Harnessing the optimization of enzyme catalytic rates in engineering of metabolic phenotypes

doi:10.21203/rs.3.rs-3915216/v1

Download PDF

Article

Harnessing the optimization of enzyme catalytic rates in engineering of metabolic phenotypes

https://doi.org/10.21203/rs.3.rs-3915216/v1

This work is licensed under a CC BY 4.0 License

Version 1

posted

You are reading this latest preprint version

The increasing availability of enzyme turnover number measurements from experiments and of turnover number predictions from deep learning models prompts the use of these enzyme parameters in precise metabolic engineering. Yet, there is no computational approach that allows the prediction of metabolic engineering strategies that rely on modification of turnover numbers. It is also unclear if modifications of turnover numbers without alterations in the host’s regulatory machinery suffice to increase the production of chemicals of interest. Here, we present a constraint-based modelling approach, overcoming kinetic obstacles (OKO), that uses enzyme-constrained metabolic models to predict in silico strategies to increase the production of a given chemical, while ensuring specified cell growth. We demonstrate that the application of OKO to enzyme-constrained metabolic models of Escherichia coli and Saccharomyces cerevisiae results in strategies that can at least double the production of over 40 compounds with little penalty to growth. Interestingly, we show that the overproduction of compounds of interest does not entail only an increase in the values of turnover numbers. Lastly, we demonstrate that a refinement of OKO, allowing also for manipulation of enzyme abundance, facilitates the usage of the available compendia of turnover numbers in the design of precise metabolic engineering strategies.

Biological sciences/Systems biology/Computer modelling

Biological sciences/Computational biology and bioinformatics

Microbial cell factories have emerged as a tractable and sustainable solution for production of important chemicals from renewable biomass [1]. Building such factories necessitates the design and implementation of systems-level metabolic engineering strategies that streamline, modify, and expand the biosynthetic capabilities of microbes serving as design chasses [2]. The in silico design of metabolic engineering strategies has been propelled by the developments of constraint-based modeling approaches that make use of genome-scale metabolic models [3–6]. These approaches have focused on in silico manipulation of fluxes, achieved in vivo by modifying the expression of genes and abundance of downstream proteins by using knock-out, knock-down, or over-expression techniques [7–13]. The production of chemicals by cell factories is, however, often impeded by insufficient catalytic activity of enzymes, resulting in negligible gains despite manipulations in protein abundance. Yet, rational manipulation of catalytic activity of enzymes has not yet been considered for in silico design of metabolic engineering strategies, despite recent advances in enzyme engineering strategies that can be readily employed to address this problem [14].

The turnover number, ${k}_{cat}$, of an enzyme denotes the maximum number of substrate molecules converted to product molecules per unit time per active site, and quantifies the enzyme catalytic activity. Recent advances in constraint-based modeling have resulted in approaches that: (i) generate enzyme-constrained genome-scale metabolic models (ecGEMs) [15, 16] by integrating turnover numbers from major repositories [17, 18] and deep learning predictions [19–21], (ii) combine fluxomics and proteomics data to estimate turnover numbers for several model organisms [22–28], and (iii) correct turnover number estimates to better match measured phenotypes [29, 30]. The essence of ecGEMs is that the rate of a metabolic reaction is bounded by the product of the turnover number and abundance of an enzyme catalyzing the reaction. These constraints allow establishing direct relations between metabolic activity, proteome allocation, physiology, and growth for organisms with available ecGEMs, including: Escherichia coli [31], Saccharomyces cerevisiae [30], Chinese hamster ovary cells [32], Homo sapiens [33], Bacillus subtilis [34], Corynebacterium glutamicum [35], Chlamydomonas reinhardtii [27] and Rhizophagus irregularis [36]. Importantly, such enzyme constraints indicate a viable way to manipulate native metabolism by designing strategies focused on modification of turnover numbers of enzymes. These strategies can be implemented using advances in deep learning of turnover numbers [19–21], in predictions of protein structures that indicate key amino acid residues driving modifications of catalytic activities [37], and in new tools for directed enzyme evolution [38].

However, the existing ecGEMs have been used to design engineering strategies based only on manipulation of enzyme abundance, following the same principles underlying flux manipulation [7–11]. For instance, an ecGEM of E. coli was used to improve lysine production, while ensuring fixed minimal growth, by using flux balance analysis (FBA) [39]. Overexpression of proteins with largest predicted abundance was used to validate the predicted increase in lysine production [31]. Similar approach was used with an ecGEM for C. glutamicum to determine enzymes with predicted differential protein abundance between low and near-optimal growth rate obtained from the in silico maximization of lysine production [35]. Another study used an ecGEM of B. subtilis to identify knockout strategies to overproduce poly-γ-glutamic acid (γ-PGA) [34]. The knock-out strategy was simulated using the well-established minimization of metabolic adjustment method (MOMA) [40], and indicated differences to strategies obtained from application of MOMA to classical GEMs; the in vivo implementation of the resulting strategies indicated a two-fold increase in the production of γ-PGA. Interestingly, these results contrast the findings based on classical GEMs which show that the overproduction of some chemicals, including many amino acids, cannot be achieved by manipulation of gene expression due to conflicts arising from the participation of one gene in the gene-protein-reaction rules of multiple reactions [11].

Motivated by developments of ecGEMs that include constraints on how fluxes depend on enzyme abundance and catalytic rates, here we devise, implement, and test constraint-based approaches to design metabolic engineering strategies that: (1) rely on manipulation of turnover numbers, without modifying enzyme abundances compared to the wild type, (2) consider the simultaneous change of turnover numbers and enzyme abundances, compared to the wild type, and (3) test the resulting strategies by deploying them with a catalogue of proteins with diverse turnover numbers from 343 fungal species. Therefore, we provide a pioneering constraint-based approach applicable with large-scale ecGEMs systematically identifying which enzyme turnover numbers need to be manipulated and in what direction to enhance the capacity of cell factories with respect to a large set of chemicals native to the hosts.

Targeting turnover numbers for engineering applications

The integration of enzymatic constraints into ecGEMs [15] facilitates the development of our optimization-based approach, termed Overcoming Kinetic Obstacles (OKO), that predicts metabolic engineering strategies targeting turnover numbers. OKO manipulates the turnover numbers of enzymes under the assumption that the abundances of enzymes in the ecGEMs of wild type and the engineered organism are not significantly changed. This setting is particularly relevant for in vivo metabolic engineering strategies, since it does not require tinkering with the underlying transcriptional and (post)translational regulatory machinery of cell factories.

OKO is formulated as a two-step approach: In the first step, we determine the maximum product yield in the wild-type model at optimal growth rate under the set of constraints imposed by ecGEMs. Next, we identify the protein allocation by minimizing the enzyme usage (see Fig. 1A, Methods). In the second step, with the obtained enzyme abundances in the wild-type model, we constrain the abundance ranges in the model of the engineered strain, to ensure no significant change in comparison to the wild type strain (Methods). By introducing a binary variable for every turnover number and a tuneable parameter, we keep track of whether or not a turnover number is considered changed. Another tuneable parameter is in turn used to define the admissible range for the modified turnover number and guarantees that its value remains within this range (Fig. 1B, Methods). The second step of OKO then minimizes the number of significantly changed turnover numbers while ensuring that a desired level of chemical production is achieved at a factor of optimal growth without affecting protein abundance compared to the wild type (Fig. 1C, Methods).

Application of OKO to two cell factories

Modification of enzyme turnover numbers enhances the capacity of wild type cell factories and marks a departure from typical engineering strategies that rely on manipulation of enzyme abundance in prioritizing product formation at the expense of biomass growth. As a result, we expect that by using OKO, the optimal growth rate in in the engineered model may remain almost unchanged in comparison to that of the wild-type, thus breaking the trade-off between product production and growth (or biomass formation) [41].

Here, we applied the proposed computational approach, OKO, to the ecYeastGEM_v8.3.4 [30] of the yeast Saccharomyces cerevisiae and the eciML1515 [31] of the bacterium Escherichia coli as cell factories. We aimed to determine modification strategies that rely on turnover numbers for the overproduction of multiple native compounds in these hosts. The ecYeastGEM v8.3.4 model contains 1148 enzymes, of which 968 are linked to ${k}_{cat}$ values, resulting in a total of 4261 available ${k}_{cat}$ values that can be modified. The eciML1515 model contains 1505 enzymes with 3392 available ${k}_{cat}$ values linked to 1259 enzymes in the model.

Domenzain et al. [42] proposed a computational method to predict optimal combinations of gene engineering targets and applied it to the ecYeastGEM_v8.3.4 model to increase the production of 102 different chemicals. Their method involves scoring genes within the model to find the magnitude and directionality of genetic modifications, and then discards genes that encode enzymes that are unfavorable for the production of the target metabolite. Finally, the approach identifies the minimal set of modifications for the transition of cells from biomass formation to metabolic production. Of the chemicals studied in [42], 49 compounds, including amino acids, are native metabolites in Saccharomyces cerevisiae. Mapping of these native compounds to metabolites in eciML1515 using KEGG IDs, CHEBI IDs and chemical formulae resulted in 41 metabolites to which the OKO method was applied (see Supplementary Table 1).

We first calculated the maximum production of each native compound at optimal growth rates, i.e. 0.38 per hour for ecYeastGEM_v8.3.4 and 0.57 per hour for eciML1515. Enzyme abundances were then calculated by using the first step of OKO (see Methods). To demonstrate that the resulting enzyme abundances can be used as a reference point, we conducted a robustness analysis relying on tailored variability analysis that specifies admissible ranges for enzyme abundance (see Methods). The results show that, on average, the logarithmic ratio of the maximum and minimum values for each enzyme abundance at the maximum production of the different chemicals of interest is 0.015 for the ecYeastGEM_v8.3.4 model and varies from $6\times {10}^{-4}$ to 0.011 for the eciML1515 model (see Supplementary Tables 1 and 2, respectively). This demonstrates that the estimated maximum and minimum abundance values for every enzyme are very close to each other, allowing the usage of the estimated enzyme abundances in the remaining computational steps of OKO.

We then used OKO to search for strategies with the minimum number of changes in ${k}_{cat}$ values that at least double the compound production while maintaining almost the same growth rates as in the wild type. The minimum number of modified ${k}_{cat}$ values for overproduction of the chemicals of interest ranges from 7 to 338 for the ecYeastGEM_v8.3.4 model and from 4 to 39 for the eciML1515 model (see Supplementary Tables 1 and 2, respectively). The two compounds with the least number of modifications required are choline and palmitoleate in the ecYeastGEM_v8.3.4 model, with seven modified turnover numbers, and proline and serine in the eciML1515 model, with four and five modified turnover numbers, respectively (see Supplementary Table 3 for the involved enzymes).

Since our goal is to double the production of a chemical of interest in comparison to the wild type, while ensuring certain growth, one may expect that only allowing for an increase in turnover numbers would suffice to address these objectives. Interestingly, however, the increase in production of the considered compounds does not necessarily entail only increases in the turnover numbers. We found that in the ecYeastGEM v8.3.4 model on average 35.5% of the enzymes require an increase in their ${k}_{cat}$ values, while in the eciML1515 model, this number is 38.5% to double the production of the selected compounds. Further, since in metabolic engineering it is easier to knock out an enzyme than to reduce its turnover number via enzyme engineering, we also identified the cases where the reduction in turnover number could be replaced by knocking out the enzyme. To the end, we inspected if an enzyme requiring a reduction in ${k}_{cat}$ value was associated with a flux of zero ($<{10}^{-6} mmol {gDW}^{-1}{h}^{-1}$) in the engineered model. On average, 53.9% of the reductions in the ecYeastGEM_v8.3.4 model and 12.9% in the eciML1515 model fell into this category. This finding indicated that decrease in turnover number, without blocking of reactions, are required to simultaneously achieve different objectives, including growth and production of the chemical of interest. Indeed, the growth rates of the engineered ecYeastGEM_v8.3.4 and eciML1515 models are on average 88% of the optimal growth rates of the wild-type models, indicating that the increase in the production of compounds following the proposed strategies does come at some, but not drastic cost of growth.

Promiscuous enzymes have been deemed reservoirs of functions that can be used in metabolic engineering, especially if particular catalytic activities are modified in a desired direction [2]. Hence, we also investigated whether enzymes targeted for modification of their turnover number were more likely to be promiscuous. We found, on average, 26.5% and 24.3% of the enzymes in the proposed strategies for the ecYeastGEM_v8.3.4 and eciML1515 models, respectively, were exhibited promiscuous functions.

OKO identifies strategies for overproduction of amino acids

Razaghi-Moghadam et al. [11] investigated the participation of enzymes in different reactions and the inclusion of complex gene-protein-reaction rules, and showed that complex rules are present in metabolic models to a considerable extent. Therefore, strategies that build on existing enzymes and pathways often lead to conflicts in the manipulation of enzyme abundances. For example, using their proposed approach, it was found that there is no feasible strategy at the native enzyme level to increase production of almost all amino acids in E. coli and S. cerevisiae. This finding motivated us to further investigate the performance of OKO to increase the production of amino acids in these cell factories. To this end, we first reviewed the primary results of OKO, which indicated the minimum number of modified turnover numbers for amino acid overproduction. This number ranges from 9 to 20 for the ecYeastGEM_v8.3.4 model and from 4 to 25 for the eciML1515 model (Fig. 2A). We found that, on average, 35% and 37.4% of the proposed enzymes in the ecYeastGEM_v8.3.4 and eciML1515 models, respectively, required an increase in their ${k}_{cat}$ values.

Furthermore, we observed that the proposed amino acid modification strategies involve a total of 83 and 80 enzymes in the ecYeastGEM v8.3.4 and eciML1515 models, respectively. Of these, 15 and 17 enzymes are required for the overproduction of at least three amino acids, respectively (see Figs. 2B and 2C). Moreover, and most importantly, the relative changes for the ${k}_{cat}$ values are small, reaching the defined limits (either ${\left({\beta }_{2}\right)}^{-1}$ or ${\beta }_{2}$) only 0.6% and 7.6% of the time for the ecYeastGEM v8.3.4 and eciML1515 models, respectively (see Supplementary Tables 4 and 5).

In addition, as shown in Figs. 2B and 2C, for each enzyme included in the proposed amino acid modification strategies, the log-fold changes are predominantly distributed to one side of zero, indicating that the proposed modifications are biased towards either increasing or decreasing the ${k}_{cat}$ values to increase the production of each amino acid. Furthermore, the boxplots in Figs. 2B and 2C show a small spread, indicating the uniformity of the estimated ${k}_{cat}$ values for each enzyme. Therefore, in vivo enzyme engineering following the proposed strategy for overproduction of amino acids is expected to benefit the increase of production of other amino acids that also relies on that enzyme.

As depicted in Fig. 2B and Supplementary Table 4, the eciML1515 model demonstrates two exceptions to the consistency of change directions. The ${\text{k}}_{\text{c}\text{a}\text{t}}$ value of dye-decolorizing peroxidase YfeX enzyme (Uniprot ID P76536) in the ferrochelatase reaction is initially 25999.42 (${\text{s}}^{-1}$) in the eciML1515 model. For the overproduction of alanine, aspartate, cysteine, glutamine, glycine, threonine, tryptophan, and tyrosine, this value must be reduced by a factor of 0.7. Conversely, overproduction of proline requires a 10-fold increase in the ${\text{k}}_{\text{c}\text{a}\text{t}}$ value. In addition, pyruvate kinase II (Uniprot ID P21599) with an initial ${\text{k}}_{\text{c}\text{a}\text{t}}$ value of 3204.01 (${\text{s}}^{-1}$) in various pyruvate kinase reactions of the eciML1515 model needs to be increased for arginine and isoleucine overproduction and decreased for tyrosine overproduction. In the proposed strategy for arginine overproduction, the ${\text{k}}_{\text{c}\text{a}\text{t}}$ value of pyruvate kinase II needs to be increased 10-fold in two reactions and 2.5-fold in another reaction.

In the ecYeastGEM v8.3.4 model, as shown in Fig. 2C and detailed in Supplementary Table 5, the estimated changes in ${\text{k}}_{\text{c}\text{a}\text{t}}$ values for two enzymes show greater variability. The isocitrate dehydrogenase [NADP] cytoplasmic (IDH) enzyme (Uniprot ID P41939) has a ${\text{k}}_{\text{c}\text{a}\text{t}}$ value of 58.30 (${\text{s}}^{-1}$) in the isocitrate dehydrogenase (NADP) reaction. This value needs to be increased by a factor of 1.3 for the overproduction of glutamine and proline, and by a factor of 10 for the overproduction of glutamate. In addition, the homoserine kinase (HK) (HSK) enzyme (Uniprot ID P17423), which has a ${\text{k}}_{\text{c}\text{a}\text{t}}$ value of 40.80 (${\text{s}}^{-1}$) in the homoserine kinase reaction, needs to be increased 1.6-fold for glycine and threonine overproduction, whereas only a 1.01-fold increase is suggested for isoleucine overproduction. These examples demonstrate that while changes in some turnover numbers can generally accommodate usage of the engineered enzymes in the implementation of engineering strategies for different compounds, there are few, notable exceptions.

Setting the ground for experimental validation

Metabolic engineering approaches that aim to use enzymes with the optimized ${k}_{cat}$ values can leverage either existing nonnative enzymes or engineered enzymes with modified substrate specificity. Methods that rely on existing enzymes have the flexibility to reuse the enzyme repository in nature and facilitate the creation of synthetic pathways for engineering purposes. This motivated us to investigate whether the identified ${k}_{cat}$ values in our engineering strategies are close to the turnover numbers of these enzymes in other organisms.

Enzyme databases such as BRENDA [17] and SABIO-RK [18] contain extensive repositories of ${k}_{cat}$ values. However, there is still a lack of high-throughput techniques for measuring ${k}_{cat}$ values, resulting in a notable disparity in the number of ${k}_{cat}$ values available compared to the vast number of organisms and metabolic enzymes in existence [28]. To fill this gap, deep learning and machine learning approaches have been proposed to predict the ${k}_{cat}$ values for different enzymes in different organisms, and have shown high performance [19–21]. To investigate whether the ${k}_{cat}$ values estimated by OKO could be found for the respective enzymes in other organisms, we used the predicted ${k}_{cat}$ values from the DLKcat approach [19]. DLKcat includes the prediction of ${k}_{cat}$ values for 651 metabolic enzymes in 343 organisms (see Supplementary Table 6).

Having mapped the two sets of ${k}_{cat}$ values from ecGEMs and the DLKcat results (see Methods), we examined each enzyme with an estimated ${k}_{cat}$ value from OKO to determine whether it was included in the list of enzymes with a predicted ${k}_{cat}$ value from the DLKcat approach. If so, we further identified the closest ${k}_{cat}$ value to the estimated one across all organisms. In the proposed amino acid modification strategies, we identified 248 and 236 estimated ${k}_{cat}$ values for the ecYeastGEM_v8.3.4 and eciML1515 models, corresponding to 83 and 80 different enzymes, respectively. As shown in Table 1, only 55.2% and 24.2% of these enzymes were included in the list of enzymes with predicted ${k}_{cat}$ values by the DLKcat approach. Furthermore, the average distance of the closest ${k}_{cat}$ values to the estimated values across all organisms was 503.15 (${s}^{-1}$) and 32188.07 (${s}^{-1}$) for the ecYeastGEM_v8.3.4 and eciML1515 models, respectively. These findings indicated that the enzymes with ${k}_{cat}$ values estimated by the OKO approach were rarely found in other organisms and could not be directly used for in vivo engineering.

Table 1

**Deep-learning-driven identification of suitable turnover numbers from other organisms**. Shown is the number of enzyme-reaction pairs in the proposed strategies for which turnover numbers can be predicted by DLKcat results. The table also includes the average distance of the ${k}_{cat}$ values predicted by DLKcat and the modifications resulting from OKO and OKO⁺.
	OKO		OKO⁺
	E. coli	S. cerevisiae	E. coli	S. cerevisiae
Found enzyme-reaction pairs	57	137	354	817
Missing enzyme-reaction pairs	179	111	0	0
Average distance (${s}^{-1}$)	32188.07	503.15	2.35	4.92

Refinement of OKO enhances its applicability

As it is more convenient to construct synthetic pathways using existing enzymes, we also proposed a refinement of OKO, termed OKO⁺. In OKO⁺, for each enzyme-reaction pair with an available ${k}_{cat}$ value in an ecGEM, we first extract the minimum and maximum of the predicted ${k}_{cat}$ values in all other organisms using the mapping established between ecGEM and DLKcat results. In total, there are 4261 and 3392 enzyme-reaction pairs with available ${k}_{cat}$ values in the ecYeastGEM_v8.3.4 and eciML1515 models, respectively, of which 1676 and 469 respected values are found in the predicted ${k}_{cat}$ values from the DLKcat approach (see Supplementary Table 7). To ensure that only enzymes with known turnover numbers are included, we introduce two additional sets of constraints in OKO⁺: (1) for the enzyme-reaction pairs with available turnover estimates from DLKcat or other resources, the predicted ${k}_{cat}$ should remain either unchanged or within the range extracted from the values obtained from DLKcat, and (2) the enzyme-reaction pairs with available ${k}_{cat}$ values in the ecGEM, for which values from DLKcat (from other organisms) are not available, are not allowed to be modified.

The introduction of these two additional sets of constraints resulted in infeasibilities to identify engineering strategies that yield the desired levels of product formation and growth. Therefore, in OKO⁺, we also allow for variation in enzyme abundance, modelled by introduction of a binary variable for each enzyme abundance indicating if it is significantly altered (with respect to a tunable parameter). This approach then minimizes the weighted average of the number of modified turnover numbers and the number of modified abundances, with preference for the former (see Methods).

By deploying OKO⁺ with the same models we found that the minimum number of modified ${k}_{cat}$ values for overproduction of the chemicals of interest ranges from 0 to 85 for the ecYeastGEM_v8.3.4 model and from 0 to 44 for the eciML1515 model (see Supplementary Tables 1 and 2), while also requiring changes in enzyme abundance. The ecYeastGEM_v8.3.4 model requires different number of changes in enzyme abundance, ranging from 2 to 240 modifications, while this number varies from 3 to 286 for the eciML1515 model. On average, 48.8% and 77% of the enzymes in the proposed strategies for the ecYeastGEM_v8.3.4 and eciML1515 models were promiscuous enzymes, respectively.

In addition, for each ${k}_{cat}$ value estimated by OKO⁺ in amino acid modification strategies, we identified the closest ${k}_{cat}$ value across all organisms. Clearly, due to the constraints imposed in OKO⁺, all enzymes with newly estimated ${k}_{cat}$ values were included in the list of enzymes with predicted ${k}_{cat}$ values from the DLKcat approach. The average distance from the estimated values to their closest counterparts across all organisms was 2.35 for the ecYeastGEM_v8.3.4 model and 4.92 for the eciML1515 model (see Table 1). The small average distance value indicates that OKO⁺ successfully identified a suitable enzyme for another organism with closely matching activity.

Inspection of the proposed strategies to increase the production of amino acids showed that the existing nonnative enzymes with ${k}_{cat}$ values closest to the predicted by OKO⁺ originate from different organisms (see Supplementary Tables 1, 2 and 8). In total, 103 different organisms contribute to the proposed modification strategies for the ecYeastGEM_v8.3.4 model and 53 for the eciML1515 model (see Supplementary Table 8). Each organism contributes a different number of enzymes, ranging from 1 to 50 for the proposed modifications in the ecYeastGEM_v8.3.4 model and from 1 to 29 for the eciML1515 model.

To further analyze the applicability of the strategies resulting from OKO⁺, we constructed two distinct ecGEMs by substituting the ${k}_{cat}$ values in the original ecGEMs with the values estimated by OKO⁺, as well as the closest values from other organisms. We then assessed the performance of the strategies with the so-modified turnover numbers in producing the compounds of interest. In each model constructed and for each compound of interest, the biomass level was set to match that of the proposed engineering strategy for the overproducing that chemical. In addition, the number of modifications to the enzyme abundance was constrained by the number of modifications in the corresponding proposed engineering strategy. Clearly, this evaluation is only applicable in cases where at least one modification to the enzyme activity was proposed by OKO⁺ and this is for 19 amino acids in the ecYeastGEM_v8.3.4 model and 12 in the eciML1515 model. With these constraints, we calculated the maximum production of each chemical of interest in the two constructed ecGEMs and determined their logarithmic ratio ($\text{l}\text{o}\text{g}\left(\frac{{v}_{max}^{\text{D}\text{L}\text{K}\text{c}\text{a}\text{t}}}{{v}_{max}^{{\text{O}\text{K}\text{O}}^{+}}}\right)$) (see Supplementary Tables 1 and 2). In the majority of cases the two constructed ecGEMs yielded the same levels of product formation. Small differences in product formation levels were only observed for glutamine in the ecYeastGEM_v8.3.4 model and for arginine and methionine in the eciML1515 model, with the smallest logarithmic ratio being $-1.3\times {10}^{-2}$.

Feasibility of strategies designed by employing OKO⁺

OKO⁺ was employed to design engineering strategies for the overproduction of 49 compounds in the ecYeastGEM_v8.3.4 model and 41 compounds in the eciML1515 model. The total number of modifications, including enzyme abundance and turnover numbers, varied from 2 to 293 in the ecYeastGEM_v8.3.4 model and from 3 to 316 in the eciML1515 model (see Supplementary Tables 1 and 2). Further analysis focused on the engineering strategies of OKO⁺ that are more feasible to implement, specifically those with a total number of modifications less than or equal to seven. Six such compounds were identified in the ecYeastGEM_v8.3.4 model and five in the eciML1515 model (see Table 2 and Fig. 3).

It is noteworthy that all modification strategies proposed by OKO⁺ to overproduce these eleven compounds involved an increase in enzyme abundance. Furthermore, the proposed engineering strategies do not only involve modification of enzyme abundance, but also adjustment of enzyme turnover numbers. For instance, the overproduction of isoamylol requires a 1.4-fold increase in the ${\text{k}}_{\text{c}\text{a}\text{t}}$ value of the 3-isopropylmalate dehydrogenase enzyme (Uniprot ID P04173), with the closest comparable value found in Candida rhagii. Similarly, for the overproduction of isoleucine, a 1.2-fold increase in the ${\text{k}}_{\text{c}\text{a}\text{t}}$ value of homoserine dehydrogenase (Uniprot ID P31116) is required, and the closest identified value comes from Blastobotrys raffinofermentans.

In the proposed strategy for spermine overproduction, a $1.5\times {10}^{-4}$-fold reduction in the ${k}_{cat}$ value of fumarate reductase 2 (Uniprot ID P21375) was proposed, with the closest corresponding value identified in Ogataea trehaloabstinens. Finally, for (S)-malate overproduction, the proposed strategy involved a 1.6-fold increase in the ${\text{k}}_{\text{c}\text{a}\text{t}}$ value of pyruvate carboxylase 1 (Uniprot ID P11154), with the closest comparable value coming from Lachancea waltii.

Additionally, for increasing homoserine production in the eciML1515 model, OKO⁺ proposed an engineering strategy involving a 1.3-fold increase in the ${\text{k}}_{\text{c}\text{a}\text{t}}$ value of aspartate-semialdehyde dehydrogenase (Uniprot ID P0A9Q9) and a 2.9-fold increase in the ${\text{k}}_{\text{c}\text{a}\text{t}}$ value of the bifunctional aspartokinase/homoserine dehydrogenase 1 (Uniprot ID P00561). The closest comparable ${k}_{cat}$ values to these proposed modifications are identified in Saturnispora zaruensis and B. anomalus, respectively. These results jointly indicate that feasible engineering strategies can be obtained when combining overexpression of enzymes with enzymes engineered towards an increase in turnover numbers.

Table 2

**Proposed metabolic engineering strategies with feasible implementation.** Shown are the compounds for which the proposed engineering strategies involve a total of seven or fewer modifications. The number of modifications to the turnover number and to the enzyme abundance are included.
		modifications of turnover number	Modifications of enzyme abundance
E. coli	Aspartate	0	5
	Citrulline	0	7
	Glycine	0	3
	Homoserine	2	3
	(S)- malate	0	6
	Acetate	0	6
S. cerevisiae	Isoamylol	1	4
	Isoleucine	1	6
	Lysine	0	2
	Spermine	1	5
	(S)-malate	1	2

Availability of enzyme turnover numbers, estimated by coupling omics data with models or relying and classical experimental techniques or predicted by machine and deep learning approaches, holds the promise for their usage in the design and deployment of precise metabolic engineering strategies. However, despite this promise, metabolic engineering has not capitalized from the availability of repositories of and models for turnover numbers. We address this gap by proposing, implementing, and testing a constraint-based approach, termed OKO, for the design of metabolic engineering strategies that allows modification of turnover numbers. Our findings indicated that the use of OKO with enzyme-constrained metabolic models of E. coli and S. cerevisiae resulted in metabolic engineering strategies that overcome the trade-off between growth and increased production of a chemical of interest. Importantly, we found that the overproduction of chemicals of interest does not only entail an increase in selected enzymes. Motivated by the need to consider the available estimates and predictions of turnover numbers for selected enzymes, we also presented a refinement of OKO that combines the modification of turnover numbers (from a well-defined range) with alterations of enzyme abundances. The resulting approach resulted in feasible strategies for overproduction of amino acids in the two hosts, which was not possible to obtained with other constrained-based approaches focused only on alteration of gene expression (as a proxy for enzyme abundance). Therefore, our study paves the way for deployment of precise metabolic engineering strategies that rely on the natural diversity of turnover numbers for given enzymes or that can use techniques for enzyme engineering.

Formulation of OKO

To determine the abundance of enzymes at the maximum product yield (${v}_{pro,wt}^{max}$) in the wild-type model, while ensuring optimal growth rate (${v}_{bio,wt}^{opt}$), we solve the following linear programming problem (LP1):

$$\underset{v,E}{\text{min}}\sum _{i=1}^{p}\left[{E}_{i}\right] \left(1\right)$$

s.t

$$\mathbf{N}\bullet \mathbf{v}=0 \left(2\right)$$

$${v}_{j}^{min}\le {v}_{j}\le {v}_{j}^{max}, 1\le j\le r \left(3\right)$$

$${v}_{pro}={v}_{pro,wt}^{max} \left(4\right)$$

$${v}_{bio}={v}_{bio,wt}^{opt} \left(5\right)$$

$${v}_{j}={k}_{cat}^{ij}\bullet \left[{E}_{i}\right], 1\le j\le r, 1\le i\le p \left(6\right)$$

$$\sum _{i=1}^{p}{MW}_{i}\bullet {[E}_{i}]\le \sigma \bullet f\bullet {P}_{total} (7)$$

where $\left[{E}_{i}\right]$ is the abundance of enzyme $i$, $p$ denotes the number of enzymes, $\mathbf{N}$ is the stoichiometric matrix, $\mathbf{v}$ is the flux distribution vector, ${v}_{j}$ is the metabolic flux through reaction $j$, $r$ is the number of reactions, ${v}_{pro}$ and ${v}_{bio}$ are the fluxes through the synthesis of the product of interest and the biomass reaction, respectively, ${k}_{cat}^{ij}$ is the catalytic rate of enzyme $i$ catalysing reaction $j$, ${MW}_{i}$ is the molecular weight of enzyme $i$, $\sigma$ is the average in vivo enzyme saturation, $f$ is the mass fraction of all measured enzymes included in the model, and ${P}_{total}$ is the total protein content.

We use the resulting obtained enzyme abundances ($\left[{E}_{i}^{wt}\right]$) to constrain the abundance range in the engineered model, using the following constraint:

$$\left(1-\alpha \right)\bullet \left(\left[{E}_{i}^{wt}\right]\right)\le \left[{E}_{i}^{eng}\right]\le \left(1+{\alpha }\right)\bullet \left(\left[{E}_{i}^{wt}\right]\right) , 1\le i\le p \left(8\right)$$

where $\alpha$ is a small parameter ($\approx {10}^{-6}$) that quantifies the insignificant deviation from the enzyme abundances in the wild-type model.

To overcome the shortcomings of abundance-based strategies [7–11], OKO opt to develop strategies that manipulate the turnover numbers. Accordingly, in the engineered model, the constraint in Eq. (6) is replaced by the following constraint:

$${v}_{j}={(k}_{cat}^{ij}+{\delta }^{ij})\bullet \left[{E}_{i}^{eng}\right], 1\le j\le r, 1\le i\le p (9)$$

where ${\delta }^{ij}$ shows the deviation from the turnover number of the wild-type enzyme, and it can be positive or negative. Eq. (9) contains a quadratic term which includes ${\delta }^{ij}$ and $\left[{E}_{i}^{eng}\right]$. To linearize this constraint a new variable ${\delta }_{e}^{ij}={\delta }^{ij}.\left[{E}_{i}^{eng}\right]$ and the following constraints are added to the optimization problem:

$${v}_{j}={k}_{cat}^{ij}\bullet \left[{E}_{i}^{eng}\right]+{\delta }_{e}^{ij}, 1\le j\le r, 1\le i\le p \left({9}^{{\prime }}\right)$$

$$-M\bullet \left[{E}_{i}^{eng}\right]\le {\delta }_{e}^{ij}\le M\bullet \left[{E}_{i}^{eng}\right], 1\le j\le r, 1\le i\le p \left(10\right)$$

where $M$ is a large number (${10}^{6}$) and Eq. (10) guaranties that $\left[{E}_{i}^{eng}\right]=0$ implies ${\delta }_{e}^{ij}=0$. As a result, Eq. (9) is replaced by Eq. (9’) to remove the quadratic constraint. The optimized turnover numbers can then be calculated by ${k}_{cat}^{ij*}={k}_{cat}^{ij}+{\delta }^{ij}={k}_{cat}^{ij}+\raisebox{1ex}{${\delta }_{e}^{ij}$}\!\left/ \!\raisebox{-1ex}{$\left[{E}_{i}^{eng}\right]$}\right.$. For each ${k}_{cat}^{ij}$, we also define two intervals (see Fig. 1B) that include the optimized value. These intervals restrict the optimized value to a range that maintains a balance distance from ${k}_{cat}^{ij}$. If $\left(1-{\beta }_{1}\right)\bullet {k}_{cat}^{ij}\le {k}_{cat}^{ij*}\le \left(1+{\beta }_{1}\right)\bullet {k}_{cat}^{ij}$, then we consider the value of ${k}_{cat}^{ij}$ to not be significantly changed; further, we prevent large relative changes by enforcing that ${\left({\beta }_{2}\right)}^{-1}\bullet {k}_{cat}^{ij}\le {k}_{cat}^{ij*}\le {\beta }_{2}\bullet {k}_{cat}^{ij}$. The two tuneable parameters ${\beta }_{1}$ and ${\beta }_{2}$ define the allowed intervals for the optimized catalytic rate (${k}_{cat}^{ij*}$). For every ${k}_{cat}^{ij}$ value, a binary variable ${y}^{ij}$ is introduced; it takes the value of 0, if the catalytic rate is significantly changed, and 1, otherwise. Based on the following constraints, the binary variable ${y}^{ij}$ enables us to switch between intervals and determine whether the ${k}_{cat}^{ij}$ can be changed or not:

$${-\delta }_{e}^{ij}-{\beta }_{1}\bullet {k}_{cat}^{ij}\bullet \left[{E}_{i}^{eng}\right]\le M\bullet \left(1-{y}^{ij}\right), 1\le j\le r, 1\le i\le p \left(11\right)$$

$${\delta }_{e}^{ij}-{\beta }_{1}\bullet {k}_{cat}^{ij}.\left[{E}_{i}^{eng}\right]\le M\bullet \left(1-{y}^{ij}\right), 1\le j\le r, 1\le i\le p \left(12\right)$$

$${k}_{cat}^{ij}\bullet \left({\left({\beta }_{2}\right)}^{-1}-1\right)\bullet \left[{E}_{i}^{eng}\right]\le {\delta }_{e}^{ij}\le {k}_{cat}^{ij}\bullet \left({\beta }_{2}-1\right)\bullet \left[{E}_{i}^{eng}\right]. 1\le j\le r, 1\le i\le p \left(13\right)$$

Here, Eq. (13) guaranties that the optimized turnover number (${k}_{cat}^{ij*}$) is in the allowed range. OKO finds a solution with the minimum number of modified turnover numbers (which is equivalent to the maximum number of unchanged turnover numbers ($\sum _{1\le j\le r, 1\le i\le p}{y}^{ij}$), while guaranteeing that: (i) the flux towards the objective is at least a given factor, ${f}_{pro} (\ge 2)$ of the maximum product yield and (ii) a certain factor, ${\alpha }_{bio} (\approx 1)$, of optimal growth is achieved. These are enforced by the following constraints:

$${v}_{pro}\ge {{f}_{pro}.v}_{pro,wt}^{max}, \left(14\right)$$

$${v}_{bio}\ge {\alpha }_{bio}.{v}_{bio,wt}^{opt}. \left(15\right)$$

The combination of the linear objective function of $\underset{v,E,{\delta }_{e},y}{\text{max}}\sum _{1\le j\le r, 1\le i\le p}{y}^{ij}$ with the linear constraints in Eqs. (2, 3, 7, 8, 9’,10–15) leads to our proposed Mixed-Integer Linear Programming (MILP) formulation of OKO (see Fig. 1C).

Formulation of OKO+

in OKO⁺, we also allow for variation in enzyme abundance. To this end, for each $\left[{E}_{i}^{eng}\right]$ value ($1\le i\le p$), we introduce an interval of $\left(\left(1-{\beta }_{e}\right)\bullet \left[{E}_{i}^{wt}\right],\left(1+{\beta }_{e}\right)\bullet \left[{E}_{i}^{wt}\right]\right)$, which defines the range of unchanged values for the abundance. In addition, a binary variable ${y}_{e}^{i}$ is introduced which takes the value of 1, if the enzyme abundance falls within the interval, and 0, otherwise. Here, ${\beta }_{e}$ is a tuneable parameter that quantifies the deviation from the enzyme abundances in the wild-type model. Based on the following constraints, the binary variable ${y}_{e}^{i}$ enables us to determine whether the $\left[{E}_{i}^{eng}\right]$ changes or not:

$$\left(1-{\beta }_{e}\right)\bullet \left[{E}_{i}^{wt}\right]-\left[{E}_{i}^{eng}\right]\le M\bullet \left(1-{y}_{e}^{i}\right), 1\le i\le p \left(16\right)$$

$$-\left(1+{\beta }_{e}\right)\bullet \left[{E}_{i}^{wt}\right]+\left[{E}_{i}^{eng}\right]\le M\bullet \left(1-{y}_{e}^{i}\right), 1\le i\le p \left(17\right)$$

where $M$ is a large number (${10}^{6}$). In OKO⁺, the constraint in Eq. (8) is replaced by the constraints in the Eqs. (16) and (17) and the objective is changed to $\underset{v,E,{\delta }_{e},y}{\text{max}}\sum _{1\le j\le r, 1\le i\le p}{y}^{ij}+w\sum _{1\le i\le p}{y}_{e}^{i}$, where $w$ is the weight reflecting the priority given to the number of changes for enzyme abundance or activity. Given that the primary aim of OKO is to identify modification strategies at the level of catalytic rates, the weight $w$ was set to 10 to prioritize minimizing the number of modifications on the enzyme abundance.

Robustness analysis of enzyme abundance

To assess the precision of the estimated enzyme abundances, for each enzyme abundance we determine the range over which the minimum enzyme usage, from LP1, remains valid. This is done by calculating the minimum and the maximum values the abundance of each enzyme can take at minimum enzyme usage (${sum}_{e}^{*}$) obtained from solving LP1, and can be done by solving the following linear programming problems (LP2):

$$\underset{v,E}{\text{min}}/\text{max} \left[{E}_{i}\right] 1\le i\le p \left(18\right)$$

s.t

$$\sum _{i=1}^{p}\left[{E}_{i}\right]={sum}_{e}^{*} \left(19\right)$$

Eqs.$\left(2\right), \left(3\right), \left(4\right), \left(5\right), \left(6\right), \left(7\right)$

Given that the minimum value is usually zero and the maximum is a very small number, we use the log-sum-exp trick [43] to calculate the logarithmic ratio between the maximum and minimum values to deal with the potential numerical instability.

OKO and OKO⁺ implementation

OKO and OKO + both have MILP formulations and are implemented in MATLAB R2022b, available at https://github.com/MonaRazaghi/OKO/. These approaches take as input an ecGEM together with one or a list of compound indices in ecGEM. The output is a list of enzymes with their respective modifications, either on enzyme turn over number or abundance. Both OKO and OKO⁺ use the Gurobi Optimizer v9.5.2 [44] as their solver to efficiently solve the corresponding MILP problems.

OKO includes several tuneable parameters, $\alpha , {\beta }_{1}$ and ${\beta }_{2}$. To increase the likelihood of finding a solution for the MILP formulation of OKO, the tuneable parameters $\alpha$ and ${\beta }_{1}$ were set to ${10}^{-1}$ and ${10}^{-8}$, respectively. In addition, the parameter ${\beta }_{2}$ was set to $10$, to avoid large relative changes in ${k}_{cat}$ values. In the case of OKO⁺, an additional tunable parameter ${\beta }_{e}$ is included. This parameter was set to ${10}^{-1}$ to have reasonable intervals for enzyme abundance.

Mapping of ${\varvec{k}}_{\varvec{c}\varvec{a}\varvec{t}}$values from ecGEMs and DLKcat

The ${k}_{cat}$ values in ecGEMs are linked to enzyme-reaction pairs, whereas the predicted ${k}_{cat}$ values from the DLKcat approach are linked to enzyme-metabolite pairs. To establish a mapping between the two sets of ${k}_{cat}$ values, we first associated the enzymes with their respective EC numbers using the Uniprot database [45]. Enzyme-reaction pairs were then converted to enzyme-metabolite pairs by including all substrates involved in the reaction. Metabolite names from the ecGEMs were mapped to the metabolites present in the DLKcat results using MetaNetX IDs.

Acknowledgements

The European Union’s Horizon 2020 research and innovation program financially supported this work through grant 862201 (to Z.N.). The KT Boost financially also supported this work through grant KT41 (to Z.R.-M.). F.S.B. acknowledges the financial support by the German Research Foundation, project number 517516852 (to Z.N.).

Cho. JS., Kim, GB., Eun, H., Moon, CW., Lee, SY. Designing microbial cell factories for the production of chemicals. JACS Au. 4;2(8), 1781-1799. doi: 10.1021/jacsau.2c00344 (2022).
Erb, TJ., Jones, PR., Bar-Even, A. Synthetic metabolism: metabolic engineering meets enzyme design, Current Opinion in Chemical Biology, 37, 56-62. doi.org/10.1016/j.cbpa.2016.12.023 (2017).
Monk, JM. et al. iML1515, a knowledgebase that computes Escherichia coli traits. Nat Biotechnol. 11;35(10), 904-908. doi: 10.1038/nbt.3956 (2017).
Lu, H. et al. A consensus S. cerevisiae metabolic model Yeast8 and its ecosystem for comprehensively probing cellular metabolism. Nat. Commun. 10 (1), 3586. 10.1038/s41467-019-11581-3 (2019).
Oh, YK., Palsson, BO., Park, SM., Schilling, CH., Mahadevan, R. Genome-scale reconstruction of metabolic network in Bacillus subtilis based on high-throughput phenotyping and gene essentiality data. J Biol Chem. 28;282(39), 28791-28799. doi: 10.1074/jbc.M703759200 (2007).
Zhang, Y. et al. A new genome-scale metabolic model of Corynebacterium glutamicum and its application. Biotechnol Biofuels, 10, 169. doi:10.1186/s13068-017-0856-3 (2017).
Burgard, AP., Pharkya, P., Maranas, CD. Optknock: a bilevel programming framework for identifying gene knockout strategies for microbial strain optimization. Biotechnol Bioeng. 20;84(6):647-57. doi:10.1002/bit.10803 (2003).
Pharkya, P., Maranas, CD. An optimization framework for identifying reaction activation/inhibition or elimination candidates for overproduction in microbial systems. Metab Eng. 8(1):1-13. doi: 10.1016/j.ymben.2005.08.003 (2006).
Ranganathan, S., Suthers, PF., Maranas, CD. OptForce: an optimization procedure for identifying all genetic manipulations leading to targeted overproductions. PLoS Comput Biol. 15;6(4):e1000744. doi: 10.1371/journal.pcbi.1000744 (2010).
von Kamp, A., Klamt, S. Growth-coupled overproduction is feasible for almost all metabolites in five major production organisms. Nat Commun. 22;8:15956. doi: 10.1038/ncomms15956 (2017).
Razaghi-Moghadam, Z., Nikoloski, Z. GeneReg: a constraint-based approach for design of feasible metabolic engineering strategies at the gene level, Bioinformatics, 37(12), 1717–1723, doi.org/10.1093/bioinformatics/btaa996 (2021).
Küken, A., Nikoloski, Z. Computational Approaches to Design and Test Plant Synthetic Metabolic Pathways, Plant Physiology, 179(3), Pages 894–906, doi.org/10.1104/pp.18.01273 (2019)
Lewis, NE., Nagarajan, H., Palsson, BO. Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods. Nat Rev Microbiol. 27;10(4):291-305. doi: 10.1038/nrmicro2737 (2012).
Goldsmith, M., Tawfik, DS. Enzyme engineering: reaching the maximal catalytic efficiency peak. Curr Opin Struct Biol. 47:140-150. doi: 10.1016/j.sbi.2017.09.002 (2017).
Sánchez, B. J. et al. Improving the phenotype predictions of a yeast genome‐scale metabolic model by incorporating enzymatic constraints. Mol. Syst. Biol. 13, 935 (2017).
Bekiaris, PS., Klamt, S. Automatic construction of metabolic models with enzyme constraints. BMC Bioinformatics. 14;21(1):19. doi: 10.1186/s12859-019-3329-9 (2020).
Jeske, L., Placzek, S., Schomburg, I., Chang, A. & Schomburg, D. BRENDA in 2019: a European ELEXIR core data resource. Nucleic Acids Res. 47, D542–D549 (2019).
Wittig, U., Rey, M., Weidemann, A., Kania, R., Müller, W. SABIO-RK: an updated resource for manually curated biochemical reaction kinetics. Nucleic Acids Research, 46, D656–D660, doi.org/10.1093/nar/gkx1065 (2018).
Li, F., Yuan, L., Lu, H. et al. Deep learning-based kcat prediction enables improved enzyme-constrained model reconstruction. Nat Catal 5, 662–672 https://doi.org/10.1038/s41929-022-00798-z (2022).
Yu, H., Deng, H., He, J., Keasling, J., Luo, X. Highly accurate enzyme turnover number prediction and enzyme engineering with PreKcat. Research Square. doi: 10.21203/rs.3.rs-2749688/v1 (2023).
Kroll, A., Lercher, MJ. Machine learning models for the prediction of enzyme properties should be tested on proteins not used for model training bioRxiv 2023.02.06.526991; doi: https://doi.org/10.1101/2023.02.06.52699.
Davidi, D. et al. Global characterization of in vivo enzyme catalytic rates and their correspondence to in vitro kcat measurements. Proc. Natl. Acad. Sci. 113, 3401–3406 (2016).
Heckmann, D., et al. Kinetic profiling of metabolic specialists demonstrates stability and consistency of in vivo enzyme turnover numbers. Proceedings of the National Academy of Sciences, 117(37), 23182-23190 (2020).
Xu, R., Razaghi-Moghadam, Z., Nikoloski, Z. Maximization of non-idle enzymes improves the coverage of the estimated maximal in vivo enzyme catalytic rates in Escherichia coli, Bioinformatics, 37(21), 3848–3855 doi.org/10.1093/bioinformatics/btab575 (2021).
Küken, A., Gennermann, K. and Nikoloski, Z. Characterization of maximal enzyme catalytic rates in central metabolism of Arabidopsis thaliana. The Plant Journal, 103(6), 2168-2177 (2020).
Hackett, S.R. et al. Systems-level analysis of mechanisms regulating yeast metabolic flux. Science, 354, 631 (2016).
Arend, M., Zimmer, D., Xu, R., Sommer, F., Mühlhaus, T., Nikoloski, Z. Proteomics and constraint-based modelling reveal enzyme kinetic properties of Chlamydomonas reinhardtii on a genome scale. Nat Commun 14, 4781 doi.org/10.1038/s41467-023-40498-1 (2023).
Ferreira, MAM., Silveira WBD., Nikoloski Z. Protein constraints in genome-scale metabolic models: Data integration, parameter estimation, and prediction of metabolic phenotypes. Biotechnol Bioeng. doi: 10.1002/bit.28650 (2024).
Wendering, P., Arend, M., Razaghi-Moghadam, Z. et al. Data integration across conditions improves turnover number estimates and metabolic predictions. Nat Commun 14, 1485 doi.org/10.1038/s41467-023-37151-2 (2023).
Domenzain, I. et al. Reconstruction of a catalogue of genome-scale metabolic models with enzymatic constraints using GECKO 2.0. Nat. Commun. 13, 3766 (2022).
Ye, C., et al. Improving lysine production through construction of an Escherichia coli enzyme-constrained model. Biotechnol Bioeng. 117(11):3533-3544. doi: 10.1002/bit.27485 (2020).
Yeo, HC., Hong, J., Lakshmanan, M., Lee, DY. Enzyme capacity-based genome scale modelling of CHO cells. Metab Eng. 60:138-147. doi: 10.1016/j.ymben.2020.04.005. (2020).
Jonathan, L., et al. An atlas of human metabolism. Sci. Signal. 13 doi:10.1126/scisignal.aaz1482 (2020).
Massaiu, I., et al. Integration of enzymatic data in Bacillus subtilis genome-scale metabolic model improves phenotype predictions and enables in silico design of poly-γ-glutamic acid production strains. Microb Cell Fact. 18, 3 doi.org/10.1186/s12934-018-1052-2 (2019).
Niu, J., et al. Construction and Analysis of an Enzyme-Constrained Metabolic Model of Corynebacterium glutamicum. Biomolecules, 12, 1499 doi.org/10.3390/biom12101499 (2022).
Wendering, P., Nikoloski, Z. Genome-Scale Modeling Specifies the Metabolic Capabilities of Rhizophagus irregularis. mSystems. 22;7(1):e0121621. doi: 10.1128/msystems.01216-21 (2022).
Jumper, J., et al. Highly accurate protein structure prediction with AlphaFold. Nature, 596(7873), 583-589 (2021).
Griesbeck, O. CRISPR/Cas9-based directed evolution in mammalian cells, Current Opinion in Structural Biology, 69, 35-40 (2021).
Orth, J., Thiele, I. & Palsson, B. What is flux balance analysis? Nat Biotechnol 28, 245–248 doi.org/10.1038/nbt.1614 (2010).
Segre`, D., Vitkup, D., Church, GM. Analysis of optimality in natural and perturbed metabolic networks, PNAS 99(23) 15112-15117 doi.org/10.1073/pnas.232349399 (2002).
Hashemi, S., Laitinen, R., Nikoloski, Z. Models and molecular mechanisms for trade-offs in the context of metabolism. Molecular Ecology, 1–11 doi.org/10.1111/mec.16879 (2022).
Domenzein, I., Lu, Y., Shi, J., Lu, H., Nielsen, J. Computational biology predicts metabolic engineering targets for increased production of 102 valuable chemicals in yeast. 10.1101/2023.01.31.526512. (2023).
McElreath, R. Statistical rethinking (1st ed.). Safari an O'Reilly Media Company Chapman and Hall/CRC. https://www.safaribooksonline.com/library/view//9781482253481/?ar (2018).
Gurobi Optimization, L. Gurobi Optimizer Reference Manual https://www.gurobi.com (2021).
The UniProt Consortium , UniProt: the Universal Protein Knowledgebase in 2023, Nucleic Acids Research, 51, D1 D523–D531, doi.org/10.1093/nar/gkac1052 (2023).

There is NO Competing Interest.

SupplementaryTables.xlsx
Tables 1-8

Download PDF

Version 1

posted

You are reading this latest preprint version

Harnessing the optimization of enzyme catalytic rates in engineering of metabolic phenotypes

Status:

Version 1

Abstract

Figures

Introduction

Results and Discussion

Targeting turnover numbers for engineering applications

Application of OKO to two cell factories

OKO identifies strategies for overproduction of amino acids

Setting the ground for experimental validation

Refinement of OKO enhances its applicability

Feasibility of strategies designed by employing OKO⁺

Conclusions

Methods

Formulation of OKO

Formulation of OKO+

Robustness analysis of enzyme abundance

OKO and OKO⁺ implementation

Mapping of \({\varvec{k}}_{\varvec{c}\varvec{a}\varvec{t}}\)values from ecGEMs and DLKcat

Declarations

Acknowledgements

References

Additional Declarations

Supplementary Files

Status:

Version 1

Harnessing the optimization of enzyme catalytic rates in engineering of metabolic phenotypes

Status:

Version 1

Abstract

Figures

Introduction

Results and Discussion

Targeting turnover numbers for engineering applications

Application of OKO to two cell factories

OKO identifies strategies for overproduction of amino acids

Setting the ground for experimental validation

Refinement of OKO enhances its applicability

Feasibility of strategies designed by employing OKO+

Conclusions

Methods

Formulation of OKO

Formulation of OKO+

Robustness analysis of enzyme abundance

OKO and OKO+ implementation

Mapping of \({\varvec{k}}_{\varvec{c}\varvec{a}\varvec{t}}\)values from ecGEMs and DLKcat

Declarations

Acknowledgements

References

Additional Declarations

Supplementary Files

Status:

Version 1

Feasibility of strategies designed by employing OKO⁺

OKO and OKO⁺ implementation