Several applications in constraint-based modelling can be mathematically formulated as cardinality optimization problems involving the minimization or maximization of the number of nonzeros in a vector. These problems include testing for stoichiometric consistency, testing for flux consistency, testing for thermodynamic flux consistency, computing sparse solutions to flux balance analysis problems and computing the minimum number of constraints to relax to render an infeasible flux balance analysis problem feasible. Such cardinality optimization problems are computationally complex, with no known polynomial time algorithms capable of returning an exact and globally optimal solution.By approximating the zero-norm with nonconvex continuous functions, we reformulate a set of cardinality optimization problems in constraint-based modelling into a difference of convex functions. We implemented and numerically tested novel algorithms that approximately solve the reformulated problems using a sequence of convex programs. We applied these algorithms to various biochemical networks and demonstrate that our algorithms match or outperform existing related approaches. In particular, we illustrate the efficiency and practical utility of our algorithms for cardinality optimization problems that arise when extracting a model ready for thermodynamic flux balance analysis given a human metabolic reconstruction.https://github.com/opencobra/COBRA.papers/2023_cardOpt with general purpose functions integrated within the COnstraint-Based Reconstruction and Analysis toolbox: https://github.com/opencobra/cobratoolbox.Open source scripts to reproduce the results are here  Systems biochemistry seeks to understand biological function in terms of a network of chemical reactions. In order to apply this approach to a particular system, one must first reconstruct the corresponding network prior to deriving a mechanistic model from it. There are various approaches to network reconstruction, depending on the type of data available and the type of computational model envisaged. Constraint-based Reconstruction and Analysis (COBRA) places strong emphasis on reconstruction of biochemical networks from complementary sources of data . Omics dMany biochemically comprehensive genome-scale biochemical networks are available, e.g. for humans , which iEven with quality control during the reconstruction process, it is not appropriate to assume that any reconstruction can be converted directly into a model and used to make predictions. A model must satisfy certain assumptions before it can be used to make reliable predictions. Depending on the type of model, these assumptions will be different. Each assumption should be chemically or biologically motivated and expressed in an unambiguous manner and preferably both, intuitively and mathematically. Flux balance analysis is a widely mathematical method used for studying genome-scale biochemical networks   . In seveTo the best of our knowledge, there exists no report of the use of nonconvex approximations to minimize the zero norm in the context of mechanistic modelling in biology. Herein, we elaborate on several important applications of cardinality optimization that commonly appear in constraint-based modelling scenarios. We approximate them with various nonconvex approximations and we solve them with difference of convex function algorithms. The results of these and alternate approaches are compared in terms of computational efficiency and the distance of the approximation to a minimal cardinality solution for a range of genome-scale biochemical models. We place particular emphasis on real scenarios that arise while converting human metabolic reconstructions, into models suitable for flux balance analysis and thermodynamic flux balance analysis. In this context, the important interplay between algorithmically and biochemically driven resolution of inconsistencies and infeasibilities is explained.stoichiometric consistency testing: finding the maximal set of stoichiometrically consistent reactions in a network  of one or more metabolites  bjective , and . If where a nonzero mization .In Problem relaxed flux balance analysis, isThe cardinality optimization problem, termed l and u) on reaction rates of the reaction rates vector v, and λ and α can be used to trade off between relaxation of mass balance or bound constraints, either globally, or for each individual lower bound, upper bound, or steady state constraint. Note that this problem is obliquely related to flux imbalance analysis, which starts with a feasible model and seeks to analyse the consequences of relaxing the steady state constraint for each metabolite individually and relate it to metabolite concentrations , (ii), (iii), (v), and (vi) are each an instance of cardinality optimization over a polyhedral convex set. However, Problem (iv) requires cardinality optimization over a polyhedral nonconvex set because the set of thermodynamically feasible fluxes is nonconvex  hydrolysis reaction where the products are adenosine diphosphate (adp[c]) and orthophosphate (pi[c]). In Recon3D, the full corresponding reaction formula isIn a flux balance model, a nongrowth associated energy maintenance requirement for synthesis of adenosine triphosphate can be represented with a lower bound on reaction When all external reactions are closed, i.e. when all external reaction bounds are set to zero, then the only net flux admissible is within a stoichiometrically balanced cycle, if and only if, the bounds on each reaction in the stoichiometrically balanced cycle simultaneously admit net flux in one direction around the cycle. Net flux around a stoichiometrically balanced cycle is thermodynamically infeasible . By furtTo illustrate the utility of relaxed flux balance analysis, which uses the DCCO algorithm, we took Recon3.01model, omitted all but one biomass reaction (VMH: ‘biomass_reaction’), set a positive lower bound on the biomass reaction to require the synthesis of biomass, and close all of the external reactions. The resulting model is therefore infeasible, i.e. no steady-state flux vector satisfies the steady-state constraints and the bound constraints required by the flux balance analysis, irrespective of the objective coefficients. By solving a relaxed flux balance analysis (Problem 2), we identified a minimal set of external reaction bounds that are required to be relaxed in order to make biomass synthesis feasible. Of the 1809 external reactions, a minimal solution returned was to relax 24 lower bounds and 2 upper bounds more than the feasibility tolerance , which is equivalent to a sum of step functions, using a difference of convex function approach to cardinality optimization. We implemented a Difference of Convex Cardinality Optimization (DCCO) algorithm, which implemented a range of different approximate step functions. Out of six different approximations tested, overall, we find that a capped-The quality of the capped-We demonstrate that a difference of convex function approach to cardinality optimization is accurate and efficient for a variety of cardinality optimization problems arising in constraint-based modelling of genome-scale biochemical networks. In particular, we demonstrate that our approach is efficient for high dimensional biochemical networks confirming the broad numerical utility of our approach. We also demonstrate the biochemical utility of a difference of convex function approach to cardinality optimization by illustrative examples that arose during the process of extracting a model, suitable for flux balance analysis (Due to its comprehensiveness with respect to metabolism, the Recon3D reconstruction exposes gaps in the biochemical literature. It contains content that is incompletely specified biochemically, often due to incomplete knowledge on the molecular mechanisms of certain biochemical reactions, e.g. incompletely specified reaction stoichiometry that is inconsistent with the remaining stoichiometrically consistent reactions. Stoichiometrically inconsistent reactions can be inadvertently present in draft genome-scale models, so it is important to them when extracting a model for flux balance analysis. Our new sequential cardinality optimization approach to finding the largest stoichiomerically consistent subset of a given network demonstrates that established approaches to detecting stoichiometric consistency (This approach assumes that the largest set of stoichiometrically consistent reactions in a reconstruction is also consistent with biochemistry. This is more likely to be an appropriate assumption for a highly interconnected biochemical network. It is conceivable that this assumption may not be an appropriate if part of a network is poorly connected, e.g. a large set of internally consistent synthesis reactions may be inconsistent with a smaller set of consistent synthesis and degradation reactions, when the former is only connected to the rest of the network by synthesis precursors.Recon3D contains reactions that do not admit a nonzero steady-state flux. Such flux inconsistencies are consequences of incomplete knowledge resulting in network gaps . AssociaDue to the high dimensionality and disparate sources of data gathered in Recon3D, the process of extracting the largest subset of the reconstruction that is suitable for a flux balance analysis provides a stiff challenge for applications of cardinality optimization in practice. Testing for stoichiometric consistency, testing for leakage or siphon of metabolites, testing for net flux consistency, testing for thermodynamic flux consistency, computing a minimal number of reactions required to be active to fulfil a certain biochemical function, and finding a minimal number of constraints to relax to make an infeasible model feasible are all cardinality optimization problems. In each case, we illustrate that a difference of convex function approach to each optimization problem does enable each problem to be efficiently solved for a variety of human metabolic networks.Comparing the stoichiometric, flux and thermodynamic flux consistency of various human metabolic networks , severalA reconstruction may specify a naming scheme for heuristic categorization of reactions into internal and external sets cf. . HoweverMany constraint-based modelling problems involve optimization of the number of nonzeros in a vector subject to polyhedral convex constraints. However, no polynomial time algorithms exist for solving such cardinality optimization problems exactly. We successfully approximated a selection of high dimensional cardinality optimization problems in constraint-based modelling by solving an approximate problem involving a difference of convex functions (btad450_Supplementary_DataClick here for additional data file.


Xanthophyll is an oxidated version of carotenoid. It presents significant value to the pharmaceutical, food, and cosmetic industries due to its specific antioxidant activity and variety of colors. Chemical processing and conventional extraction from natural organisms are still the main sources of xanthophyll. However, the current industrial production model can no longer meet the demand for human health care, reducing petrochemical energy consumption and green sustainable development. With the swift development of genetic metabolic engineering, xanthophyll synthesis by the metabolic engineering of model microorganisms shows great application potential. At present, compared to carotenes such as lycopene and β-carotene, xanthophyll has a relatively low production in engineering microorganisms due to its stronger inherent antioxidation, relatively high polarity, and longer metabolic pathway. This review comprehensively summarized the progress in xanthophyll synthesis by the metabolic engineering of model microorganisms, described strategies to improve xanthophyll production in detail, and proposed the current challenges and future efforts needed to build commercialized xanthophyll-producing microorganisms. CuThe elucidation of the natural synthetic pathways and key enzymes of several important xanthophylls has laid the foundation for xanthophyll synthesis by the metabolic engineering of model microorganisms ,18,19,20The number of articles on xanthophyll metabolic engineering in non-natural microbial producers has increased rapidly in the last decade, and the highest yield of various xanthophyll has also continuously increased over time. However, in engineered microorganisms, the yield of xanthophyll was significantly lower than that of their precursor, such as lycopene and β-carotene ,42. UndeCompared to carotene, xanthophyll has a longer synthetic pathway, resulting in a more complex microbial metabolic engineering; in addition, xanthophyll is more polarized, resulting in a more harmful effect on host cells ,44. ThesEscherichia coli, Saccharomyces cerevisiae, Yarrowia lipolytica, Pichia pastoris, and others. We summarized the progress of metabolic engineering of xanthophyll according to four categories: hydroxy-, keto-, epoxy-, and epoxy-xanthophyll derivatives. Furthermore, we highlighted strategies to increase xanthophyll production in engineering microorganisms from the aspects of the protein engineering of key enzymes, compartmentalization of metabolic pathways in organelles, enhancement of metabolic flux, network regulation of metabolic pathway, and the engineering host selection. Finally, we also extracted the common and critical issues that hinder its heterologous production and proposed some promising suggestions to break through the bottleneck mentioned above. This review aims to present relevant researchers with a holistic understanding of the current development of xanthophyll metabolic engineering and to provide a global perspective for subsequent studies.In this review, we focused on the research progress and strategies of the metabolic engineering of xanthophyll synthesis in model microorganisms, including In this section, we present the research progress of different types of xanthophyll that have been synthesized by metabolic engineering in various model microorganisms, including the basic ideas and general metabolic engineering procedures, as well as some key issues that limit the production of xanthophyll. Briefly, the microbial metabolic engineering of xanthophyll involves the docking of the exogenous pathway of xanthophyll synthesis with the endogenous core metabolism of the microbial host, allowing the flows of carbon and energy to the synthesis of xanthophyll.In model microorganisms, glucose or other carbon sources undergo glycolysis to produce acetyl coenzyme A (acetyl-CoA) and pyrurate. The acetyl-CoA and pyrurate then pass through the ergosterol synthesis pathway of the host cell, MVA  or MEP (in plants and bacteria) ,17, to pExperimental manipulation is used to introduce the genes of carotegenesis enzymes and cofactors into the microorganism and utilize the transcriptional, translational, and metabolic regulatory functions of the microbial host to control the expression of these genes. The key genetic elements involved in this process include highly active key enzyme genes, cofactor genes matching the key enzymes, various promoters and terminators, etc. The key enzyme genes and cofactor genes will be described in detail in Hydroxy-xanthophyll mainly refers to zeaxanthin, lutein, β-cryptoxanthin, zeinoxanthin, etc. The β-cryptoxanthin and zeinoxanthin are the intermediate metabolites of zeaxanthin and lutein ,21,23, rZeaxanthin is the first xanthophyll in the β-carotene branch of the xanthophyll synthetic pathway and is the precursor of various high-value xanthophyll, such as astaxanthin, violaxanthin etc. . UnfortuE. coli, S. cerevisiae, and Y. lipolytica. Zeaxanthin engineering synthesis is generally achieved by first introducing the exogenous β-carotene pathway into the host to construct a carotene chassis strain; the heterologous CrtZ is then expressed in this chassis strain to hydroxylate the β-ring at each end of β-carotene to produce zeaxanthin. The CrtZ gene has been cloned from a variety of algae and bacteria and applied to the metabolic engineering synthesis of zeaxanthin. In E. coli, compared with those from Pantoea agglomerans and Haematococcus pluvialis, the CrtZ of Pantoea ananatis has the highest β-carotene hydroxylation activity [Y. lipolytica, the catalytic activity of CrtZ from Brevundimonas Vesicularis, H. lacustris and P. ananatis was compared [P. ananatis CrtZ had the highest activity, as in E. coli. In S. cerevisiae, the synthesis of zeaxanthin was mainly used as a reporting approach to study the feasibility of experimental methods such as multi gene co-transformation [The reported model microorganisms for zeaxanthin synthesis include activity ,47,48,49compared , and P. ormation ,52; reseMassilia varians (GenBank: BDT58294.1), Xanthomonadaceae bacterium (GenBank: RZA32178.1), Oxalobacteraceae bacterium (GenBank: USX26554.1), etc. Their identities of protein sequences aligning against the CrtZ of P. ananatis are generally in the range of 60–80%, which is not lower than the identities between the above reported CrtZs. The potential of these putative CrtZ applications for the metabolic engineering of zeaxanthin also deserves further exploration.In addition to the above CrtZs, CrtZ proteins sequences of other species obtained by gene prediction or protein sequence alignment can be found on the NCBI GenBank database published in recent years, such as Another important representative of hydroxyl-xanthophyll is lutein. The metabolic engineering of lutein is more complex and difficult than zeaxanthin due to the asymmetric cyclization of lycopene. α- carotene is the direct precursor of lutein, and the β-ring and ε-ring on the two ends of α- carotene are catalyzed by lycopene β-cyclase and ε-cyclase, respectively . The hydE. coli and S. cerevisiae, and the yield is very low. In E. coli, through the screening of ε-cyclase from three sources  and CYP97C from nine sources , only the enzymes from M. polymorpha have lutein biosynthetic activity [S. cerevisiae, the synthesis of lutein can be achieved by the co-expression of β-cyclase from Xanthophyllomyces dendrorhous, ε-cyclase from Tagetes erecta, and CYP97A and CYP97C from Arabidopsis thaliana [Studies have shown that the heterologously expressed activity of β-cyclase is higher than that of ε-cyclase, leading to a preference for lycopene for the formation of β-carotene with two β-rings ,57,58. Tactivity ,59. In SH. pluvialis [Among all keto-xanthophylls , astaxanthin has received the most attention due to its strongest antioxidant activity; this promotes the most in-depth research and the highest fermentation yield, and has shown great industrialization potential. Under controlled bioreactor fermentation, the maximum yield can reach tens of mg/g DCW , which cluvialis .E. coli, S. cerevisiae, and Y. lipolytica [Kluyveromyces maximus [P. pastoris [Corynebacterium glutamicum [The most commonly used model microorganisms for the production of astaxanthin include polytica ,62. Kluy maximus ,64, P. ppastoris ,66, Coryutamicum ,68 etc.,E. coli, the combination of CrtW from Brevundimonas sp. SD212 and CrtZ from Pantoea sp. (including P. agglomerans and P. ananatis), or the CrtZ from Paracoccus sp. PC1 as a supplement to CrtZ from Pantoea sp., produces the highest astaxanthin yield [Pantoea sp. and Paracoccus sp. PC1 have different substrate preferences; a high conversion efficiency from β-carotene and canthaxanthin to astaxanthin can be achieved when the two enzymes have a combinatorial expression at a specific copy number ratio [S. cerevisiae, the higher astaxanthin production comes from the combination of the mutant BKT (H165R/V264D/F298Y/M1T/N188D/L271R) and CrtZ (L288R) of H. pluvialis, or the combination of the CrtW of B. vesicularis and CrtZ of Agrobacterium aurantiacum [Y. lipolytica, Wang [Paracoccus sp. and the CrtW from H. pluvialis yielded a higher astaxanthin production. Furthermore, the result of Wang et al. also showed that astaxanthin cannot be detected with the co-expression of CrtW and CrtZ from H. pluvialis in Y. lipolytica, On the contrary, Zhu [H. pluvialis. This contradiction needs to be further verified. In general, no matter the type of host, the bacteria CrtW and CrtZ usually have higher activity, followed by algae enzymes, and X. dendrorhous and plants  have very low or almost no activity [The first step in astaxanthin synthesis by metabolic engineering is the heterologous functional expression of CrtW and CrtZ. Since both enzymes involve two substrates, there is an issue of substrate preference. Therefore, the yield of astaxanthin is closely related to the enzymatic activity, the substrate preference, and the combination of the two enzymes. Accordingly, the first step of almost all metabolic engineering research on the heterologous production of astaxanthin is the screening and adaptability analysis of these two enzymes. In in yield ,73,74,75er ratio . In S. cantiacum ,81,82,83ca, Wang  and Ma [ca, Wang  et al. rary, Zhu  and Tramary, Zhu  reportedactivity .Almost all reports indicate that CrtZ is a rate-limiting enzyme when the astaxanthin synthetic pathway is introduced in a model microbial host, which means the conversion from β-carotene to zeaxanthin, or from canthaxanthin and echinenone to astaxanthin, which is a key step for limiting the production of astaxanthin. Thus, in addition to the CrtZs listed in E. coli [S. cerevisiae [S. cerevisiae was higher than that of axtathophyll (5.7 mg/g) when almost the same strategies and shake flask culture conditions were used. This further demonstrates the rate-limiting effect of CrtZ.Canthaxanthin is another keto-xanthophyll that is widely used commercially. At present, only E. coli  and S. crevisiae  have beerevisiae ,88, the Epoxy-xanthophyll mainly includes violaxanthin and antheraxanthin. Antheraxhanthin was mentioned mainly as the intermediate metabolite of violaxanthin, so we only focused on the engfigureineering biosynthesis of violaxanthin in this section. The biosynthesis of violaxanthin by metabolic engineering is achieved by prolonging the pathway of zeaxanthin with the introduction of ZEP into a zeaxanthin-producing microbial host. Although the cloning and heterologous expression of ZEP have been studied for nearly 30 years ,90,91,92E. coli and S. cerevisiae. In E. coli, the activity of ZEPs from seven higher-plants , one liverwort (M. polymorpha), and one algae (Phaeodactylum tricornutum) was compared [C. annuum ZEP had the highest activity, whereas that of Prunus ameniaca, Zea mays, M. polymorpha, and P. tricornutum showed extremely low activity in E. coli. Although the NADPH and electron transport system of E. coli can make ZEP active, the yield of violaxanthin is low. Exogenous redox partners, spinach ferredoxin and ferredoxin oxidoreductase, can improve the ZEP activity, whereas Nostoc sp. severely decreases its activity. The Bacillus subtilis glucose dehydrogenase as the NADPH-regenerating enzyme can increase the synthesis of violaxanthin in E. coli. Furthermore, the E. coli strains and ribosome-binding site (RBS) sequences also impacted the yield of violaxanthin. The best E. coli strain, JM101, had a yield of 231 μg/g of violaxanthin; however, the ratio of violaxanthin to total carotenoids was only 1.4–21%, which was still low. In S. cerevisiae, compared with the ZEPs of A. thaliana and Solanum lycopersicum, the Haematococcus lacustris ZEP showed the highest activity [A. thaliana can improve the violaxanthin yield, whereas the yeast mitochondrial ferredoxin-like protein and its reductase has no effect on the yield. In the best violaxanthin-producing S. cerevisiae, the final yield of violaxanthin reached 7.3mg/g, corresponding to 58.4% of total carotenoids.ZEP belongs to FAD-dependent monooxygenase and catalyzes the epoxidation of zeaxanthin in the presence of NADPH, FAD, ferredoxin (FD), and ferredoxin-NADPH oxidoreductase (FNR) ,94. Thercompared . The C. activity . The redE. coli and in S. cerevisiae, a considerable amount of upstream carotene remained, indicating that the catalytic efficiency of the heterologously expressed ZEP was low. The characterization and screening of ZEP and the matching redox partner from different species in various microbial hosts need to be further explored.From the above, in Epoxy-xanthophyll derivatives include capsanthin, capsorubin, neoxanthin, fucoxanthin, diadinoxanthin, etc. Capsanthin, capsorubin, and neoxanthin are usually considered as the last metabolites of the carotenoid synthesis pathway in higher plants. The epoxy-xanthophyll derivatives have more complex terminal groups, and they may have multiple terminal groups, such as hydroxyl, ketone, epoxy, allenic, cyclopentane, cyclohexane, etc. .Lycopersicum esculentum [S. tuberosum [Arabidopsis [Chinese Kale [L. esculentum NSY [E. coli (the substrate violaxanthin was added to the system and the yield of neoxhanthin was not mentioned), to date, neoxanthin production by microbial metabolic engineering has not been reported in detail.Except for neoxanthin synthase (NSY) and the capsanthin/capsorubin synthase (CCS), the synthases for other epoxy-xanthophyll derivatives have not yet been identified or characterized. The NSY catalyze the opening of cyclohexenyl 5–6 epoxides at one end of violaxanthin to form an allenic group through a transient carbocation . Althougculentum , S. tubeuberosum , Arabidobidopsis , and Chiese Kale  has beenntum NSY  conversiCapsicum annuum [Tiger lily [Capsanthin is the only epoxy-xanthophyll derivative whose synthesis has been achieved by microbial metabolic engineering. Capsanthin and capsorubin are synthesized by CCS catalysis from antheraxanthin and violaxanthin, respectively . Althougm annuum  and Tigeger lily  have bee+; that is, the reverse conversion from capsorubin to violaxanthin [C. annuum into β-carotene-producing E. coli, combined with greatly enhancing the expression of CCS, the production of capsanthin was realized with a titer of 0.5 mg/L [E. coli. In addition, no capsorubin was detected in this study, which was consistent with the phenotype of the capsanthin accounting for a large amount in pepper, whereas the capsorubin was only a minor product [CCS is a multifunctional enzyme with capsanthin/capsorubin synthesis and β-carotene synthesis, and its activity requires the simultaneous existence of FAD and NADPH. In addition, it was also found that CCS catalyzes the reverse reaction in the presence of NADaxanthin ,101,102.0.5 mg/L . The hig product . TherefoFrom the above, it is known that the metabolic engineering of epoxy-xanthophyll derivatives is still at the beginning stage. The cloning and characterization of key enzymes, substrate preference, and cofactor specificity need to be further investigated. From the catalytic properties of CCS, it can be speculated that the key enzymes, such as the NSY, fucoxanthin, or diadinoxanthin synthetic enzymes, may also involve multiple substrates or multiple products, which implies that the metabolic engineering of epoxy-xanthophyll derivatives is more difficult to control.After describing the overall idea and production status of xanthophyll synthesis by metabolic engineering model microorganisms, in this section, we will present comprehensive metabolic engineering strategies to improve xanthophyll production. For a certain xanthophyll synthesis, multiple strategies are usually used in combination. Since these strategies can be used universally and considered to make related works more convenient to draw on, we will present them in categories from five levels: the protein engineering of key enzymes, compartmentalization of metabolic pathway, enhancement of metabolic flux, network regulation of metabolic pathway, and microbial host selection .H. pluvialis and B. vesicularis, BKT/CrtW from H. pluvialis, Brevundimonas sp. SD212, Sphingomonas melonis, and Rhodocuccus erythropolis have been directed to evolve for functional improvement (Among the key enzymes (referring to the enzymes located downstream of lycopene or β-carotene in the xanthophyll synthetic pathway and directly synthesizing xanthophyll), the ε-LCY from Tagetes erecta, CrtZ from rovement . DirectePantoea sp. and Paracoccus sp.). Their amino acid sequence is highly consistent, but their catalytic activities and substrate specificity are different.In the conversion from lycopene to δ–carotene catalyzed by the ε-LCY, the corresponding colony color was changed from red to yellow or orange . The CrtPantoea sp. and Paracoccus sp., ZEP and CCS from pepper, ε-LCY and α- carotene hydroxylase from A. thaliana, etc., have not been reported in directed evolution.In addition, the color-based screening system is not applicable to enzymes that do not cause colony color changes, such as CrtZ and ZEP, so other high-throughput screening methods need to be established. It is reported that xanthophylls have a stronger resistance to hydrogen peroxide than carotene ,107. TheS. cerevisiae, through the directed evolution of a bifunctional enzyme CrtYB, its lycopene β-cyclase activity was eliminated, but the phytoene synthase activity was retained and the lycopene yield was correspondingly increased [In addition to catalytic activity, substrate specificity is also an important aspect of directed evolution. In a lycopene-producing ncreased . SimilarIn plants and algae, the key enzymes of xanthophyll synthesis are targeted at the plastid, such as chloroplast, chromoplast, etc. ,110. TheH. lacustris with different lengths of N-terminal truncation were expressed in S. cerevisiae, the variants with a truncation of 30 and 59 amino acids had a higher activity compared with the truncation of 80 amino acids. The catalytic activity was abolished when the truncated length reached 100 residues [A. thaliana and S. lycopersicum, and the full-length enzymes were inactive in S. cerevisiae [The length of the transit peptide is usually determined by prediction , and the real truncation site of the transport peptide in natural organisms is not accurately known. Therefore, the enzymatic activity can be optimized by testing different truncated sites around the predicted site. For example, when the ZEP variants from residues . A truncrevisiae .A. thaliana as redox partners of ZEP are used in violaxanthin-producing S. cerevisiae, the truncation of the redox partner (RFNR1 truncated at the 65th residue and FD3 truncated at the 49th residue) increased the violaxanthin accumulation 2.2-fold [In addition to the key enzymes, the redox partner proteins may also contain the transit peptide for transport to certain organelles. The N-terminal truncation of the redox partner protein in a heterologous microbial host may increase their capacity of transfer electrons. For example, when ferredoxin-NADPH oxidoreductase 1 (RFNR1) and ferredoxin 3 (FD3) from 2.2-fold .E. coli, the catalytic activity of full-length ZEP from C. annuum was higher than the truncation variant of 56 residues of the N-terminal; this truncated position was chosen according to the amino acids sequence aligned with the ZEP from A. thaliana. In addition, the full length or truncation for CCS from C. annuum has no significant effect on its capsanthin/capsorubin synthesis activity [There are also other situations. In activity .The synthesis of xanthophyll in a microbial host is usually involved in the continuous catalytic reaction of multiple enzymes, so the efficiency of the interaction between the metabolic intermediate and enzyme is a factor affecting the xanthophyll production. In addition, xanthophyll and its synthetic enzymes are mainly present in membrane localization; thus, its lateral diffusion rate in the membrane may also affect the catalytic efficiency of the enzymes. It has been found that the fusion expression of two adjacent enzymes in the synthesis pathway can improve the production of xanthophyll. This might be achieved by shortening the distance between the enzyme and the substrate or increasing the concentration of the substrate in vicinity of the enzyme, which improves the utilization of intermediate metabolites.P. ananatis and ZEP from H. lacustris on the yield of violaxanthin. They found that the CrtZ attaching as the N-terminal module was necessary for maintaining the two enzyme activities, and the rigid linker was better than the flexible one. Compared with the individual expression of the two enzymes, the fusion construct can more efficiently channel zeaxanthin toward violaxanthin in the engineering of S. cerevisiae. Nogueira et al. [Brevundimonas sp. strain SD212, on the activity of the fusion enzyme. The results indicate that the level of the target product astaxanthin in engineering E. coli was increased 1.4-fold at the fusion condition and that the size of linkers had no significant effect. From the above-mentioned fusion methods, it seems that the CrtZs from bacteria must be located at the N-terminal of the fusion construct.In order to simultaneously exert the activity of the two fused enzymes, the method of fusion, including the relative position of the two enzyme proteins and the rigidity/flexibility or length of the linker, all need to be considered. Cataldo et al.  evaluatea et al.  analyzedH. pluvialis and bacteria Paracoccus sp., respectively) through a flexible linker and found that the fusion enzyme could improve the production of astaxanthin in Y. lipolytica and that the CrtW-linker-CrtZ had a higher activity than the CrtZ-linker-CrtW. In contrast, Zhu et al. [H. pluvialis), whether through a flexible linker or RIAD/RIDD interaction peptides, decrease the yield of astaxanthin in Y. lipolytica. The above two reports implied that the CrtZ from the alga H. pluvialis did not have to be located at the N-terminal of a fusion construct. The connection mode of the two enzymes in the fusion enzyme needs to be evaluated experimentally to obtain the maximum activity.Ma et al.  combinedu et al.  reportedIn natural species, organelles, such as chloroplasts and chromoplasts, compartmentalize the metabolic pathways of xanthophyll, ensure the efficient implementation of metabolic flux, and prevent the cytotoxicity of metabolites. When the xanthophyll synthetic pathway is introduced into the heterologous microbial host, these enzymes and metabolites tend to diffuse all over the intracellular membrane, and a small fraction may also be released into the cytoplasm. This diffusion reduces the possibility of contact between the enzyme and substrate, and the excessive accumulation of intermediates may affect the cell membrane fluidity ,112.E. coli, which has no subcellular compartments, the membrane is the main targeted organelle for the xanthophyll synthetic pathway. An improvement in the load capacity of the membrane and membrane targeting of enzymes, which reduced the distance between the substrates and the enzymes, was demonstrated to increase xanthophyll production. For example, Lu et al. generated longer and larger cells through deleting the morphology/membrane-related genes (lpp and bamB), thereby increasing astaxanthin production in E. coli [E. coli using the signal peptides of OmpF and TrxA, and the yield of astaxanthin was increased 2.8-fold [E. coli using the GlpF protein, allowing for a 215.4% astaxanthin production increase [E. coli, in yeast, membrane targeting was also proven to be beneficial to the synthesis metabolites. Bian et al. localized the ε-LCY to the plasma membrane of S. cerevisiae by PMSeV-C, and the α-carotene production was increased 2.2-fold [In  E. coli . Park et2.8-fold . Ye et aincrease . In addi2.2-fold .Yeast cells contain a variety of organelles, including an endoplasmic reticulum (ER), Golgi apparatus, vacuole, mitochondria, peroxisomes, and lipid body. Each subcellular organelle has a unique physiochemical environment . Many reY. lipolytica, and the titer of astaxanthin was increased approximately two-fold compared with the fusion protein before localization. The change in ER morphology may also affect the production of xanthophyll. Although there is no relevant report on xanthophyll, the extension of ER has been proven to improve the production of upstream precursors in the xanthophyll pathway or other terpene chemicals. Kim et al. [S. cerevisiae. The deletion of the phosphatidic acid phosphatase PAH1 could also have expanded the ER that stimulated the expression of targeted enzymes and ultimately increased the production of a triterpene and its derivative [The ER is the site of protein synthesis, folding, modification, and assembly with strict dynamic regulation ,117. Them et al.  expandedrivative .+ and FAD, are located in this organelle, supplying an abundance of precursors and cofactor pools for xanthophyll synthesis [S. cerevisiae. As the precursor of xanthophyll, the increase in FPP production may also benefit the synthesis of xanthophyll.Mitochondria are the sites of tricarboxylic acid cycle (TCA) and energy synthesis. The initial precursor of the carotenoid pathway—the acetyl-CoA—and a wide range of cofactors, including NAD(P)H, NAD(P) ynthesis . Yuan etynthesis  localizePeroxisome is the site of fatty acid β-oxidation surrounded by a phospholipid monolayer . The endY. lipolytica [P. pastoris and S. cerevisiae, and has specific and potential advantages for xanthophyll synthesis. Studies show that lycopene and β-carotene are mainly localized on the cell membrane when they are produced in S. cerevisiae, and that membrane localization may lead to cytotoxicity [Y. lipolytica, lycopene and β-carotene are mainly stored in the LB [Y. lipolytica have been verified, providing the possibility of using the LB as a subcellular factory to improve xanthophyll production and the storage capacity [The lipid body (LB), also called lipid droplet (LD), is the site of the storage of triacylglycerols and steryl esters in yeast. The LB has a hydrophobic interior wrapped by the phospholipid monolayer . All thepolytica , which ctoxicity . Howevern the LB . Moreovecapacity . Neverthcapacity  found thIn addition to what was mentioned above, reports on the subcellular localization of other xanthophyll synthetic pathways are still few. Compared with carotene, xanthophyll has its own physicochemical properties, such as a relatively higher molecular polarity, stronger antioxidant activity, many key enzymes that need the synergy of cofactors, and a longer pathway bringing more by-products, which leads to a higher loss of intermediates. These inherent characteristics of xanthophyll synthesis affect the selection of subcellular organelles. Therefore, research on the adaptability between xanthophyll and different subcellular organelles may be a growth point for increasing xanthophyll production.Xanthophyll synthesis in heterologous microbes is achieved through the channeling of a series of precursors into the xanthophyll metabolic pathway flow. The metabolic flux of pathway flow directly influences xanthophyll production. Along with the evolution of key enzymes and organelle location, strengthening this metabolic flux is an important strategy for increasing the xanthophyll production. In this section, the main ways to strengthen the xanthophyll metabolic flux will be elaborated.S. cerevisiae, whereas it is lethal for the violaxanthin-producing S. cerevisiae. This phenomenon implies that S. cerevisiae is less tolerant to polar xanthophyll than hydrophobic carotenes [Increasing the gene copy numbers of key enzymes, especially for the rate-limiting enzymes, to enhance the expression of key enzymes is the common way to strengthen the xanthophyll metabolic flux. For example, increasing the gene copy number of the rate-limiting enzyme, such as ε-LCY, CrtYB, ZEP, and CrtZ, can significantly increase the production of metabolites, whereas the non-rate-limiting enzyme, such as CrtE, BKT, and CrtW, has no effect ,81,86,96In addition to the gene copy number of key enzymes, the cofactor supply is also a crucial factor for maintaining the xanthophyll metabolic flux. The cofactor is the competitive compound between the xanthophyll metabolic pathway and host metabolic network . Not onlY. lipolytica, the astaxanthin production was increased by the overexpression of phosphorgluconate dehydrogenase, which is a key enzyme for NADPH synthesis in the PPP [The types of cofactors required for xanthophyll synthesis are described in  the PPP . Meadows the PPP  reportedThe synthesis and consumption of cofactors involves multiple major metabolic pathways and affects host energy and redox homeostasis. Designing and constructing energy conserving and more efficient pathways is a promising research direction for supporting a high flux of xanthophyll pathways while maintaining cell growth. Related strategies have been shown to be feasible in the microbial synthesis of other high-value compounds ,134,135,The introduction of a heterologous pathway may unbalance the metabolic network of the host microorganism due to the deficit of the enzyme, cofactor, and energy. Meanwhile, heterologous metabolic pathways do not gain predominance and may lead to a waste of carbon and energy sources, which can also lead to a suboptimal productivity of the target metabolites.E. coli and S. cerevisiae [The real-time dynamic regulation of the global metabolic network can maintain the host microorganism growth while adapting it to the efficient accumulation of target metabolites, as well as improving the host robustness during industrial fermentation . Accordirevisiae ,139,140.E. coli in which the MVA pathway was dynamically regulated, and found that zeaxanthin overproduction in this host may be associated with the Embden–Meyerhof–Parnas (EMP) pathway, amino acid and fatty acid biosynthetic pathways, energy metabolism, and oxidative stress responses. Based on these results, they knocked out the oxidative-stress-related genes (uspE and yggE) to elevate reactive oxygen species (ROS) in E. coli cells, thereby stimulating the production of astaxanthin to cope with oxidative stress [Y. lipolytica with astaxanthin overproduction. Although omics technologies can reveal the effects of the introduction of the xanthophyll pathway on host metabolic networks in a holistic manner, these effects are complex and comprehensive, and the improvement of xanthophyll production strains through metabolic network modulation based on omics data still remains a challenge. Nowadays, several metabolic network modulation strategies for regulating precursors of xanthophyll have been established.Multi-omics technologies  offer the possibility of understanding the overall metabolic state of the host cell; the overexpression, low-expression, knockdown, and knockout can be used to regulate the expression level of enzymes; building new bridges between metabolites can optimize the inherent metabolic pathways of the host; constructing a dynamic regulatory circuit allows the host metabolic network to adapt to the metabolic flux of the target pathway in a timely manner. Shen et al.  analyzede stress . Similare stress . Throughe stress  found thE. coli, a sensing and dynamic control system, including the sensor transcriptional factor catabolite repressor/activator (Cra), the signal , and the control valve Cra-regulated promoter, was developed to regulate the glycolysis flux for mevalonate production [S. cerevisiae, rewiring the central carbon metabolism by replacing the PDH-bypass with a non-native metabolic route enables the synthesis of acetyl-CoA while reducing the energy requirements and carbon losses and improving the redox balance [S. cerevisiae, converting GPP to FPP) in combination with the use of sterol-sensitive promoters to regulate the flux of the MVA pathway can promote the accumulation of GPP while maintaining sterols at the lowest level, which ensures cell growth. Meanwhile, mediated by a diauxie-inducible promoter, it is able to reduce the accumulation of FPP, a cytotoxic downstream product of GPP, during the exponential growth phase and mitigate the toxic effects of FPP on host cells while accumulating FPP and its downstream metabolites during the post-exponential phase [In oduction . Anotheroduction . In S. c balance . Reducinal phase . Similaral phase .In general, the difficulties in constructing effective regulatory systems for xanthophyll production in model microorganisms to suit various industrial fermentation environments include the following: (1) the data on intracellular metabolic states in the xanthophyll-producing microbes are insufficient; (2) the metabolic pathway of xanthophyll is longer and more complex, which involves the coordination of multiple pathways for the synthesis and utilization of carbon sources, energy, cofactors, etc.; (3) finding the defects in metabolic networks based on metabolic state data and using genetic manipulation tools to design and construct regulatory modules or circuits that do not interfere with other necessary metabolic fluxes are challenging.In the future, a database of metabolic networks for xanthophyll-producing microbes based on integrated multi-omics analysis and experimental validation needs to be established, along with efforts on the rational design of metabolic networks based on computer modeling and machine learning. The research on the metabolic network regulation of xanthophyll-producing strains is still at the beginning stage, and there is still huge room for improvement.E. coli, B. subtilis, etc., and yeast hosts mainly include conventional yeast S. cerevisiae, and non-conventional yeast P. pastoris, Y. lipolytica, K. marxianus, C. glutamicum, Hansenula polymorpha, Candida maltosa, etc. These microbial hosts have their own specific physiological and biochemical properties and different industrial applications fields. In this section, we mainly focus on E. coli, S. cerevisiae, P. pastoris, and Y. lipolytica, which have been reported as engineered hosts for xanthophyll synthesis. Their advantages and disadvantages for xanthophyll synthesis will be discussed.At present, a variety of microorganisms have been developed as industrial microbial hosts. Prokaryotic microbial hosts mainly include E. coli is the most commonly used prokaryotic host for carotenoid metabolic engineering. By means of the lac operon, a simple multi-gene co-expression element, E. coli is the non-natural microbial host producing the most kinds of xanthophylls so far.Based on the abundance of genetic manipulation tools and its physiological and biochemical research foundation, E. coli has some inherent weaknesses in xanthophyll heterologous synthesis. (1) The efficiency of the MEP pathway in E. coli in synthesizing IPP and DMAPP, the precursors of all kinds of xantholylls, is lower than that of the MVA pathway in eukaryotic yeasts [E. coli, but it also introduces an extra cell burden and metabolic crosstalk, which may affect the engineering host metabolic network and genetic stability [E. coli, all reactions involving xanthophyll synthesis are located in the cytoplasm or cytoplasmic membrane. It is difficult to avoid the loss of precursors and intermediate metabolites, especially for the xanthophyll synthesis with a longer pathway and more cofactor requirements. (3) Almost all the enzymes in the xanthophyll synthetic pathway are membrane-related proteins. A low expression, misfolding, and inclusion body formation are common issues when a membrane protein is expressed in E. coli [E. coli produces higher levels of tetraterpenoids than yeast [However, as a prokaryotic microorganism, c yeasts ,145. Thetability . (2) Sin E. coli . It had an yeast . HoweverE. coli is still the preferred host for testing the effectiveness of a xanthophyll synthesis pathway, but considering the high industrial production demand, eukaryotic model yeasts may have greater potential.For the time being, E. coli, the MVA pathway of yeast itself can efficiently synthesize IPP, and organelle localization can improve the contact between the substrate and enzyme and reduce the loss of precursors and cofactors. A rich eukaryotic chaperone pool can help the membrane proteins to fold correctly. The common disadvantage of engineering yeast for xanthophyll synthesis may be that the transcription in a mono-cistronic manner is not conducive to multi-gene co-expression [Contrary to the above shortcomings of pression . MoreoveS. cerevisiae is currently the most common yeast species used in xanthophyll synthesis. As a conventional yeast, the strict homologous recombination of S. cerevisiae makes the genetic manipulation easier than other non-conventional yeasts [S. cerevisiae is the model strain for studying and applying multi-omics dataset mathematic analysis, CRISPR-based genome-scale engineering, GEMs -guided metabolic state prediction, etc. [S. cerevisiae to improve the xanthophyll production and host robustness. For other non-conventional yeasts, such as P. pastoris, Y. lipolytica, K. marxianus etc., the gene knock-down/out from the genome is more complex due to the non-homologous end joining (NHEJ) mechanism [S. cerevisiae is a typical Crabtree-positive yeast that produces ethanol during glucose fermentation, which is generally considered to be unfavorable for the large-scale biosynthesis of compounds because of the waste of the carbon source and limited biomass formation [S. cerevisiae as a xanthophyll-producing strain. Other non-conventional yeasts in this review are all Crabtree-negative, which is their natural advantage as microbial hosts for the industrial synthesis of xanthophyll.l yeasts . Meanwhion, etc. ,151,152.echanism . Althougormation . This maP. pastoris is a widely used heterologous protein expression chassis [P. pastoris, while the Ire1p is stress-induced in S. cerevisiae [P. pastoris over other yeast hosts [ chassis ,156 and revisiae ,158. Forst hosts .P. pastoris is a methylotrophic yeast capable of growing on methanol as the only carbon source [P. pastoris. P. pastoris is a Crabtree-negative yeast with no significant ethanol production during high-density fermentation, which comes with a higher flux of PPP and lower flux of glycolysis [S. cerevisiae, which may be more adapted to the demand of reducing power in xanthophyll synthesis. Another characteristic of P. pastoris is that the peroxisome volume can reach 80% of the cell volume under methanol- or oleate-induced conditions [P. pastoris. Although there are no related reports yet, this unique advantage of P. pastoris is a potential research focus for high xanthophyll production.In addition to the advantage in the protein expression aspect, n source . One-carn source , and it ycolysis ,163. Thenditions ,164. TheP. pastoris has been reported only as a host for astaxanthin, and the metabolic engineering of other xanthophyll and the mining of the advantages of peroxisome are barely reported.Despite its many innate advantages, Y. lipolytica has shown rapid advances as an engineering host for xanthophyll. Its unique advantages in xanthophyll production mainly include: (1) its ability to utilize various waste media sources, such as vegetable hydrolysates, waste cooking oil, and even human urine [Y. lipolytica  itsan urine ; (3) thean urine ,166. Regpolytica . So far,K. marxianus, C. glutamicum, etc., for xanthophyll production has rarely been reported. The advantages of these hosts are yet to be further explored.The use of other yeast microbial hosts, such as Xanthophyll is a natural compound with rich biological activities and wide application fields. In recent years, due to the increasing demand of the market for natural xanthophyll and for the upgrading of traditional industrial production models of high-value compounds, the research on the production of this kind of compound using various model microbial hosts has developed rapidly. However, the xanthophyll produced by microbial metabolic engineering has not yet realized industrialization. Although the shift in the industrial production model of natural xanthophyll is related to a variety of factors, such as industrial inertia, the environment policy, etc., the most important is that the production costs of microbial engineering are not sufficient to cover the cost of the industrial model update. Therefore, the breakthrough in the xanthophyll production by engineering microbial hosts will still be a hot research topic in the future.From the above factors and strategies that affect the production of xanthophyll, it can be concluded that future microbial metabolic engineering research on xanthophyll synthesis needs further efforts in the following aspects:(1) The catalytic activity and substrate specificity of key enzymes of xanthophyll synthesis are usually low in the non-natural microbial host. At present, random mutation is still the main method for improving the activity and specificity of these enzymes. However, only one to two meaningful amino acid mutation sites can be obtained in each round of screening, so the efficiency and possibility of obtaining ideal mutants is very low. The three-dimensional structure of enzymes is an important basis for understanding their catalytic mechanism . In termE. coli and S. cerevisiae, synthetic organelles have been demonstrated for the functional localization of heterologous metabolic pathways [(2) The biochemical characteristics of xanthophyll itself result in a limited capacity of the host cell to accommodate it. Compared with carotene, xanthophyll, as an exogenous compound with a stronger antioxidant activity and relatively higher polarity, has a more detrimental effect on the physiological and biochemical status of the host . Membranpathways ,180,181.pathways ,183. Altpathways ,185, or pathways ,186, are(3) The overall metabolic network in the host is not fully adapted to the efficient synthesis of xanthophyll. A longer xanthophyll synthesis pathway inevitably has an impact on the balance of the complex metabolic network of the host cell. At the same time, the metabolic network of the host does not match the efficient synthesis of xanthophyll due to the lack of natural screening and evolution. The metabolic engineering synthesis of xanthophyll is still in its beginning stage. The next step, using the systems and synthetic biology tools based on the combination of biotechnology and information technology and through the “design–build–test–learn” cycle  to achieS. cerevisiae into E. coli was able to increase the yield of zeaxanthin. In 2019, Takemura et al. [E. coli with violaxanthin synthesis was obtained by screening different sources of ZEP and oxygen reduction pairs. However, this study did not utilize the MVA introduction strategy described above. Similarly, in 2021 [E. coli was carried out independent of the previous synthesis strategies of zeaxanthin and violaxanthin. Because the synthesis pathway of various xanthophylls is a cascade reaction, different strategies should be comprehensively considered and combined. This is also a feasible way to improve the production of xanthophyll.(4) Various strategies were used piecemeal and could lead to the duplication of effort. In 2016, Shen et al.  reporteda et al.  reported in 2021 , the synH. pluvialis and Paracoccus carotinifaciens produce cis-astaxanthin, whereas X. dendrorhous produces trans-astaxanthin [Besides the host cell metabolic engineering, the fermentation engineering optimization, bioavailability enhancement, product extraction, and packaging process improvement are also important issues in the process of xanthophyll industrialization. Among these, bioavailability is an important consideration for carotene and xanthophyll to exert health-protective effects. The bioavailability of carotenoid is low due to its instability and hydrophobicity, although that of xanthophyll is higher than that of carotene . The bioaxanthin . The conE. coli and S. cerevisiae, among others, have achieved the use of xylose, one of the main hydrolysis products of lignocellulose, as a carbon source for growth and metabolism [S. cerevisiae and K. marxianus synthesized lycopene, carotene, and astaxanthin using xylose and glucose as carbon sources [In addition to the production of high-value products, microbial metabolic engineering for the uptake and utilization of cheap waste biomass is also developing rapidly . Lignocetabolism . Recentl sources ,197,198.In conclusion, xanthophyll synthesis by the metabolic engineering of model microorganisms holds great industrialization prospects and is expected to revolutionize the industrial production mode of natural xanthophyll.


A sensitivity analysis of model parameters was performed, revealing an interplay between growth rate, cell-specific metabolic rate, and extracellular enzyme activity. This approach allowed us to identify plausible growth trajectories consistent with the observed bacterial densities in the cryopeg brines. We found that the cell-specific metabolic rate in this system is relatively high compared to marine sediments. We attribute this finding to the need to invest energy in the production of extracellular enzymes, for generating bioavailable carbon from particulate organic carbon, and the production of extracellular polysaccharides for cryoprotection and osmoprotection. These results may be relevant to other isolated systems in the polar regions of Earth and to possible ice-bound brines on worlds such as Europa, Enceladus, and Mars.Cryopeg brines are isolated volumes of hypersaline water in subzero permafrost. The cryopeg system at Utqiaġvik, Alaska, is estimated to date back to 40 ka BP or earlier, a remnant of a late Pleistocene Ocean. Surprisingly, the cryopeg brines contain high concentrations of organic carbon, including extracellular polysaccharides, and high densities of bacteria. How can these physiologically extreme, old, and geologically isolated systems support such an ecosystem? This study addresses this question by examining the energetics of the Utqiaġvik cryopeg brine ecosystem. Using literature-derived assumptions and new measurements on archived borehole materials, we first estimated the quantity of organic carbon when the system formed. We then considered two bacterial growth trajectories to calculate the lower and upper bounds of the cell-specific metabolic rate of these communities. These bounds represent the first community estimates of metabolic rate in a subzero hypersaline environment. To assess the plausibility of the different growth trajectories, we developed a model of the organic carbon cycle and applied it to three borehole scenarios. We also used dissolved inorganic carbon and nitrogen measurements to independently estimate the metabolic rate. The model reconstructs the growth trajectory of the microbial community and predicts the present-day cell density and organic carbon content. Model input included measured rates of the  Their prevalent physiological state is understood to be energy-limited . For exa14C) measurements suggest the brines have been enclosed for approximately 40 ka BP  to dissolved organic carbon (DOC) in the brine. POC represents the dominant form of organic carbon in surrounding permafrost yet is not available to bacteria until hydrolyzed to smaller molecular weight compounds (DOC).Finally, we compared the model predictions to the available observations, which together allowed us to propose the system’s microbial history under energetic isolation. We produced plausible simulations hinging on the precision of key parameters, and thus could identify research areas that would further advance understanding of bacterial energetics in extreme environments.2.To provide context for our model we outline the relevant environmental characteristics of cryopeg brines in this section. The physical characteristics guided the development of the equations governing environmental interactions in the model. Microbial energetics of the bacteria found in the cryopeg brine constrained our analyses and provided an understanding of the biology that the model attempts to resolve. Together, the physics and biology of the cryopeg brine underlie the design of our work, and the thoughts behind the analyses conducted.2.1.Cryopeg brines are volumes of hypersaline water that occur in cryopeg, a basal layer in permafrost of unfrozen sediment perennially at subzero temperatures . The briThe Utqiaġvik cryopeg system presents brines encased by marine sediments, as previously observed in other cryopegs, as well as those newly discovered to be encased by massive ice, respectively called intra-sediment and intra-ice brines . Intra-iin situ oxygen measurements have been made in these or other tunnel boreholes, but anaerobic conditions are expected within the brines  cycle and glyoxylate shunt. The glyoxylate shunt bypasses the production of carbon dioxide and may play a role in oxidative stress response . As a substitute for glycolysis, it encodes the Entner–Doudoroff pathway, considered an adaptation for energy efficiency at low temperatures  contact than occur in seawater. Increased cell-to-cell contact rates exacerbate resource and space competition. An analysis of cryopeg brine metagenomes found high abundance of cells associated with the type VI secretion system and microcin C, both tools to lyse neighboring competitors . This miMoreover, cryopeg brines host abundant viral communities of marine origin that appear to have mediated the exchange of genetic information . Viral iThe required production of certain compounds may also increase the energetic cost of life in this system. Subzero brines are relatively viscous , and mus5 cells mL−1 will not require the same amount of energy as one at 108 cells mL−1. More complex trajectories could also have occurred, such as when a microbial community declines due to insufficient energy, then recovers after an energy input .Although the current genomic data available provide promising insights into the metabolisms supported by cryopeg brines, they do not allow us to determine whether these brines have supported energetically isolated microbial communities for 40,000 years. To understand the energetics of the Utqiaġvik brines, their energetic histories need to be reconstructed. This effort necessarily involves the reconstruction of the microbial growth trajectory over the lifespan of the brine. 3.GitHub. The contents of this paper were generated from the most recent commit on the “paper” branch. Python v3.9 and Julia v1.8.2  at 2°C. The resulting supernatant was decanted and filtered into a clean EPA vial using a 0.2-μm syringe filter, then frozen until analyzed. The tube of leftover sediment was reweighed for porewater/sediment normalization. DOC was measured using a Shimadzu TOC-VCSH DOC analyzer according to standard protocols in the Marine Chemistry Lab . In the case of massive ice, we lacked suitable samples for DOC analysis, so measurements of dEPS  were use3.2.14C dating procedure  was measured for a sample of CBIW brine taken in 2017 as an auxiliary to the rocedure . Brine s3.3.We considered three separate scenarios for modeling purposes. Each scenario is based on a unique occurrence of cryopeg brine below the permafrost tunnel. The scenarios are named after the borehole that yielded the brine they describe: CB1, CB4, and CBIW. The following variables define a scenario: brine cell density, brine POC and DOC concentration, surrounding POC and DOC concentration, post-enclosure carbon addition, bacterial growth rate, and carbon content per cell.Marinobacter sp., its growth rate and a literature-informed approximation of its carbon content were used to represent the microbial community.The CB1 scenario was chosen to represent the multiple intra-sediment brines in the Utqiaġvik region of common geology and microbial composition. It was paired with organic carbon measurements made on regional permafrost from the nearby Barrow Environmental Observatory (BEO). As the dominant organism in this brine was the newly isolated Psychrobacter sp. The published growth rate and carbon content for Arctic Psychrobacter sp. . We then took the difference between starting TOC and TOC measured in the brines. This calculation accounted for any carbon addition during the 40,000-year period by adding it to the starting TOC quantity. We subtracted from this difference the quantity of organic carbon diverted toward biomass.To obtain bounds for our approximation we considered two cases of cell growth. The lower bound case requires the available quantity of organic carbon to be divided among as many cells as possible to minimize this per-cell quantity. This case corresponds to one in which no growth occurs . The upp5 cells mL−1 and the observed ending cell density. The resulting rate is called the “minimum growth rate.” This approach assumes that the microbial community was growing over the entire lifespan of the enclosed brine, and hence does not allow for death or dormancy. Inherent to To calculate the slowest possible rate of exponential growth, we determined the growth rate of a community over the simulation time of 40,000 years by fitting an exponential function between the starting cell density of 10The cell-specific metabolic rate, 5 cells mL−1, the order of magnitude of cell densities observed in coastal sea ice , is encompassed in the cell-specific metabolic rate. Each unit of organic carbon respired is removed from the DOC pool and added to the DIC pool. The quantity of DIC in the model runs presented here are modified solely by this cellular respiration of DOC. Cells grow according to an equation relating their maximum growth rate to substrate concentration . As a ceAs used in the CBIW scenario, the model allows for the addition of organic carbon to the system, beyond that available at time zero. A model feature not used here would allow consideration of a punctuated or a constant input of DIC through processes other than respiration, such as carbonate dissolution. Possible chemoautotrophy to remove DIC and generate new biomass  would re3.7.Due to the sparse data available on cryopeg brines, reconstructing their microbial history requires assumptions to obtain the first-order approximation of their energetics. These assumptions inherently introduce limitations to our results. We address the central assumptions here to contextualize our results.A key assumption in our analyses is that the cryopeg brines started with an amount of organic carbon equivalent to the quantity observed in their contemporary surroundings. This assumption is required, as obtaining precise information on a cryopeg system at the time of its formation 40,000 years ago is not possible. The assumption is not unreasonable given the hydrological isolation of the brines and the near-constant temperatures that have kept their surroundings frozen throughout their lifetimes .in situ microscale observations of these remote systems, we cannot parameterize niches or differentiate the energetic requirements of inhabiting them. For the purposes of conducting an overarching energetic analysis of the system, the lack of diffusivity may not be a critical limitation. The analysis is simply spread uniformly across the environment and the microbes.Our model does not account for diffusion of material throughout the brine, which neglects the likelihood of environmental niches . WithoutWe assumed that every cell in the system grows at the same rate. Of course, different subpopulations of cells express different phenotypes and levels of activity, including dormancy, at different times in their life histories. This assumption likely leads to an overestimation of the community growth rate and, in turn, an underestimation of the cell-specific metabolic rate. However, as will be seen in our results, the cell-specific metabolic rate compares reasonably well to existing estimations.We also assumed that every cell in the system has the same carbon content throughout its lifetime. Of course, bacterial communities exhibit a range of cell sizes, with size and potentially content changing as a function of growth conditions, growth phase, starvation conditions, and dormancy. Until distribution data for cryopeg brines are obtained, the use of a uniform distribution of cell size and carbon content in our analyses leaves some uncertainty to our results. As will be seen, our model simulations are not overly sensitive to this parameter.We have attributed cell death to starvation, but other processes can lead to cell death in these cryopeg brines. In particular, cell lysis following viral infection and “bacterial warfare” may contribute significantly . Use of We assumed that microbial community kinetics could be represented by those of the dominant bacterium. Many bacterial species exist within the cryopeg brine, each with presumably distinct kinetics. However, overall diversity was low and the dominant species was strongly dominant in each scenario considered, accounting for half or more of the community. Making this assumption allowed a first-order approximation despite the unknown complexities of community kinetics.We assumed that all POC is inaccessible to the brine community until hydrolyzed enzymatically to DOC, and that all DOC is accessible and labile. An absence of data on the chemical composition and lability of either of these pools of organic carbon limits our analysis, as does the assumption that EEA rate is constant. Bacteria regulate their production of extracellular enzymes in response to environmental substrates, but we lack data to model this kinetic or enzyme lifetime. These assumptions could lead to biased results in EEA rate calculations and final carbon quantities .Finally, we assumed that organic compounds are the only limiting source of carbon, nutrients and energy for cell respiration and growth. Sources of inorganic nutrients are plentiful in cryopeg brines , but are3.8.The model was solved using the DifferentialEquations.jl package v7.6.0  using a The growth term, equation  that rele is DOC :A logistic growth term has been added to cap the growth as the cell density, The death term, arvation :This term accounts for the assumption that cells will lyse if they do not have enough substrate to maintain their integrity, i.e., cannot satisfy their metabolic need  for each of the three cryopeg scenarios under different boundary conditions. Each simulation represents one of 8 unique combinations of the lower or upper bound of three variables: 3.10.To understand how the accuracy of our estimates affect model results, we conducted a sensitivity analysis of model parameters. Using GlobalSensitivity.jl package v2.1.2  we execuBriefly, this variance decomposition method varies each parameter within given bounds and measures the corresponding variance of the output. The resulting first-order Sobol index of a parameter is a measure of how much variance in the output can be attributed to that parameter. The total-effect Sobol index encompasses interactions between the variance of that parameter and the others in the analysis. The bounds passed for each parameter aim to encompass the range of microbiologically plausible values; these can be found in The sensitivity analysis was executed on the CB1 scenario, excluding environmental parameters. This choice was made to understand the influence of bacterial parameters, such as carbon content per cell and growth rate, on our results. Furthermore, these constitute the few parameters that future lab work may attempt to quantify, whereas more accurate environmental data is elusive.4.Here we provide the results of the different measurements made to fill gaps and complement the datasets available in the literature, and thus enable our model simulations. These measurements include sediment carbon and nitrogen content of cryopeg and regional sediments and brine DIC for one borehole sample. Estimates of cell-specific metabolic rate and extracellular enzyme rate are shown for the three different scenarios examined. Finally, a sensitivity analysis of model parameters and the model predictions are presented.4.1.−1 at a depth of 367–383 cm (n = 4). The porewater salt concentration was 6‰. The concentration of DOC in this porewater was 51.2 μg C mL−1. The nitrogen content of the sediment was 0.0016 ± 0.00005 μg N μg sediment−1, for a molar C:N ratio of 15.8 mol C mol N−1.To improve the accuracy of our model, we measured the quantity of organic carbon in sediment permafrost previously sampled at two locations in the BEO. The average value for POC was 0.0232 ± 0.0006 μg C μg sediment−1 (n = 3). The porewater salt concentration ranged between 22‰ and 30‰. The concentration of DOC in this porewater at 187-cm depth was 1,286 μg C mL−1. The nitrogen content of the sediment was 0.0010 ± 0.00015 μg N μg sediment−1. CB4 sediment thus had a C:N ratio of 15.8 mol C mol N−1.We also measured the concentration of organic carbon in sediment surrounding the CB4 cryopeg brine. For POC, the average value in this sediment layer was 0.0136 ± 0.0012 μg C μg sediment4.2.10 fg C mL−1. The dissolved inorganic carbon content of frozen sediment from CBIW (in 2018) was 4.9 × 10 × 1010 fg C mL−1. We do not have DIC measurements for other brines.The dissolved inorganic carbon content of CBIW brine (in 2017) was measured as 6.93 × 104.3.−1 day−1 , the estimated bounds of EEA rates were 0.806 and 0.584, with a predicted timespan of 48,700 years, much closer to the observed age of the cryopeg system. In all cases, this independent estimation of the system’s timespan is near to or less than double the measured timespan, well within the goal of obtaining order of magnitude estimates.We calculated the EEA rate required to hydrolyze the difference between surrounding sediment POC and brine POC. In the case of the CB1 scenario, the bounds of estimated EEA rates were 0.195 and 0.802 fg C cell4.5.A sensitivity analysis of model parameters revealed the importance of the three parameters at the heart of the Monod growth term : growth 4.6.In two of the eight sets of conditions used for model simulations, our model fully or partially succeeds in explaining the cell densities observed at 40,000 years. With conditions of minimum growth rate paired with low cell-specific metabolic rate and calculated EEA, all three cryopeg brine scenarios reach their observed cell densities . With meBy When the maximum growth rate is used, the microbial populations rapidly reach the system carrying capacity –H. Once 5.Our overall approach can be considered a bulk energetic analysis. We have made the fundamental assumption that the total energy use of the system corresponds to the difference in organic carbon between the permafrost and the cryopeg brine, assuming these started with equal amounts. This approach mitigates the lack of a secondary metabolic state  in our model. In this way, our cell-specific metabolic rate calculations provide bounds on the average energy requirement of a bacterium in this setting.11 fg C mL−1, two orders of magnitude below the quantity produced by our assumption. This calculation is expected to produce a lower bound quantity given that it does not consider nitrogen cycling or the concentration of other nitrogen species in the brine. Thus, this quantity does not contradict our assumption or prediction. Similarly, the DIC value measured is three orders of magnitude below our expectations based on DOC consumed in CBIW. This analysis indicates that we may be overestimating DIC in the model by not accounting for the complexities of the inorganic carbon system in a subzero brine  marine sediments.Extracellular enzyme activity has been documented in cryopeg brines . Produci5 cells mL−1, we obtain maximum doubling times on the order of 103 years. This result is microbiologically feasible, based on similarly long doubling times  calculated for other, related energy-limited environments, particularly marine and deep subsurface sediments .In all but two (of 8) sets of conditions for simulations, the model fails to reconstruct a cell growth trajectory that yields the observed cell densities. In these cases, cell density collapses to zero due to the lack of available DOC to meet community energetic requirements. However, in most cases, plenty of POC, a potential source of energy, remains . The extWhile the half-velocity constant presents high Sobol indices, this result must be nuanced. First, the chosen value is orders of magnitude lower that the quantity of DOC present in the system. Thus, the impact of this term at the beginning of the simulation is low, and growth proceeds unimpeded. A higher value might slow growth, but the timespan here is long enough that the effect would be negligible. When the quantity of DOC in the system is closer to or below the value chosen, the community is typically on a trajectory toward extinction in the model. Hence, the half-velocity constant, while important because it modulates growth, does not alone explain why the model is limited in explaining our observations.Simulations based on the CBIW scenario provide some insight on model success versus failure in predicting the observations. In this scenario, the lower bound cell-specific metabolic rate is lower than the extracellular enzyme activity rate used, whether the calculated or measured value ,B. Obserin vitro and in situ measurements may represent another. Future research on extracellular enzyme production and kinetics at subzero temperatures and high salinities, coupled with cell-size measurements, could allow for an improved understanding of bacterial energetics in cryopeg brines.Clearly, the EEA rate has the potential to make bioavailable a significant energy source in the system: POC. We note that the observed cell-specific rate of EEA used in the simulations is the average of activities measured on only three substrates in CBIW brine. This rate is kept constant throughout every simulation. This simplification does not accurately reflect the number and specificity of enzymes produced in a cryopeg brine, their complex kinetics, the regulation of their production, or their lifetimes under subzero brine conditions. The cell-specific EEA rate surely fluctuated over the lifespan of the brine as a function of cell density, DOC concentration, and extracellular enzyme turnover time. We were thus led to calculate the range of EEA rates that would allow for enough POC to be hydrolyzed to sustain the microbial community. For the CB1 and CB4 scenarios, these calculated rates are an order of magnitude higher than the measured rate used. Conversely, we calculated the amount of time needed for the chosen EEA rate to hydrolyze the required amount of POC. The results point to a longer lifespan for the cryopeg brines than the measured 40,000 years (by carbon dating), as high as 81,200 years in one case. This discrepancy, based on the chosen EEA rates being too low, provides one explanation as to why our model fails in many cases to explain the observed cell densities. A lack of data to account for cell size differences between in-situ conditions, and hydrogen sulfide concentrations are not known. However, the presence of sulfur-oxidizing and sulfur-reducing bacteria was recorded in these brines . GK also received support from a private sponsorship and the Karl M. Banse professorship to JD.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.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.