Quantitative analysis of experimental metabolic data is frequently challenged by non-intuitive, complex patterns which emerge from regulatory networks. The complex output of metabolic regulation can be summarised by metabolic functions which comprise information about dynamics of metabolite concentrations. In a system of ordinary differential equations, metabolic functions reflect the sum of biochemical reactions which affect a metabolite concentration, and their integration over time reveals metabolite concentrations. Further, derivatives of metabolic functions provide essential information about system dynamics and elasticities. Here, invertase-driven sucrose hydrolysis was simulated in kinetic models on a cellular and subcellular level. Both Jacobian and Hessian matrices of metabolic functions were derived for quantitative analysis of kinetic regulation of sucrose metabolism. Model simulations suggest that transport of sucrose into the vacuole represents a central regulatory element in plant metabolism during cold acclimation which preserves control of metabolic functions and limits feedback-inhibition of cytosolic invertases by elevated hexose concentrations. Introducing the reversible formation of an enzyme-substrate complex (E + S → ES), a release of product P from ES (ES → E + P), and the simplifying assumption that formation of ES is much faster than its decomposition into E and P, finally yields the Henri–Michaelis–Menten kinetics . If concentration dynamics are considered (only) over time, ordinary differential equations (ODEs) are applied while partial DEs account for more than one independent variable, for example, time and space.The quantitative study of biochemical reaction networks represents an interdisciplinary research area of (bio)chemistry, physics and mathematics. Enzymes catalyse chemical reactions under physiologically relevant conditions. Enzyme activity directly depends on temperature, pH, ion strength and redox potential of a cell or compartment showing characteristic optima Ineffluxes :(3)KM in a low-millimolar range . Invertases play a central role in diverse processes of plant metabolism, development and response to environmental stress Koch, . Plant ie Sturm, . Invertae Sturm, . While be Sturm, . Previoue Sturm, . Here, m2.Arabidopsis thaliana under ambient (22°C) and low (4°C) temperature  = rin − rinv. Simulation results of different sucrose concentrations were plotted against glucose and fructose concentrations (f(Suc), J and H for one sucrose concentration (a detailed definition of concentrations is provided in the figure legend). Although sucrose concentrations used for 4°C simulations were up to 8-fold higher than under 22°C, resulting absolute values and dynamics of f(Suc) were significantly lower than under 22°C . As expected, under conditions of low product concentration, f(Suc) became minimal under both temperatures due to increased rates of sucrose cleavage (f(Suc) was due to increased hexose concentrations (inhibitors) and a reduced Vmax of invertase (see Table 1). As a result, also the dynamic range of J and H decreased across all simulated scenarios by several orders of magnitude  induced by (slight) changes of glucose and fructose concentrations, respectively. At 22°C, high glucose concentrations (~ 2.5−3 μmol gFW−1) minimise j13 and, with this, also the regulatory effect of fructose dynamics on f(Suc) (see −1) also lead to minimal values of j13, which were, however, still significantly higher than j12 (see p < .001). This discrepancy became also visible in the curvature of f(Suc), that is, in the Hessian matrix  see . At 4°C,n matrix .j12 ≈ j13, that is, These observations suggest that, under ambient conditions and (increased) glucose concentrations, it is 3.Arabidopsis leaf mesophyll cells were estimated as previously described assuming the cytosol to comprise 5% and the vacuole 80% of the total cell volume  1 g fresh weight of Arabidopsis leaf material  across a physiologically feasible range of metabolite concentrations at 22°C revealed higher variability of vacuolar metabolic functions than in the cytosol  due to lowered invertase inhibition by glucose and fructose. At 4°C, the discrepancy between concentration effects on f(Suc) in cytosol and vacuole became stronger due to significant cold-induced sugar accumulation (f(Suc) in the cytosol was almost invariant across the simulated sucrose concentration range of 25.6–51.2 mM (f(Suc) (f(Suc) which revealed dynamics of vacuolar fructose concentration to have the strongest regulatory effect within the simulated scenario . Hence, lowered effective metabolite concentrations in the vacuole resulted in higher elasticity of mulation . Under t–51.2 mM  while dy (f(Suc) . This wascenario .f(Suc) and provide further evidence for a dominant role of fructose in regulation of sucrose cleavage under low temperature. Previous studies have shown that sugar accumulation, in general, plays a central role in plant cold response and acclimation  in the cytosol and vacuole by fructose directly connects sucrose dynamics with the stabilisation of many other cellular pathways. In future studies, a combination of the presented kinetic approach with subcellular sugar analysis of mutants being affected in sucrose cleavage and subcellular sugar transport might reveal further detailed insights into the regulatory network of plant sucrose metabolism.Together with the findings of the whole cell model , these o4.n-dimensional functions and surfaces, their extrema and their curvature .
In summary, I am convinced that this article is of high interest for the readership of Quantitative Plant Biology. I would be pleased to publish it within your journal and thank you in advance for editing my manuscript.
Sincerely yours,
Thomas Nägele
 Comments to Author: Prof. Nägele presents a theoretical study in which he applies the Jacobian and Hessian matrix of metabolic functions to analyse a simple model of invertase-driven sucrose hydrolysis. Using a recently published set of carbon uptake rates and kinetic parameters from Arabidopsis thaliana, accession Col-0 at ambient temperature and cold stress the author studies the potential regulatory role of metabolite dynamics during plant cold acclimation. The manuscript is well written and sound. However, as the concept of applying partial derivatives to study metabolite dynamics is not novel, the manuscript is currently lacking convincing insights that can be gained from the presented analysis. Thus, I have a few major and minor suggestions, most importantly:The manuscript would gain matter if the author elaborated more on the biological insights of this computational analysis and how sucrose hydrolysis affects metabolism under normal conditions and cold stress.Minor points:The term “metabolic function” can have different meanings in different scientific communities and contexts. Thus, defining this term even more explicitly, both in the abstract and the introduction, could avoid confusing the reader.It would be insightful for the reader if this analysis was placed in a larger context and to learn in which other studies the Jacobian and/or Hessian matrix has been used to study metabolite dynamics.Although the manuscript is well written and enjoyable for an expert reader it might be challenging to follow for a non-expert reader. However, I guess that might be expected from a manuscript to be published in Quantitative Plant Biology. Comments to Author: The paper of Nägele entitled “Metabolic regulation inferred from Jacobian and Hessian matrices of metabolic functions” introduces a mathematical modeling framework based on the estimation of Jacobian and Hessian matrices of a metabolic network at a steady state to describe influences of metabolites and conditions on fluxes and metabolite concentrations. It is applied to a simple model of invertase-driven sucrose hydrolysis using literature data under two different temperatures.The interdisciplinary combination of experiments and systems theoretic analysis is generally interesting and promising. However, while reading the paper, I had several difficulties in understanding the overall aim of the study and to follow the line of argumentation. I was not able to extract the main research results. I suggest to re-structure the paper in this respect and hope that my detailed comments below help to do so. Moreover, I recommend considering teaming up with a partner from the mathematical/modeling field, to clarify the issues on the mathematical side.Major points:I found the paper difficult to read, mainly due to the structure and line of argumentation:- The introduction contains a short explanation the complexity of enzyme activities in cellular systems, explains the well known law of mass action and states that metabolic systems can be described by differential equations.In an introduction, I would rather expect that the intro describes current state of work in the field, their limitations and open research questions / problems, and then states how (some of) these are addressed in the paper and which methods are used, and probably a short outlook on the main results of the paper.- The section “Deriving a Jacobian matrix to study ….” (p4ff) still reads as a kind of introduction / review for a derivation of the MM kinetics. When the sucrose hydrolysis system was introduced as a model (Eq4), it was not clear to me that this is the particular application system for the paper. In the following, product inhibition of invertases are described . Since this is crucial also for the following, I suggest to improve the reaction scheme to make this dependence clear, and probably cast it into a Figure, which illustrates the example system that is analyzed here. In connection with the mathematical model (Eq 8-11).- I also suggest to design a figure that illustrates the methodological pipeline. Key messages do not become clear from only one Figure in the end of the paper.- p6: are equations 8,9 extracted from other literature sources? Please clearly indicate-p7, first line: Now that the model is introduced, one expects the description of questions and goals in the context of this model latest; instead, a description of linearization to study stability of a steady state follows. I do not understand the message of this paragraph. The model introduced on p6 clearly reaches a dynamic steady state with constant in- and effluxes, if I am not mistaken. The time scale of this convergence of course depends on initial concentrations and parameter values for rate constants and Michaelis constants. Now it is stated that plant metabolism can hardly be described as in steady state due to its external and internal dynamics, which is, however, not included in the model. The motivation why the analysis via Jacobian and Hessian matrices makes sense at all if the steady state assumption is not fulfilled is not clear to me. Moreover, the assumption that the velocity of an enzymatic reaction linearly depends on substrate concentration is in contrast to the before mentioned MM kinetics, where the order of the reaction velocity with respect to the substrate changes from one to zero with increasing substrate concentration.- It is not completely clear what the Jacobian matrix can be used for. It is argued that the spectrum of J_f indicates stability of a steady state, but is stability really a relevant issue for the particular system at hand? Without knowing the Jacobian matrix and the exact dynamics, I would intuitively say that this is a stable system with respect to perturbations of any concentrations of species in the network in a steady state.- A critical discussion of limitations of the method / results is missing. How do results relate to other similar studies? Is this approach e.g. related to Modular response analysis, which is to my knowledge derived from Metabolic Control Analysis?- The application in connection with the data gathered in Table 1 is interesting, but the description is not sufficient to understand the key points: what is the goal of this application / what are the questions, how are r_inv rates exactly calculated, what do we learn from the results?Minor- p3: explanation mass action law: “This probability is proportional to (I) the concentration of reactants, (ii) to the number of molecules which participate in a reaction”: this is a misleading wording. The number of molecules usually appears in stochastic descriptions, where molecule numbers are low. Otherwise, concentrations are used in the law of mass action.- p3, Equation 1, similarly: what are S_i and P_j, are these concentrations or molecule numbers?-p7, Jacobian matrix: I would rather explain linearization by the ODE system for the dynamics of a small perturbation from a steady state, i.e. \dot (\Delta x)=J_f(\bar x)\Delta x, where \Delta x=x-\bar x is the deviation from the steady state \bar x and J_f(\bar x) is the Jacobian matrix of the ODE system evaluated at the steady state (which is important but missing in the text).- p8, sentence: Further, these equations show:… is this clear from the equations? I think this is generally intuitively clear when using MM kinetics to describe substrate conversions- p8: what is a “square decrease towards zero”?-p8, equ. 16 not clear to me. If hexose is present in large amounts, this inhibits r_inv and, if r_in is constant, this leads to an accumulation of Suc, right? Can’t this be seen just by the reaction scheme with known feedback influences? Comments to Author: Dear Prof. Nägele,
we have now received the required number of review reports. Unfortunately, both reports are critical and request major rewriting of your manuscript.
I suggest that you take into account the comments of the reviewers and revise the manuscript accordingly. In its current form the manuscript is not appropriate for publication in Quantitative Plant Biology.
Kind regards,
Christian Fleck No accompanying comment. Dear Dr. Hamant,
Dear Dr. Fleck,
I am submitting a fully revised theories article to be considered for publication in your journal Quantitative Plant Biology. Based on reviewer comments, the article is now entitled “Metabolic regulation of subcellular sucrose cleavage inferred from Jacobian and Hessian matrices of metabolic functions”. I have addressed all comments raised by both reviewers and have extended my theoretical analysis to a subcellular level of metabolism. My findings provide strong evidence for an important role of vacuolar sucrose transport during cold acclimation. To my opinion, this provides strong evidence for the applicability and usefulness of my approach. I have further added a methodological pipeline graph to indicate how metabolic functions and their dynamics might be numerically analysed to reveal detailed insights into metabolic regulation. To facilitate further review activities, I have highlighted all changes made (yellow background).
In summary, I am convinced that this revision has improved article is of high interest for the readership of Quantitative Plant Biology. I would be pleased to publish it within your journal and thank you in advance for editing my manuscript.
Sincerely yours,
Thomas Nägele Comments to Author: The author has addressed all my suggestions and questions in a satisfying manner. The revised version of the manuscript has much gained from the addition of more biological context. I only have two minor comments left.Axis labels of Figure 1 and especially Figure 3 are fairly small and could be increased for better readability.Figure 2 seems to be corrupted during the submission process. Comments to Author: I apologise for the considerable time it took to review the manuscript, but we had difficulties to find the needed number of reviews. One reviewer decided to stay anonymous. I therefore attach the review below.
I recommend to carefully consider the comments of this reviewer. In particular, I would like to remind the author that a research article is not a review article. I suggest to shorten the introductory material as also proposed by the reviewer.
Report from anonymous reviewer:
In my opinion, the revised manuscript has improved compared to the original one. In particular, some of the newly added paragraphs about the interpretation of the findings of the study in the biological context are helpful. However, I still think that the manuscript needs some major revisions in order to make it accessible to a broad readership.
My major concern is about the structure of the paper. While this has partly improved in the revised version, I still think that it contains too much text about „standard knowledge“ . It takes the reader a long time until the first results are presented. Moreover, at this point the „study design“  is still not completely clear. I could also not find a concise summary of the major findings of the paper.
To my knowledge, the theory about metabolic networks is vast, and interpretations of Jacobian  matrices can also be found elsewhere. So I suggest to re-structure the content of the paper and to 1. shorten standard knowledge considerably, 2. think about how to even more emphasize and illustrate the major findings, 3. refer to existing literature about using J and H for an analysis of metabolic networks.
It is also still not completely clear to me what is to be estimated. The Jacobian and Hessian matrix of a steady state are just matrixes with fixed entries that can readily be calculated if all model parameters are given. And if I understand correctly, this is what is done to produce the results. However, the author elaborates on estimating Jacobian matrices from experimental data, which is a much harder problem. I do not see the connection to his results.
The added paragraph on p7 about why a steady state assumption is justified is helpful, but should be integrated earlier in the manuscript.
 No accompanying comment. Dear Dr. Hamant,
Dear Dr. Fleck,
based on your and reviewer comments, I have revised my article entitled “Metabolic regulation of subcellular sucrose cleavage inferred from quantitative analysis of metabolic functions”. I have addressed all comments raised by you and both reviewers. I have added a supplemental file to explain the mathematical basics behind the analysis to prevent having too much text in the main manuscript/introduction.
I hope I can convince you that this revision has improved the article and can be considered for publication in Quantitative Plant Biology.
Thank you very much for editing my manuscript!
Sincerely yours,
Thomas Nägele Comments to Author: Dear Dr. Nägele,
I find your manuscript now sufficiently improved and ready for publication in QPB.
Kind regards,
Christian Fleck No accompanying comment.


We constructed a methanol assimilation pathway to produce poly-3-hydroxybutyrate (P3HB) using the MCC pathway, which included the ribulose monophosphate (RuMP) pathway for methanol assimilation and non-oxidative glycolysis (NOG) for acetyl-CoA (precursor for PHB synthesis) production. The theoretical product carbon yield of the new pathway is 100%, hence no carbon loss. We constructed this pathway in E. coli JM109 by introducing methanol dehydrogenase (Mdh), a fused Hps–phi (hexulose-6-phosphate synthase and 3-phospho-6-hexuloisomerase), phosphoketolase, and the genes for PHB synthesis. We also knocked out the frmA gene  to prevent the dehydrogenation of formaldehyde to formate. Mdh is the primary rate-limiting enzyme in methanol uptake; thus, we compared the activities of three Mdhs in vitro and in vivo and then selected the one from Bacillus methanolicus MGA3 for further study. Experimental results indicate that, in agreement with the computational analysis results, the introduction of the NOG pathway is essential for improving PHB production . We demonstrated that PHB can be produced from methanol via metabolic engineering, which provides the foundation for the future large-scale use of one-carbon compounds for biopolymer production.The naturally occurring one-carbon assimilation pathways for the production of acetyl-CoA and its derivatives often have low product yields because of carbon loss as CO Escherichia coli, have gained great attention in the bioconversion of methanol [E. coli, as the expression of only three heterologous enzymes is sufficient for methanol assimilation [E. coli to enable methanol assimilation [E. coli, demonstrating the possibility of in vivo conversion of methanol into a specialty chemical [The increasing demand for energy and resources from rapid economic development has prompted research on possible alternatives. Some alternative sources, such as biogas, bioethanol, and biomethanol, have been widely produced from some waste materials ,2. Over methanol . There amethanol . Among tmilation . Muller milation . Whitakechemical .E. coli, methanol utilization via the RuMP pathway involves CO2 loss and ATP expenditure in the synthesis of acetyl-CoA–derived products [2, thereby reducing the maximum carbon yield of acetyl-CoA to 67%. Similarly, two other methanol assimilation pathways—the serine pathway and the XuMP pathway—also reduce the carbon yield to 54% and 67%, respectively, which are not optimal pathways for maximizing the yields of acetyl-CoA–derived metabolites [Although the RuMP cycle is the most applicable methanol assimilation pathway in products . Specifiabolites . To solvabolites  designed2 and H2O, resulting in a significant reduction in “white pollution” [E. coli and convert methanol to the acetyl-CoA–derived product PHB. An extended metabolic network model of E. coli incorporating the methanol assimilation pathway and the PHB synthesis pathway is used to identify the optimal pathway. Then, the functional modules for methanol assimilation, PHB synthesis, and NOG are introduced into E. coli, thereby constructing the entire bioconversion pathway from methanol to PHB.As a derivative product of acetyl-CoA, poly-3-hydroxybutyrate (PHB) has excellent biodegradability. Within a certain period of time, microorganisms can break down PHB into COllution” ,14. PHB llution” ,16,17. Allution” . To thisE. coli metabolic network model based on iML1515 was used to calculate the optimal production pathway and yield of PHB by performing flux balance analysis (FBA) [E. coli, the methanol utilization reaction converting methanol to formaldehyde and reactions of the MCC pathway ) were added to the iML1515 model. The FBA calculation was performed using the COBRApy [An extended genome-scale is (FBA) ,20. PHB  COBRApy . In the mdh2  from Bacillus methanolicus MGA3, mdh-CT  from Cupriavidus necator N-1 [TaADH  from Thermoplasma acidophilum DSM 1728 [E. coli BL21 (DE3) for protein expression. The fused Hps–phi gene was synthesized  according to the sequence reported by Orita et al. [The primers used in the plasmid construction were obtained from GENEWIZ  and are listed in ator N-1 , and TaADSM 1728  were synT7 promotors in the expression vector pACYCDuet-1 were replaced by the Trc promotor from pTrc99a to reconstruct a new vector called pZQ for the C1 assimilation module according to Golden Gate cloning [T7 promotor of the mcs1 region with primers 09 and 10 . The re-amplified sequence was then re-circled by enzyme-cut and link-up with BsaI and T4 DNA-ligase . Finally, the re-circled plasmid was finally transformed to E. coli JM109, and positive vectors were verified by colony PCR and Sanger sequencing.Two  cloning . The vec9 and 10 , which w1 and 12  was desiT7 promotor was operated based on the first T7 promotor. The differences between the two were that (i) the initial vector was pACYCDuet-1, in which the T7 promotor changed to the Trc promotor, and (ii) the primers for the lining vector and re-amplifying primers  was first introduced into the multiple cloning site 1 of plasmid pZQ, individually with primers 17 and 18, 19 and 20, and 21 and 22, respectively (the restriction enzyme cutting sites are listed in A C1 assimilation module was built by introducing methanol dehydrogenase (Mdh), hexulose-6-phosphate synthase (Hps), and 3-phospho-6-hexuloisomerase (Phi) into a reconstructed plasmid pZQ. Each methanol dehydrogenase gene (The NOG module was constructed on plasmid PBHR68 containing the PHB production module . The fxpE. coli strain JM109-NOG were used as the chassis strain for further genome modification [frmA (glutathione (GSH)-dependent formaldehyde dehydrogenase); this deletion method was conducted according to a 1-step inactivation of chromosomal genes [The wild-type JM109 and the previously constructed fication . Plasmidal genes . The funE. coli strain BL21 (DE3) with constructed pET-28a vectors grew in lysogeny broth  at 37 °C and 200 rpm with 50 µg/mL kanamycin  to an absorbance ranging from 0.6 to 0.8 (600 nm). Gene expression was induced by adding 0.1 mM isopropyl-b-D-thiogalactopyranoside , and the cells were incubated at 18 °C for 16 h. The bacterial cells were harvested by centrifugation  and re-suspended in a lysis buffer ). The cells were disrupted by passing the cell suspension three times through a high-pressure homogenizer (JN-3000 PLUS) at 6,894,757 Pa (1000 Psi). Cell debris and membrane fractions were removed by centrifugation . The supernatant was loaded onto a Ni–NTA agarose column  equilibrated with the lysis buffer . The column was washed with 2 column volumes of the lysis buffer and 2 column volumes of the wash buffer . The proteins were finally eluted with a gradient elution buffer  imidazole, 50 mM Tris HCl, 150 mM NaCl; pH = 7.5). The purified proteins were desalted using an ultrafiltration tube  with a desalting buffer  [The H = 7.5) . ProteinH = 7.5)  with a B2HPO4 buffer containing 5 mM MgSO4, 500 µM NAD+ , and 200 µg protein; 0.5 M methanol  was added [The reaction was conducted in 3-paralleled 200 µL in pre-heated (37 °C) 50 mM Kas added . The proas added .2HPO4, 2.5 mM NADP+, 5 mM MgSO4, 10 U G6PD, and 10 U Pgi. To start the reaction, 5 mM formaldehyde was added to the reaction mixture. Each sample was tested in 3 parallels.The fused enzyme activity of purified Hps–phi was assayed by measuring the NADPH formation via coupled reactions catalyzed by glucose-6-phosphate dehydrogenase (G6PD) and phosphoglucoisomerase (Pgi) at 37 °C as described previously ,34. Subs600 of the culture and the assumption that 1 L culture with an OD600 of 1 contains 0.250 g of biomass, half of which was assumed to be protein.Enzyme activity assay for methanol dehydrogenase and Hps–phi was conducted in vivo using a method similar to that described in the study by Muller et al. . Cells wE. coli strains were grown overnight in an LB medium with antibiotics. The following morning, 1 mL bacteria solution was used to inoculate in main cultures containing 50 mL of MS medium with 100 mM ribose  in 250 mL baffled shake flasks to an OD600 of 0.8. Subsequently, 0.1 mM IPTG was added to the solution. Cells were grown at 20 °C, shaking at 220 rpm for 10 h.Constructed g for 4 min at room temperature and re-suspended with water. They were then centrifuged and re-suspended twice. The pellet was re-suspended in 50 mL standard MS medium without glucose or ribose, and the actual OD600 was measured. The re-suspended cells were inoculated at 37 °C, shaking at 150 rpm as 0.5 M methanol was added. After inoculation for 22 h, the re-suspended cells  were freeze-dried to determine the PHB concentration.Cells were centrifuged at 10,000× w/w %) was quantified by gas chromatography  with an HP-5 capillary column [w/w %) was defined as the percent ratio of PHB concentration (dry weight per liter of culture broth) to cell concentration (dry weight per liter of culture broth).The PHB content  to form the MCC pathway, the PHB production rate was improved to 1.5 mmol/gDCW/h from 6 mmol/gDCW/h methanol consumption  exhibits the highest activity both in vitro (11.4 mU/mg) and in vivo (9.2 mU/mg). Therefore, mdh2 was selected to construct the C1 assimilation module in the engineered strains.The C1 assimilation module included methanol dehydrogenase and the fused Hps–phi enzyme. The Hps–phi enzyme was chosen based on the study by Orita et al. , which rmdh2 could successfully enable the conversion of methanol to formaldehyde in strain JM109-Δfrm-mdh2, whereas the formaldehyde could not be further utilized. With the further introduction of Hps-phi fusion, the formaldehyde concentration could be reduced in strain JM109-Δfrm-C1, which indicated that formaldehyde was converted into the RuMP pathway. However, a significant amount of formaldehyde remained that could be utilized. This might be owing to the lack of ribulose-5-phosphate, which was a key intermetabolite for the condensation of formaldehyde  was conducted in a previous study [fxpk from Bifidobacterium adolescentis into the genome of JM109-Δfrm-C1-PHB, obtaining the strain JM109-NOG-Δfrm-C1-PHB. To increase the Fxpk expression, the fxpk gene was also inserted into the PHB synthesis plasmid pBHR68 for the formation of a new plasmid, pBHR70. Plasmid PBHR70, replacing PBHR68, was introduced into JM109-NOG-Δfrm-C1 to obtain a new strain JM109-NOG-Δfrm-C1-PHB-NOG with improved phosphoketolase expression.The construction of plasmid pBHR68 for PHB production  when supplied with methanol. Moreover, the PHB content of JM109-Δfrm-C1-PHB strain on methanol (3.51%) was higher than that of the control group JM109-Δfrm-PHB (3.39%). These results indicated that methanol was indeed converted to PHB with the addition of the C1 module. However, both the increases in PHB content were relatively low, implying that the classic RuMP pathway, solely, might not be sufficient for efficient PHB biosynthesis from methanol in E. coli.To evaluate whether the C1 and NOG modules contribute to PHB biosynthesis, PHB production was conducted with or without methanol . A statiAfter the introduction of the NOG module, the PHB content of JM109-NOG-Δfrm-C1-PHB strain in the methanol group (3.75%) was about 22.5% higher than that in the non-methanol group (3.06%). The PHB content of strains with the NOG module (3.75%) was 6.8% higher than that of strains without the NOG module (3.51%) with methanol as a carbon source, which indicated that the addition of the NOG module could facilitate PHB biosynthesis from methanol. With the further overexpression of the NOG module using multi-copy plasmid in strain JM109-NOG-Δfrm-C1-PHB-NOG, its PHB content from methanol (6.19%) was 85% higher than that without methanol (3.33%) and was 65.1% higher than that produced by JM109-NOG-Δfrm-C1-PHB (3.75%). This indicated that the expression level of NOG is important in the methanol bioconversion using the MCC pathway. The comparison of the above results shows that the overexpression of the MCC pathway can significantly facilitate PHB biosynthesis from methanol, which is consistent with the in silico calculation result.Considering the low cost of methanol and the continuing efforts to convert abundant natural gas and coal into methanol, developing technologies to convert methanol into other industrial products has drawn interest . In receE. coli by introducing the Mdh and RuMP genes into the host. Whitaker et al. [B. stearothermophilus and demonstrated that the engineered strain could convert methanol to flavanone naringenin. However, both studies used the natural RuMP pathway for methanol assimilation, which is not favorable for the production of acetyl-CoA–derived products (such as PHB) resulting from carbon loss during pyruvate decarboxylation, as described by Bogorad et al. [Muller et al.  were ther et al.  further d et al. .E. coli to improve product yield. The MCC pathway is the combination of the RuMP pathway with the NOG pathway [On the basis of previous studies and guided by the optimal pathway for PHB production determined by genome-scale network analysis, we first engineered the MCC pathway in  pathway , which cmdh2 from B. methanolicus MGA3 and Hps–phi fusion [frmA gene coded the enzyme converting formaldehyde to formate would greatly reduce the availability of formaldehyde to Hps–phi , and PHB production from different organisms. Compared with the strain containing only the RuMP pathway for C1 assimilation, the strain with the complete MCC pathway produced more PHB by assimilating methanol. Despite the low PHB content relative to that from strains growing on glucose, the results indicate that the introduction of the MCC pathway in E. coli can improve its ability for C1 compound bioconversion. To our knowledge, the present study is the first metabolic engineering research on the conversion of methanol to PHB in E. coli. This study provides a basis for subsequent studies to further improve product yield from methanol.On the basis of metabolic network analysis, we found that the MCC pathway can convert C1 compounds into acetyl-CoA–derived products, such as PHB, without carbon loss. We engineered this pathway in


The inborn errors of metabolism (IEMs or Inherited Metabolic Disorders) are a heterogeneous group of diseases caused by a deficit of some specific metabolic pathways. IEMs may present with multiple overlapping symptoms, sometimes difficult delayed diagnosis and postponed therapies. Additionally, many IEMs are not covered in newborn screening and the diagnostic profiling in the metabolic laboratory is indispensable to reach a correct diagnosis. In recent years, Metabolomics helped to obtain a better understanding of pathogenesis and pathophysiology of IEMs, by validating diagnostic biomarkers, discovering new specific metabolic patterns and new IEMs itself. The expansion of Metabolomics in clinical biochemistry and laboratory medicine has brought these approaches in clinical practice as part of newborn screenings, as an exam for differential diagnosis between IEMs, and evaluation of metabolites in follow up as markers of severity or therapies efficacy. Lastly, several research groups are trying to profile metabolomics data in platforms to have a holistic vision of the metabolic, proteomic and genomic pathways of every single patient. In 2018 this team has made a review of literature to understand the value of Metabolomics in IEMs. Our review offers an update on use and perspectives of metabolomics in IEMs, with an overview of the studies available from 2018 to 2022. The Inborn errors of metabolism (IEMs or Inherited Metabolic Disorders) are a heterogeneous group of genetic disorders, usually inherited as recessive disorders or, in smaller proportion, as the result of spontaneous mutations. These diseases are caused by a defect in metabolic pathways involved in the metabolism of small  and large molecules , coenzymes, vitamins, etc. The defect results in an alteration of the body concentrations (increase or reduction) of these molecules. This may lead, for instance, to an excessive accumulation of macromolecules, or a deficit of the energy pathways, etc. The clinical expression of the defect and the organ damage depend on the metabolic pathway involved ,2.Although IEMs are disorders genetically transmitted the model ‘one gene-one enzyme-one disease’ can no longer be considered appropriate .Indeed, each patient has a peculiar phenotype that requires a personalized approach to these complex and rare diseases. Thus, Metabolomics, the global study of metabolites, small molecules within a mass range of 50 or 1500 daltons, can plays a central role in the study of IEMs, leading to a better understanding of the pathogenesis and pathophysiology, contributing to improving the processes of diagnosis, therapy and prognosis. Integrating genomics and metabolomics data represents the current challenge to improve the diagnosis and prognosis of IEM ,4,5.The purpose of this narrative review is to offer an update on the use and perspectives of metabolomics at IEMs.This review will focus on an overview of comprehensive studies, available from 2018 to 2022, and some interesting studies from 2017.IEMs are monogenic, often untreatable, disorders, in which a single enzyme or protein causes a distinct metabolic signature. Different variants in some proteins can lead to either deficiency or increase activity, with drastically different phenotypes. Due to their remarkable heterogeneity, IEMs are classified according to clinical, pathophysiological, affected enzymes, affected organelles and many other criteria. Nevertheless, numerous biochemical phenotypes that do not cause clinical disease have been described .Saudubray, et al. classified IEMs into three groups: intermediate metabolism disorders affecting small molecules, disorders involving primarily energy metabolism, and disorders involving complex molecules . FurtherTaken alone, IEMs are rare, however, globally they affect about 0.5–1 in 1000 people .For these reasons, awareness of these diseases, their presentations, and their evaluation is critical for healthcare professionals because they can occur at any age .The investigation of Inborn Errors of Metabolism has already benefitted from metabolomics as a tool to facilitate diagnosis by finding appropriate biomarkers in human samples .Metabolomics, one of the “omics” sciences, is a technique that investigates and detects the whole and comprehensive set of metabolites  present in a given biological system, organs, and biological fluids, portraying their phenotypes. This has proven to be very useful in the investigation of the human health since this technique is able to spot very rapidly every metabolic change induced by pathophysiological stimuli such as diseases, drug administration, environmental changes and nutrition .The study of the complex metabolic fingerprint and the comparative analyses of metabolomes are performed by a combined approach of spectrometric and spectroscopic techniques and computer programs. The most common metabolomics analyses techniques are nuclear magnetic resonance (NMR) spectroscopy, gas or liquid chromatography-mass spectrometry (GC-MS and LC-MS) ,11.Both NMR spectroscopy and mass spectrometry (MS) are widely used in metabolomics research. NMR spectroscopy is a powerful technique for the identification of small molecules and the analysis of their structure and dynamics. It is a non-destructive technique that does not require the separation of the metabolites prior to analysis, making it a suitable tool for the analysis of complex mixtures, such as biological fluids. In contrast, MS is a destructive technique that requires the separation of the metabolites before analysis. The separation step is usually performed using either gas or liquid chromatography. MS is capable of providing more accurate quantification of metabolites, and can detect a wider range of metabolites than NMR spectroscopy.According to Emwas et al., NMR spectroscopy is best suited for the analysis of low molecular weight compounds, while MS is more suitable for the analysis of high molecular weight compounds. NMR spectroscopy is also less sensitive than MS, which can be a limitation when analyzing low-abundance metabolites. However, NMR spectroscopy is more robust and reproducible than MS, making it a valuable tool for large-scale metabolomics studies.In summary, both NMR spectroscopy and MS have their strengths and weaknesses, and the choice of which technique to use depends on the specific goals of the study and the characteristics of the metabolites being analyzed ,13,14.Timely newborn screening and genetic profiling are crucial in early recognition and treatment of IEMs. Diagnostic delay may result in acute metabolic decompensation, progressive neurologic injury, or death .In most developed countries, and many developing countries, each newborn is screened for IEMs by dry blood spot (DBS) testing. In 1980s, targeted metabolomics with tandem mass spectrometry (MS/MS) was introduced as a reference technique for newborn screening, because of its capacity to screen a wide range of previously unscreened IEMs by a single test performed on a DBS.From their introduction in public health care, newborn screening programs have expanded to include now more than 50 inherited metabolic disorders, including aminoacidopathies, organic acidemias, fatty acid oxidation disorders, and lysosomal storage disorders. Despite its absolute clinical value and its primary role in public health care, newborn screening offers only a snapshot of minimal subset of metabolic alterations, and several IEMs are not identifiable by routine newborn screening programs ..20].However, Haijes et al., in 2019, showed that the direct-infusion high-resolution mass spectrometry (DI-HRMS) based non-quantitative metabolomics could correctly capture the biochemical profile of patients with an IEM in CSF. Eleven patient samples, harboring eight different IEM, and thirty control samples were analyzed. This analysis of patient CSF profiles resulted in correct ‘most probable diagnoses’ for all eleven patients, including non-ketotic hyperglycinaemia, propionic aciduria, purine nucleoside phosphorylase deficiency, argininosuccinic aciduria, tyrosinaemia type I, hyperphenylalaninemia and hypermethioninaemia .Therefore, Klinke et al., in 2020, developed an extendable targeted LC-MS/MS platform for the analysis of multiple metabolites in CSF, providing reference concentrations for several biomarkers. They demonstrated that a smaller sample volume (200 μL) is required with a single analytical platform resulting in faster diagnostic results while reducing preanalytical problems .,29.28,29A strict low-Phe diet eliminates all animal proteins and consists of a controlled amount of natural protein from plant sources to provide minimum Phe requirements and relies on the consumption of either elemental amino acid medical foods (AA-MFs) or glycomacropeptide medical foods (GMP-MFs) to provide the majority of dietary nitrogen and variable amounts of calories, carbohydrates, fats, minerals, and micronutrients ,30.metaIn the last years, metabolomics studies have focused on understanding the efficacy, collateral effect and difference between different nutritional regimens.Indeed 2017, a metabolomic study analyzed metabolites and neurotransmitters derived from Tyrosine and Tryptophan in plasma and urine samples from subjects with PKU consuming both AA-MF and GMP-MF. These authors confirm their hypothesis that differences in the composition of the intestinal microbiota occur with ingestion of AA-MF compared with GMP-MF, with a higher degradation of Tyr in AA-MF diet, thus reducing its bioavalability for synthesis of neurotransmitters . TherefoMoreover, a year later, another study investigated adults and adolescents with PKU on a low-Phe diet and with AA-MF and GMP-MF to evaluate lipid metabolism though metabolomics analysis. They observed significantly difference in total plasma cholesterol concentrations in classical PKU, variant PKU patients and controls .While, in patients with fatty acid oxidation (FAO) disorders, metabolomic was used to evaluate changes in metabolic pathways according to a different diet approach with the ingestion of ketone esters (KE). In fact, in patients with a maladaptive shift from fat to carbohydrate (CHO) oxidation during exercise this is thought to underlie myopathy and exercise-induced rhabdomyolysis. Thus, they tested this hypothesis in patients with very long-chain acyl-CoA dehydrogenase deficiency (VLCADD) . The resTargeted metabolomic was also applied in another recent study on oral ketone ester supplementation in patient with McArdle disease, to detect pyruvate, lactate, and acetoacetate in plasma and hydroxybutyrate, glucose, and glycerol in plasma and in breath samples .Finally, another application of metabolomics in this field, is represented by a study on resveratrol as a supply that can improve exercise capacity in patients with fatty acid oxidation (FAO) disorders .In the less studied IEMs, the studies still focused on researching some diagnostic and severity markers. In this process, targeted and untargeted metabolomics has been widely used. In 2021, Ning Liu et al., to examine the utility of untargeted metabolomics, tried to use the traditional metabolomic screening approach for many potentially treatable IEMs not included on NBS panels, nor covered in standard, first-line biochemical testing. A total of 14 IEMs were detected, including 3 conditions not included in the Recommended Uniform Screening Panel for NBS. Screening also identified 128 unique cases with IEMs, giving an overall diagnostic rate of 7.1%. In total, 70 different metabolic conditions were determined, including 49 states not presently included on the Recommended Uniform Screening Panel for NBS. These findings suggested that untargeted metabolomics provided a 6-fold higher diagnostic yield than the conventional screening approach and identified a broader spectrum of IEMs. Notably, with the expansion of NBS programs, traditional metabolic testing approaches identify few disorders beyond those covered on the NBS. These data support the capability of clinical untargeted metabolomics in screening for IEMs and suggest that broader screening approaches should be considered in the initial evaluation for metabolic disorders  37]..37].For example, in IEMs of the non-oxidative branch of the pentose phosphate pathway, untargeted metabolomics was able to identify novel biomarkers, thereby expanding the current knowledge of TKT e TALDO conditions and providing further insight into potential underlying pathophysiological mechanisms. Furthermore, untargeted metabolomic testing offers the advantage of having a single effective biochemical screening test for identification of rare IEMs, that may otherwise go undiagnosed due to their generally non-specific clinical presentations .Finally, the untargeted approach can also assess further perturbations of the metabolic network of disease in patients under ongoing treatment. For example, the metabolic defect in glycogen storage disease type I (GSDI) results in fasting hypo-glycemia and typical secondary metabolic abnormalities . Thus, GSDI has profound effects on various metabolic pathways in addition to the known typical exceptions. These alterations are present despite optimized dietary treatment, which may contribute to the risk of developing long-term complications, an inherent problem of GSDI which appears to be only partly modified by current therapy .Today the challenge is to interpret the metabolic pathways involved in each metabolic pathology. Indeed, metabolite perturbations are assessed based on current knowledge of specific metabolic deficits. Furthermore, the qualitative diagnostic process may have limitations that make it difficult to evaluate the clinical aspects observed in the patient.To address this gap, Karlien et al. proposed a single-platform, non-targeted quadrupole time-of-flight (QTOF) LC metabolic profiling method that can be applied for diagnostic screening of metabolic deficits present in each patient called Next Generation Metabolic Screening (NGMS).Through disease-specific filters, the authors identified a panel of 340 clinically relevant metabolites known to be diagnostic or to evaluate the efficacy of therapeutic interventions. The method would reduce the complexity of the data obtained and to extract the necessary diagnostic information.Thus, targeted analysis can be used to confirm the specificity of new disease biomarkers. For example, plasma NGMS analysis or evaluating of metabolic pathways of genetic variants of uncertain significance are applicable to type II xanthinuria. NGMS can also be used for non-targeted metabolomic results, be filtered using a panel of disease-associated metabolites. In fact, with this approach it was possible to obtain a correct diagnosis for 42 out of 46 IEMs by identifying potential new biomarkers known and still unknown .Another example concerned the identification of N-acetylmannosamine, which was increased in the body fluids of patients with severe developmental delay and dysmorphism. This marker identified a new metabolic pathology due to N-acetylneuraminic acid phosphate synthase (NANS) deficiency  15,40].,40.15,40Such metabolites relationships can also be formalized as networks, where the nodes correspond to the metabolites or features , and edges connect nodes if the corresponding metabolites are related. Several networks can be built from a single dataset (or a list of metabolites), where each network represents different relationships, such as statistical (correlated metabolites), biochemical (known or putative substrates and products of reactions), or chemical  .Moreover, in 2022, Thistlethwaite et al., tried to improve upon manual diagnosis of IEMs in the clinic by developing novel computational methods to analyse untargeted metabolomics data. They employed an automated computational diagnostic method that “connects the dots” (CTD) between metabolite perturbations observed in individual metabolomics profiling data and modules identified in disease-specific metabolite co-perturbation networks learned from prior profiling data. Their approach can be used to supplement information from biochemical pathways and has the potential to significantly enhance the interpretation of variants of uncertain significance uncovered by exome sequencing .metabolThe benefit of CTD-based metrics can be compelling when applied undiagnosed individuals by current methods. By quantifying the likeness of individuals metabolite perturbations with perturbation patterns observed in many diseases, candidate diagnoses can be ranked and possible diagnoses can be recommended. Furthermore, if genetic sequencing data are available for individuals exhibiting strong disease-specific metabolite perturbation patterns, VUSs can be re-interpreted given the available evidence provided by untargeted metabolomics. While CTD-based metrics cannot eliminate manual review entirely, they can expedite it and increase the confidence by which clinical laboratory directors make diagnostic decisions. Finally, disease-specific network models can be automatically and continuously updated as new case profiling data accumulates, ensuring stronger network stability and improved diagnostic performance .The expansion of metabolomic in clinical biochemistry and laboratory medicine communities as brought these approaches into clinical practice. Metabolomic has a part in newborn screenings in most developed countries and an important role in the differential diagnosis between IEMs. Moreover, Metabolomic can help in evaluating metabolites in follow-up as markers of severity or efficacy of diet and therapies. It is still crucial detecting new IEMs while performing untargeted metabolomic studies, new markers of well-known IEMs and in the characterization of metabolic pathway diseases to find new or different therapy approaches. Lastly, several research groups are trying to profile metabolomics, proteomics and genomics data in network platforms to have a holistic vision of of every single patient.In conclusion, metabolomics has a predominant and well-characterized role in IEMs, both in scientific research and current clinical practice.


The formation of spheroids during epithelial ovarian cancer progression is correlated with peritoneal metastasis, disease recurrence, and poor prognosis. Although metastasis has been demonstrated to be driven by metabolic changes in transformed cells, mechanistic associations between metabolism and phenotypic transitions remain ill-explored. We performed quantitative proteomics to identify protein signatures associated with three distinct phenotypic morphologies  of the high-grade serous ovarian cancer line OVCAR-3. We obtained disease-driving phenotype-specific metabolic reaction modules and elucidated gene knockout strategies to reduce metabolic alterations that could drive phenotypic transitions. Exploring the DrugBank database, we identified and evaluated drugs that could impair such transitions and, hence, cancer progression. Finally, we experimentally validated our predictions by confirming the ability of one of our predicted drugs, the neuraminidase inhibitor oseltamivir, to inhibit spheroidogenesis in three ovarian cancer cell lines without any cytotoxic effects on untransformed stromal mesothelia.  •Proteomic signatures acquired for distinct morphological OVCAR-3 cell phenotypes•Captured perturbed reaction modules associated with phenotype transition using GSMM•Model predicts oseltamivir to reverse metabolic flux-driven phenotypic transition•Oseltamivir inhibits spheroidogenesis across three ovarian cancer cell lines Physiology; Mathematical biosciences; Proteomics; Cancer Our objective was to predict the transition-specific perturbation modules responsible for disease progression and disrupt it through targeting its regulatory points. We reconstructed context-specific metabolic models for OVCAR-3 samples of three morphological stages using Recon3DHigh-throughput proteomics was performed in this study using the mass spectrometry data-dependent top10 approach. The data contains the expression of 3,122 proteins across the three biological replicate samples of each morphological stage of the OVCAR-3 cell line see A, namelyDifferentially expressed proteins between progressive morphological stages of OVCAR-3 were identified by applying a cutoff of 1 on lues see C. Among lues see . MetabolTo acquire a better understanding of how the morphological changes during tumor progression are associated with metabolic reprogramming, we used a generic human metabolic model Recon3D.The central premise of these MEMs is to extract reactions corresponding to highly expressed genes preferentially. However, cellular metabolic functionalities are not always preserved after model extraction. The study by Opdam et al.Following the results from the previous section, the iMAT-Th1 models of all three morphological stages were considered for further investigation. The iMAT-Th1 models had a high metabolic functionality score and were less sensitive to the threshold selection; therefore, they were considered for further investigation. Constraint-based modeling (CBM) flux sampling technique was used to evaluate the steady-state flux values,Metabolic alterations drive OVCAR-3 cancer cells to gain a metastatic phenotype and form spheroids in the peritoneal cavity. Perturbations directing the transition of morphological stages of the OVCAR-3 cell line were obtained in previous section. A low correlation of 0.0284 and 0.0352 ascertained the significant shift in the metabolic flux profiles during transitions 1 and 2, respectively. Both common and transition-specific reactions were large in number, and targeting such large perturbations is biologically infeasible. Therefore, we defined an approach for finding an optimal set of metabolic reactions whose perturbation is responsible for the transition of the morphological stages of the OVCAR-3 cell line. This technique was aimed at finding small modules of reactions whose modulation increases the correlation between the flux profiles of perturbed reactions in the modulated and initial stage model of the transition see A. In sinThe reactions present in top modulation strategies see  of both Alterations in the flux values of metabolic reactions were observed during the transition from the initial stage to the later stages of OVCAR-3. Targeting genes catalyzing the perturbed reactions can be a potential strategy for reversing the metabolic alterations that occur during morphological transitions. For this, we filtered out a total of 651 and 626 genes catalyzing reactions that were perturbed during transition 1 and transition 2, respectively. We sifted 495 and 462 non-essential genes see A and 5B.DLST, GALE showed a significantly high correlation, i.e., were able to rectify the metabolic profile altered during transition 1. Multi-pathway targeting genes HSD17B10, HADHB, and ACAA2, were among the top 5 gene knockout results of transition 1 (see SLC) genes such as SLC17A4, SLC17A2, SLC25A1, and others (see GNPAT and GPAM implicated in the triacylglycerol synthesis pathway (lipid metabolism) were among the top gene knockout results of transition 2  obtained from Genomics of Drug Sensitivity in Cancer (GDSC) for the OVCAR-3 cell line.Z score describes whether a cell line is sensitive or resistant to a drug compared to other cell lines screened against the same drug. A negative score means the cell line is more sensitive to the drug, while a positive score means less sensitive. The Z score of a drug for a particular cell line is defined as:x is the IC50 value of the drug in question (over OVCAR-3 cell line), μ is the mean and Z score) for only 16 drugs  pathway was predominantly involved in the top reaction modules of the inter-spheroidal transition. The TAG pathway has been known to promote cancer growth by acquiring free fatty acids from tri-acyl glycerides to the cellular pool of fatty acids.SLC) genes such as SLC17A4, SLC17A2, and SLC25A1 were found to inhibit the metabolic perturbation involved in the inter-spheroidal transition significantly. Consistent with this, over-activation of SLC25A1 has been observed in ovarian cancer, and its inhibition improved cancer cell sensitivity to platinum-based chemotherapy.GNPAT and GPAM involved in this pathway were able to block transition 2. Interestingly, it has been previously observed that GPAM silencing reduced cell migration and tumor xenograft development in ovarian cancer cells.ALDOB, ADH1B, NEU1, and NT5E block the metabolic alterations during both transitions concur with previous studies that show suppression of ovarian cancer growth upon silencing these genes.,,Targeting the metabolic perturbations involved in the phenotypic transition of cancer cells can impair ovarian cancer progression toward its more metastatic and aggressive stage. Genome-level mapping of the perturbed metabolic reaction through our models provided the gene targets. Essential genes were scrupulously filtered out using the normal ovarian data from GTEx data appertaining the impact of these genes on growth rate following a knockdown. Thus, single gene knockout was performed using genes that catalyze metabolic reactions altered in morphological phenotypic transitions but are not involved in cell survival. For example, solute carrier (NEU1) showed larger overlap values and higher pathway perturbation. Oseltamivir is an anti-viral drug used to treat influenza A and B virus; it inhibits the neuraminidase enzyme in humans.Drug repurposing opens a feasible space for devising a single/multi-gene targeting strategy in different indications. Using the metabolic models of spheroidal morphologies, we evaluated the impact of metabolism-targeting drugs retrieved from the DrugBank database. Canagliflozin, oseltamivir, gemcitabine, and pentoxifylline target the proteins that catalyze reactions perturbed during both transitions. Among these, the drug oseltamivir .Request for further information for resources and reagents should be directed to and will be fulfilled by the lead contact Dr. Samrat Chatterjee (This study did not generate new unique reagents.The ovarian cancer cell lines used in the study were a kind gift from Dr. Rajan Dighe (OVCAR-3 and SK-OV-3); COV362 was purchased from ECACC. The cell lines had been tested for mycoplasma contamination and also authenticated using short tandem repeat (STR) analysis.The studies described here were carried out in accordance with the guidelines of IISc Bioethics and Safety Committee.The ovarian cancer cell line OVCAR-3  was used for this study. Cells were maintained and cultured in suspension following the protocol used in our previous study.10 normalized, and the metabolic genes data was further used for building the models.The high throughput proteomics data contains the expression of 3122 proteins across triplicates of the distinct phenotypic morphologies monolayer, moruloid spheroids, and blastuloid spheroids. We first removed proteins absent in all nine samples of the data. Next, 2720 proteins expressing in We constrained the carbon-source exchanges to a maximum uptake of 10 mmol In order to determine the expression data associated with each metabolic reaction, we used the GPR rules present in Recon3D. GPR rules describe the association between the reaction and the gene product catalyzing it. A function named ‘GPRparser’ of COBRA Toolbox1.model (Recon3D),2.reaction’s expression array,3.lower threshold ,4.upper threshold The iMAT implementationThe algorithm aims to include the high expression reactions and remove the low expression reactions while building the model. The two threshold values used in our study for this algorithm are:Threshold 1 (Th1): lower expression threshold: 2.4861 , and upper expression threshold: minimum value of top Threshold 2 (Th2): lower expression threshold: mean(exp) where, ‘exp’ is the expression array of reactions in the model, and ‘std’ is the standard deviation.1.consistent model (flux consistent subset of Recon3D),2.core reactions FASTCORE is an algorithm to build context-specific models with the advantage of fast computation and compactness of the output model.The two threshold values used in our study for this algorithm are:Threshold 1 (Th1): minimum value of top Threshold 2 (Th2): 2.4861 INIT is a model extraction algorithm,1.model (Recon3D),2.weights for each reaction (must be same length as model.rxns)Reactions with positive weights were considered to have high expression, whereas reactions with negative weights were considered as less expressed. A weight of The two threshold values used in our study for this algorithm are:Threshold 1 (Th1): minimum value of top Threshold 2 (Th2): 2.4861 iMAT has been designed to use two different threshold values (lower and upper), where the lower threshold is used to filter reactions with expressions below this value and regard them as ‘non-expressed’. While the upper threshold is used to filter reactions with expressions above this value as ‘expressed’. On the other hand, FASTCORE and INIT use a single threshold for filtering reactions based on the reaction expression. Even though iMAT uses two thresholds, it still works on involving reactions with a high expression which is the same case with the other two methods. Moreover, the threshold defining the involvement of a reaction  in all three methods is approximately the same  maximized the flux through sink reaction corresponding to each essential metabolite. If the flux value of the sink reaction was above the reaction activity threshold (ri) <0 then,if ref flux (ri) = 0 and model.lb (ri) = ref flux (ri)model.ub (ri) > 0 then,if ref flux (ri) = ref flux (ri) and model.lb (ri) = 0model.ub . Otherwise, the modulation of that particular reaction was not added to the model. Following this way, the iteration goes up to the length of the total number of perturbed reactions. The resultant model and the corresponding correlation coefficient were again put to another level of sequential reaction modulation in the same manner. This is defined as different levels of reaction modulation. So iteratively, in each level, if the sequential modulation of a reaction results in a significant increase in correlation coefficient, it was added to the model, and the model was sent to the next level until the correlation between consecutive levels becomes less than 0.01 .The cut-off for reaction modulation was chosen to obtain a high correlation between profiles in a transition, with an optimal number of reactions in the modules. We evaluated various pairs of internal and external cut-offs, of which 0.001 as internal cut-off and 0.01 as external cut-off gave the highest mean correlation with a minimum mean number of reactions in the modules. The distribution of the mean correlation value and mean number of reactions in modules for different cut-offs (in both transitions) is shown in ,For reversible reaction: For irreversible reaction: The Genotype-Tissue Expression (GTEx) database was used to extract RNA sequence data of 166 normal ovarian samples.To observe the knockout effect of a gene on the growth rate of normal ovarian models, the bounds of reactions catalyzed by the queried gene were set to zero. The Flux balance analysis (FBA) was then performed using Cobratoolbox’s function ‘Optimizecbmodel’ to determine the growth rate.In-silico gene knockout in metabolic models is a method of suppressing the function of a gene to assess the impact on the overall metabolic profile. To execute single gene knockout, the lower and upper flux bounds of reactions catalyzed by the queried gene were set to zero. The metabolic flux profiles were then examined and compared to the flux profiles of the transition’s reference/initial model. The metabolic model corresponding to monolayer will be the reference/initial model for transition 1, while the metabolic model corresponding to 24-h spheroids will be the reference/initial model for transition 2.The aim is to determine the minimum percentage inhibition or reduction in the flux bound of reactions catalyzed by metabolic targets of the drug that can produce a maximum effect, i.e., a high correlation coefficient. We varied the percentage inhibition of the flux bounds from 10%  to 100% (complete inhibition). For both transitions, the correlation coefficient between the flux values of the perturbed reactions in the drug infused metabolic model and the initial stage model was evaluated. The extent of positive correlation indicates the drug’s potential to revert the transition.in vitro systems,OVCAR-3 cells were maintained in RPMI-1640  medium  along with 10% FBS . The non-cancerous mesothelial cells, MeT-5A, were cultured in complete Medium 199 supplemented with 10% FBS, 5 μg/mL insulin, 0.5 μg/mL hydrocortisone, 2.6 ng/mL sodium selenite, 27 pg/mL β-estradiol, 10 μg/mL transferrin, 10 ng/mL hEGF, and 20 mM HEPES buffer. All the cells were maintained in a 5% Spheroids were cultured in 3% polyHEMA-coated  dishes in basal medium supplemented with 250 ng/mL insulin , 0.5 μg/mL hydrocortisone , 2.6 ng/mL sodium selenite , 10 μg/mL transferrin , 27.3 pg/mL estradiol  and 5 μg/mL prolactin . These were maintained in culture for 1 to 7 days. Spheroids were visualized using the Olympus IX73 fluorescence microscope.Spheroids were first pelleted in a sterile 15-mL tube. Cells were then fixed using 3.7% formaldehyde  at To determine live and dead cells in the culture, cells were stained with 0.5 mg/mL Calcein AM  for 15 min. Cells were washed with PBS, counterstained with Propidium Iodide  for 5 min, and imaged under the Olympus IX73 fluorescence microscope.A cell-permeable redox indicator resazurin  was used to assess the viability of ovarian cancer cells. Viable cells with active metabolism reduce resazurin to a pink fluorescent compound resorufin, and the amount of resorufin produced is proportional to the number of viable cells. The assay was performed by seeding 3000 cells per well of a 96 well plate. After 24 h, they were treated with different concentrations of oseltamivir phosphate and were incubated for 48 h. Puromycin (1 μg/mL) was used as a positive control for cell death. After the incubation period, 10 μg/μL resazurin was added to each well and incubated for 1.5 h. Fluorescence was measured using a microplate fluorometer equipped with a 560 nm excitation/590 nm emission filter set. IC50 values were calculated using a dose-response curve in Prism Graphpad.We assessed the significance of the metabolic functionality score evaluated for each context-specific model. We computed the metabolic functionality score of 1000 random models of the same size as the queried model under investigation. These models were generated by randomly removing reactions from the parent model Recon3D while ensuring the model’s consistency. Then, we defined the p value as follows:The workflow describing the complete methodology adopted in this study and the workflow showing the steps to identify metabolic perturbations during the phenotypic transitions are provided in Supplementary see  and S8.


Introduction: Targeted Radionuclide Therapy is used for the treatment of tumors in nuclear medicine, while sparing healthy tissues. Its application to cancer treatment is expanding. In particular, Auger-electron emitters potentially exhibit high efficacy in treating either small metastases or single tumor cells due to their short range in tissue. The aim of this paper is to study the feasibility of a large-scale production of thulium-167, an Auger-electron emitter radionuclide, in view of eventual systematic preclinical studies.Methods: Proton-irradiated enriched erbium-167 and erbium-168 oxides were used to measure the production cross sections of thulium-165, thulium-166, thulium-167, and thulium-168 utilizing an 18-MeV medical cyclotron equipped with a Beam Transport Line (BTL) at the Bern medical cyclotron laboratory. The comparison between the experimental and the TENDL 2021 theoretical cross-section results were in good agreement. Additional experiments were performed to assess the production yields of thulium radioisotopes in the BTL. Thulium-167 production yield was also measured irradiating five different target materials  with proton beams up to 63 MeV at the Injector II cyclotron of Paul Scherrer Institute.Results and Discussion: Our experiments showed that an 8-h irradiation of enriched ytterbium-171 oxide produced about 420 MBq of thulium-167 with a radionuclidic purity of 99.95% after 5 days of cooling time with a proton beam of about 53 MeV. Larger activities of thulium-167 can be achieved using enriched erbium-168 oxide with a 23-MeV proton beam, obtaining about 1 GBq after 8-h irradiation with a radionuclidic purity of  The radionuclide is bound to a targeting agent, expressing an affinity towards tumor-associated antigens. The selection of a suitable targeting molecule favors the accumulation of the radiopharmaceutical preferentially in the proximity of malignancies, sparing healthy cells from excessive dose  stands out as a nuclear medicine technique capable of targeting tumors of different sizes. This task is achieved by targeting molecules labeled with specific radionuclides. According to the radionuclide selected, a suitable particle radiation  decay) and significant emittance of low-energy electrons  of 208 keV  168Er2O3, c) natTm2O3, d) natYb2O3, e) 171Yb2O3, mainly inducing the following nuclear reactions using proton beams with various energies:167Er 167Tma) 168Er 167Tmb) 169Tm 167Yb →167Tmc) natYb167Lu →167Yb →167Tmd) 171Yb167Lu →167Yb →167Tme) The present paper focuses on two complementary objectives: i) the investigation of production cross sections of relevant thulium radionuclides using enriched erbium-167 and erbium-168 oxides as target materials with an 18-MeV medical cyclotron and ii) the investigation of different cyclotron production routes using a 72-MeV proton beam. In addition, the production yield results from the medical cyclotron were compared to those obtained using a 72-MeV research cyclotron . The folThe two objectives of this study were achieved using two different cyclotrons. The cross-section measurements were performed at the Bern medical cyclotron laboratory utilizing an 18-MeV medical cyclotron (IBA Cyclone HC 18 MeV). The production yield measurements were conducted using a 72-MeV separated-sector high-intensity isochronous cyclotron, called Injector II, the second stage of the High-Intensity Proton Accelerator (HIPA), installed at PSI. Targets were prepared according to the requirements of each facility and irradiation purposes.natYb2O3 and 2) 99.999 %natTm2O3. Isotopically enriched target materials were purchased from ISOFLEX United States  168Er2O3 97.2% and 98.3%, and 3) 171Yb2O3 95.5%. All target materials consisted of oxide powder of different lanthanides. Target materials with natural isotopic composition were purchased from ChemPUR  with thed States  with theμL of erbium oxide in ethanol. The target mass was gradually deposited pipetting about 5 μL and waiting for the ethanol evaporation; the process was repeated until the entire central pocket was covered by the target mass. After deposition, the target mass was measured with an analytical balance . Prior to irradiation, the disk was covered in 13-μm thick aluminum foil to prevent radioactive material from spreading after the irradiation. Because of the low solubility of erbium oxide in ethanol, shaking the vial with the suspension before pipetting helped facilitating the material deposition over the whole pocket surface. However, a uniform surface distribution of the target mass is improbable using the sedimentation technique. For this reason, the cross-section measurements were performed with a technique developed by the Laboratory of High Energy Physics (LHEP) group  group . Each ta<10 nA)  and with<10 nA) . The pro<10 nA) ). The be<10 nA) . The tarnterSpec . Each menterSpec . The EoBμm thick aluminum lid  ainum lid . The eve167Er2O3, b) 168Er2O3, c) natTm2O3, d) natYb2O3, e) 171Yb2O3. The authors explored direct  by following the intended product through the chemical separation. This quantity is defined as the fractional activity of the target radionuclide with respect to the total activity of the sample.Thulium-167 production was investigated using five different target materials: a) d direct . They caμA current is peeled off from the main beam of 2.5 mA delivered by Injector II. Behind the beam splitter, the proton beam is directed towards an irradiation station named IP2  mechanical stability of the target disk and ii) potential undesired production of radionuclidic impurities. From experimental evidence it was observed that the target disk is fragile, if the thickness is less than 250 t1/2 < 1 day). Afterward, the irradiation time was increased to 2 h and, subsequently, to 8 h for the most promising production routes.An irradiation procedure was established in order to validate the experimental and theoretical cross sections reported in the literature. In general, three energies covering the expected highest production cross-section peak of thulium-167 were selected for each target material. At least two targets of 40-mg mass were irradiated for each energy. The proton currents impinging on target surface were calculated with the program Beam Delivery Simulation (BDSIM)  and TRANn detector  connected to a data acquisition system from Canberra (Mirion®) (France) using their Genie 2000 software package for spectrometry analysis (RRID:SCR_021933). Each measurement was performed with a dead time The activity was measured by means of gamma-ray spectrometry with a HPGe type u (t1/2) ≈ 0.2%, u (Iγ) ≈ 5%, in particular σ level of confidence.Several independent contributions affect the cross-section uncertainties: target mass Enrichment levels of enriched target materials were assessed by means of inductively coupled-plasma mass spectrometry (ICP-MS) in collaboration with the Laboratory of Radiochemistry of Politecnico di Milano. The results are tabulated in 167Er2O3 and 168Er2O3, respectively. The cross-section results of The production cross sections were investigated from 6.5 MeV to 18.2 MeV proton beam energy. The excitation functions of theoretical production cross sections and the experimental data are shown in 167Er 165Tm: Experimental data and theoretical calculation are in good agreement  reaction. It was also possible to experimentally observe the steep raise due to the 167Er  reaction in the high energy range. Thulium-165 activity was measured at least 2 days after EoB to let thulium-166 decay due to an overlap between the main gamma line of thulium-165 (Eγ = 242.9 keV) and a coincidence sum peak between the most intense X-ray  of thulium and a gamma line of 194.7 keV (Iabs = 0.83%) that originated from the thulium-166 decay. It is noteworthy that a considerable amount of thulium-166 was produced at the selected irradiation conditions using enriched erbium-167 oxide as target material.greement . The mai167Er 166Tm: Data points and TENDL 2021 curve show a similar trend  reaction.ar trend . In this167Er 167Tm: According to 167Er 168Tm: Experimental data across the peak in 168Er  reaction appears to be evident. In contrast, it is uncertain whether the slight increase at higher proton energies could be attributed either to the 170Er  reaction or the error attributed to the measurement method.168Er 165Tm: In 166Er  reaction likely dominates in this production route. In this case, it is worth mentioning that thulium-166 is produced in considerably lower activity. As a result, no significant cooling time was required.168Er 166Tm: 167Er  reaction.168Er 167Tm: The theoretical calculations and the experimental data are in good agreement and they are shown in 168Er  reaction.168Er 168Tm: In 168Er  reaction should provide the major contribution to the production.The thulium-167 cross-section uncertainties are dominated by the uncertainty of the branching ratio of its main gamma line (207.8 keV), which shows a high relative error of approximately 19% . ConsideMoreover, the production cross sections measured in this study were also employed to derive the nuclear cross sections contributing to the production of the relevant thulium radioisotopes. A technique based on the inversion of a linear system of equations was used to achieve this objective . This me3 density (1-σ error). The following equation was adopted to evaluate the thin-target product yield ) the mass stopping power as a function of the proton beam energy (Ep), Ein the inlet proton energy at the target entrance surface, Eout the exiting proton energy from the target rear surface, σ(Ep) the interpolated cross section based on numerical values experimentally measured as a function of the proton beam energy. The EoB thin target yield (TTY) is calculated with:ti is the irradiation time. For the evaluation of the production yield, the physical thin target yield was adopted and calculated with the following equation:λ ⋅ ti ≪ 1. In addition, the radionuclidic purity as a function of the proton energy (Ep) was calculated as follows:The experimental cross-section results were validated in the BTL. The experimental production yields of each relevant thulium radioisotope were compared with calculations based on nuclear cross sections of the predominant nuclear reactions within the investigated energy spectrum (6.8 MeV–18.2 MeV) . Numericct yield :y=NAv⋅η167Er2O3 and 168Er2O3, respectively, maximizing thulium-167 production. However, analyzing the production yields for 168Er2O3, it can be supposed that higher proton energies might lead to higher values. The experimental results are plotted in 167Er2O3 and 168Er2O3, respectively. The numerical values are reported in 167Er2O3 as target material deviates significantly from experimental measurements. This deviation might be caused by considering the uncertainty of the exiting proton energies. From simulations it was observed that this energy can be found mostly in the energy range of (9–10) MeV, which corresponds to the region where the production cross section exhibits a steep increase. In this case, the uncertainties on target characteristics, especially target density, may play a significant role, since they highly affect the calculated exiting proton energies. The exiting proton energies were calculated with SRIM . Figure 167Er2O3, 168Er2O3, natTm2O3, natYb2O3, 171Yb2O3). The production tests data are summarized in 168Er2O3 and 171Yb2O3. The first target material showed high production yields when irradiated with rather low proton energies (18.7 MeV–24.6 MeV). However, the maximum produced activity, unexpectedly, was found to be at 22.8 MeV. Based on the findings derived from the proton irradiation of natural erbium as documented by 168Er 167Tm reaction, irrespective of isotopic distribution. The same reaction mostly contributes in the production of thulium-167 for proton-irradiated PSI targets of enriched erbium-168 oxide. Therefore, it is reasonable to qualitatively compare the theoretical production yield trend calculated using the production cross sections of t1/2 = 51.5 m), with respect to the irradiation time. On the other hand, predictions for the same irradiation period show that proton irradiations of enriched erbium-168 oxide using a 23-MeV proton beam could yield 1 GBq of thulium-167 activity.At PSI, the project involved the assessment of thulium-167 production yields using five different target materials 168Tm reaction and due to the suppression of the 167Er 168Tm reaction. Focusing on enriched erbium-168 oxide, irradiations with higher proton energies might have enabled a larger thulium-165 production through the 167Er  reaction, despite a lower enrichment level of erbium-167.The radionuclidic purity was also evaluated for each target material. A cooling time of 5 days was selected for its assessment to neglect the contribution of thulium-166, while minimizing thulium-165 content. The first was never detected due to long cooling time. High activities of longer-lived radionuclides (mainly thulium-167 and thulium-168) prevented performing gamma-ray spectrometry before its activity was below the minimum detectable activity (MDA). On the other hand, thulium-165 was occasionally measured due to low production and long cooling periods. For this reason, upper limits of the radionuclidic purity are reported in 2O3 and Yb2O3) was also dictated by the elimination of a production channel for thulium-168 due to the presence of stable ytterbium-168. As a matter of fact, the highest radionuclidic purity was observed using 171Yb2O3 as target material exploiting the high proton energies accessible at the IP2 target station. The sole thulium-168 was detected among thulium radioisotopes due to long cooling periods. Furthermore, only prolonged irradiation periods (tirr ≥ 1 h) enabled the production of a sufficient activity of this radionuclide, thereby enabling its detection through gamma-ray spectrometry. Consequently, the irradiations of natural ytterbium oxide showed a 100% radionuclidic purity due to short irradiation periods.The decision to investigate indirect production routes . By solving the Bateman equations considering an 8-h irradiation, it is possible to determine: i) a suitable cooling time, approximately 7.5 h, and ii) thulium-169 content A crucial aspect might be represented by the possibility of having the stable thulium-169 in the final product. This isotope originates from the decay chain of the isobars with mass number 169  studies  showed tμAh was obtained at PSI, in contrast to the 8.3 MBq/μAh measured at the Bern medical cyclotron laboratory. The discrepancy might be attributed to an imperfect control over the parameters of the proton beam, e.g., the proton current, when impinging on the target surface. Future work will be devoted to experimentally assess these beam characteristics and improve the beam positioning at the IP2 target station. At the current stage, simulation results are used to evaluate the proton current impinging onto the target at the IP2 target station projecting the 50-μA current measured inside the vacuum chamber. These objectives will be achieved by exploiting monitor cross sections and by implementing a new beam monitor system, respectively. The latter will consist of four sets of thermocouples installed prior to the aluminum vacuum window.A slight difference in the enriched erbium oxide data was observed when comparing the production yield results measured at PSI and at the Bern medical cyclotron laboratory. For example, by employing a comparable beam energy for enriched erbium-168 oxide, a production yield of 7.0 MBq/168Er2O3 could potentially yield approximately an activity of 1 GBq with a radionuclidic purity of tcool = 5 d, 0.5% of activity impurity assigned to thulium-168). This can be achieved by bombarding a target measuring 40 mg in mass and 6 mm in diameter, under the following irradiation conditions: 8 h irradiation time, 22.8 MeV proton beam energy, 19.3 μA (from simulations) proton current. Unfortunately, large production of thulium-167 with 171Yb2O3 is impractical due to the saturation of its short-lived parent nuclide lutetium-167 (t1/2 = 51.5 m). However, this production route is still appealing for its high level of radionuclidic purity , although the highest registered thulium-167 activity was of 420 MBq after 8 h irradiation time. This result was obtained irradiating a 40-mg, 6-mm-diameter target disk using a proton beam with the following characteristics: 51.1 MeV proton beam energy, 21.4 μA (from simulations) proton current.In conclusion, the proton irradiation of μAh (Ep = 12.7 MeV) and 8.3 MBq/μAh (Ep = 18.2 MeV) were measured for 167Er2O3 and 168Er2O3, respectively. However, the large uncertainty of the emission intensity of the 208-keV gamma ray (urel = 19%) significantly affects the precision of thulium-167 cross-section data. To achieve more accurate cross-section measurements, future metrological research will be addressed to improve the precision and accuracy of 208-keV gamma line of thulium-167.In this study, the production of the medically relevant radionuclide thulium-167 was investigated using both medical (18 MeV) and research (72 MeV) cyclotrons. In general, the comparison between experimental results and theoretical predictions of TENDL 2021 exhibited a good agreement. Experimental cross-section data were validated by performing production yield measurements. The production yields of 2.4 MBq/167Er2O3, 168Er2O3, natTm2O3, natYb2O3, 171Yb2O3) for the thulium-167 production allowed to determine the most promising production route for medical applications. 168Er2O3 stood out as the most favorable candidate target material for the production of thulium-167 on a large scale with a radionuclidic purity of tcool = 5 d). An efficient and robust radiochemical separation technique will be devised to pursue high specific activities of thulium-167 in view of its future medical applications. Further studies should also be conducted to ascertain whether the radionuclidic impurity levels, specifically thulium-168, could potentially impose constraints in relation to radiation protection and patient dosimetry.The systematic investigation of the production yields using various target materials (This study and the following steps will enable subsequent preclinical investigations aimed at exploring the eventual use of this radionuclide in therapy and imaging.


Mammalian cells produce up to 80 % of the commercially available therapeutic proteins, with Chinese Hamster Ovary (CHO) cells being the primary production host. Manufacturing involves a train of reactors, the last of which is typically run in fed-batch mode, where cells grow and produce the required protein. The feeding strategy is decided a priori, from either past operations or the design of experiments and rarely considers the current state of the process. This work proposes a Model Predictive Control (MPC) formulation based on a hybrid kinetic-stoichiometric reactor model to provide optimal feeding policies in real-time, which is agnostic to the culture, hence transferable across CHO cell culture systems. The benefits of the proposed controller formulation are demonstrated through a comparison between an open-loop simulation and closed-loop optimization, using a digital twin as an emulator of the process.  First principles models can be used for prediction; however, the extent of prediction capability greatly depends on the extensiveness of the experimental information on which the model is built. In particular, if data is available for a limited range of process conditions, the model parameter values will likely differ as the operating conditions change. Additionally, the existing data might not capture all the underlying phenomena - a ubiquitous feature in most biological processes Two key physicochemical phenomena involved in culture processes at the cellular level are transmembrane transport, which governs nutrient uptake and product secretion, and the metabolic reactions in the intracellular environment. Transport phenomena and metabolic reactions are interrelated, so mathematical descriptions of cell culture dynamics should take both into account. Cell culture dynamics can be described at the extracellular level using a Monod-type kinetic model, which, despite being unstructured, can satisfactorily describe cell growth and transport phenomena At an intracellular level, a kinetics-based approach is intractable as the substantial number of reactions inside the cell would make estimating related kinetic parameters a computationally and experimentally challenging task Saccharomyces cerevisiaeEscherichia coli cells Stoichiometric metabolic models provide a static picture of what is happening inside a cell at a given instance. Several authors have solved the models dynamically, optimizing the model for a cellular objective for a time interval. Although the formulation becomes more complex, it allows for the coupling with a model-based control strategy, which requires dynamic integration with time. Several authors have proposed solutions which fit into two major categories: iteratively find a solution for the linear programming problem and integrate the ordinary differential equations for a fixed time until the end of the simulation (Static Optimization Approach) or optimize over the entire solution time (Dynamic Optimization Approach) While some researchers have used statistical design of experiments to derive transfer functions for control, including pH control using the Plackett–Burman design method Moving to online control, some studies have proposed simpler control strategies such as glucose setpoint control using Raman spectroscopy for feedback control Although several authors have claimed that MPC has the potential to provide increased product yield, as it has for other industries, it is not widely used either academically or industrially Model uncertainty and measurement noise are typical problems associated with bioprocesses, directly affecting the generalizability of cell culture models. Besides the technical challenges of implementing MPC, there is also an investment challenge, as online control requires measuring and acting frequently, thus resulting in an infrastructure cost of sensors, actuators and control systems. Lastly, the pharmaceutical industry is heavily regulated, and a change of control system would require approval from regulatory agencies in silico multi-parametric approach to control the feed flow rate, which is projected to show to lead to higher productivity. Harcum et al. E. coli based on dynamic FBA. Each of the papers mentioned above showcases some alternatives for controlling cell culture processes. However, certain strategies such as nonlinear MPC In the present work, we propose a MPC strategy that would not require additional investment costs and could be integrated within an already established fed-batch process. Our control strategy circumvents the need for frequent online measurements by considering long control intervals when compared to conventional MPC approaches, presented in the literature 21.y Get current state 2.Using the current state and the reactor model, compute the optimal control policy (Controller)3.Implement optimal control policy for control interval 1 in the digital twin of the reactor 4.Repeat steps 1–3 until the end of the simulationThe controller (described in Both the metabolic model and the control optimization were performed using gPROMS ModelBuilder v.7.1.1 (Process Systems Enterprise Ltd). Each component of the control framework will be discussed in the following sections.2.1The reactor model consists of differential and algebraic equations describing the mass balances for each component  and the corresponding specific uptake and production rates. The cell culture dynamics is described by Monod-type kinetics. The model includes a description of 22 metabolites and an estimation of 35 model parameters. We evaluated the prediction capability of this new model structure using the experimental set-up presented in Kyriakopoulos and Kontoravdi 2.2The control strategy is composed of two main optimization steps. The first is to find the glucose flux that leads to optimal cell growth. The second is to determine the optimal feeding strategy that leads closer to that optimal cell growth. The metabolic model is described in 2.2.1S is the stoichiometric matrix, v the fluxes of all reactions, virrev the fluxes of the irreversible reactions, LBi the lower bound of flux i and UBi the upper bound. This optimization was performed for each of the five fed-batch stages: early exponential, mid-exponential, late exponential, early stationary and late stationary. The difference between the five stages is expressed in the bounds of the fluxes, which constrain the space to the limits expected for that particular cellular stage. As a result, there will be a set of constant optimal fluxes per culture stage.The metabolic model uses a network of 101 metabolites, and 144 reactions In the original paper of the metabolic network, the maximization of biomass is shown to achieve worse predictions than an alternative multi-optimization strategy 2.2.2OF is the objective function, ui,k the manipulated variable i over the control interval k, t time, Topt the optimization time horizon, j and The controller optimization is cast as a minimization between the current and optimal glucose flux computed by the metabolic model  control decisions. Additionally, the formulation of the optimization problem might be the root cause for such different feeding strategies. In Case A, the optimizer is more restricted than in Case B, given that it has to minimize the trajectory of 22 metabolites . This added flexibility to the controller makes it more susceptible to the control interval.To mitigate the sudden jumps in control inputs, a penalty to the rate of change was added to optimization case B. Two different rate of change penalties were tested: + ∕ − 10 and + ∕ − 5 mmol/L  as that variable was the one pushing for the sudden jumps. The shorter the control interval, the larger was the effect of the rate of change penalty. This is agreement with the fact that the longer the control interval, the smaller the peaks of the control inputs. The results show that the addition of the rate of change is a useful tool to mitigate sudden changes of control inputs, in case they are difficult to implement during an experiment.Another aspect to consider is the actual amount of glucose that is being predicted to be fed in both cases. The rate of change penalty was considered as well. 3.3In both cases, shorter control intervals lead to higher antibody yield. This result is in agreement with other authors: Papathanasiou et al. The closed loop results are compared against an experiment that used a designed feed that had already increased antibody yield up to 3.5-fold compared to batch culture 3.4In all case A examples, the glucose feed rises slightly for the first 50–100 h, decreasing for the next 50–100 h and stabilizing at its lowest level in the later stages of the batch. The shorter the control interval, the more piecewise the trajectory is.Unlike case A, in case B, there is no piecewise trajectory. Glucose feed remains constant in a low value for the first 50–100 h, increasing in peaks as the batch progresses. As discussed in It is evident that in both cases A and B, the target glucose flux  solver built into gPROMS ModelBuilder v7.1.1 and run on an Intel(R) Core(TM) i7–10810 U CPU @ 1.10 GHz 1.61 GHz, and each optimization took less than 10 s. There is no significant difference between optimization case A and B. As such, both are computationally inexpensive and suited for online control.4Herein, we presented a model predictive controller for the production reactor of CHO cell cultures. The control strategy leverages a reduced metabolic network model of a CHO cell to calculate glucose and amino acid uptake rates that will lead to optimal cell growth for each cell phase. These fluxes are used as control targets to compute the optimal feeding strategy. The optimal feeding strategy is then used in a digital twin of the production reactor. Our results demonstrated that this control strategy has the potential to lead to higher antibody production for different cases. Furthermore, our findings support the existing literature by emphasizing the advantages of using shorter control intervals. This suggests that utilizing shorter sampling windows can lead to better controller performance and, consequently, higher productivity. The control framework is flexible and transferable across different CHO cell culture systems. Furthermore, it can include more complex metabolic models, such as genome-scale models. We believe this strategy is an appropriate first step towards advanced process control in the bioprocessing industry as it does not require extensive computational power and can be implemented without extra infrastructure costs.Mariana Monteiro: Conceptualization, Formal analysis, Investigation, Methodology, Writing – original draft. Sarah Fadda: Formal analysis, Investigation. Cleo Kontoravdi: Conceptualization, Funding acquisition, Supervision, Writing – review & editing.The authors have no conflict of interest to declare.