewable resources into useful metabolic products through fermentation and other biological conversions
Flux balance analysis (FBA) has emerged as an important framework
The use of computational tools operating on metabolic reconstructions to identify strain modifications is becoming commonplace. Nevertheless, a number of shortcomings plague all existing approaches. All are sequential in nature generating a single engineering strategy per run thus requiring multiple restarts to generate a set of candidate list of alternatives (i.e., typically less than ten) that is dwarfed by the myriads of engineering possibilities afforded by genome-scale models spanning thousands of reactions. Furthermore, in the absence of kinetic descriptions OptKnock and other methods rely on the maximization of surrogate biological fitness functions (e.g. maximization of biomass yield
The key concept of OptForce is to maximally resolve which fluxes (or combinations thereof) must depart away from the range of values allowed to span in the wild-type strain in response to an overproduction target. This maximal range of flux variability for the wild-type strain can be elucidated by iteratively maximizing and minimizing each flux
Contrasting the flux ranges for the (wild-type) metabolic network against the ones consistent with the overproduction target(s) provides the cornerstone of OptForce.
We refer to reaction fluxes that must increase (see
The next step of OptForce is to identify how the collective set of changes (encoded within the MUST sets) can be imparted on the wild-type metabolic network with the minimal number of direct interventions (i.e., knock-up/down/outs). The identified MUST sets encode Boolean choices regarding which fluxes (or combinations thereof) must change in value. Upon the incorporation of these constraints, an optimization formulation is proposed (see Appendix C in
The optimization formulations for computing the allowable flux values for all reactions in the wild-type metabolic network are provided in Appendix A (see
In this section, we benchmark the OptForce framework by identifying metabolic interventions that lead to the overproduction of succinate using the latest genome-scale metabolic model for
While results for MUSTU and MUSTL involve primarily intuitive negations of by-products formation, sets MUSTUU, MUSTUL and MUSTLL allude to more complex flux re-allocations (see
Figure 3a shows the list of reaction pairs in the MUST sets. Figure 3b shows the network of interacting reactions formed the list of all reaction pairs from Figure 3a. Reactions in green ovals indicate that its flux increases and red ovals indicate the decrease in flux values. Figure 3c represents the minimal set of network changes identified using Boolean logic that together span the entire network shown in Figure 3b.
Network of all the interacting components (Figure 4a) and the minimal set of network modifications (Figure 4b) for reactions in the MUSTUUU, MUSTUUL, MUSTULL and MUSTLLL sets.
We next used the bilevel optimization formulation (refer Appendix C in
Figure 5a shows the interventions for cases 1 and 2 before adding the PYC reaction and Figure 5b shows the interventions after adding the PYC reaction. Reaction names shown in green ovals indicate the FORCE set whose fluxes must be increased while the red ones indicate the ones that must be decreased. Reaction names adjacent to small red triangles represent knockouts.
Despite the differences in the MUST sets between cases 1 and 2 the corresponding FORCE sets of reactions were identical. Up-regulations for PPC, CS, MALS, ICL and ACONTa and down regulations for reactions along the pathways leading to competing by-products were required for the 98% succinate yield case. Even though the membership of the FORCE set is the same the corresponding required levels of up or down-regulation are slightly different.
Blue lines indicate the wild-type flux ranges. The orange (case 1) and green (case 2) lines indicate the flux values beyond which these reactions must be engineered to guarantee the overproduction of succinate.
Pyruvate carboxylase (PYC) has been overexpressed in
Figure 7a shows the list of MUSTU, MUSTL and MUSTX set of reactions. Figures 7b and 7c shows the minimal set of network modifications required for the doubles and triples, respectively, for case 3.
The FORCE set of engineering interventions for this scenario is contrasted against cases 1 and 2 and is shown in
In this paper, an optimization-based methodology called OptForce was introduced for predicting all possible metabolic modifications that could guarantee, subject to the model stoichiometry and conditions, a pre-specified overproduction level of a desired biochemical. The results for succinate overproduction in
Many of the suggested interventions recapitulate existing strain redesign strategies for succinate synthesis. For example, experimental evidence suggests that the overexpression of PPC from
The up-regulation of citrate synthase (CS), aconitase (ACONTa/b) and reactions from the glycolytic pathway (PGK and TPI) are engineering strategies suggested by OptForce that to the best of our knowledge have not yet been implemented for succinate production. Heterologous overexpression of the
The genetic interventions predicted by OptForce underscore the importance of up-regulating key fluxes along the succinate pathway in addition to the knockouts for by-products. Existing strain optimization procedures (e.g. OptKnock
Results from OptKnock | Results from OptReg | Results from OptForce | ||||
Number of metabolic interventions (K) | Knockouts | Minimum guaranteed flux for succinate (*) (mmol/gDW.hr) | Metabolic Interventions | Minimum guaranteed flux for succinate (*) (mmol/gDW.hr) | Metabolic Interventions from FORCE sets | Minimum guaranteed flux for succinate (mmol/gDW.hr) |
K = 2 | ALCD2x, GLUDy | 5.5 (84.1) | PFL (×)PPC (↑) | 2.1 (79.4) | PPC (↑), CS (↑) | 84.6 |
PFL, LDH | 1.2 (76.8) | - | - | PPC (↑)MDH (↓) | 50.8 | |
K = 3 | ALCD2x, PFL, LDH | 5.9 (85.7) | PFL (×), PPC (↑), ALCD2x (↓) | 2.8 (84.3) | PPC (↑), CS (↑)MDH (↓) | 100.2 |
ALCD2x, ACKr, PTAr | 1.1 (84.6) | - | - | PPC (↑), ACONT (↑)MDH (↓) | 100.2 | |
K = 4 | ALCD2x, ACKr, PTAr, PYK | 4.9 (88.8) | PPC (↑), PDH (↓)ALCD2x(↓), CS(↑) | 2.8 (88.4) | PPC (↑), CS (↑)PFL (↓), MDH (↓) | 100.2 |
ALCD2x, ACKr, PTAr, TKT1 | 2.1 (87.4) | - | - | PPC (↑), ACONT (↑)PFL (↓), MDH (↓) | 100.2 |
(*) The values within parentheses denote the maximum flux values for succinate from OptKnock and OptReg.
The OptForce procedure allows for the complete enumeration of engineering modifications consistent with an overproduction target(s). The incorporation of metabolic flux information about the wild-type network allows for a sharper elucidation of engineering interventions. The engineering interventions predicted by OptForce depend on the available flux measurements for the initial strain. OptForce can be modified to predict globally valid metabolic interventions by utilizing biological objectives (i.e. maximization of biomass) when sufficient metabolic flux data are not available. Furthermore, the procedure can hierarchically be applied at intermediate stages of a metabolic engineering project by re-calculating the set of engineering interventions as new flux data for (multiple) mutant strains become available. The restriction of minimality in the calculated FORCE set can be relaxed allowing for the exploration of less parsimonious engineering interventions. For example, we studied the case for identifying additional interventions after retaining the best eight out of the ten interventions originally identified by the OptForce method (for cases 1 and 2). However, we found that even after allowing seven additional interventions (i.e. K = 15), the resulting FORCE set was not sufficient to increase the yield to more than 80% of the theoretical maximum. In addition, reactions that cannot (e.g., diffusion limited transport, non-gene associated reactions, etc.) be directly manipulated can be excluded from consideration during the derivation of the FORCE set. It is to be noted that the OptForce procedure provides targets for genetic manipulations at the metabolic flux level. The lack of a completely quantitative mapping between gene expression and flux levels implies that multiple rounds of experimental strain modifications may be needed to translate the FORCE set of reaction fluxes to the required gene expression levels. An algorithmic implementation of the procedure is available as supplementary material (see supporting information -
Appendix A: Computing flux variability for the wild-type and overproducing networks
(0.09 MB DOC)
Appendix B: Bilevel formulation for the identification of MUST sets
(0.05 MB DOC)
Appendix C: Bilevel formulation for the identifying the FORCE set
(0.07 MB DOC)
Results for MUST considered four-at-a-time (quadruples)
(0.12 MB DOC)
Prototype Implementation for the OptForce Algorithm
(0.06 MB DOC)
Minimal set of network modifications for reaction quadruples.
(2.08 MB TIF)
MUST set of reactions for 98% yield of succinate. Figure S2a shows the list of reactions in the MUSTU and MUSTL sets. Figure S2b and S2c shows the network of interacting reactions and the minimal set of network modification for the doubles and triples, respectively, identified for case 2.
(3.34 MB TIF)
The authors wish to thank Anthony P. Burgard and Vinay Satish Kumar for helpful suggestions and discussions.