Metabolic alterations can serve as targets for diagnosis and cancer therapy. Due to the highly complex regulation of cellular metabolism, definite identification of metabolic pathway alterations remains challenging and requires sophisticated experimentation.We applied a comprehensive kinetic model of the central carbon metabolism (CCM) to characterise metabolic reprogramming in murine liver cancer.We show that relative differences of protein abundances of metabolic enzymes obtained by mass spectrometry can be used to assess their maximal velocity values. Model simulations predicted tumour-specific alterations of various components of the CCM, a selected number of which were subsequently verified by in vitro and in vivo experiments. Furthermore, we demonstrate the ability of the kinetic model to identify metabolic pathways whose inhibition results in selective tumour cell killing.Our systems biology approach establishes that combining cellular experimentation with computer simulations of physiology-based metabolic models enables a comprehensive understanding of deregulated energetics in cancer. We propose that modelling proteomics data from human HCC with our approach will enable an individualised metabolic profiling of tumours and predictions of the efficacy of drug therapies targeting specific metabolic pathways. However, despite all these advances, the overall death rate for cancer has declined at a much slower pace in the past 40 years compared to other major causes of mortality such as cardiovascular and infectious diseases.2 This is, to a large extent, explained by suboptimal long-term anti-proliferative efficacy of newly developed molecular-targeted drugs.3 Cancer cells display a marked capability to compensate for the inactivation of signalling pathways—and other growth-promoting mechanisms—that are considered essential for neoplastic progression.5 This translates into the emergence of therapy resistance, a major obstacle of clinical oncology.6 To achieve effective and long-lasting therapy responses it is therefore of pivotal importance to identify processes that are at the same time essential and unique, thereby avoiding resistance via usage of alternative pathways. Metabolism represents such a process as it is essential for cellular survival and growth, e.g. by providing energy, reductive power and building blocks for anabolic reactions. In light of the uniqueness of metabolic pathways, their functional inactivation can usually not be compensated, resulting in robust cellular damage and/or death.7Numerous initiatives around the world in conjunction with the unprecedented development of high-throughput analytical methodology have spiralled up the molecular knowledge about cancer in dizzying heights.8 However, it also became evident that a reliable analysis of metabolism, especially under in vivo situations, is challenging to perform.9 This is due to various factors, such as the rapid turnover of substrates and products, the intricate complexity of the metabolic network, the central importance of external stimuli such as hormones, growth factors and the cellular microenvironment.10 One main reason for the insufficient understanding of metabolic changes in tumours is the strong focus on changes in the expression level of metabolic enzymes and transporters. The importance of downstream kinetic regulation, for instance by allosteric effects or reversible phosphorylation, has been underestimated or completely disregarded in the last two decades.11 Choosing glucose metabolism of the liver as an example, we have recently demonstrated the necessity to combine existing knowledge on gene expression changes with the complex kinetic regulation of enzymes in order to understand the metabolic response of the liver to varying external challenges.12 Here, we present an innovative concerted approach to study cancer metabolism by combining a novel physiology-based kinetic model of the central metabolism,13 with high-quality quantitative proteomics data and molecular biological experimentation to elucidate metabolic differences between liver cancer  and the normal liver in a murine model. Using relative changes in the expression level of metabolic enzymes in HCC and normal liver cells to scale maximal enzyme activities, we simulate the metabolic response of HCC and the normal liver to variations in the metabolite and hormone profile of the blood plasma. This enables the definition of conditions at which the metabolism of the tumour becomes severely impaired while the metabolism of normal liver cells remains largely unaffected. We strongly believe that the herewith presented approach bears translational potential and will outline a basic roadmap to achieve this.The notion that tumours display specific metabolic alterations that can be exploited for diagnosis and therapy of cancer has received widespread attention in recent years.14 Briefly, male ASV-B mice express the early region of the SV40 large T (SV40lT) oncogene under control of the mouse antithrombin III promoter. ASV-B mice show time-dependent liver tumour development with first evidence of dysplasia at 8 weeks, adenomas at 12 weeks and hepatocellular carcinoma (HCC) at 16 weeks of age. All mice were maintained under specific pathogen-free conditions under a 12 h light/dark cycle with free access to food and drinking water and cage enrichment at the animal facilities in Berlin (Charité) and Aachen . Animal procedures were performed in accordance to approved protocols  and followed recommendations for proper care and use of laboratory animals. For tissue preparation, 16-weeks-old ASV-B or tumour-free male control mice  were sacrificed by cervical dislocation and liver tissue samples were snap-frozen in liquid nitrogen. Further analyses of tissue samples were performed within 2–4 weeks.The murine HCC model  was established and initially characterised by Dubois and co-workers.13 The model was used to simulate the impact of nutrient supply (including oxygen), hormonal stimuli and protein abundance of metabolic enzymes on the functional output of the liver. The model comprises the central hepatic metabolic pathways of: glycolysis, gluconeogenesis, glycogen synthesis, glycogenolysis, fructose metabolism, galactose metabolism, the creatine-phosphate/ATP shuttle system, the pentose phosphate cycle composed of the oxidative and non-oxidative branch, the citric acid cycle, the malate aspartate redox shuttle, the glycerol-3-phosphate redox shuttle, the mitochondrial respiratory chain, the beta-oxidation of fatty acids, fatty acid synthesis, ketone body synthesis, cholesterol synthesis, triglyceride synthesis and degradation, the synthesis and hydrolysis of triglycerides, the synthesis and export of the very-low density lipoprotein (Vldl), the urea cycle, the metabolism of the amino acids serine, alanine, glutamate, glutamine, aspartate and ethanol metabolism. Furthermore, the model contains the key electrophysiological processes of the inner mitochondrial membrane including the mitochondrial membrane potential, mitochondrial ion homeostasis and the generation and utilisation of the proton motive force. All modelled reactions and transport processes are depicted in our previous publication . The metabolic model is coupled to a phenomenological model of hormonal signalling by glucagon and insulin affecting the short-term regulation of metabolic enzymes by reversible phosphorylation (see below). Uptake, metabolisation and generation of glucose, fructose, galactose, pyruvate, lactate, glycerol, ammonia, serine, alanine, glutamate, glutamine, fatty acids, ethanol, acetate, urea, acetoacetate, β-hydroxybutyrate, oxygen and VLDL particles are being described by the model.We have recently developed a comprehensive kinetic model of the central metabolism of hepatocytes.15 Glycolysis and gluconeogenesis as well as fatty acid synthesis and β-oxidation are inversely regulated by glucagon and insulin signalling via phosphorylation and de-phosphorylation of key regulatory enzymes. In the model, the plasma concentration of insulin and glucagon is directly translated into the phosphorylation state of interconvertible enzymes by a phenomenological sigmoid function (γ-function) also used in the work published by Bulik et al.12 Moreover, we used phenomenological transfer functions to compute the plasma concentrations of insulin and glucagon and of non-esterified fatty acids (NEFA) directly from the plasma level of glucose. This setting rests on the assumption that the release of insulin and glucagon from pancreatic islet cells is mainly controlled by the plasma glucose level and that high concentrations of glucagon and epinephrine stimulate the hormone-sensitive lipase (HSL) in adipose tissues, thus creating an inverse relationship between the plasma level of glucose and NEFA.The metabolism of the liver is strongly controlled by hormones, in particular insulin and glucagon.16 and the eluates dried and reconstituted to 20 µl of 0.5% acetic acid in water. Five microliters were injected in duplicate on a UPLC system (Eksigent Technologies) coupled to a LTQ Velos Orbitrap (Thermo Fisher Scientific), using a 240 min gradient ranging from 5 to 45% of solvent B . For the chromatographic separation 30 cm long capillary (75 µm inner diameter) was packed with 1.9 µm C18 beads . On one end of the capillary nanospray tip was generated using a laser puller, allowing fretless packing. The nanospray source was operated with a spray voltage of 2.1 kV and an ion transfer tube temperature of 260 °C. Data were acquired in data dependent mode, with one survey MS scan in the Orbitrap mass analyzer  followed by up to 20 MS/MS scans in the ion trap on the most intense ions. Once selected for fragmentation, ions were excluded from further selection for 30 s, in order to increase new sequencing events.Murine liver samples were immediately frozen in liquid nitrogen and re-suspended in urea buffer  containing 100 µl of zirconium beads for protein extraction. Samples were homogenised on a Precellys 24 device (Bertin Technologies) for two cycles, 10 s at 6000 rpm. After centrifugation to remove beads and tissue debris, protein concentration was measured by Bradford colorimetric assay and 100 µg were taken for protein digestion. Leftover samples were frozen at −80 °C. The disulfide bridges of proteins were reduced in DTT 2 mM for 30 min at 25 °C and successively free cysteines alkylated in iodoacetamide 11 mM for 20 min at room temperature in the dark. LysC digestion was then performed by adding 5 µg of LysC  to the samples and incubating it for 18 h under gentle shaking at 30 °C. After LysC digestion, the samples were diluted three times with 50 mM ammonium bicarbonate solution, 7 µl of immobilised trypsin (Applied Biosystems) was added and samples were incubated 4 h under rotation at 30 °C. Eighteen micrograms of the resulting peptide mixtures were desalted on STAGE Tips17 and maintained in Dulbecco’s modified Eagle’s medium  containing 10% foetal bovine serum and 1% penicillin-streptomycin (Thermo Fisher Scientific) in collagen-coated flasks. All experiments were conducted within four days after primary cell isolation. HCC cells were isolated from 16-weeks-old ASV-B mice and cultivated in the medium described above. After an initial adaptation period of one to two months they started to proliferate and grow stably under cell culture conditions.Primary hepatocytes from C57Bl/6 J were isolated as described earlier18 with slight modifications. Mouse livers were perfused with ice-cold University of Wisconsin organ preservation solution (UW), submerged in UW and kept on ice. Cylindrical cores with a diameter of 5 mm were prepared using a manual biopsy punch  and placed in a Krumdieck tissue slicer  containing ice-cold oxygenated Krebs-Henseleit buffer . William’s E Medium  supplemented with 2.75 mg/ml D-glucose and 50 µg/ml gentamycin (Sigma–Aldrich) was used as the standard culture medium. To assess urea synthesis under stimulated conditions, DMEM (high glucose) with additional urea cycle substrates (2 µM ornithine and 10 µM NH4Cl (both Sigma–Aldrich)) was used. To determine the effect of complex I inhibition, PCLS were cultured in DMEM standard medium with or without 0.5 mM metformin . Slices were incubated in a 6-well culture plate containing three slices per well and 3.5 ml medium. After 1 h of pre-incubation, slices were transferred to fresh medium and incubated for 24 h. Viability of the cultured tissue was confirmed by quantification of ATP with the Bioluminescence Assay Kit CLSII (Merck) and results were normalised to total protein content. Culture medium was collected and stored at −80 °C for later analysis of urea production. The concentration was determined by the University Hospital RWTH Aachen Central Laboratories applying standard diagnostic procedures.Precision cut liver slices (200 µm thickness) were prepared from both normal and tumour-bearing murine livers based on a published protocol20 with the mouse UniProt database  and a common contaminants database (247 protein entries). Carbamidomethylation of cysteines was chosen as fixed modification, oxidation of methionine and acetylation of N-terminus were chosen as variable modifications. Two missed cleavage sites were allowed, and peptide tolerance was set to 7 ppm. The search engine peptide assignments were filtered at 1% FDR at both the peptide and protein level. The ‘match between runs’ feature was not enabled, ‘second peptide’ feature was enabled, while other parameters were left as default. For protein quantification LFQ intensities calculated by MaxQuant were used.21 The minimum LFQ ratio count was set to 2 and a MS/MS spectrum was always required for LFQ comparison of the precursor ion intensities; only unique and unmodified peptides were used for LFQ quantification, in order to keep the LFQ calculation isoform specific. Before comprehensive data analysis, data quality was evaluated using the in-house developed quality control software PTXQC.22Proteomics raw data were analysed using the MaxQuant proteomics pipeline v1.4.1.2 and the built in Andromeda search engine23 This package assesses the significance of fold changes using parallel linear models sharing variance parameters. This method was originally developed for microarray data but turns out to be particularly suited for shotgun proteomics as it alleviates the scarcity of the measurement matrix by sharing the variance between proteins. Out of 2124 detected proteins, 1579 were used and tested for significance of their fold changes (detected in at least two samples in each condition). Nine hundred and thirty four proteins were found to have significant fold changes (FDR 5%). Metabolically relevant pathways for mouse were obtained from the GSKB R package,24 which propose a pre-processed metabolic pathway collection. The Piano R package was used to estimate the significance of the directional regulation of the pathways.25 The methods used to generate a consensual p-value in PIANO were: mean, median, sum, maxmean, stouffer, fisher, reporter, tailStrength, wilcoxon and PAGE. The FDR and t-values yielded by the LIMMA package were used as gene level statistics. The scripts and data can be accessed here: https://github.com/adugourd/Berndt_Egners_Mastrobuoni.In total, 28 proteomic samples were analysed, coming for 14 mouse livers, with seven healthy and seven tumourous livers. Hence, the dataset comprised seven biological replicates for each condition, with two technical replicates per mouse liver. All bioinformatic analyses were performed in R. For each protein, technical replicates were averaged. Box and density plots were generated to assess the homogeneity of the sample distributions. Clustering was performed over complete cases of proteomics samples using the complete method and Euclidean distance (see pheatmap and hclust R packages) as well as principal component analysis. Differential analysis was performed using the LIMMA R package.t-test using the GraphPad Prism 5.0 software (GraphPad Software) if not denoted otherwise. Differences were considered statistically significant at p < 0.05.All data are presented as mean ± standard error of the mean (SEM). Statistical analysis was performed by unpaired, two-tailed Students 13 We used the protein abundance data obtained from the murine samples to scale the activity  values) of the metabolic enzymes to generate tumour-specific kinetic models. These tumour-specific kinetic models were constructed by scaling the maximal activity of each enzyme and transporter in the network according totumour and Econtrol denote the LFQ intensity of the enzyme in the tumour and the control tissue. 13 EquationFor the generation of the tumour-specific kinetic model we used the quantitative proteomics data together with Hepatokin1, a fully kinetic model of the central carbon metabolism of the liver.20 The proteomics experimental design consisted of 2 conditions (HCC and control (ctr)), seven biological replicates per condition and two technical replicates per biological replicate. In total, 2124 proteins were detected across the 28 samples. Each pair of technical replicates was averaged resulting in 14 biological samples  and Gapdh  are significantly upregulated in HCC tissues  of the respective enzymes to generate a kinetic model of the central metabolism of murine HCC. To assess the functional consequences of alterations in metabolic enzyme expression, we applied the model to a typical 24 h physiological plasma concentration profile of exchangeable metabolites and the hormones insulin and glucagon. We used the plasma profile as model input and computed the diurnal variations in the concentrations of all model metabolites and fluxes for normal liver and murine HCC , explaining its antidiabetic properties.29 Using the reported inhibition concentrations of metformin of 0.5 mM for complex I28 and 0.055 mM for G3pdh,29 we simulated the effect of metformin on HCC and healthy liver. We put the external conditions to their mean value over one day and varied the metformin concentration from 0 to 1 mM. Figure We hypothesised that the reduced capacity of oxidative phosphorylation in HCC can be exploited for cancer therapy by serving as a metabolic target to selectively impair HCC metabolism while leaving healthy liver intact. This was further strengthened by modelling the oxygen consumption as a function of mitochondrial complex I activity, demonstrating consistently lower values of tumour compared to control liver Fig. . The ant30 However, exploitation of metabolic vulnerabilities to identify effective and specific anti-cancer agents remains challenging. The advancement of analytical technologies like shotgun proteomics opened the way for global snapshots of the molecular makeup of healthy tissues and tumours.32 The increased sensitivity of these technologies together with improved data reproducibility enable for the first time to map the biochemical network in its totality.9 However, due to (i) enormous plasticity and dynamics, (ii) multi-level regulatory mechanisms and (iii) a highly complex network of reactions, cellular metabolic processes are difficult to study. Mathematical models are useful tools to unravel this complexity, and various tools have been established to develop and analyse genome-scale metabolic models cells.33 Using omics data to scale cell-wide network models of metabolism has led to the identification of novel drug targets and biomarkers.34 Naturally, mathematical models are always simplifications of multi-level biological phenomena; however, hitherto published metabolic models of liver metabolism specifically lack important regulatory aspects, e.g. hormonal influences and allosteric parameters. In addition, they are very often not based on data that have been established experimentally but on information solely extracted from published literature.The fundamental metabolic reprogramming processes that tumour cells undergo to support growth and survival have received widespread attention in recent years and are now considered as an emerging hallmark of cancer.13 The influence of fluctuating nutrient (like glucose and glutamine) and oxygen concentrations within a physiological range are also taken into account. As demonstrated by us earlier, these parameters are at least equally important for modelling the metabolic performance as the changes in enzyme abundance . Applying the model to the central metabolism of HCC, we took advantage of the fact that HCCs originate from hepatocytes,35 i.e. metabolic enzymes in normal and malignant cells only differ in their expression level. This enabled us to re-parameterise the hepatocyte model by scaling the enzyme activities between HCC and normal hepatocytes according to the observed changes of protein abundances that we assessed by quantitative mass spectrometry. It has to be taken into account that relative abundances of cell types other than HCC cells also contribute to the determined protein expression profiles to a certain extent. Immunohistochemistry staining, however, demonstrated negligible infiltration of immune cells in HCC tumour nodules. We therefore assume that the contribution of other cell types to the final proteomics datasets is rather small. This assumption is substantiated by the fact that experimental results obtained from isolated HCC cells were well in line with calculated model predictions. The present study proves that our approach is able to transform mass spectrometry protein data into biologically and clinically meaningful metabolic predictions about the HCC tissue turnover activity of various metabolites. Comparison of simulated normal and HCC liver metabolic performance reveals fundamental differences. We validated several of the calculated model output parameters successfully using different experimental approaches. Glycolytic and respiratory activity were determined by measuring the extracellular acidification and oxygen consumption rates, confirming that HCC cells show increased glycolytic and reduced mitochondrial activity. These findings are well in line with earlier reports using transcriptomics, metabolomics or enzyme activity measurements on different murine HCC models.38 Increased glycolytic activity is consistently found in independent analyses of human HCC tissue with different omics approaches and non-invasive imaging (NMR spectroscopy), pointing towards the Warburg effect as a metabolic hallmark of human liver cancer.41Here, we used a comprehensive kinetic model of the central carbon and lipid metabolism of hepatocytes that incorporates not only the metabolic reaction network but also enzyme regulation by allosteric effectors and by reversible phosphorylation due to changing insulin and glucagon signalling as in Berndt et al.42 Butler et al. showed that the human hepatocellular carcinoma cell lines Huh-7, HepG2 and LH86 do not express the urea cycle enzyme carbamoyl phosphate synthetase 1.43 A comprehensive microarray analysis of 521 patient-derived HCC samples revealed suppression of urea cycle-associated enzymes.44 On the other hand, arginase I and carbamoyl phosphate synthetase (Cps) were found overexpressed in human HCC and their detection via immunohistochemistry was suggested to improve the histopathological diagnosis of HCC.45 Our approach now reveals—for the first time—reduced urea cycle activity in a murine HCC model, nicely confirming that systematic integration of protein expression data is a prerequisite to comprehend metabolic pathway activity.46 The analysis of HCC-specific changes of lipid metabolism has received a lot of attention recently (over 20 studies using human samples and different omics approaches were published in the last 10 years47). The reported results are very heterogeneous, precluding the identification of an HCC-specific lipid metabolism pattern. If anything, activation of fatty acid catabolism (most importantly β-oxidation) could be considered a hallmark of HCC-specific lipid metabolism as it was reported by the majority of publications.47 Of note, the activity of anabolic lipid metabolism pathways in HCC has received significantly less attention. Our approach of combining quantitative proteomics with mathematical modelling predicted reduced activity of several anabolic lipid pathways in HCC, e.g. synthesis of triacylglycerides, cholesterol and fatty acids as well as VLDL secretion. We were able to functionally validate the calculated reduction of triacylglyceride synthesis, underscoring the eligibility of the comprehensive kinetic model to forecast alterations of lipid metabolism in HCC. In summary, the results of all validation experiments show striking consistency with the calculated model simulations indicating that our kinetic model is indeed a powerful tool to reproduce HCC metabolism in a reliable manner.The kinetic model predicted HCC-specific alterations of urea and triacylglyceride synthesis as well as glycogen storage, all of which represent key functions of normal liver. The functionality of the urea cycle in HCC tissue has been under debate for quite some time. It had been established rather early on that HepG2 cells, one of the most widely used human HCC cell lines, harbour a defective urea cycle and it was later shown that this is due to ornithine transcarbamylase and arginase I deficiency.48 Metformin was subsequently shown to exert anti-tumour effects against established human HCC cell lines and in HCC xenografts in nude mice.49 Our results confirm the cell line data reported by Miyoshi et al. and furthermore show that primary hepatocytes are not affected by metformin at the doses found to inhibit HCC cells. These results demonstrate the versatility of our kinetic model as, in addition to depicting metabolic activities, it is able to predict metabolic vulnerabilities. We propose that the herewith outlined experimental approach will also be able to identify innovative targets for the therapy of human HCC. One could even envision an application in a clinical setting where mathematical modelling of biopsy-derived quantitative mass spectrometry-based proteomics data could assist the design of a personalised therapy tactic. Future work with patient samples will need to thoroughly test this hypothesis before a potential exploitation for HCC therapy.The feasibility of the translational application of our kinetic model to estimate and evaluate the performance of therapeutic agents with prediction of possible adverse effects is demonstrated by calculating the outcome of metformin treatment on HCC viability. The antidiabetic drug metformin received a lot of attention in recent years after it was reported to reduce cancer risk and mortality in diabetic patients.supplemental material, figures and figure legends in one fileexecutable SBML file of Hepatokin1


Streptomyces coelicolor M1152 is a widely used host for heterologous expression of BGCs, a systemic understanding of how its genetic modifications affect the metabolism is lacking and limiting further development. We performed a comparative analysis of M1152 and its ancestor M145, connecting information from proteomics, transcriptomics, and cultivation data into a comprehensive picture of the metabolic differences between these strains. Instrumental to this comparison was the application of an improved consensus genome-scale metabolic model (GEM) of S. coelicolor. Although many metabolic patterns are retained in M1152, we find that this strain suffers from oxidative stress, possibly caused by increased oxidative metabolism. Furthermore, precursor availability is likely not limiting polyketide production, implying that other strategies could be beneficial for further development of S. coelicolor for heterologous production of novel compounds.Many biosynthetic gene clusters (BGCs) require heterologous expression to realize their genetic potential, including silent and metagenomic BGCs. Although the engineered   •Time-series transcriptomics and proteomics of S. coelicolor M145 and M1152•Application of GEM to interpret changes in the proteome on the systems level•Limited effect of improved precursor supply on enhanced production in M1152•Reduced rate of germicidin in M1152 suggests a need for other expression hosts Systems Biology; Omics; Metabolic Engineering Streptomyces coelicolor has been the de facto model actinomycete for the production of antibiotics. Being known for over 100 years, the interest in this organism predates the golden age of antibiotic research. With its complex life cycle, featuring mycelial growth and differentiation, spore formation, programmed cell death, and the ability to produce multiple colored secondary metabolites, it has assisted greatly in our understanding of how streptomycetes sense their surrounding   . Heterols (BGCs) . These Bormatics .S. coelicolor as a heterologous production host relies on a metabolism that has evolved to provide the necessary precursors to produce a broad range of complex molecules. Many of these molecules are produced when the strain is experiencing nutrient-limiting conditions that lead to growth cessation and complex re-modelling of its metabolism (S. coelicolor M145 (S. coelicolor A3(2)  . This haor A3(2) .S. coelicolor M145 as a host for heterologous BGC expression, strain M1146 was created by the sequential deletion of its four major BGCs   . This shibiotics . Up to nibiotics  and is tS. coelicolor M1152 has been confined to transcriptome profiling of batch fermentations  open access and contribution, (2) version control, (3) continuous development and integrated quality control with memote  newh memote , baker'sh memote , and Chih memote . The recS. coelicolor, while tracking development using Git for version control  and abundances. The GECKO toolbox modifies the structure of an existing GEM to integrate turnover rates and proteome data. Consequentially, this constrains the range of estimated fluxes to a biologically feasible range as determined by the amount and efficiency of each enzyme. Note that this approach regards the maximum catalytic activities but does not consider other kinetic parameters such as affinity constants. The overall flux variability of the resulting enzyme-constrained model (EcSco-GEM) is drastically reduced compared with the classic genome-scale model (1) flux variability. As reactions with high variability result in low certainty in the estimated fluxes, the observed reduction in flux variability is therefore a qualitative measure of the increased accuracy achieved by constraining the range of possible fluxes to those satisfying the limitation in protein allocation.To include explicit constraints regarding enzymes catalyzing metabolic reactions, the GECKO formalism  was applle model G, particIn our endeavor to describe the metabolic differences between M145 and M1152 we generated in total 17 time- and strain-specific enzyme-constrained models by combining EcSco-GEM with estimated growth, secretion, and uptake rates, as well as proteome data from cultivations that are detailed and analyzed later in the article.S. coelicolor Sco-GEM models can simulate behaviors of  earlier . Culture earlier A and 2B. earlier . Both D-depleted . The RNAdepleted  and weredepleted  , an increase in oxidative phosphorylation, and a decrease in fatty acid biosynthesis D and S4.Amycolatopsis sp. , delaying phosphate depletion by M1152 to 47 h after inoculation  biosynthesis in elicolor , one canelicolor . MalonylAlthough the proteome data are an integral part of the EcSco-GEM models, RNA-seq data were used to both verify the trends and to gain further insights into the regulatory changes that are not captured by the metabolic models. As the proteomic data, the RNA-seq data showed large global differences between M1152 and M145, revealing 499 differentially expressed genes with a significance threshold of p < 0.01.Unsupervised clustering of the significantly changed genes reveal differences in regulatory systems related to redox regulation, signaling, and secondary metabolism. The significantly changed genes were clustered into seven groups with K-means clustering, with clusters 1–3 containing genes that are upregulated in M1152 compared with M145, and clusters 4–7 vice versa . A Gene The enriched processes upregulated in M1152 point to increased oxidative stress : antioxiscbA (SCO6266) and its downstream gene scbC (SCO6267), which stands out by being almost 6-fold upregulated in M1152. This high expression level is likely due to the deletion of scbR2 (SCO6286), the last gene selected to be part of the cpk BGC  to this enzyme introduction of a (secondary) copy of germicidin synthase gene y of gcs . Thus, trpoB mutation, and increased oxidative metabolism and oxidative stress. As Act itself works as an electron acceptor one may hypothesize that its presence could relieve some of this stress. Another approach is to reintroduce scbR2 to avoid influencing the related regulators of development and secondary metabolism.Although earlier work has suggested a competition for common precursors between fatty acids and secondary metabolites biosynthesis , our resS. coelicolor seems to have a complex and not fully elucidated regulatory system, several studies have shown that manipulation of regulatory genes can affect the production of secondary metabolites .Further information and requests for resources and reagents should be directed to and will be fulfilled by the Lead Contact, Eduard J Kerkhoven . Here, the latest version of the Sco-GEM is available in both YAML and SBML level 3 Version 1. In addition, users can contribute to further model development by posting issues or suggest changes. The proteomics data are available from ProteomeXchange: PXD013178 via the PRIDE partner repository (GSE132487 (M145) and GSE132488 (M1152). Normalized counts are also found in The models and scripts generated during this study are available at GitHub (pository . NormaliAll methods can be found in the accompanying


Pichia pastoris (Komagataella phaffii) is currently considered one of the most promising hosts for recombinant protein production (RPP) and metabolites due to the availability of several tools to efficiently regulate the recombinant expression, its ability to perform eukaryotic post-translational modifications and to secrete the product in the extracellular media. The challenge of improving the bioprocess efficiency can be faced from two main approaches: the strain engineering, which includes enhancements in the recombinant expression regulation as well as overcoming potential cell capacity bottlenecks; and the bioprocess engineering, focused on the development of rational-based efficient operational strategies. Understanding the effect of strain and operational improvements in bioprocess efficiency requires to attain a robust knowledge about the metabolic and physiological changes triggered into the cells. For this purpose, a number of studies have revealed chemostat cultures to provide a robust tool for accurate, reliable, and reproducible bioprocess characterization. It should involve the determination of key specific rates, productivities, and yields for different C and N sources, as well as optimizing media formulation and operating conditions. Furthermore, studies along the different levels of systems biology are usually performed also in chemostat cultures. Transcriptomic, proteomic and metabolic flux analysis, using different techniques like differential target gene expression, protein description and 13C-based metabolic flux analysis, are widely described as valued examples in the literature. In this scenario, the main advantage of a continuous operation relies on the quality of the homogeneous samples obtained under steady-state conditions, where both the metabolic and physiological status of the cells remain unaltered in an all-encompassing picture of the cell environment. This contribution aims to provide the state of the art of the different approaches that allow the design of rational strain and bioprocess engineering improvements in Pichia pastoris toward optimizing bioprocesses based on the results obtained in chemostat cultures. Interestingly, continuous cultivation is also currently emerging as an alternative operational mode in industrial biotechnology for implementing continuous process operations.The methylotrophic yeast  In recent years, recombinant protein production (RPP) technology has given rise to a multibillion-dollar market offering products for a wide range of industrial activities such as food, detergent, paper, chemical, cosmetic, and pharmaceutical production. For example, more than 400 RPP-based pharmaceutical products are currently available on the market  cells , Kluyveromyces lactis, Yarrowia lipolytica, or Komagataella phaffii (Pichia pastoris)  has arisen as an efficient and versatile cell factory for obtaining a wide spectrum of biotechnological products including recombinant proteins and metabolites of diverse origins  and the ability to perform post-translational modifications as well as to secrete the products extracellularly , a strong and tightly regulated promoter, was the first used obtaining efficient production rates of several proteins of interest   of the microorganism used  (chemostat or turbidostat-based approaches)  and deceleration-stats (De-stats), which are used to study the increase or decrease the specific growth rate, respectively , where an environmental parameter is continuously changed while the dilution rate is kept constant  studies Bull, , but alsTranscriptomic, proteomic, metabolomics, and fluxomic data, can be jointly integrated into a systems biology approach shown in  in orderTranscriptional analysis is usually the first step in systems biology studies as it is also the first stage in the information flow from genomic data  , which quantify the number of transcripts present in a sample by whole transcriptome sequencing, have arisen as helpful workhorses. In fact, these methods provide a robust overview of all transcripts  was examined by using the RNAseq SOLiD platform. In addition, further RT-PCR analysis showed a constitutive splicing of HAC1 gene transcript across the different phases of RPP induction independent of the lysozyme misfolding level. The importance of this finding is based on the fact that Hac1p corresponds to a key transcription factor in the triggering of UPR response  is one other limiting factor for RPP  improved with increasing specific growth rate (μ), gene transcription had no influence on the latter, indicating a constitutive nature of PTHI11.Furthermore, it has been observed that transcriptional analysis provides useful information for characterizing native and engineered promoters. Thus, Landes et al.  characteG1, corresponding to a high-affinity glucose transporter (GTH1), exhibited strong and tight regulation under carbon-limiting conditions. Also, further characterization of this promoter at variable specific growth rates in chemostat cultures revealed the optimal specific production rate at a dilution rate D = 0.07 h−1.In similar work intended to develop alternatives to the methanol-based expression system, Prielhofer et al.  identifiP. pastoris producer clones growing at controlled specific growth rates in chemostat cultures have also enabled further transcriptional characterization and expansion of existing knowledge about the impact of this key parameter for improvement of the cell factory. Thus, Rebnegger et al. . In order to generate an alternative model for Warburg effect studies, Ata et al.  under AOX1 promoter . As confirmed by ROL transcriptional levels in a ddPCR analysis, optimal specific extracellular lipase activity was obtained with the 2C clone. By contrast, transcriptomic analyses with microarrays revealed constraints with increasing ROL gene dosage on the transcriptional machinery  . As revealed by specific analysis with ddPCR, methanol uptake was found to have a positive effect on the transcriptional response; the effect, however, resulted in no increase in product activity , global stress-related transcription factors and with nutrient responses reveal an adaptation of low substrate availability at near-zero growth rates. This finding reinforces the reduction observed in the maintenance coefficient (ms), in comparison to chemostat cultures growing at higher μ. Otherwise, protein synthesis in retentostat cultures exhibited insubstantial transcriptional regulation, so further research, for example with RP-expressing clones, to determine whether the alternative cultures could be useful with P. pastoris and to outperform S. cerevisiae translational capacity at low μ is proposed.Although most transcriptional analyses have been performed in chemostat cultures, some have been conducted in retentostats. Rebnegger et al.  performeAccording to the central dogma of molecular biology, the protein level falls at the last stage of the information flow . A metabolic phenotype is defined by the actual activities of the metabolic reactions in cells . Because they are rarely constant, reaction rates are usually determined under steady-state or pseudo-steady state conditions and commonly referred to as “metabolic fluxes,” which are thus key indicators of the physiological status of cells.in vivo values for kinetic parameters are usually unavailable. A number of techniques have thus been developed to quantify metabolic fluxes collectively that are known as “metabolic flux analysis” (MFA) or, simply, “fluxomics.” Many of them have been applied to P. pastoris and the most salient are discussed below. Using those techniques for metabolic engineering improves existing knowledge of the physiological properties of biological systems, thus enabling the rational design of cell factories and efficient metabolic engineering cycles.Determining metabolic fluxes remains difficult despite major technological advances in quantifying all components involved. In fact, it is not always possible to determine the concentrations of all relevant components; also, As stated above, MFA is widely used for comprehensive analysis of the physiological effects of environmental changes or genetic engineering modifications. Metabolic fluxes  provide an excellent operational picture of cell operation. A continuous culture provides a simple, convenient tool for maintaining a stable (in steady state) cell metabolism over long periods of time. Comparing metabolic flux distributions under different conditions allows a deeper understanding of the effects resulting from the genetic or environmental changes.13C labeling . Using GEMs in combination with steady-state data should in theory allow one to calculate metabolic fluxes. Unfortunately, the intricate interconnections among metabolites, and the small number of flux measurements typically available , prevent the accurate determination of most of the metabolic fluxes, which requires the combined use of mathematical models, optimization methods and/or experimental techniques such as Genome-scale metabolic models have become essential tools for MFA and rational-based strain engineering. These models are mathematically structured knowledge bases containing descriptions of all biochemical reactions, metabolites, and metabolic genes for a specific organism—a Biochemical, Genetic and Genomic (BiGG) knowledge base  or their mixtures   rate, but also by the methanol fraction in mixed feeds. Experiments using chemostat cultures have shown environmental factors such as oxygen-limited conditions or low temperatures to have a strong impact on MFA  and building block production  while reducing biomass yield  requires a deep physiological understanding of the cell factory. For the topic discussed in this review, such knowledge is expected to eventually allow the rational development of feasible and competitive bioprocesses with shorter times to market. The overall approach is usually not straightforward due to the complexity of the different interactions occurring at many cell physiology levels. Thus, since the interactions between the cell factory performance and the bioprocess conditions define key parameters of interest (KPI) of the production, an empirical determination of those are required. In this sense, to obtain this kind of information accurately, chemostats are considered the most usual continuous cultivation applied  and concretely, batch or fed-batch cultures to determine oxygen requirements  However, currently, continuous cultivations should be considered a preferred option to assess the effect of any culture conditions. The fact of working in steady state conditions in whichever cell population is considered homogeneous allows to obtain very accurate and reliable results. In contrast, dynamic processes such as batch of fed-batch cultures are expected to be less robust and present more deviations due to possible drifts in culture conditions. Furthermore, also parameter determination such as kinetic rates and yields is also considered to be more complex in dynamic processes.Bioprocess performance is influenced by some physical conditions of cultures including temperature (T), pH and dissolved oxygen (DO). The optimum conditions for production may differ from those for growth due to their effect on several factors including protein-specific characteristics, kinetics and sensitivity of products to proteolytic degradation.P. pastoris bioprocesses is about 30°C, above 32°C protein expression is suppressed and cell growth rapidly decays  by P. pastoris in continuous cultures growing at the same μ but at different temperature (22 or 30°C). Overall, the lower temperature led to lower specific productivities irrespective of the co-substrate used. Strikingly, lowering temperature produced an increase in biomass concentration.Berrios et al.  examinedAs a conclusion of the studies focused on the T effect, the efficiency of a low cultivation temperature depends on the target protein, so this effect should be studied for each case.P. pastoris cultures is commonly set at 5.0–6.5  by having the bioreactor operate at a constant agitation rate and using air or oxygen-enriched air as the inlet gas in order to ensure fully aerobic conditions . Chemostat cultures have been used to examine the boosting effect of oxygen-limiting conditions on RPP. For example, Garcia-Ortega et al. . Also, a high osmolarity decreased biomass yield due to the increased energy maintenance requirements.The composition of the cultivation medium also has a direct impact on osmolarity. Dragosits et al.  examinedP. pastoris and constitutive promoters such as PGAP, glycerol and glucose are widely used as carbon sources because they result in high specific growth rates that are usually accompanied by adequate specific production rates  far enough from μ+ strain for PAOX1-driven heterologous production of a sea raven antifreeze protein. The specific product formation rate (qP) and product-based volumetric productivity (QV) increased throughout the range of dilution rates used (0.01–0.10 h−1). Similarly, Boze et al. (V or qP increased relative to the use of methanol as sole carbon source at the same dilution rate (0.01 h−1). However, the substrate concentration ratio was not optimized in either study.D'Anjou and Daugulis  used a se et al.  studied P. pastoris Mut+ strain expressing recombinant avidin at a constant dilution rate D = 0.06 h−1. With methanol fractions higher than 0.6 C-mol C-mol−1, qP was like cultures performed with methanol as sole carbon source.Jungo et al.  studied Rhizopus oryzae lipase (Rol) as a model system to investigate the application of methanol-glycerol feeding mixtures in the P. pastoris Mut+ producer clone. Cultures were grown in a simple chemostat system and response surface methodology was used to evaluate the effects of D and the methanol/glycerol ratio in the feed as experimental variables. The optimum conditions provided qP values similar to, and QV values higher than those of processes using methanol alone as substrate. Furthermore, Berrios et al.  , and product formation (qP) are Monod for cell growth, Pirt's as a maintenance energy model and Luedeking–Piret as linear μ-dependence for substrate uptake and product formation, respectively. However, saturation patterns, non-monotonic behaviors or bell-shaped types have also been observed, especially in substrate-inhibited systems for cell growth and non-constitutive RPP , substrate uptake  usually exhibit different production kinetics. Thus, the PAOX1-driven expression system often exhibits non-monotonic kinetics, possibly as a consequence of the metabolic burden resulting from methanol uptake and/or protein processing, and from secreting limitations due to outstanding expression levels . For other proteins, studies performed in chemostat   and the YP/X values were always higher in continuous mode at similar μ comparing to those obtained in fed-batch cultivation.In terms of absolute values, only in the case of Fab 3H6 and hSA production, the specific production rate (V) has been also included in Additionally, since productivities could be one of the main performance criteria from an industrial point of view, volumetric productivity  including productivities  production with the constitutive promoter PGK in continuous and fed-batch cultures. They found volumetric and specific productivity to peak at the highest μ levels, which indicated a direct correlation between growth and production.de Macedo Robert et al.  comparedProduction kinetic profiles for other proteins have also been obtained in other continuous cultures that were used as references to develop optimal feeding strategies adjusted to cell factory performance. The result was a marked increase in production in terms of volumetric productivity and product titer for some Fab fragments  in chemostat cultures growing under a steady state. Alternatively, it can also be assured with periodic changes in dilution rate or the aeration conditions . Adaptation of the yeast to growth on methanol over 250 generations was examined and observed a complex correlation among carbon source, cell growth and RPP. Increased specific growth rates on rich and minimal growth media was studied at the level of both population and single clone. Selected clones displayed strain-dependent variations for the yield of PAOX1-based recombinant protein expression, one showing up to 2-fold increase in terms product titer.Gasser and Mattanovich  reportedr et al.  investigFrom a bioprocess engineering perspective, process variability often results in issues arising from changes in critical process parameters (CPPs), key parameters of interest (KPIs), or critical material attributes (CMAs), all of which in turn affect critical quality attributes (CQAs). CPPs can change throughout a culture and require using appropriate control strategies to reduce process variability. Advances in process analytical technology (PAT) and quality by design (QbD) approaches have substantially reduced times for process development. According to Hernandez , in the P. pastoris have been described for batch and fed-batch operations. Besides the common sensors used for the monitoring and control of culture conditions and gas analysis, just scarce applications have been reported for continuous mode  was running 6 weeks at μ = 0.14 h−1. In this case, considering the unproductive time spent in setting up, draining out, cleaning and reassembling in fed-batch operation, the overall CalB production was 5.8 times greater than the fed-batch process  was maintained working for 2 weeks reaching similar levels of product titer than at the end of a fed-batch culture. Specifically, QP. pastoris is presented in Finally, a summary including the main items required to address toward the industrial implementation of continuous cultivation with the cell factory P. pastoris is considered an outstanding cell factory alternative for its industrial use in production processes of both metabolites and recombinant proteins. Despite the excellent features of this host, in general, most of the bioprocesses based on fermentation technology are considered still far from achieving the maturity of other industries. In this sense, the present trends toward their optimization are provided by two complementary approaches: Strain development and bioprocess engineering. In order to achieve relevant progresses in the long road to bioprocess optimization it is essential to acquire robust and reliable knowledge of the system used. This knowledge is considered with the objective to be able to design and implement rational developments from any of the both approaches mentioned. In this context, continuous cultivation emerges as an excellent tool to accurately characterize the performance of the cell factory in terms of physiological and production parameters. Furthermore, the steady state conditions achieved during the continuous cultures and the high degree of cell population homogeneity makes this operational mode, an excellent tool toward the development of a wide range of systems biology studies including transcriptomics, proteomics, metabolomics and other cutting edge “-omics” studies.The yeast P. pastoris. It illustrates the different approaches that, based on the results obtained in continuous cultivation (chemostat), allow to achieve rational improvements at both strain and bioprocess engineering level.In P. pastoris has the most relevant challenges with the identification of efficient and methanol-free alternative promoters, the integration of upstream and downstream, reaching short process development times with minimal risks on quality/regulatory requirements through PAT and QbD approaches and, finally, to evaluate the impact of long-term continuous operation on genetic stability and cell physiology.Besides, the current trends of industrial biotechnology is promoting the transition from batch/fed-batch-based processes toward the continuous biomanufacturing due to the numerous advantages that present this operation mode in terms of ensuring a robust and very high product quality as well as, among others, to reduce running costs and minimizing equipment requirements. The potential implementation of biomanufacturing processes with MN-T and XG-O contributed writing the Abstract and the Introduction sections. MN-T and JA wrote the section: Continuous cultivations provide an excellent tool for systems biology research. JM-S and FV wrote the section: Bioprocess characterization with chemostat cultures. XG-O, JM-S, and FV wrote the section: Is continuous cultivation a real alternative for its use in industrial Pichia pastoris processes? XG-O, JM-S, and FV wrote the Conclusions section. All authors read, reviewed, and approved the submitted version.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


The first discovery of metabolic alterations in cancer cells refers to Otto Warburg’s observations. Cancer metabolism results in alterations in metabolic fluxes that are evident in cancer cells compared with most normal tissue cells. This study applied protein expressions of normal and cancer cells to reconstruct two tissue-specific genome-scale metabolic models. Both models were employed in a tri-level optimization framework to infer oncogenes. Moreover, this study also introduced enzyme pseudo-coding numbers in the gene association expression to avoid performing posterior decision-making that is necessary for the reaction-based method. Colorectal cancer (CRC) was the topic of this case study, and 20 top-ranked oncogenes were determined. Notably, these dysregulated genes were involved in various metabolic subsystems and compartments. We found that the average similarity ratio for each dysregulation is higher than 98%, and the extent of similarity for flux changes is higher than 93%. On the basis of surveys of PubMed and GeneCards, these oncogenes were also investigated in various carcinomas and diseases. Most dysregulated genes connect to  Recent developments in omics data, such as genomics , transcrA better understanding of the genome-scale human metabolic network may enable the identification of disease genes and related pathways, thereby offering better targets for drug development. The release of genome-scale human metabolic networks, such as Recon 1 and 2 ,10, EdinHuman tissues have diverse metabolic functions, which are complex and specialized in different tissues and cell types. Mapping out these tissue-specific metabolisms in GSMMs will advance our understanding of the metabolic basis of various physiological and pathological processes. Nevertheless, for the in-depth study of specific cell phenotypes, the development of tissue- or cell-type-specific metabolic models is necessary. Automated reconstruction algorithms developed to date can be broadly categorized into flux-dependent and pruning methods ,20,21,22The metabolic network reconstruction processes are described in m is the number of metabolites and n is the number of reactions; FBA is a constraint-based modeling approach where the stoichiometry of the underlying biochemical network constrains the solution. The stoichiometric matrix of a typical metabolic system is underdetermined, and infinite solutions are possible. The FBA formulates a metabolic network as a linear programming problem, as shown in Equation , wherein signals ; thus, tFBA assumes that metabolic networks will reach a steady state constrained by the stoichiometry. Even though the stoichiometric constraints lead to an underdetermined system, the bounded solution space of all feasible fluxes can be identified, that is, a large set of alternative flux distributions with an identical objective value. We minimized the squared sum of all internal fluxes for FBA to ensure efficient channeling of all fluxes through all pathways to eliminate numerous flux distributions in Equation . The EucEquation , and ΩInminvf/b∑iWe introduced a tri-level optimization problem (TLOP) to simulate gene screening procedures in a wet lab to infer oncogenes. The flowchart of the in silico experiment is presented in The hierarchical multiple objectives are considered in the outer optimization problem in Equation . The firHere Equation  indicateEquation .The second and third objectives are determining that the similarity ratios of the flux reprogramming are maximized. The similarity ratios provided  to illusThe TLOP framework must decide which genes are selected for mutation. Most optimal strain design methods ,31,32,33The pseudo-enzymes are then used as upper-level variables in Equation  to selecThe candidate genes in Equation  are reprThe TLOP framework in Equation  considerThe metabolic model of Recon 2.2 consists of 5324 species, 7785 reactions, and 1675 associated genes A. Until Total 565 choke-point metabolites (metabolites involve in only one synthesis or degradation reaction) in the normal and cancerous metabolic networks were determined by topology analysis. Due to that different uptakes can lead to a bias of the computational results, same uptakes  for normCAT, G6PD, and CDO1) obtained from the NHDE algorithm are FAP-associated genes. Therefore, the results reveal that the inference optimization framework is a useful computer-aided oncogene detection system.The NHDE algorithm was applied to solve the TLOP, and the top 20 one-hit oncogenes were determined; their average similarity ratios are presented in t-test was used to analyze the RNA-sequencing data, and a p-value less than 0.05  is statistically significant. The result shows that 17 out of the 20 oncogenes are significant as shown in We also applied RNA-sequencing data of the healthy and cancerous colorectal tissues obtained from the TCGA database  on the aCAT, is an essential antioxidant enzyme that catalyzes the decomposition of hydrogen peroxide (H2O2) to water and molecular oxygen. CAT catalyzes three decomposition reactions of H2O2 in the cytoplasm, peroxisome, and mitochondria of the GSMN model. Based on the computation results, we determined that a 78% downregulation of CAT could increase the production of reactive oxygen species (ROS) that exhibits carcinogenic effects [CAT is related to apoptosis, proliferation, and cell growth signaling pathways . However, the reaction-based approach only determined r0249 with average similarity ratio of 0.981 and extent of flux changes of 0.935. The proposed pseudo-enzyme strategy was then applied to regulate both reactions. An average similarity ratio of 0.955 and average flux change ratio of 0.771 were obtained, which were smaller than that obtained using the reaction-based approach. Following the posterior procedures, we observed that the gene HMGCL could obtain an identical result through the reaction-based approach, but it also catalyzed another reaction HMGLx and included the isozyme HMGCLL1. The gene PRODH2 achieved the same result but catalyzed four reactions. Finally, CAT regulated three reactions , but each reaction achieved different results.Furthermore, we applied a reaction-based approach to determine oncogenes in order to illustrate the performance of the proposed pseudo-enzyme strategy. Six top-ranked one-hit reactions are presented in To avoid the solution bias of FBA used in the TLOP problem for evaluation of flux alterations, flux variability analysis (FVA) was applied to compute the minimum and maximum values of each metabolite for the normal model and the mutants. The flux ranges were compared between mutant and normal models, and each flux difference between mutant and normal models was classified into seven categories according to the definition presented in This study introduced a tri-level optimization framework that incorporated protein expressions of normal and tumor tissues for inferring oncogenes. The protein expression data or RAN-sequencing data, input of the optimization framework, was acquired from public databases such as HPA or TCGA. To enable provision of personalized medical treatment, the input of the optimization framework can be replaced with a patient’s protein expressio data. The proposed TLOP is an NP-hard problem, and no commercial software programs could be used to solve the problem. The NHDE algorithm with hierarchical objectives was applied to solve the problem. Moreover, this study introduced enzyme pseudo-coding numbers for expressing gene association to avoid the performing posterior decision-making that is necessary for the reaction-based method. CRC was applied as the case study, and the NHDE algorithm inferred 20 top-ranked oncogenes that cause various carcinomas and diseases based on surveys of PubMed and GeneCards. Notably, the evidence illustrated that the inference optimization framework enables oncogene prediction.


E. coli that exchange molecules with their environment, express the genes required for chemotaxis, swim, grow, and divide. This model is developed incrementally, highlighting cross-compartment mechanisms that link E. coli to its environment, with models for: (1) metabolism and transport, with transport moving nutrients across the membrane boundary and metabolism converting them to useful metabolites, (2) transcription, translation, complexation, and degradation, with stochastic mechanisms that read real gene sequence data and consume base pairs and ATP to make proteins and complexes, and (3) the activity of flagella and chemoreceptors, which together support navigation in the environment.The degree to which we can understand the multi-scale organization of cellular life is tied to how well our models can represent this organization and the processes that drive its evolution. This paper uses Vivarium—an engine for composing heterogeneous computational biology models into integrated, multi-scale simulations. Vivarium’s approach is demonstrated by combining several sub-models of biophysical processes into a model of chemotactic  The fundamental unit of life—the cell—is a compartment of active molecular processes that operate together as an integrated whole. When we look up close, we see dynamics governed by fluxes of matter and energy that drive molecular reactions, reconfigurations, and transport. When we take a step back, we see the cell is embedded in, and interacts with, an environment filled with other cells, chemical gradients, and physical barriers. Cellular life is fundamentally multi-scale—the physiology and behavior observed at the cellular scale (of micrometer length and second/minute duration) are driven by events occurring at spatio-temporal scales that are both greater and smaller. This paper focuses on multi-scaling of bacterial cells —the multTo confront the complexity of cellular biology, we can encode molecular mechanisms into integrated computational models and simulate them to observe how the hypothesized mechanisms operate as a whole. Where the simulation output matches experimental observations, there might be truth to the proposed mechanisms; where the output diverges, we know something is wrong. Cellular phenotypes emerge through diverse mechanisms operating both internally and externally to the cell—to capture this emergence in realistic detail requires a multi-scale modeling approach that decomposes cellular processes into independent sub-systems, defines them with the most appropriate computational representations, and integrates them into unified and executable models.E. coli is an ideal target for multi-scale cell modeling. These minimal organisms—rod-shaped bacteria about 2 microns long—have undergone more scientific scrutiny than any other organism, being the model organism used to discover the genetic code, DNA replication, and genetic regulation, and they are now a cornerstone of modern synthetic biology. This is why, as early as 1973, Francis Crick and Sydney Brenner talked about coordinating a world-wide effort toward “the complete solution of E coli” [E. coli has also been a model organism for the molecular biology of behavior, with every aspect of its chemotaxis—E. coli’s primary mode of navigation—as the focus of intense scientific investigation [ E coli” ,6,7,8,9.tigation . Analysitigation ,12, the tigation , and tratigation . Howevertigation —this is E. coli chemotaxis has, for the most part, been studied in isolated subsystems, with mechanisms proposed for practically every active molecular process. There are models published on the activity of chemoreceptors [E. coli chemotaxis is a highly cross-modal phenotype with many integrated subsystems that coordinate their activities. As a consequence, E. coli can achieve a diverse range of chemotactic behavior as it moves between different physiological states and environments [eceptors , signal eceptors ,18, and eceptors , as welleceptors ,21. In tronments ,23. As aVivarium is a novel simulation engine that addresses computational biology’s dual challenges of model reuse and multi-scale integration by explicitly separating the interface that connects models from the frameworks that implement them. This contrasts with standardized modeling approaches, such as the Systems Biology Markup Language (SMBL), which support reuse through a standardized specification of models . ExistinE. coli chemotaxis. E. coli in three subsections with the progressive integration of new modules:  multi-scale representation of a compartment hierarchy with modular processes, (2) multi-scale simulation with multiple timescales and distributed computation, and (3) multi-scale development of models with modules that can be reused and recombined into increasingly complex computational experiments. This paper’s focus is the application of Vivarium to modeling bigraph  of embedded compartments, based on the writings of Robin Milner [topology is a bipartite graph of processes that connect to stores  a next_update method, which takes the current state and a time-step, runs the model and returns an update; finally, (4) a composite of multiple processes declares a topology that defines how processes are wired together through shared stores. Composites can also accept parameters, which are passed to their processes’ constructors to override the defaults.Any model that can take a state and transform it for an interval of time can be made into a process by implementing a process interface. The interface is designed to be as simple as possible—it requires the following protocol: (1) A constructor that accepts a list of parameters that configure the model—this overrides default parameter values and allows easy access to parameters by users or by learning algorithms; (2) a experiment. A basic simulation cycle has processes view their declared states, run their mechanisms for a set time, and return an update that modifies the states  Custom modules specific to a given biophysical system. These are the easiest way to adapt models from prior publications, and can be used for their single function. This paper demonstrates these with the chemoreceptor and flagella processes. (2) Wrapper modules built around external modeling libraries—if other platforms are available that can be imported to accomplish the modeling task, they should be reused. This paper demonstrates such processes with pymunk  for the Further modularity comes from the separation of functions in different software libraries. The Vivarium engine is available as its own library, which is required for implementing the process interface and running a simulation. Individual modeling projects can release their processes, composites, and data in separate libraries. This streamlines model development, allowing users to (1) write their own processes and composites, (2) import libraries from different projects to access their processes, reconfigure them, and combine them to quickly prototype new models, and to (3) make incremental changes  and iterate on model designs that build upon previous work. Finally, Vivarium is released under the MIT license, permitting open development and reuse. By open-sourcing the software, future scientists can build upon existing models by adding new processes, making new predictions, and testing against new data.E. coli can live in a variety of environments of different molecular compositions, which drive patterns of growth, behavior, and evolution. Their small size, of micron scale, exposes them to very different physics from our own. The low ratio of inertial to viscous forces (a low Reynolds number) overwhelms any inertia they might carry [ht carry . They armulti-body physics and diffusion—these operate on the states of agent bodies and molecular fields  becomes disinhibited and begins to express LacY protein. With sufficient LacY in the membrane, lactose is taken up, the metabolism shifts to lactose metabolism, and growth resumes.Consider glucose–lactose diauxie as an example of this dynamic process ,40. WhenMetabolism: We begin with a dynamic flux balance analysis (dFBA) model of metabolism. Flux balance analysis (FBA) is an optimization-based approach, which takes network reconstructions of biochemical systems and applies linear programming to determine flux distributions in the absence of kinetic parameters. It assumes a steady state, with fluxes across a stoichiometric network of reactions all balanced for each individual molecular species. Constraints are imposed on individual fluxes, setting their upper and lower limits. An objective function is then optimized; the model in this paper optimizes the production of biomass based on known composition of metabolic end-products [products . FBA is products  that caniAF1260b, which comes from the BiGG model database [E. coli strains, Salmonella, and even some human cells. iAF1260b includes 2382 reactions controlled by 1261 genes, which transform 166 metabolites. iAF1260b was selected because it includes the relevant transport reactions and generates the four nucleotides and twenty amino acids required for the gene expression processes in The metabolism process is configurable and can run any properly formatted metabolic network. The chosen network is a genome-scale metabolic model called database . The metWhen a metabolism process is placed in a compartment and run on its own, it takes up metabolites from the environment and grows its internal pools of metabolites, exponentially increasing in mass and reproducing the expected 40 minute doubling time in minimal glucose media a. If metTransport: If we take the perspective of an individual cell in a colony, the influx of nutrients can no longer be explained by the optimization of biomass production. External molecules are brought into the cells by transporters embedded in their membranes, and it takes an optimized composition of transporters to maximize influx—this composition is under complex mechanistic control involving gene regulation networks and competition with other proteins. Glucose is transported into the cell by two primary transport systems [ systems ,44: (1) The transport process uses a generalized form of the Michaelis–Menten kinetic rate laws called convenience kinetics . The minGene expression: To demonstrate the dynamics of kinetic transport, we need to express transporters and have their state control transport flux. A minimal, stochastic ordinary differential equation (ODE) process for gene expression is used for LacY transporters, which is informed by the schematic of the models and parameters described in [ribed in ,46. Thisv), with transport setting the dynamic uptake rates, and metabolism using them as flux constraints on the FBA problem. This works because transport reactions operate on the boundary of the metabolic network, and metabolism is limited to use what is supplied by these flux constraints. Transport and gene expression are coupled through a protein store (p), which holds the transporter proteins, and metabolite store (m), which holds the internal metabolite pools that are built up by metabolism and regulate gene expression. As internal metabolite pools change, this triggers changes to the expression of transporters, which influences the transport rates and, hence, the flux constraints on metabolism.The integrated model can be placed in the environment and run—it grows and divides, with each daughter cell having its own transport kinetics, metabolism, and gene regulation. This results in, for the first time to our knowledge, genome-scale models of colonies that are implemented on an individual cell basis, with heterogeneous cells distributed in a spatial environment—each carrying out its own FBA instance with dynamic flux constraints. This is already a fairly large model compared to a standard agent-based model.The model demonstrates the emergence of glucose/lactose diauxic shifts. We now replace the ODE-based gene expression process of the previous subsection with more detailed, configurable, and stochastic processes for transcription, translation, degradation, and complexation. These processes operate on gene and protein sequence data, transcription unit structure, binding propensities, and other parameters to express mRNA, proteins, and protein complexes. They use a Gillespie algorithm —a discreAfter describing the four processes, they are integrated with the metabolism and transport of the previous subsection and configured to implement a detailed model of flagella expression; in the following section, these flagella will be given a function that enables them to generate forces in the environment.Transcription: E. coli’s genome is organized in operons, in which multiple genes are expressed as transcription units that are transcribed together as mRNA. The synthesis of a transcription unit starts at a promoter sequence in the chromosome, where RNA polymerase (RNAP) binds to begin transcription, and ends at a terminator, where the RNAP unbinds. The RNAP uses the sequence of nucleotides in an operon as a template to synthesize a matching mRNA transcript, itself a sequence of nucleotides. The energy cost of transcription comes from ATP hydrolysis, with one ATP for each nucleotide elongation.The transcription process used here can be configured with any chromosome data that include gene sequence data as well as promoters’ and terminators’ locations. The process operates on the state of RNAPs, nucleotides, ATP, and mRNA. The binding of RNAP is implemented by the Gillespie algorithm, with affinities determined by transcription factors for each promoter. Each promoter has a number of binding sites that can be occupied by a number of different transcription factors . The affinity of the RNAP to bind to a given promoter is modulated by the concentration of transcription factors, which either activate or repress that promoter. The higher these thresholds, the more concentration is required to turn it from an empty state to an occupied state, providing a means to gradually introduce components as determined by changing concentrations of the transcription factor. Once bound to a promoter, the RNAP occludes binding of additional RNAPs—it elongates at a rate of 50 base pairs per second and frees up the promoter region when at a distance of 30 base pairs—which allows a transcription unit to be occupied by many RNAPs at different locations.Translation: The translation process operates on the available mRNAs, amino acids, ATP, and free ribosomes; this process does not include tRNA charging. A ribosome binds to an mRNA and uses it as a template for polymerizing a sequence of amino acids at a rate of 22 amino acids per second, with two ATPs used per amino acid for ATP hydrolysis. The same mRNA can be translated by many ribosomes at once, given a minimum occlusion distance of 50 base pairs between them. Upon termination, the protein and ribosome are released into the appropriate stores, and their counts increased. Each transcript, as a potential operon containing the code for many separate proteins, has a series of separate binding affinities for the gene products it encodes. The affinities of these binding reactions are parameters that can be supplied to the model, and can be targeted by parameter selection algorithms.Complexation: Most protein function comes from the activity of complexes, which are composed of many individual protein monomers. These complexes can be constructed in steps, with intermediate complexes combining to form larger complexes. The stoichiometry of a complexation network describes how monomers combine into complexes, and sub-complexes into larger complexes. The complexation process uses the Gillespie algorithm to determine which monomers or complexes combine and when. The propensities for these reactions are parameters that can be supplied for this model; since these values have not been reported, we used the order-of-magnitude estimate of Degradation: The degradation process uses basic enzyme kinetics (here provided by the enzyme endoRNAse) to reclaim the nucleotide bases from mRNA at a steady rate, with a cost of one ATP per nucleotide degraded. These transcripts are removed from the cytoplasm, and the bases that compose them are returned to the pool of available nucleotides. Proteins are not degraded in the model due to their much longer degradation time in real cells—the loss of protein concentration is due to dilution from growth and division, and this is the loss that has to be countered by ongoing gene expression.The gene expression processes can be configured by providing an expression network that includes all of the parameters described above—gene sequences for the operons, promoter and terminator locations, transcription factors for each promoter with threshold values for RNAP binding, and complexation reaction stoichiometry. To demonstrate the integrated function of these processes, we curated a flagellar expression network from the EcoCyc database , shown iE. coli’s gene expression machinery has been experimentally demonstrated to perform “just-in-time” expression, with proteins synthesized in roughly the order they are required [Flagella are large protein complexes that require the coordinated expression of many individual monomers. To coordinate the expression of these monomers, required , and proThe key to this expression pattern is a multi-gene feedback loop in the network with two transcription factors—FlhDC and FliA—that get expressed and then take over the regulation of additional required genes. The components’ progressive expression is achieved by an increasing sensitivity to the concentration of FlhDC and an inverse sensitivity to FliA, which is itself regulated by FlhDC. When both are present, FlgM binds FliA and prevents its interaction with RNAP, thus inhibiting FliA-dependent transcription. When the flagellum’s basal body is assembled, FlgM is exported from the cell, initiating the next stage with FliA-dependent transcription. This pattern of transcription activation is configured using a binary sum logic gate blueprint and activation coefficients .E. coli [E. coli function. The model shown here does not express the full E. coli genome, so it is initialized with reduced counts of RNAPs and ribosomes to keep flagella from being over-expressed by an entire cell’s worth of polymerases. Based on an assumption of even distribution based on final protein mass, an average of four flagella were estimated to require 20 ribosomes and 10 RNAPs—these polymerases are themselves not expressed in the model, so they are kept constant for all flagellum-expressing cells and reset upon division.Next, polymerases need to be initialized so that they can express the provided flagella genes. There are about 10,000 RNAPs and 20,000 ribosomes in a single E. coli , which iAs shown in E. coli flagellum is a reversible rotary motor that is embedded in the cell membrane and generates thrust in the environment [An ironment . It is pChemotaxis takes this baseline motility and alters it for directed navigation. The key to navigation is chemoreceptors, which sense changing concentrations in the environment and trigger signal cascades that alter the state of the flagellar motor switch, and thus influence the flagellar rotation direction. This elongates the time of runs when moving up an attractant gradient or down a repellent gradient, generating a biased random walk that brings the cell toward favorable and away from adverse conditions.E. coli chemoreceptors—Tar and Tsr for amino acids and other stimuli, and Trg, Tap, and Aer more specifically for sugars, dipeptides, and redox potential. The cell’s chemoreceptors cluster together at its poles—typically one or two clusters in an entire cell. A cluster activates and deactivates together as a single entity; this amplifies detected signals and increases sensitivity [There are several classes of sitivity . ChemoreSignal transduction between chemoreceptors and flagellar motors is mediated by a well-known protein interaction network . CheA isThis subsection takes the flagella expressed in the previous subsection and adds them to the cell as individual sub-compartments with rotational states. Their combined thrust is applied to the agent bodies in the environment, introducing motility. A proton-motive force is integrated to drive their activity, and a chemoreceptor cluster is integrated to sense the environment, trigger signals that control the flagellar rotational states, and generate directed chemotaxis up an attractant gradient.Flagellar activity: Individual flagella synthesized by the gene expression processes are added to the compartment hierarchy as sub-compartments of a cell. The rotational states of each flagellum are modeled as a stochastic bistable system in which the transition rates between CCW and CW are functions of the phosphorylated protein CheY (CheY-P) [(CheY-P) —the resu(CheY-P) .agents’ boundary store , with energy values based on ligand concentration and methylation levels. This results in four energy levels: on without ligand, on with ligand, off without ligand, and off with ligand. Sensory adaptation comes from the methylation of chemoreceptors, which alters the free-energy offset and transition rate to favor the on state; attractant ligand binding favors the off state. Adaptation can be seen in The activity of a chemoreceptor cluster is modeled using a Monod–Wyman–Changeux (MWC) model from  and is sE. coli are well suited to navigate up exponential gradients [radients .The resulting thrust and torque are saved in a boundary store and are read by the environment’s multi-body physics process. These motile forces are applied directly to the agents’ bodies along their outer boundary, which pushes them in the environment. A “run” applies the force at a normal angle to the agent’s back end, and a “tumble” applies the force at a random angle. This combines with forces from the environment, such as the viscous force, which dampens inertia, and jitter force, which applies random impulses that randomize the cell’s orientation. The resulting behavior, shown in 4.2 μm/s ), an ave4.2 μm/s .An insight coming from this integration is that the activities of chemoreceptors, flagella, and the environment are more closely coupled than many internal processes need to be to each other. The timescale for chemoreceptors and flagella to achieve successful chemotaxis is a maximum of 0.01 s—longer timescales make the cell miss important gradient information. Additionally, this required the timescale of the environmental processes to also be set at 0.01 s so that they could apply the generated forces and update the cells’ external ligand concentration at a rate that maintains the cell–environment coupling. This can be compared to internal coupling between metabolism and gene expression, which were safely set at E. coli can move at a velocity 10 body lengths per second. Because of this, significant additional work will be required to analyze the consequences of the described model.The simulation time required to approximate growth is in the timescale of hours—six orders of magnitude higher than the required timescale for chemotaxis. The chemoreceptors and flagellar processes could have achieved this, but in order to have the transport/metabolism system respond to environmental changes, they too would need to be brought to a comparable timescale—at a huge computational cost. Furthermore, the spatial scales of the environment required for simulations of growth are enormous relative to the cellular scale because E. coli cell model with a rich internal state and dynamics, which can grow into colonies of heterogeneous cells and move around within a dynamic, spatial environment. The scope of this model is large, and we only scratched the surface of the phenomena implied by the full set of integrated processes. Metabolism, transport, gene expression, flagellar activity, and chemoreception have many reported cross-dependencies that could be more carefully evaluated with a model such as the one described here. Some interesting examples include: (1) Metabolism and chemoreception are linked by the Aer chemoreceptor, which detects redox changes and is thought to respond to the metabolic state of the cell rather than any particular ligand [This paper took us through a quick tour of the multi-scale development of a chemotactic r ligand . (2) Trar ligand ,64. (3) r ligand . More brr ligand . The oppThis multi-scale model is the first application of the interface provided by Vivarium. Building a complete whole-cell model will require a larger project that harnesses the collective effort of many scientists. Each individual cell type has unique mechanisms that have to be curated, with parameters that need to be reconciled, and with distinct phenotypes that have to be validated. For such projects to reach their full potential, we need to refine our modeling frameworks and collaborative coding practices. Vivarium provides an interface for these efforts—a plug-in system that simplifies the integration of alternate process models into complex hybrid, multi-scale simulations. This will lower the barrier to contribution so that new users can encode new processes and plug them into existing models. With good computational design and the assistance of learning algorithms, such a framework will support incremental progress, which, through collaborative effort, can build up an increasingly accurate representation of cells and will one day make them “whole”.