Current address: IBIVU Systems Bioinformatics, Amsterdam, The Netherlands
Conceived and designed the experiments: BT AW LJ RAN EJS. Performed the experiments: AW LJ. Analyzed the data: BT AW LJ RAN. Contributed reagents/materials/analysis tools: RAN. Wrote the paper: BT AW RAN EJS.
The authors have declared that no competing interests exist.
In the study of metabolic networks, optimization techniques are often used to predict flux distributions, and hence, metabolic phenotype. Flux balance analysis in particular has been successful in predicting metabolic phenotypes. However, an inherent limitation of a stoichiometric approach such as flux balance analysis is that it can predict only flux distributions that result in maximal yields. Hence, previous attempts to use FBA to predict metabolic fluxes in
Being able to predict the metabolic fluxes and growth rate of a microorganism is an important topic in microbial systems biology. One approach, constraint-based modeling, uses a reconstructed metabolic network and optimization techniques to make such predictions. Although widely used, the success of this approach depends on a number of important assumptions. First, it assumes that evolutionary forces have shaped the metabolism towards optimality of, in most cases, growth rate. Second, through the nature of the modeling approach, it assumes that microorganisms maximize the growth rate through optimizing the yield on the growth substrate. Despite successes of the approach in model organisms such as
The role of mathematical modeling in the study of microbial physiology has increased considerably by the development of genome-scale metabolic models
In many of these studies flux balance analysis (FBA) was used. FBA uses optimization of an objective function to find a subset of optimal states in the large solution space of possible states that is shaped by mass balance and capacity constraints
However, we have recently demonstrated that
To fully appreciate these results, it is crucial to understand very precisely what FBA assumes and what it predicts. Under many conditions, especially in the laboratory and under adaptive evolution protocols, growth rate is a good proxy for fitness. Thus, an optimization with respect to growth rate seem an appropriate modeling strategy, and that is what FBA does: it most often optimizes the growth rate (
Where
(A) A stoichiometric network can be used, with FBA, for optimization of maximal yield of biomass on a certain nutrient. (B) by providing an experimentally measured input rate (capacity constraint in constraint-based modeling terms), FBA predicts a specific growth rate. The two situations are, however, exactly the same except for some scaling factor (indicated in bold). In both cases, a flux distribution through the stoichiometric network will be found that maximized the yield of biomass on the nutrient.
There are potentially other strategies that lead to enhanced fitness. These include a very fast (but metabolically inefficient) consumption of substrates, closely related to high growth rates
In line with the above reasoning, we realized that even though the behavior of
These results provide a thorough understanding of the limitations to methods that predict flux states after adaptive evolution based on FBA, but also provides handles (in the forms of specific cultivation conditions) to overcome them.
Glycerol is a substrate that is not unknown to lactobacilli, but often is co-fermented with a fermentable carbon source
When we tried to cultivate
After two months and approximately 20 generations, the OD600 values increased substantially (from 0.1 at day 0 to 0.4, measured after 48 h). At this point we tried to grow the adapted culture again under respiratory conditions, and growth was now possible and higher OD's were reached (OD600 of 0.4 versus 0.8 for anaerobic versus respiratory, respectively). Hence, from this point on the adaptive evolution protocol was continued under respiratory conditions.
Closed circles represent the behaviour of the culture, the closed triangle shows the behaviour of the isolated strain NZ1405. There is variability that seems related to the specific batch of medium, which is chemically defined but rather complex. Within one batch of medium, the variability is indicated for strain NZ1405 (closed triangles, standard deviation of four replicates).
We characterized growth and product formation in the original shake-flask that was used for the adaptive evolution (
Uptake or production (mmol gDW−1) | Shake flask | Fermentor | Model constraints robustness analysis | |||||
Average | ± | Stdev | Average | ± | Stdev | LB | UB | |
Growth rate (h−1) | 0.26 | − | 0.01 | 0.23 | − | 0.04 | 0 | ∞ |
Glycerol | −40.0 | ± | 2.41 | −47.1 | ± | 2.11 | −42.1 |
−38.0 |
citric acid | −1.91 | ± | 0.25 | −0.40 | ± | 0.09 | −2.1 | −1.7 |
Lactate | 33.5 | ± | 1.40 | 30.7 | ± | 0.89 | 0 | ∞ |
Pyruvate | 0.15 | ± | 0.06 | 0.01 | ± | 0.06 | 0 | ∞ |
Formate | 0 | ± | 0 | 0 | ± | 0 | 0 | ∞ |
Acetate | 5.83 | ± | 0.51 | 4.76 | ± | 0.78 | −∞ | ∞ |
Ethanol | −4.27 | ± | 0.53 | −5.35 | ± | 1.22 | −∞ | ∞ |
Acetoin | 0.74 | ± | 0.02 | 1.14 | ± | 0.10 | 0 | ∞ |
Succinate | 0 | ± | 0 | 0 | ± | 0 | 0 | ∞ |
Oxygen | ND | −22.3 | ± | 3.14 | Robustness parameter |
Data presented are yield data averaged over 2–4 independent experiments during growth between an OD600 of 0.2 and 0.7. Yield data are in mmol gDW−1. Negative values indicate uptake of the compound. The last two columns indicate the constraints used for the robustness analysis of
ND not determined; LB lower bound; UB upper bound.
Presented unit is in mmol gDW−1 for comparison to measured fluxes. To get to flux constraints with unit mmol h−1 gDW−1 (as presented in
The endpoint of adaptive evolution as characterized above was compared to optimal behavior predicted by the genome-scale model under respiratory conditions. During the very first simulations, however, we noticed that very high biomass yields could be obtained, with concomitant production of only CO2 and water as final products. The simulations implicated phosphoketolase (PKL) in the reverse direction than usual, the usual direction being cleavage of the xylulose 5-P as phosphoketolase is involved in pentose catabolism in many lactic acid bacteria
The complex medium that was used, created another problem that needed to be solved: How to set reasonable constraints on the many medium components present in the medium? When all measured fluxes, including the amino acid fluxes, were set as constraints and biomass yield was optimized, a growth rate of 0.324 h−1 was found, which fits reasonably well with, but is clearly higher than, the rate of 0.26 h−1 found experimentally. There are two possible reasons for the discrepancy. First, through the adaptation, the (stoichiometric) efficiency of some metabolic processes may have improved that have not been incorporated in the model. These relate to possible changes in efficiency of transport systems, to efficiencies in proton leakage and/or ATPase stoichiometry (number of protons pumped per ATP molecule), or to the assembly of biomass precursors into new cells (the growth-related ATP coefficient). Improvements in these processes, however, would lead to lower
Reassuring as this result may be, the main question is, whether we can predict fluxes. Since we have so many input fluxes, the issue is what the minimum set of input fluxes is that needs to be fixed by experimental observations in order to prevent the system from becoming unbounded. This issue has not been specifically addressed before, as most studies have been performed on organisms that grow on minimal salts media with one carbon source
To tackle this problem, we first dismissed a major impact of amino acid metabolism in the light of the smaller fluxes compared to primary metabolism (
We found 2669 EFMs and 531 different overall EFM stoichiometries with net ATP production (see
Since most EFM's were dependent on variable amounts of oxygen we decided to fix the uptake rates of citrate and glycerol at the measured values, leave the acetate and ethanol capacity constraints unrestricted, and predict the growth behavior as a function of the oxygen uptake rate (
(A) Impact of oxygen uptake on optimal lactate (green), acetate (red) and ethanol (black) fluxes. Dashed box indicate the oxygen consumption rate measured experimentally. Above and uptake rate of 13 mmol h−1 gDW−1 growth is no longer energy limited, resulting in variability in fluxes: the diverging lines indicate the maximum and minimum flux value at each oxygen uptake rate. (B) Impact of oxygen uptake on the growth rate. (C) Experimentally derived fluxes are included for comparison.
Initially, however, it was a surprise that FBA predicted lactate formation as an optimal strategy, and not acetate (which at first sight would yield more ATP). To understand this result from the robustness analysis, we went back to the elementary flux modes. We applied a constraint-based optimization on all 2669 EFMs to ask which combination of EFMs would lead to the highest ATP production yield, given the measured fluxes of oxygen, glycerol and citrate as constraints (see
Thus, EFMs 2, 3 and 174 (numbered according to the table in the
The anaerobic conversion of citrate and ethanol into acetate and succinate (EFM2) was unexpected, since no succinate is being formed experimentally. Rather, acetoin was formed, a well known product from citrate metabolism implied in pH homeostasis
In summary, the constraint-based EFM analysis provided valuable additional mechanistic insight in the many options that the metabolic network had (as a function of the oxygen consumption rate), and strikingly, the adapted strain selected out of the 2669 possibilities the 3 EFMs that were (almost) optimal for ATP production under oxygen uptake limitation. The use of elementary flux modes to decipher the optimal use of multiple nutrients is a new application of the EFM concept, underpinning the optimality of the solution used by the adapted strain. Under these relatively poor conditions, realizing an optimal yield appears the best strategy to win the battle of fitness. However, this is provided a restricted uptake of oxygen, and so one may argue that yield maximization is still not predictive in our case, the optimum being full oxidation to acetate. Indeed, the situation is analogous to the suboptimal acetate production by
This study shows how rational design of the selection conditions can be used to steer the strategy for fitness of an organism into a desired direction. It appears, at first glance, that this conclusion was reached before, especially by the studies of the Palsson group on
A clear understanding of the difference will be crucial in appreciating the usefulness and limitations of optimization techniques in systems and synthetic biology. For example, the recently developed OptKnock strategy took the idea of being able to predict adaptive evolution one step further by identifying knockout targets that would result in the alignment of growth rate and byproduct formation as optimization objective, thereby forcing cells to increase fitness by increasing product formation
The bacterial strain used in this study was
At the end of the adaptation process, judged by no further growth improvements, 96 single colony isolates were isolated from a CDM agarose plate (CDM medium containing 1–1.5% Agar, LABM Limited, Bury, UK) and grown overnight in a KC Junior, micro-titer reader (Bio-Tek, Vermont) shaken with intermediate intensity at 37°C. OD600 and growth rates were compared. Subsequently, one isolate (NZ1405) was chosen for further characterization.
Strain NZ1405 was cultivated in Erlenmeyer shake flasks as described above (4 independent experiments). At mid-log phase (OD600 of 0.7), samples were collected for analysis of amino acids, organic compounds and dry weight, as described previously
The average oxygen consumption rate during mid-exponential growth (OD600 0.2–1) was used.
The previously developed genome-scale metabolic model of
The robustness analysis presented in
Elementary flux modes were calculated using Metatool 4.9
Here,
Model capacity constraints. This file contains amino acid uptake rates and corresponding flux constraints used in the model, and more details on model results.
(0.24 MB DOC)
Model details. This file contains the abbreviations, reactions and the gene-protein-reaction associations of
(0.28 MB XLS)
The phosphoketolase cycle. This file contains more information on the phosphoketolase cycle that was discovered in the network of
(1.60 MB DOC)
Elementary Flux Mode analysis. This file contains the Metatool input file used for elementary flux mode analysis, and the resulting EFMs.
(0.66 MB DOC)
The authors wish to thank anonymous referees, Matthias Heinemann, and Stefan Schuster for valuable help in improving the manuscript.