Model-driven analysis of experimentally determined growth phenotypes for 465 yeast gene deletion mutants under 16 different conditions
- Evan S Snitkin1,
- Aimée M Dudley2,
- Daniel M Janse3,
- Kaisheen Wong^,
- George M Church4 and
- Daniel Segrè1, 5Email author
© Snitkin et al.; licensee BioMed Central Ltd. 2008
Received: 27 June 2008
Accepted: 22 September 2008
Published: 22 September 2008
Understanding the response of complex biochemical networks to genetic perturbations and environmental variability is a fundamental challenge in biology. Integration of high-throughput experimental assays and genome-scale computational methods is likely to produce insight otherwise unreachable, but specific examples of such integration have only begun to be explored.
In this study, we measured growth phenotypes of 465 Saccharomyces cerevisiae gene deletion mutants under 16 metabolically relevant conditions and integrated them with the corresponding flux balance model predictions. We first used discordance between experimental results and model predictions to guide a stage of experimental refinement, which resulted in a significant improvement in the quality of the experimental data. Next, we used discordance still present in the refined experimental data to assess the reliability of yeast metabolism models under different conditions. In addition to estimating predictive capacity based on growth phenotypes, we sought to explain these discordances by examining predicted flux distributions visualized through a new, freely available platform. This analysis led to insight into the glycerol utilization pathway and the potential effects of metabolic shortcuts on model results. Finally, we used model predictions and experimental data to discriminate between alternative raffinose catabolism routes.
Our study demonstrates how a new level of integration between high throughput measurements and flux balance model predictions can improve understanding of both experimental and computational results. The added value of a joint analysis is a more reliable platform for specific testing of biological hypotheses, such as the catabolic routes of different carbon sources.
Recent advances in both high-throughput experimental approaches and computational analysis techniques have provided opportunities to explore biological function at the system level. An area in which this research has flourished is the study of genome-scale metabolic networks. Genome-scale metabolic network stoichiometries, encompassing all known metabolic reactions for a given organism, have been published for a diverse set of organisms, ranging from Escherichia coli  to human . These network stoichiometries have been used to build quantitative models capable of producing biologically informative and experimentally testable predictions [3, 4]. In particular, constraint-based flux balance techniques have established a set of tools for the study of metabolic network behaviors using a steady state approximation and optimality criteria [5, 6].
Although flux balance predicted distributions represent rough approximations of the complex reality of cellular metabolism, numerous studies have demonstrated the ability of flux balance models to reproduce various types of experimental results [7, 8]. A type of experimental data that has been frequently used for model assessment is the measurement of growth phenotypes under different genetic and environmental backgrounds. The ability to determine growth phenotypes in a high-throughput manner, both experimentally [9, 10] and in flux balance models, has contributed to making model comparisons to single deletion mutant growth phenotypes a community standard in the assessment of new models [11–13].
The high predictive capacity of genome-scale models, as inferred from these assessments, has also stimulated their use in studies that address questions currently at the edge of experimental feasibility. These studies have typically taken advantage of the speed of flux balance model computations to make system-level observations that are experimentally challenging or unfeasible. They include the exploration of global patterns of epistasis [14–16], essentiality under combinatorially diverse environmental conditions , processes of adaptive or reductive evolution [4, 18], complex metabolic engineering optimization , and the study of microbial communities .
As models become increasingly reliable and useful as discovery tools parallel to experimental methods, new paradigms for the integration of experimental and computational analyses may be explored. It is particularly important to understand how such integration can be used to gain novel biological insight beyond that attainable from independent experimental and modeling studies. Recent integrated analyses have employed iterations of experiments and modeling to drive biological discovery [21–24].
Here, we use model predictions and high-throughput experimental data in a bidirectional and synergistic manner. Specifically, we compare yeast flux balance model predictions with a new compendium of single gene deletion phenotypes under 16 different conditions. Contrary to the usual direction of refinement (whereby models are refined based on experimental data), we start by using computational predictions to identify potential weaknesses in the experimental results. This model-based refinement leads to the identification of several mutant defects, increasing our confidence that discordances are the result of model deficiencies. Based on this refined data, we evaluate the predictive capacity of different modeling frameworks, using an array of statistical metrics, and describe the global features of a yeast metabolism growth phenotype map. In addition, by combining the growth phenotype maps with automated visualization of detailed flux predictions, we present a case study (glycerol utilization) that provides additional insight on the power and limitations of stoichiometric models. Finally, we show how an integrated data analysis approach allows us to discriminate between different hypotheses on the mechanism of raffinose utilization in yeast.
Results and discussion
Media conditions implemented in compendium of deletion phenotypes
Synthetic complete (SC) medium
SC, adenine drop out
SC, arginine drop out
SC, inosine drop out
SC, lysine drop out
SC, methionine drop out
SD minimal media
SC, amino acid drop out
Yeast peptone (YP), glucose is primary carbon source
YP, ethanol is primary carbon source
YP, galactose is primary carbon source
YP, glycerol is primary carbon source
YP, actetate is primary carbon source
YP, lactate is primary carbon source
YP, raffinose is primary carbon source
YPTE no glucose
YP with ergosterol and zymosterol, no glucose
YPTE no O2
YP, with ergosterol and zymosterol, anaerobic condition
Computational analyses of single gene deletion mutants were performed using the steady state approach of flux balance analysis (FBA) and its minimization of metabolic adjustment (MOMA) variant. In these approaches, mass conservation laws translate into linear constraints on reaction rates (fluxes). The additional constraints imposed by gene knockouts are implemented by setting the values of the corresponding fluxes to zero (see Materials and methods). Within the space of flux distributions compatible with such constraints one can identify biologically meaningful states (the flux balance predictions) by computing the optima with respect to an objective function hypothesized to mimic the result of evolutionary or physiological adaptation. FBA predictions of gene deletion effects are often obtained by maximizing biomass production ('growth')  whereas in MOMA the fluxes of the knockout are predicted to minimally deviate from their natural wild-type state  (see Materials and methods for more details). The search for alternative objective functions constitutes in itself an interesting and active area of research [30–32].
Summary of available yeast models
Number of genes
Number of reactions
Number of metabolites
Number of metabolites in biomass reaction that are not included in the biomass in both of the other two models
Refinement of experimental phenotype data
While most studies only use experimental data to refine models, we started by asking whether the model predictions could be used to improve the quality of experimentally determined phenotypes. Previous comparisons between flux balance predictions and experimental measurements of growth phenotypes for gene deletion strains have reported accuracies upwards of 90% [11, 13]. A similar fraction of correct predictions (94%) was obtained in the first comparison of our own experimental data and iFF708 model predictions. These numbers indicate a high predictive capacity of the models, supporting the possibility that computational estimates of phenotypes might serve as a good reference for critically analyzing experimental data. Minimization of experimental errors in this type of study is of great importance for several reasons. First, for the purpose of model refinement based on comparisons with experimental data, experimental inaccuracies could result in either the propagation of model errors or in erroneously fitting models to faulty experiments. Second, such experimental inaccuracies could lead to incorrect conclusions, when used as benchmarks for biological hypothesis testing. Finally, increased accuracy of the experimental data itself is critical in the generation of valid biological insight.
A clustered map of mutant phenotypes reveals diversity of metabolic behaviors
Flux balance models predict essentiality under diverse conditions
After utilizing the model results to refine the experimental phenotypes, we next took advantage of this refined data set to build a benchmark for assessing model performance across different conditions through multiple statistical metrics. In addition to assessing model predictions using the current compendium of deletion mutant data, we also included mutants that have no growth under YPD, so that we could gain a more complete picture of model performance. Specifically, genes required for growth under YPD were assumed to be required under all conditions. While this assumption is not universally valid, it is likely to be largely correct due to the fact that most nutrients provided under other conditions are also provided under YPD.
The tendency for the different models to vary in their relative performance when considering different metrics can largely be explained by considering their previously mentioned differences. For example, the observation that the iLL672 model predicts more essential genes than the other models is predominantly due to its altered biomass definition. Specifically, the fact that the biomass definition for the iLL672 model contains 12 additional metabolites dictates that genes in pathways leading to the production of those metabolites will be required for growth. Therefore, in the absence of an exogenous supply of a given biomass metabolite, the corresponding biosynthetic genes will be predicted as being essential. It should be noted that because the definition of biomass for a given model is independent of the condition, changes in the biomass definition will not improve the ability of the model to differentiate between the metabolic requirements under different conditions. For instance, ubiquinol, a cofactor required for respiratory function, is one of the 12 metabolites added to the biomass definition for the iLL672 model. As a consequence of this imposed requirement for ubiquinol, ubiquinol biosynthetic genes are correctly predicted to be essential in the presence of non-fermentable carbon sources, where respiratory function is required. On the other hand, in the presence of fermentable carbon sources these genes are incorrectly called essential, as respiratory function is no longer essential to growth (Figure S1 in Additional data file 1).
Model predictions of condition-specific essential genes
In addition to tabulating the number of condition-specific essential genes identified using the assumption of maximal mutant growth, we determined how many additional genes could be identified by implementing the alternative optimization criterion of MOMA . Rather than assuming that the flux distribution of a deletion mutant will necessarily be optimal for growth, MOMA is based on the hypothesis that the mutant flux distribution will be minimally distant from that of the wild type. This approach is motivated by the fact that one should not necessarily expect an organism to respond optimally to a gene deletion. Rather, in the absence of an evolved response to the sudden removal of a gene, one might hypothesize that the metabolic network will tend to stay close to the unperturbed steady state. The MOMA hypothesis has been supported by experimental studies in yeast, as well as other organisms, where the flux response to gene deletions was determined using C13 tracer experiments [40, 41]. These studies observed a local rerouting of metabolic fluxes around the reactions compromised by gene deletions in viable deletion mutants, consistent with the MOMA hypothesis of minimal flux redistribution. An important step in the implementation of MOMA is the selection of wild-type flux predictions, from which the distance is minimized. Ideally, one should use a wild-type solution constrained by experimental flux measurements [13, 29], but experimental flux measurements were not available for all the studied conditions. Therefore, we used the FBA predicted optimal solution, with a secondary optimization that minimizes the sum of the absolute values of the fluxes. This secondary optimization is necessary to select a specific set of fluxes among the alternative flux solutions equally optimal for growth. The biological relevance of this flux minimization criterion has been previously reported [42, 43].
Focusing on our condition specific essentiality predictions, we found that utilization of MOMA led to the correct identification of an additional six (average among three models) condition-specific essential genes, beyond the set identified using the assumption of optimality (Figure 6). Using a slightly more stringent definition for model agreement with experimental results (see Materials and methods), we found that, on average, 14 condition-specific essential genes are identified using MOMA with the different models, relative to FBA. Especially striking was the observation that under the condition when glycerol is provided as the primary carbon source, 9 and 10 additional essential genes were identified by MOMA in the iFF708 and iND750 models, respectively. Additional inspection revealed that these additional essential genes identified by MOMA under glycerol conditions all functioned in respiratory metabolism.
Automated visualization for detailed assessment of flux predictions
Assessment of the concordance between computationally and experimentally determined mutant growth phenotypes provides a coarse evaluation of a model's propensity to correctly reproduce metabolic function. To more rigorously establish that a metabolic model accurately depicts metabolic behavior under a particular condition, one must judge the accuracy of the predicted flux distribution underlying the predicted growth rate [29, 30]. Unfortunately, experimentally measured fluxes are only available for a few organisms, under a small number of conditions, making global model assessment in this manner incomplete. One can, however, employ a more qualitative assessment by simply verifying that the predicted fluxes match biological knowledge, as supported by other types of data. A major hurdle in making such a qualitative assessment is the difficulty of automatically visualizing metabolic fluxes in a way that would allow immediate biological insights. While static networks, as well as platform-specific or model-specific visualization methods, are widely available [44–48], a general platform for metabolic network visualization is still lacking. To address this problem, we developed a visualization pipeline, which holds the potential to evolve into a general purpose platform. Our metabolic flux representation pipeline uses the freely downloadable VisANT network visualization software . Specifically, we used VisANT to create a standard layout of the reactions of central energy metabolism that are present in the iFF708 and iLL672 models, and then loaded previously computed flux distributions for visual analysis (see Materials and methods for details on network visualization). As a supplement to this work we have provided an online tool that allows for interactive visualization of flux distributions predicted by the iLL672 model for all single deletion mutants .
Detailed evaluation of fluxes under glycerol growth condition gives insight into model behavior
We used our visualization framework to explore the underlying basis of some of the model predictions. Specifically, we examined in detail the fluxes predicted by the iFF708 model for mutants in the respiratory chain under glycerol conditions. As described previously, these mutants were incorrectly predicted to be able to grow under this condition using the FBA assumption of optimality, and correctly predicted as non-growers using MOMA. Examination of these mutants was especially interesting as it had the potential to provide insight into why yeast does not utilize the predicted optimal metabolic route when confronted with such gene deletions. Previous studies have indeed found that E. coli grows suboptimally in glycerol, and that the FBA-predicted optimum is achieved only upon several generations of in vitro evolution . The mutations underlying the improved glycerol growth phenotype caused major regulatory changes, likely detrimental to growth under more commonly encountered conditions, and therefore absent in the wild type [51, 52].
To elucidate the route by which FBA circumvents the apparent redox imbalance that should occur in the absence of respiratory function, we visualized the flux distribution predicted by FBA when complex III of the ETC was knocked out. As can be seen in Figure 7b, the flux entering the ETC has been diverted from complex III to another reaction, which is catalyzed by Ura1. Ura1 catalyzes a redox reaction that is the fourth step in pyrimidine biosynthesis . In the iFF708 model this reaction utilizes the ETC intermediate ubiquinone as an electron acceptor or donor depending on the direction in which the reaction proceeds. While it is common in other yeast species for the reaction catalyzed by the ortholog of Ura1 to utilize the ETC as an electron donor/acceptor, in S. cerevisiae the Ura1 enzyme is cytosolic, and uses fumurate as an electron acceptor [54, 55]. Therefore, we conclude that the redox imbalance is averted in the FBA solution through the utilization of a reaction that is misrepresented in the model. This conclusion was further confirmed by the observation that when the Ura1 reaction is excluded from the model, FBA correctly predicted the inability of respiratory mutants to grow under glycerol conditions. This was a critical validation, as it excluded the possibility that there were alternative optimal flux solutions that did not use the Ura1 reaction .
The finding that a subset of the predictions discordant between FBA and MOMA were in this case due to an inaccurate model reaction, and not a biologically meaningful difference between MOMA and FBA, illustrates the value of verifying model-based conclusions at the level of fluxes. Analysis of predicted fluxes revealed that the discordant predictions were attributable to the propensity of FBA, and not MOMA, to drastically reroute fluxes so as to utilize the incorrect model reaction. While the growth maximization objective exploits the misrepresented flux, the minimal adjustment objective, lacking the foresight of how to rearrange fluxes optimally, identifies a solution that uses this flux minimally, and fails to produce some biomass components. Had we simply taken the differing phenotypic predictions between FBA and MOMA at face value, we might have reached the conclusion that their predictions differed due to the fact that S. cerevisiae does not exhibit optimal responses to gene deletions in the respiratory chain under glycerol conditions, possibly because glycerol is a non-preferred carbon source. This case illustrates the fact that a correct interpretation of model results may require a detailed examination of the flux predictions underlying the phenotypic predictions. While it is unreasonable to examine all flux predictions in such detail, our results suggest that there is value in validating major conclusions at this level.
Discriminating between alternative pathways for raffinose utilization
As the central difference between the two hypothetical pathways is the presence of an α-galactosidase enzyme, our analysis focused on determining whether available experimental data and models support the presence of this enzymatic activity. In order to clearly determine the contribution of model predictions to this analysis, we started by consulting genome-scale experimental data alone, independent of the models. We hence first asked whether the phenotypic data support the participation of the putative α-galactosidase, Ybr184w, in raffinose utilization. To this end we identified those genes that were experimentally determined to be essential only under the raffinose condition. This analysis revealed that the only gene uniquely essential under this condition is the β-fructosidase, Suc2. The fact that only SUC2 was identified as essential, and not YBR184W, is a first indication that Ybr184w does not participate in raffinose utilization in yeast.
To gain further insight into the role of SUC2 and YBR184W in raffinose metabolism, we looked at the expression of these two genes in the presence of a variety of carbon sources, utilizing a publicly available set of mRNA micorarray experiments . Examination of the expression pattern of SUC2 mRNA revealed that it has almost a two-fold increase in expression in the presence of raffinose, relative to the other carbon sources tested. In contrast, YBR184W mRNA does not show an increase in expression in the presence of raffinose, or any of the other carbon sources tested. The lack of an altered expression level or a growth defect for the ybr184w deletion mutant in the presence of raffinose suggests that YBR184W does not participate in raffinose utilization and is likely misannotated as an α-galactosidase.
Deletion phenotypes predicted differently under raffinose conditions by iLL672 builds with and without α-galactosidase activity
Experimental phenotype of deletion under YPRaff
Predicted phenotype of deletion mutant made by iLL672 build with α-galctosidase
Predicted phenotype of deletion mutant made by iLL672 build without α-galctosidase
Reason for incorrect prediction made by iLL672 build with α-galactosidase activity
Galactose is produced when α-galactosidic bond in raffinose is cleaved. Therefore, in build with α-galactosidase, Gal genes are required to metabolize galactose produced during raffinose catabolism
See explanation for Gal1
See explanation for Gal1
YBR184W is the putative α-galactosidase and is essential by definition of the model build
The galactose produced when the α-galactosidic bond is cleaved can be used as the primary carbon source, with the remaining sucrose unit being excreted
Pgi1 catalyzes the reversible conversion of glucose-6-phosphate to fructose-6-phosphate in glycolysis and gluconeogenesis. The pentose phosphate pathway can be used to bypass the deletion of this gene to maintain glycolytic function Without the α-galactosidase only the fructose unit of raffinose is usable, making Pgi1 essential for its role in gluconeogenesis
Evaluation of the two model builds based on their relative concordance with the phenotype data provided strong support for the build lacking an α-galactosidase, in agreement with previous reports [61, 62]. While in this instance standard biochemical assays could have been performed to differentiate between the two proposed routes for raffinose catabolism, this may not be true or easy in general. Therefore, genome-scale metabolic models and data can be thought of as broadly applicable tools, usable for hypothesis testing in conjunction with molecular biology tools.
While the cases examined above illustrate specific examples of how the combination of experimental and computational data can help gain biological insight, we expect that most discrepancies between the refined experimental data and model predictions could yield additional useful information and novel testable hypotheses. Guidelines on how to interpret the results of the comparison between experimental phenotype data and FBA and MOMA model predictions, along with potential strategies for validation, are presented in Table S7 in Additional data file 2. By applying these guidelines systematically to our data, we generated an easily accessible list of all inconsistencies unresolved between model and experiment, together with possible biological interpretations (Table S8 in Additional data file 2). Paired with the online interactive flux visualization tool described above, this list might be used 'on demand' to help understand specific pathways, or as the starting point for further systematic analyses, such as integration with other data sets.
By generating a yeast compendium of experimentally determined phenotypes for single gene deletion mutants of metabolic genes and predictions from stoichiometric models, we explored ways in which genome scale experimentation and modeling can be utilized synergistically. We found that utilizing the models to explore the experimental data proved useful in both experimental quality control and hypothesis testing. These analyses demonstrated that genome-scale models are not only useful in addressing questions beyond experimental tractability, but can function in parallel with experimentation to drive biological discovery. At the same time, our analysis of predicted intracellular fluxes was essential for drawing accurate conclusions in cases otherwise wrongly predicted based on phenotype comparisons, indicating that all outcomes of flux balance models should be critically analyzed for biological interpretation.
Genome-scale studies often aim to systematically extract biological information from model-data comparisons. As such systematic comparisons are increasingly common in different organisms, it is important to understand how experimental data imperfection, stoichiometric model choice and output interpretation can affect biological conclusions. We hope that our assessment of models and data, based on a new publicly available data set will provide a platform for more informed future systematic understanding. Moreover, increased awareness of the advantages and potential drawbacks of these approaches should help promote the fact that large-scale systems biology methods are not limited to providing high-level insights, but can also be used to expand our knowledge of specific biological pathways.
Materials and methods
Strains and media
We measured the growth phenotypes of the 465 homozygous diploid mutants (Table S1 in Additional data file 1) present in both the yeast FBA model  and the yeast deletion set . Each mutant contains a precise deletion of an open reading frame in the strain BY4743 (MATa/α his3Δ1/his3Δ1, leu2Δ0/leu2Δ0, ura3Δ0/ura3Δ0, met15Δ0/MET15, lys2Δ0/LYS2) . The growth of each homozygous deletion mutant was examined at 30°C under 16 conditions. Unless indicated, all media recipes are referenced in . Six rich (YP) media conditions were used to test carbon source utilization, including YPGly (3% glycerol), YPLac (2% lactate), YPEtOH (2% ethanol), YPOAc (2% potassium actetate), YPGal (2% galactose/1 mg/ml antimycin A), YPRaff (2% raffinose/1 mg/ml antimycin A). Anaerobic growth was measured using YPDTE (2% glucose/20 mg/ml ergosterol/0.5% Tween 80/0.5% ethanol) media  and the BBL GasPak Plus anaerobic system catalyst and indicator strips (Becton/Dickinson, Franklin Lakes, NJ, USA). We also tested YPTE (20 mg/ml ergosterol/0.5% Tween 80/0.5% ethanol) under aerobic conditions as an example of a poorly characterized condition that could be metabolically modeled. Six minimal media were used to measure various auxotrophies, including lysine (SC-Lys), adenine (SC-Ade), tryptophan (SC-Trp), inositol (SC-Ino), arginine (SC-Arg), and minimal medium supplemented with only the nutrients required by the parental strain (SD + histidine, leucine, and uracil) . YPD and SC complete media  were used as controls for the growth rate of each mutant under rich and minimal media conditions, respectively.
The 465 strains of interest were selected from the 4,710 strain homozygous diploid yeast deletion set (Open Biosystems, Huntsville, AL, USA) and re-arrayed into a 96-well format. Strains in 96-well format were grown to saturation in liquid YPD, transferred to agar plates containing each of the 16 media conditions by replica pinning, and grown at 30°C until the wild-type controls had reached a sufficient growth level. All conditions were performed in duplicate. Mutant growth under each condition was quantified using an automated system that uses image analysis software to quantify strain growth . Plates were digitally photographed using a GelDoc Station (Bio-Rad Laboratories, Hercules, CA, USA) with images saved as 8-bit TIFF images and converted to 16-bit TIFFs using Adobe Photoshop. Images were batch processed using the GenePix image analysis software (Molecular Devices, Sunnyvale, CA, USA), and data corresponding to the 96 spots per plate were saved as tab-delimited text files. General growth differences between plates or conditions were normalized by assuming that only a small subset of spots would deviate from wild-type growth and calculating the average diameter and intensity measurements of all spots on a plate. Spots differing from this average by empirically determined standard deviations (SD) were deemed slow-growers or non-growers. Spots scored as absent by the GenePix scoring algorithm or with a diameter of 40 pixels or less were scored as non-growers, spots with intensities less than 2.5 SD and diameters less than 1 SD or with intensities less than 1 SD and diameters less than 3 SD were scored as slow growers, all other values received a wild-type growth score. The relative growth of each strain under an experimental condition was then normalized by comparison to its growth on the control medium (YPD or SC), distinguishing condition-specific growth defects from general slow growth. For the purpose of comparison to the model predictions, growth rates were discretized into wild-type growth (2) slow growth (1), and no growth (0).
The variability and sensitivity of this method for determining mutant growth phenotypes have been evaluated in a prior study . To evaluate the variation and potential error in this specific data set, we performed two sets of analyses. First, we analyzed the variability between replicates. After filtering systematic errors due to the failure of the strain to grow on the YPD or SD control plate, less than 3% of the data points in the initial data set differed between replicates. Second, we compared our growth values to published results  for the same strains under the same conditions, but measured using a different experimental system, competitive growth assayed by microarray hybridization (Figure S2 in Additional data file 1).
Selection of mutants for experimental refinement
Mutants were selected for experimental refinement on the basis of disagreement of the experimental growth phenotype with the corresponding prediction made by the iFF708 model, under at least one of the 16 conditions. A prediction was deemed discordant if the difference between mean growth rate of the two duplicate growth measurements differed from either the MOMA or FBA predicted growth rate by more than a selected threshold (see below). A total of 87 mutants were flagged with this approach, of which 77 were retested with PCR and linkage analysis (see next section).
Confirming phenotypes by PCR and linkage
To confirm the presence of the correct gene deletion in the original strain screened, the homozygous diploid mutant was examined by PCR (Table S2 in Additional data file 1). To test whether the observed phenotypes were linked to the deleted gene, we developed a high-throughput genetic linkage strategy. Strains of interest were selected from the BY4741 (MATa his3Δ1, leu2Δ0, ura3Δ0, met15Δ0) haploid deletion set (Open Biosystems, Huntsville, AL, USA) and gridded in 96-well format. These strains were crossed to YAD641 (MATα can1Δ:: pMFA1-HIS3, his3Δ1, lys2Δ0, leu2Δ0) by replica plating the grid to a YAD641 lawn and allowing cells to mate overnight on YPD at 30°C. Diploids were selected by growth on SD +histidine +leucine +G418  for two days at 30°C, transferred to sporulation medium  by replica plating, and allowed to sporulate for 6 days at room temperature. Sporulated tetrads were then digested with 1 mg/ml zymolyase for 30 minutes at 37°C and deletion-containing MATa haploid progeny were selected by growth on SC -histidine -arginine +canavanine +G418 . For each strain, 10 single colonies were chosen and re-screened for all phenotypes of interest. Strains with colonies that showed differences in growth rates on any of the media were dismissed as having unlinked mutations present in the strains.
Flux balance analysis
FBA is a constraint-based approach for predicting steady state reaction rates (fluxes) in a metabolic network, and has been described in detail elsewhere . FBA relies on the hypothesis that, on average, the concentrations of all metabolites in an asynchronous population of cells can be considered constant in time. This implies that the net sum of the fluxes producing and consuming any intracellular metabolite is zero. The network of reactions is uniquely defined by a stoichiometric matrix S, whose element S ij represents the stoichiometry of metabolite i in reaction j, positive if a metabolite is produced, negative if it is consumed. Exchange reactions, representing the fluxes of metabolites in and out of the system, are incorporated into the S matrix. The steady state constraint is hence formally expressed as:
S·v = 0
where v is the vector of reaction fluxes. In addition to the steady state assumption, inequality constraints can be imposed to set upper and lower bounds on individual fluxes (α i ≤ v i ≤ β i ). As done before, we use these constraints to impose maintenance requirements and irreversibility of specific reactions, and to set limits on nutrient uptake rates. See Table S4 in Additional data file 2 for bounds used to implement each of the modeled conditions.
Previous work has shown that when working with genome scale metabolic models, the above linear program can have multiple solutions [29, 56]. In other words, for a given set of constraints, there can be several different sets of fluxes that result in an optimal value for v growth . For predicting growth rates using FBA the alternative optima are not a problem, but for establishing wild-type fluxes to use with MOMA and for analyzing specific fluxes underlying model predictions, it was important that we did not arbitrarily select among the multiple optimal solutions. To address this issue we performed a secondary optimization in which we selected, among all flux vectors that had the maximal value for v growth , the one that had the minimum sum of absolute values of fluxes. The motivation for this secondary optimization is that an organism may attempt to maximize growth with a minimum investment of resources. We utilized the commercial software Xpress (Dash Optimization, Englewood Cliffs, New Jersey, USA) to carry out all linear optimizations, as well as quadratic optimizations (see below).
In order to implement the deletion of a gene g, additional constraints are added, which set the flux through all reactions requiring the protein product of gene g to zero. Before comparing model predictions of mutant growth to the discretized experimental growth rates (see above), model growth rates were first normalized to be between 0 and 2. This allowed for a direct comparison of experimental growth rates and model predictions. If the difference between the mean experimental growth rate for two duplicates and the normalized model growth rate was less than or equal to one, then the model prediction was deemed correct. For comparison between FBA and MOMA, this threshold was lowered to 0.9, in order to identify more differences between the two optimization approaches.
Minimization of metabolic adjustment
Yeast models were retrieved either from authors' websites or supplementary materials [11, 13, 25, 68]. Subsequent to retrieving the models, some adjustments were made to each to allow for mimicking of the experimental media conditions (Table S5 in Additional data file 2). In particular, modifications were made to each model to allow for raffinose metabolism, as all models were lacking raffinose transporters. In addition, to mimic the experimental strains used in this study, the reactions encoded by His3, Leu2 and Ura3 were constrained to have zero flux.
Flux visualization using VisANT
VisANT is a Java-based, platform-independent tool for the visualization and analysis of biological networks and is freely available for download over the web at . VisANT provides a platform for analyzing diverse types of biological data through integration with many popular biological databases (for example, GenBank, SwissProt, and KEGG) and is capable of performing complex calculations of specific network properties. Metabolic networks were represented in VisANT as bipartite graphs, with the two classes of nodes being reactions and metabolites. Edges can either go into or come out of a reaction depending on whether the connected metabolite is a reactant or product, respectively. The weight and corresponding thickness of an edge between a metabolite and a reaction is representative of the normalized flux carried by the given reaction. All fluxes are normalized by the maximal flux in a given network, such that the maximum weight is unity.
In order to standardize the layouts of the network graphs, such that they more closely resembled traditional textbook representations of the corresponding biochemical pathways, we extracted the node coordinates from a template network. This was done by parsing the VisML file associated with the template network. VisML is an XML formatted representation that contains the necessary information to reconstruct a VisANT network. Once the node coordinates were extracted, different flux distributions could be overlaid on the same network map. As a supplement to this paper we have provided an online interface through which the flux predictions made by the iLL672 and iFF708 models, for all single deletion mutants, can be visualized in VisANT .
Additional data files
electron transport chain
flavin adenine dinucleotide
flux balance analysis
minimization of metabolic adjustment
AMD is supported by a Genome Scholar and Faculty Transition award (K22 HG002908) from the NIH/NHGRI. DS acknowledges support by the US Department of Energy, the National Institute of Health and the NASA Astrobiology Institute. The authors would also like to thank Zhenjun Hu for help with flux visualization in VisANT and Dan Fraenkel for comments on the manuscript. It is with sadness that we report the premature passing of our co-author Kaisheen Wong, who participated enthusiastically and productively in this project as a high school student.
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