Escherichia coli and Pseudomonas putida grown in different media and with phenotype predictions of gene knocked-out Escherichia coli mutants. Our neural-mechanistic models systematically outperform constraint-based models and require training set sizes orders of magnitude smaller than classical machine learning methods. Our hybrid approach opens a doorway to enhancing constraint-based modeling: instead of constraining mechanistic models with additional experimental measurements, our hybrid models grasp the power of machine learning while fulfilling mechanistic constrains, thus saving time and resources in typical systems biology or biological engineering projects.Constraint-based metabolic models have been used for decades to predict the phenotype of microorganisms in different environments. However, quantitative predictions are limited unless labor-intensive measurements of media uptake fluxes are performed. We show how hybrid neural-mechanistic models can serve as an architecture for machine learning providing a way to improve phenotype predictions. We illustrate our hybrid models with growth rate predictions of  Mechanistic models estimate the phenotype of microorganisms in different environments but may have limited predictive capabilities. Here, authors develop trainable hybrid models with improved predictability using mechanistic insights and smaller training sets than conventional machine learning techniques. In this study, we present an approach that combines machine learning (ML) and mechanistic modeling (MM) to improve the performance of constraint-based modeling (CBM) on genome-scale metabolic models (GEMs). Our hybrid MM-ML models are applied to common tasks in systems biology and metabolic engineering, such as predicting qualitative and quantitative phenotypes of organisms grown in various media or subjected to gene knock-outs (KOs). Our approach leverages recent advances in ML, MM, and their integration, which we briefly review next.1, which in the last CASP14 competition predicted structures with a precision similar to structures determined experimentally. Following this foot step, one may wonder if in the future we will be able to use ML to accurately model whole-cell behaviors. The curse of dimensionality2, i.e. the fact that fitting many parameters may require prohibitively large data sets, is perhaps the biggest hurdle that prevents using ML to build cell models. Obviously, cells are far more complex than single proteins and since the amount of data needed for ML training grows exponentially with the dimensionality2, as of today, ML methods have not been used alone to model cellular dynamics at a genome scale.The increasing amounts of data available for biological research bring the challenge of data integration with ML to accelerate the discovery process. The most compelling achievement within this grand challenge is protein folding, recently cracked by AlphaFold3 for one of the latest models). These models encompass metabolism, signal transduction, as well as gene and RNA regulation and expression. Cellular dynamics being tremendously complex, MM methods are generally based on strong assumptions and oversimplifications. Ultimately, they suffer from a lack of capacities to make predictions beyond the assumptions and the data used to build them.For the past decades, MM methods have been developed to simulate whole-cell dynamics  and possibly secondary objectives . As we shall see later and as discussed in O’Brien et al.5, FBA suffers from making accurate quantitative phenotype predictions.Flux balance analysis (FBA) is the main MM approach to study the relationship between nutrient uptake and the metabolic phenotype  of a given organism, e.g., 6 where ML is used after FBA as a post-process to classify enzyme essentiality. Similarly, Schinn et al.7 used ML as a post-process to predict amino acid concentrations. Freischem et al.8 computed a mass flow graph running FBA on the E. coli model iML15159 and used it with a training set of measured growth rates on E. coli gene KO mutants. Several ML methods were then utilized in a post-process to classify genes as essential vs. non-essential. As reviewed by Sahu et al.10, ML has also been used to preprocess data and extract features prior to running FBA. For instance, data obtained from several omics methods can be fed to FBA, after processing multi-omics data via ML13.The MM and ML approaches are based on two seemingly opposed paradigms. While the former is aimed at understanding biological phenomena with physical and biochemical details, it has difficulties handling complex systems; the latter can accurately predict the outcomes of complex biological processes even without an understanding of the underlying mechanisms, but require large training sets. The pros of one are the cons of the other, suggesting the approaches should be coupled. In particular, MMs may be used to tackle the dimensionality curse of ML methods. For instance, one can use MMs to extend experimental datasets with in silico data, increasing the training set sizes for ML. However, with that strategy, if the model is inaccurate, ML will be trained on erroneous data. One can also embed MMs within the ML process, in this strategy, named hybrid-modeling, ML and MM are trained together and the model parameters can be estimated through training, increasing the model predictive capacities. To improve FBA phenotype predictions, ML approaches have been used to couple experimental data with FBA. Among published approaches, one can cite Plaimas et al.10, the interplay between FBA and ML still shows a gap: some approaches use ML results as input for FBA, others use FBA results as input for ML, but none of them embed FBA into ML, as we do in this study with the artificial metabolic network (AMN) hybrid models.In all these previous studies, and as discussed in Sahu et al.14, Biologically-Informed Neural Networks15) with recent solutions based on recurrent neural networks (RNNs)16. Hybrid models have also been developed in physics to solve partial differential equations, such as Physics Informed Neural Network17 (PINN), available in open-source repositories like SciML.ai18. The goal of these emerging hybrid modeling solutions is to generate models that comply well with observations or experimental results via ML, but that also use mechanistic insights from MM. The advantages of hybrid models are two-fold: they can be used to parametrize MM methods through direct training and therefore increasing MM predictability, and they enable ML methods to overcome the dimensionality curse by being trained on smaller datasets because of the constraints brought by MM.The main issue with hybrid modeling is the difficulty of making MM amenable to training. Overcoming this difficulty, solutions have recently been proposed under different names in biology for signaling pathways and gene-regulatory networks . Our approach bridges the gap between ML and FBA by computing steady-state metabolic phenotypes with different methods that can be embedded with ML. All these methods rely on custom loss functions surrogating the FBA constraints. By doing so, our AMNs are mechanistic models, determined by the stoichiometry and other FBA constraints, and also ML models, as they are used as a learning architecture.5. Indeed, realistic and condition-dependent bounds on medium uptake fluxes are critical for growth rate and other fluxes computations, but there is no simple conversion from extracellular concentrations, i.e., the controlled experimental setting, to such bounds on uptake fluxes. With AMNs, a neural pre-processing layer aims to capture, effectively, all effects of transporter kinetics and resource allocation in a particular experimental setting, predicting the adequate input for a metabolic model to give the most accurate steady-state phenotype prediction possible. Consequently, AMNs provide a new paradigm for phenotype prediction: instead of relying on a constrained optimization principle performed for each condition , we use a learning procedure on a set of example flux distributions that attempts to generalize the best model for accurately predicting the metabolic phenotype of an organism in different conditions. As shown in the results section, the AMN pre-processing layer can also capture metabolic enzyme regulation and in particular predict the effect of gene KOs on phenotype.We showcase our AMNs with a critical limitation of classical FBA that impede quantitative phenotype predictions, the conversion of medium composition to medium uptake fluxesVin, to simulate environmental conditions for the GEM of an organism  that replace the Simplex solver while producing the same results Fig. . The thrV0, for the flux distribution to limit the number of iterations of the mechanistic layer. The initial flux distribution is computed from medium uptake flux bounds, Vin, when the training set has been generated through FBA simulations, or medium compositions, Cmed, for experimental training sets. For all AMNs, the training of the neural layer is based on the error computation between the predicted fluxes, Vout, and the reference fluxes, as well as on the respect of mechanistic constraints. It is important to point out that AMNs attempt to learn a relationship between Vin (or Cmed) and the steady-state metabolic phenotype, generalizing this relationship for a set of conditions and not just only one as in FBA. In the upcoming subsections, Fig. We next used the MM models as a component of AMN hybrid models that can directly learn from sets of flux distributions Fig. . These fVin after training. Indeed, once the AMN has been trained on adequate FBA-simulated data, we can fix its parameters, resulting in a gradient backpropagation compatible reservoir that mimics FBA. The AMN reservoir can then be used to tackle the above-mentioned issue of unknown uptake fluxes: adding a pre-processing neural layer and training this layer with an experimental dataset, one can predict uptake fluxes from the media composition. Results of the pre-processing neural layer can directly be plugged into a classical FBA solver and the neural layer can be reused by any FBA user to improve the predictive power of metabolic models with an adequate experimental set-up. We showcase AMN-Reservoir results in Fig. E. coli and P. putida.Finally, we developed a non-trainable AMN-Reservoir to showcase how the predictive power of classical FBA can be improved Fig. . This arLet us first recall that the methods described in this subsection are mechanistic models (MMs) that replace the Simplex-solver used in FBA and allow for gradient backpropagation, but without any learning procedure performed. As far as medium uptake fluxes are concerned, we consider in the following two cases: (1) when exact bound values (EB) for medium uptake fluxes are provided, and (2) when only upper bound values (UB) for medium uptake fluxes are given.16, recursively computes M, the vector of metabolite production fluxes, and V, the vector of all reaction fluxes (cf. “Wt-solver” in “Methods” and in Supplementary Information for further details). The vectors M and V are iteratively updated using matrices derived from the metabolic network stoichiometric matrix S and from a weight matrix, Wr, representing consensual flux branching ratios found in example flux distributions . Since the mass conservation law is the central rule when satisfying metabolic networks constraints, these ratios play a key role in the determination of the metabolic phenotype, i.e. the paths taken by metabolites in the organism. In this approach, we assume that the flux branching ratios remain similar between flux distributions with different bounds on different uptake fluxes. A simple toy model network is shown to demonstrate the functioning of the Wt-solver in Supplementary Fig. Our first method (Wt-solver), inspired by previous work on signaling networksWhile the Wt-solver is simple to implement it suffers from a drawback. As discussed in Supplementary Information “AMN-Wt architecture”, a consensus set of weights leads to a solution when upper bounds (UB) for uptake fluxes are provided, but not when exact bounds (EB) for uptake fluxes are given  or upper bounds (UBs) for uptake fluxes (Vin). That method makes use of Hopfield-like networks, which is a long-standing field of research21 inspired by the pioneering work of Hopfield and Tank22. As with the Wt-solver, the LP-solver iteratively computes fluxes to come closer to the steady-state solution (Vout). However, calculations are more sophisticated, and the method integrates the same objective function (e.g. maximize growth rate) as the classical FBA Simplex solver. The solver iteratively updates the flux vector, V, and the vector, U, representing the dual problem variables also named metabolites shadow prices23 (cf. “LP-solver” in “Methods” and in Supplementary Information for further details).The second method (LP-solver), derived from a method proposed by Yang et al.24. With PINNs, solutions are first approximated with a neural network and then refined to fulfill the constraints imposed by the differential equations and the boundary conditions. Refining the solutions necessitates the computation of three loss functions. The first is related to the observed data, the second to the boundary conditions and the third to the differential equations. As detailed in “Methods”, we similarly compute losses for simulated or measured reference fluxes, Vref, the flux boundary constraints, and the metabolic network stoichiometry. As in PINN we next compute the gradient on these losses to refine the solution vector V. Unlike with the LP-solver, we do not provide an objective to maximize in the present case, but instead reference fluxes, consequently the method is named QP because it is equivalent to solving an FBA problem with a quadratic program.The third approach (QP-solver), is loosely inspired by the work on physics-informed neural networks (PINNs), which has been developed to solve partial differential equations matching a small set of observationsE. coli core model25 taken from the BiGG database26. To generate with Cobrapy package19 a training set of 100 growth rates varying 20 uptake fluxes, following the procedure given in “Methods”. Results can be found in Supplementary Fig. To assess the validity of the LP and QP solver, we used the V0) from bounds on uptake fluxes (Vin) or media compositions (Cmed). This solution enables the training of all AMNs with few iterations in the mechanistic layer. In the remainder of the paper, we name AMN-Wt, AMN-LP and AMN-QP, the hybrid model shown in Fig. While the above solvers perform well, their main weakness is the number of iterations needed to reach satisfactory performances. Since our goal is to integrate such methods in a learning architecture, this drawback has to be tackled. As illustrated in Fig. E. coli metabolic models, E. coli core25 and iML15159. These models are composed respectively of 154 reactions and 72 metabolites, and 3682 reactions and 1877 metabolites . In all cases, the training sets were generated by running the default Simplex-based solver (GLPK) of Cobrapy19 to optimize 1000 growth rates for as many different media. Each medium was composed of metabolites found in minimal media (M9) and different sets of additional metabolites  taken up by the cell (more details in Methods “Generation of training sets with FBA”). These training sets have as variables a vector of bounds on uptake fluxes  along with the Cobrapy19 computed growth rate. For the ANN training set, to enable loss computation on constraints, we replaced the growth rate by the whole flux distribution computed by Cobrapy19 (cf. Methods “ANN architecture”).The performances of all AMN architectures  and a classical ANN architecture  are given in Fig. Q²) for the growth rates of the aforementioned models. All results shown are computed on 5-fold cross-validation sets. Additional information on hyperparameters and results on independent test sets are found in the Supplementary Information. In particular, Supplementary Fig. E. coli core model with different neural layer architectures and hyperparameters, justifying our choices for the neural layers of AMNs (one hidden layer of dimension 500 and a training rate of 10−3). Similar results were found for AMN-LP and AMN-Wt. Additionally, in Supplementary Table Figure E. coli core25 and iML15159. It is interesting to observe the good performances of AMN-Wt when UB training sets are provided. Indeed, while counterexamples can be found for which AMN-Wt will not work with EB training sets , thus the number of training data points is substantially larger than for AMNs . Despite requiring larger training sets, ANNs also need more learning epochs than AMNs to reach satisfying constraint losses and growth rate predictions for E. coli core . We determined which compositions to test by choosing all the 1-carbon source media compositions and randomly picking one hundred of the 2-, 3- and 4-carbon sources media compositions . The growth of E. coli was monitored in 96-well plates, by measuring the optical density at 600 nm (OD600) over 24 h. The raw OD600 was then passed to a maximal growth rate determination method based on a linear regression performed on log(OD600) data (more details in Methods “Growth rate determination”).To train AMNs on an experimental dataset, we grew Cmed, and growth rates, Vref, was used to train all AMN architectures . These architectures are those shown in Fig. Cmed as input. In all cases the mechanistic layer was derived from the stoichiometric matrix of the iML151520E. coli reduced model . Following Fig. Cmed was entered as a binary vector (presence/absence of specific metabolites in the medium), the vector was then transformed through the neural layer into an initial vector, V0, for all reaction fluxes (therefore including the medium uptake fluxes) prior to be used in the mechanistic layer and the loss computations. Prediction performances are provided in Fig. The resulting experimental dataset of media compositions, For displaying meaningful results and to avoid any overfitting bias, we show in Fig. Cmed  reach a regression performance of 0.71 ± 0.01 with the same dataset and cross-validation scheme, indicating AMNs can outperform regular machine learning algorithms.As a matter of comparison, a decision tree algorithm predicting only the growth rate from Q² values could be interpreted differently if taking this variability into account. To study this further, we estimated the best possible Q² that can be reached at a given experimental variability. Precisely, for each experimental data point, we randomly drew a new point from a normal distribution with a mean and variance equal to what was experimentally determined for the original point. This point can be considered as an experimental randomized point. After doing this for all points and computing the Q², repeating this process 1000 times, we obtain a mean Q² = 0.91 with a standard deviation of 0.02. Consequently, the best possible Q² accounting for experimental variability is 0.91, and the performance of Q² = 0.77 (or 0.78) must be interpreted considering that value. Furthermore, substituting each point by a box defined by standard deviations of both measurement and prediction, we find that 79% for AMN-QP (76% for AMN-LP and 74% for AMN-Wt) of the boxes intersect the identity line indicating that these points are correctly predicted within the variances.As one can observe in Fig. 28 a dataset of 17,400 growth rates for 145 E. coli mutants. Each mutant had a KO of a single metabolic gene and was grown in 120 media with a different set of substrates. Our AMNs training set, were therefore composed of medium composition and reaction KOs, both encoded as binary vectors, alongside the measured growth rates. More details can be found in Methods “External training sets acquisition”. Results are presented in Fig. RKO). Importantly, we also added a term to the custom loss in order to respect the reaction KOs (cf. Methods “Derivation of loss functions” for more details).Our results show that AMNs can learn on FBA-simulated training sets and make accurate predictions while respecting the mechanistic loss, as shown in Fig. Q² = 0.81  yields a regression performance of 0.75, with the same cross-validation scheme and dataset.The AMN regression performance in Fig. .81 Fig. . For comE. coli, iML15159, an accuracy >90% was found for a dataset of growth assays based on media compositions (classification task predicting growth vs. no growth). Consequently, we also show in Fig. 30, we threshold the growth rate measures  to binary values . With classifications, one can compute ROC curves, and these are shown in Fig. The performance of classical FBA is poor, as no correlation can be found between measured and calculated growth rate Fig. . Such pe31. With this dataset, composed of 31 fluxes measured for 64 single regulator gene KO mutants of E. coli grown in 2 media compositions, our AMN reaches a variance averaged Q² value of 0.91 in 10-fold cross-validation.Overall, the results presented in Fig. E. coli nutrients, as well as their relation to external nutrient concentrations, remain largely unknown: the uptake flux for each compound may vary between growth media. In classical FBA calculations, this is usually ignored and the same upper bound  is used in all cases. Our results for KO mutants suggest that this strongly reduced regression performance of classical FBA, while in classification the effect is less severe. Nonetheless, for regression or classification the problem remains: how can realistic uptake fluxes be found?As already mentioned in the introduction section, the uptake fluxes of 32, we call this architecture “AMN-Reservoir”  by random weights.In the following, we show a way to find these uptake flux values and improve the performances of classical FBA solvers (for both regression and classification). Once an AMN has been trained on a large dataset of FBA-simulated data, we can fix its parameters and exploit it in subsequent further learning in order to find uptake flux values that can be used in a classical FBA framework. Loosely inspired by reservoir computingr” Figs.  and 5a. E. coli growth rates, and the second is a growth assay of P. putida grown in 296 different conditions33 . The procedure used for the two datasets is the same. First, the AMN-Reservoir is trained on FBA simulations. For E. coli we used as an AMN-Reservoir the AMN-QP of Supplementary Table P. putida we used the AMN-QP of Supplementary Table 33 UB dataset. Second, as shown in Fig. E. coli growth rates and a classification task for P. putida growth assays (growth vs. no-growth). After training on media compositions and measured growth rates (for both E. coli and P. putida), we extract the corresponding uptake fluxes (Vin). These uptake fluxes are then taken as input for a classical FBA solver for growth rate calculation, as shown in Fig. We benchmarked our AMN-Reservoir approach with two datasets. The first one is the one used in Fig. E. coli dataset  to 0.97 (panel c) and we raised the accuracy on P. putida growth assays from 0.81 (panel f) to 0.96 (panel e). We note that these uptake fluxes were found for the training set of the AMN-Reservoir, but we also show the performance of FBA with uptake fluxes found for cross-validation sets  enabling gradient backpropagation within metabolic networks. The models exhibited excellent performance on FBA generated training sets Fig. . We alsoies Fig. .In classical FBA, all biological regulation mechanisms behind a flux distribution are ignored and flux computation relies entirely on bounds set on uptake or internal fluxes. Therefore, when performing classical FBA, one needs to set uptake bounds individually for each condition to reliably predict metabolic phenotypes. AMNs attempt to capture the overall effects of regulation via the neural layer while keeping the mechanistic layer for the metabolic phenotype. Indeed, as shown in Fig. E. coli growth rates and P. putida growth assays). Figure For improved adaptability, we also trained AMN-Reservoirs on large FBA-simulated training sets and used these to improve FBA computations on two experimental datasets  gives uptake fluxes for the metabolites used in our benchmarking work with ida Fig. , and the9. However, these experiments are limited in number, and biomass coefficients are usually determined only once, for a single experimental setup, and are hardly extrapolated to all possible conditions. Some studies already underline this issue and attempt to efficiently integrate experimental data in the biomass reaction parametrization40. With AMNs, a trainable layer containing the biomass coefficients could be added, adapting the biomass reaction to any experimental setup. Another possible application of AMN is to enhance GEMs reconstruction based on quantitative prediction performance. Indeed, the method we developed for KOs could be adapted to screen putative reactions in a metabolic model so that its predictions match experimental data. This task should be performed after a manual curation, of course, to rely on existing literature knowledge and databases.Making FBA suitable for machine learning as we have done in this study opens the door to improve GEMs. For instance, in addition to estimating uptake fluxes, AMNs could be used to estimate the coefficients of the biomass reaction based on measurements. So far, these coefficients are derived based on literature, but also using experimental data: growth rate, fluxes, and macromolecular fractions measures can help finding optimal coefficientsE. coli core25 show that at least 500,000 labeled data (reference fluxes) are needed in the training sets to reach losses below 0.01  with performances slightly under those of AMN. However, with these algorithms, nothing is learned regarding the mechanistic constraints and results produced by these methods cannot be fed back to classical FBA, as we do in Fig. Returning to the curse of dimensionality issue mentioned in the introduction, we systematically studied at which training set sizes ‘black-box’ ML methods would yield performances similar to our AMN hybrid models. To that end, we trained a simple dense ANN model on training sets of increasing sizes. Results obtained with 41, and AMNs could be used to build a similar device in vivo by adding a trainable layer after the mechanistic layer whose purpose would be to select metabolite production fluxes that best split positive from negative samples.Beyond improving constraint-based mechanistic models and black-box ML models, AMNs can also be exploited for industrial applications. Indeed, since arbitrary objective functions can be designed and AMNs can be directly trained on experimental measurements, AMNs can be used to optimize media for the bioproduction of compounds of interest or to find optimal gene deletion and insertion strategies in typical metabolic engineering projects. In this latter case, reactions would be turned off via a trainable layer, which would be added prior to the mechanistic layers of our AMNs. Another potential application is the engineering of microorganism-based decision-making devices for the multiplexed detection of metabolic biomarkers or environmental pollutants. Here, AMNs could be used to search for internal metabolite production fluxes enabling one to differentiate positive samples containing biomarkers or pollutants from negative ones. Such a device has already been engineered in cell-free systems19 and screens for all two-sided reactions, then duplicating them into two separate reactions; and writes a new version of the model with bi-directional reactions split into separate forward and backward reactions. To avoid confusion, we add a suffix to these reaction names, either “for” or “rev” respectively designating the original forward reaction and the reversed reaction. The uptake reactions were also duplicated, even if encoded as one-sided, and their suffix was set to “i” for inflow reactions (adding matter to the cell), and “o” for outflow reactions (removing matter from the system).The set-up of our AMNs requires all reactions to be unidirectional; that is, the solutions must show positive-only fluxes . To split reactions of a given metabolic network into separate forward and reverse reactions, we wrote a standardization script that loads an SBML model into Cobrapy9 model is large, comprising 3682 reactions and 1877 metabolites. A substantial number of reactions in this model have zero fluxes for many different media, and it is unnecessary to keep these reactions during the training process. Prior to training, we therefore generated a reduced model by removing reactions having zero flux values along with the metabolites no longer contributing to any reactions. Using that procedure, we were able to reduce iML15159 model to only 550 reactions and 1083 metabolites.As detailed in the next subsection, our unidirectional models are used to build flux data training sets. The duplicated iML151519, with different models of different sizes. Throughout this paper, when “reference FBA-simulated data” is mentioned, it refers to data computed with this method.Our reference flux data were obtained from FBA simulations, using the GNU Linear Programming Kit  on Cobrapy26. The models were used to generate data using Cobrapy19 following a precise set of rules. First, we identified essential uptake reactions for the models we used (E. coli core25 and iML15159) which we defined in the following way: if one of these reactions has its flux upper bound set to 0 mmol gDW−1 h−1, the biomass reaction optimization is impossible, even if all other uptake fluxes bounds are set to a high value, e.g., 1000 mmol gDW−1 h−1. In other words, we identified the minimal uptake fluxes enabling growth according to the models. For E. coli core25 we found seven of such obligate reactions . For iML151520 we had the same 7 obligate reactions and additional salt and ions uptake reactions . With iML15159, we also added as obligate reactions the uptake of four amino acids  in order to be consistent with our experimental training set where the four amino acids were systematically added to M9 . During reference FBA-simulated data generation, the upper bounds on these obligate reactions were set to 10 mmol gDW−1 h−1.Reference FBA-simulated data for metabolic flux distributions were generated using models downloaded from the BiGG databaseE. coli core model25 we added 13 variable uptake reactions . For each generated medium, a set of variable uptake reactions was selected, drawn with a binomial distribution B with n = 13 and p = 0.5, p being a tunable parameter related to the ratio of selected reaction. Consequently, the mean number of selected variable uptake reactions was n × p = 6.5. Next for each selected reaction, the upper bound continuous value of the reaction flux was randomly drawn from a uniform distribution between 2 and 10 mmol gDW−1 h−1. For the iML15159 model, to limit the combinatorial search space, the selected variable uptake reactions were those of the experimental training set and consequently between 1 and 4 variable uptake reaction were added . The upper bound values for each selected variable reaction were chosen randomly between 0 and 2.2 mmol gDW−1 h−1 (0 excluded). The 2.2 threshold was chosen to produce predicted growth rates that were in the range of those observed experimentally. For the P. putida iJN146333 model, we used the same approach with variable uptake reactions selected from the experimental training set, and consequently 1 variable uptake reaction was added to obligate reactions  for each element of the training set. The upper bound values for each selected variable reaction were chosen randomly between 0 and 10 mmol gDW−1 h−1 (0 excluded).To generate different media compositions, we added to the obligate reactions a set of variable uptake reactions. For the E. coli core25, iML15159 and iJN146333 we ran FBA in Cobrapy19 for each medium and recorded all steady-state fluxes including the growth rate (flux of the biomass reaction). These fluxes were used as a training set for all models presented in Fig. 19 to generate the training set. For EB training sets, the variable uptake flux values were those calculated by Cobrapy19 at steady state.After generating the set of growth media for Loss functions are necessary to assess the performances of all MM solvers and all AMN architectures  and also to compute the gradients of the QP solvers. In the following and subsequent subsections, all vectors and matrices notations are defined when they are first used and can also be found in Supplementary Table n reactions and m metabolites. Let S the m × n stoichiometric matrix of the model. We assume some metabolites can be imported in the model through a corresponding uptake reaction. Let Vin be the vector of nin upper bounds  for these uptake reactions, and let nin × n projection matrix such that Vref be the vector of reference flux data (FBA-simulated or measured). With Pref the nref × n projection matrix for measured fluxes. V is calculated by solving the following quadratic program (QP):To compute loss, we consider a metabolic model with V, of Eq. (L1 is the loss on the fit to the reference data. L2 ensures the respect of the network stoichiometric constraint (S V = 0). L3 ensures the respect of the constraints on input fluxes that depend on medium composition (L4 ensures the respect of the flux positivity (V ≥ 0). The losses are normalized, respectively by nref for the fit to reference data, m for the stoichiometric constraint, nin for the boundary constraints, and n for the flux positivity constraints.For each solution, , of Eq. , four loL is:Summing the four terms, the loss More details about each loss term can be found in the Supplementary Information “QP-solver equations”.L5, for ensuring a null value for fluxes that have their reaction KO:RKO is a vector of length nKO describing which reactions are KO, and PKO the projection matrix mapping the whole flux vector V to KO fluxes.When reaction KOs are added to the input of AMNs  for vector V can be arbitrary as long as the uptake medium bounds are respected. Vectors V and M are iteratively computed until convergence using the following equations:Wr is a consensus weight matrix representing flux branching ratios, S is the stoichiometric matrix, sj,i the stoichiometric coefficient of row j and column i, zi the number of strictly negative elements in column i of S, and ⊙ the Hadamard product operation. Additional details on the procedure and the associated matrices are provided in Supplementary Information section “Wt-solver equations”.The Wt-solver describes a metabolic state by two vectors 20 where the authors used gradient descent on both primal and dual variables of the problem.The LP method aims at solving linear constrained problem similar to the ones solved by FBA. It relies on the results from Yang et al.Sint is the stoichiometric matrix with uptake fluxes zeroed out (i.e. fluxes that add matter in the system). In other words, Sint is the internal stoichiometric matrix. Let us consider bFBA, a vector of dimension m with bi corresponding to uptake fluxes of medium metabolite mi  and cFBA, the objective vector of dimension n , the FBA problem can be written as:U being the dual variable of V:This problem can be written in its dual form with V and its dual U through gradient descent:t is the iteration number and dt the learning rate.As mentioned before, the problem given by Eq.  can be s20 as it has been proven to converge to global optimum independently from the initial values of V and U. Detailed expressions and derivations of gradients for U and V are provided in Supplementary Information “LP-solver equations” along with Figs. Note that initialization of LP with uptake fluxes is not mandatory with the method from Yang et al.V that minimizes the loss (L in Eq. (Vcan thus be found by solving V is computed iteratively with iteration number t and learning rate dt.The QP solver solves the quadratic program given by Eq. . While tL in Eq. ). The grs in Eq. , V is coDetailed expressions and derivations for the gradient Vin, and the output layer corresponds to the set of all fluxes Vout. In order to assess losses with the ANN architecture, which does not have any mechanistic layer, each entry of the training set contained all flux values . Consequently, the training process with ANN consists in fitting all predicted fluxes to reference flux data . To compare results with the other architectures, R² and Q² are computed for the growth rate, and constraint losses are computed using predictions for all fluxes, using the formulation given in the subsection Methods “Derivation of loss functions”.The ANN architecture is a “black box” dense neural network. As with the other architectures the input layer corresponds to the medium uptake fluxes, nin for medium uptake fluxes (Vin) and then transform it via a dense neural network the input vector into an initial vector of size n for all fluxes (V0), which is refined through an iterative procedure computing nin × n weight matrix transforming Vin to V0 is learned during training, and we name this transforming layer the neural layer. With AMN-LP/QP, n × m weight matrix (Wr). That weight matrix can be directly computed from training data when all fluxes are provided or can be learned during training, when only a fraction of fluxes are provided . In our implementation (cf. “Code availability” section) AMN-Wt is embedded in a RNN Keras cell42 and both matrices Wi and Wr are learned during training. ANN-Wt is further detailed in Supplementary Information “AMN-Wt architecture”.As shown Figs. V corresponding to Vin are not updated in the neural nor mechanistic layers when training with exact values for medium uptake (EB training sets).With all AMN architectures, the values of 1 in Eq.  for meaReference data parameters: reference data can either be FBA-simulated or experimental. For FBA-simulated data, we can tune the size of the training set to be generated. We can also modify the mean number of selected variable intake medium fluxes, and the number of levels (i.e. the resolution) of the fluxes. We can also modify the variable uptake reactions list, but this modifies the architecture of the model , so we kept the same list for each model in the present work. The lists can be found in the subsection “Generation of training sets with FBA”.Model hyperparameters: during learning on FBA-simulated or experimental data, ANN and AMN have a small set of parameters to tune: the number and size of hidden layers, the number of epochs, the batch size, the dropout ratio, the optimizer and learning rate, and the number of folds in cross-validation. These numbers are provided in Supplementary Table The parameters used when training ANNs and AMNs, there are two types:19 by simply searching for the maximum R² between experimental and FBA-predicted growth rates for scalers ranging between 1 and 10.The goal of this optimization was to find the best scaler for fluxes to best match experimentally determined growth rates, by using “out-of-the-box” FBA, simply informing the presence or absence of the flux according to the experimental medium composition. The optimal scaler used in Figs. −1 in our M9 preparations. The selected carbon sources enter different parts of the metabolic network: 6 sugars enter the upper glycolysis pathway, and 4 acids enter the lower glycolysis pathway or the TCA cycle. With a binary  approach when generating the combinations to test for making the experimental training set, we generated all possible combinations of 1, 2, 3 or 4 carbon sources simultaneously present in the medium. Naturally, we picked all 1-carbon source media combinations for experimental determination (only 10 points). Then, we randomly selected 100 more combinations to experimentally determine, by randomly picking 20 points from the 2-, 40 points from the 3- and 40 points from the 4-carbon source combinations sets. The python scripts to generate these combinations and pick the ones for making our experimental training set are available on our Github package43 (cf. “Codes availability” section). After picking the combinations to test, we experimentally determined the maximum specific growth rate of E. coli for each combination of carbon sources in M9 (cf. next two subsections). The mean over replicates for each media composition was computed as the corresponding growth rate value to make the final experimental training set (cf. Methods “Growth rate determination”).Ten carbon sources were picked for being the variables of our training sets: Ribose , Maltose , Melibiose , Trehalose , Fructose , Galactose , Acetate , Lactate , Succinate , Pyruvate . These could ensure observable growth as a sole carbon source with a concentration of 0.4 g lE. coli DH5-α (DH5a) was a M9 medium prepared with those final concentrations: 100 µM CaCl2 ; 2 mM MgSO4 ; 1X M9 salts: 3 g l−1 KH2PO4 , 8.5 g l−1 Na2HPO4 2H2O , 0.5 g l−1 NaCl , 1 g l−1 NH4Cl ; 1X trace elements: 15 mg l−1 Na2EDTA 2H20 , 4.5 mg l−1 ZnSO4 7H2O , 0.3 mg l−1 CoCl2 6H2O , 1 mg l−1 MnCl2 4H2O , 1 mg l−1 H3BO3 , 0.4 mg l−1 Na2MoO4 2H20 , 3 mg l−1 FeSO4 7H2O , 0.3 mg l−1 CuSO4 5H2O , solution adjusted at pH = 4 and stored at 4 °C; 1 mg l−1 Thiamine-HCl ; 0.04 g l−1 amino acid mix so that L-Alanine , L-Proline , L-Threonine , Glycine  were each at a final concentration of 5 mg l−1 in the medium. The additional carbon sources that could be added were individually set to a final concentration of 0.4 g l−1. The pH was adjusted at 7.4 prior to a 0.22 µm filter sterilization of the medium. Pre-cultures were recovered from glycerol −80 °C stocks, grew in Luria-Bertani (LB) broth overday for 7 h, then used as 5 µl inoculate in 200 µl M9 (supplemented with variable compounds) in 96 U-bottom wells plates overnight for 14 h. Then 5 µl of each well was passed to a replicate of the plate on the next day for growth monitoring. The temperature was set to 37 °C in a plate reader , with continuous orbital shaking at maximum speed, allowing aerobic growth for 24 h. A monitoring every 10 min of the optical density at 600 nm (OD600) was performed. A figure for summarizing the experimental workflow is available in Fig. The base medium for culturing 600) data in each window. We then retrieve the maximum specific growth rate as the maximum regression coefficient over all windows. If several growth phases are visible, one can omit a part of the growth curve for the maximal growth rate determination . Eight replicates for each medium composition were performed (on a single column of a 96-well plate). Outliers were manually removed after visual inspection of the growth curves or clear statistical deviation of the computed growth rate from the remaining replicates. The numbers of replicates kept range from 2 to 8, with an average of 4.6 (±1.6) replicates per medium composition. Means and standard deviations over replicates were computed to be used for training AMNs and making figures. All raw data and the code to process it are available in the Github repository43 (cf. “Code availability”).The maximal growth rate was determined by sliding a window of 1 h-size, performing a linear regression on the log grown in 120 conditions (each with a different set of substrates) from Biolog phenotype microarrays44. The final training set can be found in the source data, provided as a Source Data file (cf. “Data availability”).The dataset was downloaded from the ASAP database (Mutant Biolog Data I for K-12 mutant strains)RKO in Fig. For practical reasons, we converted the information about metabolic gene KOs information into binary vectors describing which reactions are directly affected by a gene KO, called −1 h−1 was found to be the best value in terms of regression performance) for each substrate in the dataset when it is present (otherwise 0). To simulate a KO, we set the lower and upper bound of a reaction to zero.For the FBA computation Fig. , we set 30, we applied a threshold of 0.165 h−1, which is equal to 5% of the maximum growth rate (3.3 h−1) found in the dataset. Therefore, the classification task can be seen as the ability for the model to classify growth rates below and above the threshold value.To transform the measured growth rates from continuous values into binary values  for P. putida’s GEM. This state-of-the-art GEM of P. putida KT2440 contains a few hundred more genes and reactions from the previous models, allowing better coverage. The dataset corresponds to growth assays with 188 carbon and 108 nitrogen sources. For each condition, we verified that an uptake reaction flux was present in the iJN146333 model. Fifty-five conditions contained a nutrient source without a corresponding uptake reaction in the model. For all those conditions, the AMN input would be the minimal medium. In order to avoid biasing the training set with 55 identical conditions, we kept one condition describing the minimal medium for carbon sources and one condition describing the minimal medium for nitrogen sources. The 55 conditions were added back to compute the final score. The training set can be found in the source data, provided as a Source Data file (cf. “Data availability”).The dataset used to generate Fig. 33, reporting a set of uptake fluxes upper bounds. When testing a carbon (nitrogen) source, glucose (NH4) was removed from the minimal medium, and the respective nutrient source metabolite was added. Using these simulated growth media, accuracies on growth predictions using Cobrapy . For more details on the statistics and reproducibility of these external training sets, please refer to the original studies.Further information on research design is available in the Supplementary InformationPeer review fileReporting SummarySource data


Introduction: Genome-scale metabolic models (GEMs) are organism-specific knowledge bases which can be used to unravel pathogenicity or improve production of specific metabolites in biotechnology applications. However, the validity of predictions for bacterial proliferation in in vitro settings is hardly investigated.Methods: The present work combines in silico and in vitro approaches to create and curate strain-specific genome-scale metabolic models of Corynebacterium striatum.Results: We introduce five newly created strain-specific genome-scale metabolic models (GEMs) of high quality, satisfying all contemporary standards and requirements. All these models have been benchmarked using the community standard test suite Metabolic Model Testing (MEMOTE) and were validated by laboratory experiments. For the curation of those models, the software infrastructure refineGEMs was developed to work on these models in parallel and to comply with the quality standards for GEMs. The model predictions were confirmed by experimental data and a new comparison metric based on the doubling time was developed to quantify bacterial growth.Discussion: Future modeling projects can rely on the proposed software, which is independent of specific environmental conditions. The validation approach based on the growth rate calculation is now accessible and closely aligned with biological questions. The curated models are freely available via BioModels and a GitHub repository and can be used. The open-source software refineGEMs is available from https://github.com/draeger-lab/refinegems. Human life and substantial cultural achievements depend on prokaryotes. While a minority of bacterial species cause invasive diseases, humans could not exist without beneficial microbes colonizing the gut and the body surfaces. Additionally, the metabolic capacities of microbes flavor and preserve our food, detoxify the environment, or allow the production of antibiotics to treat infections. Without the ability to identify and grow microbes under defined conditions within laboratory surroundings, many modern comforts would be unthinkable. Remarkably, we are only beginning to appreciate the enormous diversity of bacterial life, and even with state-of-the-art techniques to grow bacteria, the vast majority remains uncultivated .As a huge metabolic capacity is slumbering within these “unculturable” bacteria, efforts for their cultivation should be intensified . ComputeAmong other benefits, GEMs permit predicting an appropriate media composition that should allow proliferation for any organism. However, up to date, this potential seems hardly exploited as it needs combined efforts of bioinformaticians to make predictions and of microbiologists to test the same systematically. Most published models lack sufficient experimental validation, or the designators of the components contained in the models only allow preliminary conclusions to be drawn about tangible cell components. These shortcomings reduce the validity or interpretability of the predicted results. Only if modelers and experimenters work closely together can they check predictions made by the model and, if necessary, change the structure of the model or the experimental setup to gradually arrive at a meaningful representation of reality in the model that yields reliable results .de novo created GEMs to predict in vitro growth characteristics of Corynebacterium striatum. At the time of writing, no genome-scale systems biology models are available that characterize this species. C. striatum is a Gram-positive, non-sporulating rod discovered in the early 20th century. It was considered a commensal within the healthy human skin microbiota for a long time . Thus, four additional strains with BacDrive sequence information were obtained from DSMZ  and PATRIC were used to search for complete genome sequences of rom DSMZ . All seqrom DSMZ .C. striatum exists in the Virtual Metabolic Human (VMH) database. The VMH offers GEMs of organisms interesting for human microbiomes. Most models within the VMH database are used as a basis to build simulatable microbiomes. Additionally, all VMH GEMs use specific entity IDs of which some overlap with biochemically, genomically, and genetically structured . It assumes that the goal of any organism is to increase its biomass toward cell division. The returned objective value was then interpreted as growth rate in mmol Growth rates from simulations with COBRApy are given in mmol 600 nm (OD600) was measured at t = 0 h and at t = 24 h. Fold changes were calculated by dividing OD600 (t = 24 h) by OD600 (t = 0 h).All media compositions are available in the Corynebacterium glutamicum minimal medium version 12 (CGXII), For each of the four strains, one colony grown on Tryptic Soy Agar (TSA) Blood plates was inoculated in 10 mL of TSB. Precultures were incubated overnight at 37°C and 150 rpm and diluted to an OD of 0.05 in TSB, Brain-Heart-Infusion Broth (BHI), Roswell Park Memorial Institute cell culture medium 1640 (RPMI), Lysogeny Broth (LB), M9 minimal medium (M9), and ® file and were then read using pandas , OD0 is the OD at time 0, d refers to the displacement along the x-axis. Multiple columns with OD values are possible. Coming from the plate reader, technical replicates were averaged before fitting. The wells representing the blank were also averaged and subtracted from the averaged technical replicates.Growth data were extracted from the plate reader in a Microsoft Excelg pandas . The logoptimize . This uscurve_fit was always initialized with p0 = np.asarray, the function is defined in Python asFor the logistic fit, def logistic :return K/(1+((K-y0)/y0)*np.exp(-r*t))During the tests on different media, the models were continuously monitored, and simulations were run to obtain missing metabolites that might help to recover growth on the minimal media of interest. We noticed that the models had no exchange reactions for sodium which was changed to reflect the ability of sodium uptake of the respective organisms.C. striatum is currently available. However, within the gut microbiota resource of the VMH database ], we used three more strains, namely, FDAARGOS_1197 (1197), FDAARGOS_1115 (1115) and FDAARGOS_1116 (1116), whose genome sequences have been completely assembled. In addition to these four strains, we also investigated the strain KC-Na-01 (KC), which is well characterized by the KEGG database, but unlike the other four strains, it is not available from the DSMZ. For this reason, for strain KC, we exclusively performed an in silico analysis.We decided to work with multiple strains to get a comprehensive picture of the strain-specific properties of The strain-specific models were named following the guidelines given by The models created in this study are composed of 1,053–1,382 metabolites, 1,541–2,002 reactions, and 719–772 genes. This is within the usual range of bacterial GEM . FigureReactions can be classified into different types using the SBO terms. SBO analysis showed that all four models follow a similar reaction type distribution , suggestThe metabolic reconstructions were used for a detailed comparison of the five strains. This showed an overlap of 47 % for all metabolites and an overlap of 35 % for all reactions across all models . With 16in vitro data for the microorganism of interest is available. However, the accuracy of GEMs in predicting in vitro characteristics is frequently unclear. Therefore, we decided to compare model predictions to in vitro growth characteristics under various nutritional conditions.GEMs can be used to predict growth characteristics of bacterial species under defined nutritional conditions . This cain vitro unclear. As defined media, we used RPMI  or even in continuous culture systems where a constant refreshment of medium with an inflow of metabolites can be used. It is well known that varying growth conditions impact the achieved cell densities and growth rates significantly. However, the influence such conditions have on, e.g., gas exchange rates, are difficult to reflect within GEMs.We, therefore, decided to test the accuracy of the model to predict the growth characteristics of the strains under two distinct growth conditions .1. Growth in high volume flasks for determination of binary phenotypes. Higher volumes of media (10 mL in 50 mL flasks) were inoculated to an optical density of 0.2, and the optical density was assessed after 0 and 24 h to determine binary growth phenotypes (growth vs. no growth). Binary phenotypes are used to assess the accuracy of a GEM where a simulation can be run, e.g., on different carbon sources that can then be tested in the laboratory.in vitro experiments. We used a volume of 150 µL per medium in a 96-well plate and automated the assessment of OD600 over time to determine growth kinetics. From the growth curves captured via a plate reader the doubling time at the inflection point of the sigmoidal curve can be extracted and compared to those predicted by the GEM.2. Microtiter format to assess growth kinetics. Besides binary phenotypes, the prediction of metabolites or additional nutrients that increase/decrease growth rates is of high relevance for the planning of d-ribonucleotide (nmn). A putative nmn transporter is predicted by the GEM, supporting the existence of an auxotrophy to this compound. In contrast, transporters for the precursors of nmn (nicotinate or nicotinamide) were not predicted. This caused the GEM to predict a specific need for nmn which was not available in the in silico formulation of LB. Interestingly, all strains were able to grow in LB in in vitro experiments  than strains 1115 and 1116 (45.92 min⋅generation−1 and 40.38 min⋅generation−1 respectively)  . These d2+, Cu2+, Fe2+, Mn2+ and Zn2+) for all strains while 1116 lacked additionally nmn as observed before. However, all strains grew, effectively in flasks in vitro . Investigating this phenomenon showed a lack of the trace elements  to 100 min  or nmn and pantothenic acid (strain 1116). The addition of the respective nutrients in silico allowed simulated proliferation for all strains  which is known to have growth stimulatory effects on Corynebacteria  was poor for all strains  and SBO term annotation refinement via its integrated SBOannotator . Other imain.py script and the corresponding config.yml file, which is available on GitHub b) it can be installed via pip and the functions can be accessed individually Comprehensive documentation is available online, which is accessible via GitHub. The scope of the different modules of refineGEMs is outlined in RefineGEMs can be used in two different ways: a) as a standalone script using the Corynebacterium striatum. Only strains whose genome has been entirely sequenced and available in the German Collection of Microorganisms and Cell Cultures (DSMZ) were selected as strains to be studied. In doing so, this work comprises three principal objectives: First, developing a unified infrastructure for creating systems biology models was and making it publicly available. Second, using this infrastructure to create GEMs for selected strains of the bacterium C. striatum and to make them freely accessible. Finally, experimentally verifying and using these strain-specific GEMs for their further refinement based on generated predictions of bacterial growth in the presence of defined nutritional environments.This study aimed at building strain-specific genome-scale metabolic models (GEMs) for The GEMs’ prediction of bacterial growth have enormous potential for laboratory-based microbiology as it might help to quickly adjust culture conditions to optimize growth rates and growth yields, to optimize fermentation processes or even to enable growth of so far not-culturable bacteria. However, while GEMs are nowadays created for many different species and even for multiple strains of the same species, their ability to correctly predict biological phenotypes is hardly investigated.C. striatum strains and used them to make predictions about proliferation of the strains under defined nutritional conditions. These predictions were then compared to biological data sets gained in the laboratory. All models are available for download from the BioModels database.In a typical scenario, published computer models are initially developed as a theoretical foundation and only checked against previously published data, if available . In othein vitro growth while GEMs predicted a growth failure. This phenomenon can have two different underlying reasons. Firstly, it is possible that certain nutrients are present in vitro that were not included in in silico formulation of the nutritional composition. This highlights that the in silico assembly of the nutritional composition of laboratory media needs to be approached deliberately. Trace metals are important to mention in this regard. These nutrients are hardly mentioned on ingredient lists of commercial media . Similarly, not all trace metals are purposely added to defined media  produced in laboratories around the world. However, the amount needed is extremely low and physiologically relevant concentrations are available in most media as long as special action for their removal  is avoided. Accordingly, media formulations used with GEMs should reflect that trace metals are most likely not limiting factors in experimental setups.Our experiments identified several pitfalls reducing accuracy of model prediction. We found several examples of “false negative” predictions, referring to in silico composition of media to increase the accuracy of growth prediction.Furthermore, for complex media ingredients such as yeast, tryptic soy or meat extracts that are frequently used in microbiological practice, the precise composition of these extracts are unknown. However, they contain excess of amino acids, vitamins, ribonucleotides, etc. which should be included in the Secondly, false negative predictions can also be caused by inappropriate transport activities within GEMs. One example in this regard is nicotinic acid transport. The GEM of strain 1116 predicts nmn to be a crucial metabolite for this strain. Supplementation of the medium with the precursors nicotinic acid or nicotinamide is regarded as insufficient as specific transporters for their import are not predicted within the genome. In contrast to this prediction, we found the strain to proliferate in the presence of nicotinamide (growth in RPMI) as well as in the presence of nicotinic acid (M9 medium), strongly suggesting that both intermediates can be acquired by the bacterium and enable the synthesis of nmn. However, additional experimental evidence is needed to validate this hypothesis and the responsible transport systems remain to be identified.in vitro. These inconsistencies are more problematic, as they reduce the usefulness of GEMs for laboratory-based experiments. Unfortunately, the reasons for this are less clear and the issues are more difficult to address. However, one reason might be that GEMs are based on genetic information while information about expression of the respective metabolic pathways is missing. Although genes for biosynthesis of aminoacids or vitamins might be present within a strain of interest, a failure to express the same might entail physiological auxotrophies. This phenomenon is known for the amino acids Leucin and Valin for Staphylococcus aureus (C. striatum in CGXII and M9 media.We also observed “false positive” predictions, referring to GEMs predicting growth, while proliferation is not observed s aureus . Along tin silico assumptions are frequently not directly transferable to in vitro conditions. GEMs assume homogeneously mixed cells under isothermal and isobaric conditions whose compartments maintain constant volumes. Molecular concentrations are assumed abundant enough to be effectively continuous. In addition, for simplicity, some physicochemical factors, such as osmotic pressure or electroneutrality, are not considered. The modeled cells would also remain steady, resulting in constant molecular concentrations. These assumptions are by far not met in vitro which can also account for discrepancies between model experimental results. Taken together, GEMs have high potential to support experimental microbiologists. However, close interactions and repetitive cycles of prediction experimental validation and model refinements are needed to improve accuracy of the predictions.Additionally, in vitro growth of Corynebacteria. It is currently impossible to incorporate such findings into GEMs.Inclusion of experimental observations into GEMs represents another task for the future. Exemplarily, it is known that addition of Tween 80 improves C. striatum models were performed by standardized Python scripts in a directory structure based on version control and made available, the modeling process can be traced in detail. Thus, a software infrastructure comprehensively tested on several genuine and relevant case studies is available, which can be applied to further reconstruction projects.Since all individual steps for reconstructing these five strain-specific The tools and models created in this work through close collaboration between the dry and wet laboratories provide a valuable working basis for subsequent studies. The software infrastructure developed and the models created have been extensively tested and validated using standard methods.C. striatum strains described herein in order to provide even more accurate and thus more meaningful predictions.However, since no computer model, no matter how carefully developed, can ever exhaustively represent all processes of a cell type under investigation, subsequent work will be necessary to elucidate further the metabolism of all five Concerning the underlying model assumptions, extensions for gene expression would also be beneficial. Modeling approaches are already available as ME models [for Metabolism and Expression ]. On theFurther developments on the experimental side would also be beneficial: since the predictive power improves the more precisely the media composition is known, the substance concentrations of their components should be clarified more precisely for model development using human microbiota. Due to biovariability, only average values can be expected, but knowledge of the standard deviation across subjects also allows conclusions to be drawn and enables computer experiments under variation with higher accuracy.Since no biological system can live in isolation, the interaction with other members of the microbiota remains an essential aspect for subsequent research to understand the diverse interactions with commensals, other pathogens, and the human host in a larger picture. Basic approaches in this direction are already available, with which the models developed here can also be combined .The models, Python programs, and Git-based version management working template presented with this work can be directly applied and used for subsequent projects immediately and can be independently further developed. Thus, an infrastructure extensively tested on several relevant reconstruction efforts is available and can be applied to any GEM.


Chlamydomonas reinhardtii, a model eukaryotic microalga accessible to metabolic engineering, is 17-fold smaller compared to the heterotrophic cell factory Saccharomyces cerevisiae. Here we generate quantitative protein abundance data of Chlamydomonas covering 2337 to 3708 proteins in various growth conditions to estimate in vivo maximum apparent turnover numbers. Using constrained-based modeling we provide proxies for in vivo turnover numbers of 568 reactions, representing a 10-fold increase over the in vitro data for Chlamydomonas. Integration of the in vivo estimates instead of in vitro values in a metabolic model of Chlamydomonas improved the accuracy of enzyme usage predictions. Our results help in extending the knowledge on uncharacterized enzymes and improve biotechnological applications of Chlamydomonas.Metabolic engineering of microalgae offers a promising solution for sustainable biofuel production, and rational design of engineering strategies can be improved by employing metabolic models that integrate enzyme turnover numbers. However, the coverage of turnover numbers for  Closing a major gap in photosynthetic metabolic modelling, the authors provide over 500 estimates of in vivo enzyme catalytic rate in C. reinhardtii, which considerably improves predictions on how enzyme mass is allocated to different pathways. However, the economic feasibility of photosynthetic bioreactors requires further optimization of desired biotechnological objectives4, including the production of lipids6, pigments7, or hydrogen8. Our ability to rationally engineer metabolism for biotechnological applications scales with our understanding of the metabolism of organisms used as cell factories. Genome-scale metabolic models (GEMs), as mathematical representations of knowledge about metabolism, along with constraint-based modeling, have facilitated the design of metabolic engineering strategies9. Moreover, enzyme-related constraints that rely on turnover numbers (kcat) have been shown to accurately predict various phenotypes, including overflow metabolism12, even without the usage of measurements of uptake fluxes12. Further, these protein-constrained GEMs (pcGEMs) have been used to successfully identify engineering targets for biotechnological applications, such as increased production of lysine13 or of high-value compounds15 in Escherichia coli as well as the increase of the heme protein yield in Saccharomyces cerevisiae by 70-fold16.Microalgae can synthesize a wide range of high-value compoundskcat data used in most pcGEM studies are obtained by laborious purification of the enzyme of interest and quantifying its maximum catalytic efficiency in an in vitro experiment12. For organisms with available quantitative proteomic and physiological data, it is also possible to estimate the maximal apparent catalytic rate 18 to obtain estimates of each intracellular flux and find their ratio to the abundance of the corresponding enzymes; this results in condition-specific kapp values which are subsequently compared over the investigated experimental conditions to identify the largest. The latter is then used as the maximal in vivo catalytic rate for the enzymatic reaction, kcat in metabolic models that explicitly describe protein biosynthesis has also been employed as a strategy for parameter estimation20.The kcat and E. coli show high concordance17, for eukaryotic organisms like S. cerevisiae18 and Arabidopsis thaliana21 lower correlation values between kcat and 22 and SABIO-RK23. While these databases offer comprehensive kinetic data for E. coli, only 10% of the entries in the union of the two databases cover enzymes of the Viridiplantae taxon. Further, the databases contain a total of only 85 turnover numbers (0.0012% of entries) specific to green algae. Thus, to render the powerful pcGEM modeling framework applicable with organisms from this biotechnologically relevant taxon, we must substantially increase the knowledge of organism- and taxon-specific turnover numbers.While it has been shown that 25 to acquire a comprehensive set of protein abundance values from cultures of Chlamydomonas reinhardtii wild type and mutant strains grown under various conditions. We used this data set together with the recently developed minimization of non-idle enzyme (NIDLE) approach26 to estimate 21, extending the available literature data on C. reinhardtii by ~ 10-fold. In total, we obtained kcat and kcat values in pcGEMs of C. reinhardtii with Here we used cutting-edge mass spectrometry techniquesC. reinhardtii, we generated a comprehensive, high-quality proteomics data set, encompassing 27 samples from various strains and growth conditions sampled at steady state. The absolute protein abundance data were generated based on the QConCATapproach25. QConCAT employs an isotopically labeled artificial protein containing concatenated peptides of multiple endogenous proteins as external standard to allow for absolute quantification of protein abundance. Using the concatamer to obtain a calibration curve we were able to obtain absolute protein quantification for up to 3708 (median: 3376) proteins  annotated in the S. cerevisiae model28. The large number of enzymes present in C. reinhardtii leads to a lower relative coverage, although we quantified the abundance of 11% more enzymes in comparison to what has been attained in S. cerevisiae.To obtain mentclass2pt{minimi27 Fig. . In totaC. reinhardtii’s metabolic states.We observed a smaller number of quantified proteins in the UVM4 strains compared to CC1690 Fig. . HoweverC. reinhardtii. To calculate apparent catalytic rates on a genome scale we used the NIDLE approach that minimizes the number of idle enzymes , representing the principle of effective usage of cellular resources26. NIDLE does not rely on maximizing growth as a cellular objective, but rather includes constrains from measured specific growth rates. It is formulated as a mixed-integer linear program (MILP) and does not enforce any proportionality between the measured enzyme abundance and reaction flux. The condition-specific flux distributions obtained by this MILP formulation are then used together with the absolute protein quantification to calculate the apparent catalytic rates, following established approaches26.Our main aim is to make use of the proteomics data to extend the sparse knowledge of enzyme kinetic properties in kapp values using a linear or quadratic formulation (see Methods). Based on this extension we were able to determine enzyme kinetic data for 18 and 41 reactions with multiple expressed isozymes based on the linear and quadratic formulations, respectively  in at least one of the experimental conditions  of 2 s−1 but the distribution is skewed with a maximum of 1011.2 s−1)  Fig. . This fiC. reinhardtii available at BRENDA22 and SABIORK23 about tenfold. Further, for 448 of the reactions with assigned The set of ism Fig. , thus exion Fig. . Aside fS. cerevisiae18 and A. thaliana21 found that in vitro determined turnover numbers provide a rather poor proxy of in vivo turnover number estimates. Thus, we were interested to identify if curated literature kcat values for C. reinhardtii correspond to the determined in vivo 30 to assign the phylogenetically closest available kcat values from BRENDA22 to reactions  of −1.4; Supplementary Fig. p-value > 0.05); however, “Cofactor and Modification” and “Lipid” metabolic systems terms showed larger interquartile ranges then the other terms Fig. . The scaons Fig. . Moreoveons Fig. . This inkcat values from literature. While we observed ~4-fold higher Spearman correlation with the kcat values for the endogenous C. reinhardtii enzymes  deemed the comparison interesting for scenarios in which pcGEMs of photosynthetic eukaryotes without available chemostat growth data are built, preventing the application of the GECKO correction procedure unavailable, and (ii) aimed to disentangle the effect of GECKO correction from the effect of 30, we found that the raw GECKO models of C. reinhardtii with and without usage of kcat correction step and refitting σ. For heterotrophic conditions, σ was fitted to ~0.4 of the value in autotrophic in mixotrophic conditions  Fig. . The RMSC. reinhardtii. Here we made use of this resource to considerably expand the information for green algae. Due to the extended NIDLE formulation we were able to estimate 568 (24% of enzymatic reactions) E. coli17 and S. cerevisiae18, respectively. To our knowledge, we present here the data set with the highest 13 in the biotechnologically relevant taxon of green algae. The next step to further improve the accuracy of estimated parameters is to integrate metabolic flux measurements from isotopic labeling of the investigated culture conditions. This methodical milestone has not yet been achieved in eukaryotes, where in vivo kcat estimation studies relied solely on constrained based modeling21. However, the feasibility of such a study has been proven in E. coli19. Recent methodical improvements in C. reinhardtii metabolic flux analysis34 put this promising combination of experimental data in reach. Future interdisciplinary efforts to improve our understanding of photosynthetic metabolism in green algae and their descendants will focus on achieving this milestone.We presented a protein abundance data set with extensive coverage of the proteome response to various perturbations. This data set comprises a valuable resource for systems biology studies in ons Fig.  indicateC. reinhardtii data sets included data from previously published QConCAT studies available under PRIDE35 data set identifier PXD018833  [https://www.ebi.ac.uk/pride/archive/projects/PXD018833] and were further augmented by data sets measured as part of this study and made publicly available under the PRIDE identifier PXD037599 [https://www.ebi.ac.uk/pride/archive/projects/PXD037599]. As control cultivation conditions for C. reinhardtii CC1690 cells, cultures were grown for 48 h in tris-acetate-phosphate (TAP) medium using a rotatory shaker operating at 2 turns per second, while being constantly illuminated at 100 µmol photons m−2 s−1 at and held at 24 °C. Data sets differing from control conditions were created by alteration of listed growth parameters , incorporating BamHI/HindIII restriction sites for subsequent cloning steps. The synthesized PS-Qprot coding sequence was cloned into the pET-21b expression vector (Novagen) using the BamHI and HindIII restriction sites. M9 minimal medium was prepared with 9.2 mM 15NH4Cl  and 100 µg ml−1 ampicillin. The transformed E. coli ER2566 cells harboring pET-21b-PS-Qprot were inoculated into the 15N-labeled M9 minimal medium. The culture was incubated under appropriate conditions to allow protein expression and 15 N incorporation. After sonication, supernatant was applied to a Co-NTA column (G-Biosciences) for purification based on the His-tag present on the PS-Qprot protein. The column was washed three times with Urea Buffer  containing 5 mM, 25 mM, and 100 mM imidazole, respectively. The eluted protein was concentrated and dialyzed into phosphate buffered saline. The concentration of the PS-Qprot protein was determined spectroscopically at 280 nm using a NanoDrop spectrophotometer. The concentration was calculated based on the Lambert-Beer’s law, assuming a molecular weight of 39,945.63 g/mol for PS-Qprot and an extinction coefficient of 86,860 M−1 cm−125. The extinction coefficient values were determined using the ExPASy ProtParam tool.The coding sequence for the PS-Qprot protein was codon-optimized for 25. Quantitative analysis of MS/MS measurements was performed using ProteomIQon 0.0.736. Peptide searches were performed upon the assembly of a peptide database based of the Chlamydomonas proteome based on version JGI5.5 of the C. reinhardtii genome blended with the sequences of spiked-in QconCAT proteins. The search space included methionine oxidation and acetylation of protein N termini as variable modifications and was extended by 15N-labeled variants of Chlamydomonas proteins. False discovery rate thresholds for peptide spectrum matches and protein group identifications were set to 1%. Following peptide spectrum matching, ion abundances were estimated by integration of the areas of extracted-ion chromatograms.After cell harvesting and protein extraction, all samples were spiked with a master mix of Chlamydomonas-specific QConCAT proteins and digested tryptically. Peptides were separated using a reversed phase chromatography system consisting of a trapping column  and an analytical column . The separation was performed at a flow rate of 4 µl/min. The chromatographic separation was achieved by employing a gradient elution method with HPLC buffer A  and HPLC buffer B . The gradient profile ranged from 2% to 35% of buffer B over the course of the separation. Measurement was performed via LC–MS/MS 15N-labeled peptides originating from spiked-in QConCAT proteins allowed to estimate absolute protein abundances for a multitude of different C. reinhardtii proteins25, as previously described38. With these high-quality QconCAT-based abundance measurements at hand, we were able to create calibration curves by regressing the latter on the preliminary protein abundance estimators, and thus to compute proteome-wide absolute abundance estimates.To obtain absolute protein abundances, we first aggregated ion species to the modified peptide level by summation . Differently modified versions of the peptides were aggregated to the peptide and then protein-group level by median-based aggregation, yielding preliminary protein abundance estimates. Computing the ratio between native, unlabeled peptides and A data set entry is considered to have ambiguous entries if its quantification is based on a peptide that is non proteotypic ; otherwise, the protein is defined to have an unambiguous entry. For ambiguous entries, an iterative approach was used to remove them in each sample. If an unambiguous entry of one of the mapped proteins was present, the corresponding concentration was subtracted from all ambiguous entries of this protein and the protein ID was removed from the ambiguous entries. If the cellular concentration of an ambiguous entry was smaller than 0 after subtracting, the entry was removed from the sample. This procedure was repeated until no further protein IDs could be removed from ambiguous entries. The remaining ambiguous entries were removed from the sample data. Proteins that were only quantified in one of the three biological replicates were removed from the data set. For the remaining data the median over the measured replicates was used in the downstream analyses.Chlamydomonas reinhardtii “iCre1355”27 was employed. The erroneous reaction formular of ‘CAT’ was updated to “2 h2o2[c] → 2 h2o[c] + o2[c]”. GPR rule syntax was updated to not include “… and (GENE1 or GENE2 …) …” rules. All model modifications and mathematical programs solved in this study was carried out using the COBRA toolbox39 and GUROBI solver40 in MATLAB41.The most recent SBML and COBRA compatible model of 27 with the respective culture conditions used in the proteomics experiments. The NIDLE approach is formulated for positive, real valued flux variables; therefore, the models were converted to irreversible by splitting each reversible reaction into irreversible forward and backward reactions. All uptake reactions were constrained by the model supplied bounds except for acetate uptake. For mixotrophic conditions a linear regression model was fitted based on the mixotrophic chemostat culture measurements from Imam et al.27, in which acetate uptake rate was predicted based on growth rate. The model was fitted using the R lm function42 with default options, and the model predicted uptake rate increased by the standard error of prediction was used as an upper bound on the acetate uptake rate for the mixotrophic culture scenarios27. For the heterotrophic condition the maximum measured acetate uptake rate from the Imam et al. heterotrophic chemostat data was set as an upper bound , given in the followingIn the case that multiple isoenzymes have been measured by mass spectrometry we integrated information from different conditions to decompose the contribution of different isoenzymes to the observed flux. We took advantage of the fact that in the mixotrophic standard growth conditions best approximate the maximum apparent catalytic rate for the majority of enzymes , and the obtained chemostat experiments27 corresponding pcGEMs were created. Scripts were adapted according to the README instructions . For compatibility with the GECKO toolbox, the JGI gene ids in iCre135527 were converted to Uniprot ids and introduced duplicates where removed. The protein content used for biomass rescaling and limiting of the enzyme pool reaction was taken from the measurements of Boyle & Morgan44. For all pcGEM simulations the uptake rate bounds of the macronutrients ammonium, phosphate, and carbon dioxide where set to 1000f . Growth associated maintenance was not refitted. A corrected model based on the observed chemostat growth measurements in the model publication27 was created using GECKOs objective control coefficient heuristic to correct over constraining kcat values, and the sigma factor was fitted. The NIDLE pcGEMs were generated by substituting GECKO-assigned kcat values for each enzyme pseudometabolite in the augmented stochiometric matrix with the maximum of all NIDLE obtained The GECKO toolboxkapp values obtained from the tested condition. The same condition specific uptake flux constraints as in the NIDLE problems were used. Flux trough the biomass reaction was fixed to 0.99 of the observed growth rates and the flux through the “draw enzyme pool” reaction was minimized.The pcGEM fitted with chemostat data from “Mixotrophic_Rep3” and “Heterotrophic_Rep1” were used for the simulation of enzyme usage in the proteomics experiments of the respective growth scheme. In the NIDLE models used for enzyme usage comparison the substituted 22 and SABIO-RK23 databases (status 07/2022) and joint. For the reactions with EC-number annotation in iCre135527 the following matching criteria for enzymes with fully matching EC-number where tried in the given order:Chlamydomonas taxon & substrateChlamydomonas taxonViridiplantae taxon & substrateViridiplantae taxonTurnover numbers of non-mutated enzymes together with organism and EC-number information were downloaded as text files from BRENDAkcat values in the first criteria with non-zero number of matches was assigned as comparison kcat.The maximum of all −4 times the lowest estimated kapp value was added to all values prior to log10-transformation. kapp values were reaction-wise mean centered. The Euclidian distance between the kapp vectors was calculated using the R function dist from the stat package42. In case two compared vectors didn’t have a single pair of comparable entries due to NA values resulting from missing enzyme quantifications, the distance was set to 1050. Hierarchical agglomerative clustering using the single linkage approach was applied as implemented in the R stat package42.A pseudocount of 10Details on the statistical approaches used are given in the figure captions and methods section. Proteomics data were acquired in triplicates to assess reproducibility. For all other statistical tests sample size is given in the text or figure caption. No statistical method was used to predetermine sample size. Peptides that were only determined in one replicate were excluded from the analysis. The experiments were not randomized. The Investigators were not blinded to allocation during experiments and outcome assessment.Further information on research design is available in the Supplementary InformationPeer Review FileDescription of Additional Supplementary FilesSupplementary Data 1Supplementary Data 2Supplementary Data 3Supplementary Data 4Reporting SummarySource Data