Determining the biodegradation of functionalised cellulose esters.
Recently, there has been an increased interest in developing functionalised carbohydrates, such as cellulose palmitate, as novel replacements for petroplastics. The functionalisation gives the materials excellent water barrier properties, as well as processability and mechanical properties akin to PET, while potentially having superior biodegradability to conventional first-generation biopolymers. However, the true biodegradability of these novel polymers is still unknown with some recent reports suggesting that it is limited. In this study, we investigated the potential of cellulose palmitate to biodegrade under controlled laboratory conditions, comparing the polymer to cellulose acetate. To this end, studies using specific enzymes, targeted whole cell fungal degradation and model edibility experiments were devised to study the biodegradability at end-of-life. On an enzymatic level, a combination of cellulase and lipase enzymes were found to hydrolyse the fatty acid linkages, allowing the cellulases to access the carbohydrate chain and release glucose. Under optimal conditions the biopolymer was completely hydrolysed within 6 hours. A soil fungi was then isolated from a compost heap that had been loaded with the functional material, to establish the most suitable species for whole cell degradation. This common soil fungi, Mucor sp., was then grown successfully under lab conditions on the functional material as a 95% carbon source. Finally, an edibility experiment was designed, using pepsin and pancreatic enzymes at precise pH concentrations found in the gastrointestinal tract to mimic real life conditions of ingestion by birds. While cellulose acetate broke down under just the acidic conditions, with no enzymes, the cellulose palmitate was found to be stable at the acidic conditions, but hydrolyse over 7 days when the enzymes were present. To the best of our knowledge this is the first study to confirm the biodegradability of functionalised cellulose highlighting the large promise of functionalised carbohydrates as a sustainable alternative to petrochemical plastics within the packaging industry.
- Research Article
53
- 10.1093/ps/78.11.1561
- Nov 1, 1999
- Poultry Science
Evaluation of dietary supplements of lipase, detergent, and crude porcine pancreas on fat utilization by young broiler chicks
- Research Article
20
- 10.1097/00007611-199409000-00005
- Sep 1, 1994
- Southern Medical Journal
Hyperamylasemia of pancreatic origin has been noted in patients with severe head injury without abdominal trauma or evidence of pancreatitis. Thirty-eight patients with intracranial bleeding of various types were evaluated for elevated pancreatic amylase and lipase enzymes without associated pancreatitis. Twenty-five patients had elevated serum lipase; 17 of 25 also had elevated amylase without pancreatitis. Most lipase elevations occurred earlier than those of amylase. Six clinical variables--mannitol, ceftriaxone, nimodipine, steroids, Glasgow Coma Score, and total parenteral and enteral hyperalimentation--were evaluated to determine relationship to the enzyme elevations. A significant relationship exists between patients not treated with steroids and elevated lipase and amylase enzyme activities. Multivariate analysis revealed a significant interaction between lipase elevation and decreasing Glasgow Coma Score, indicative of increasing severity of intracranial bleeding. Proposed causes of enzyme elevations in intracranial bleeding include vagal stimulation, altered modulation of the central control of pancreatic enzyme release, and release of cholecystokinin from the brain. Physician awareness of the association of intracranial bleeding with the elevation of amylase and lipase without pancreatitis can save the patient needless cost and manipulation.
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5
- 10.1016/j.advms.2015.01.003
- Jan 19, 2015
- Advances in Medical Sciences
Monitoring changes in plasma levels of pancreatic and intestinal enzymes in a model of pancreatic exocrine insufficiency – induced by pancreatic duct-ligation – in young pigs
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208
- 10.1016/j.ijbiomac.2020.03.163
- Mar 19, 2020
- International Journal of Biological Macromolecules
Cellulose from sources to nanocellulose and an overview of synthesis and properties of nanocellulose/zinc oxide nanocomposite materials
- Discussion
13
- 10.1100/tsw.2002.281
- Jan 1, 2002
- The Scientific World Journal
In this work, investigations were performed under laboratory conditions of the degradation ability by a common soil fungus, Aspergillus niger, toward chlorsulfuron and metsulfuron-methyl. The results were very encouraging (79% for chlorsulfuron and 61% for metsulfuron-methyl of total degradation), especially compared to those registered in our previous studies with a Pseudomonas fluorescens strain B2 (about 21 to 32%). Furthermore, the chemical degradation of the two compounds was studied and two products (1[2-methoxy-benzene-1-sulfonyl]-7-acetyltriuret and 1[2-chlorobenzene-1-sulfonyl]-7-acetyltriuret) were isolated and characterised by hydrolysis in acidic conditions. Our aim in the future will be the identification of intermediate metabolites by HPLC and LC-MS analyses in order to identify the degradative pathway by the fungal strain and to compare this to those obtained by chemical degradation and by P. fluorescens strain.
- Abstract
- 10.1016/j.pan.2013.04.095
- May 1, 2013
- Pancreatology
Exocrine pancreas ER stress differentially induced by different fatty acids
- Research Article
9
- 10.1079/bjn19870111
- Nov 1, 1987
- The British journal of nutrition
1. The effect on pancreatic digestive enzyme levels of fasting and changes from a diet containing trypsin inhibitor (raw soya-bean flour, RSF) to diets free of trypsin inhibitor (heated soya-bean flour, HSF, or commercial rat chow) was studied in rats for up to 7 d. 2. In RSF-fed rats killed without fasting, enzyme levels were low, but after fasting for 24 h before killing there was a marked increase in all enzyme levels. Histological studies showed that pancreatic acinar cells from RSF-fed rats killed without fasting were devoid of zymogen granules, but following a 24 h fast there was a marked accumulation of zymogen granules which extend into the basal cytoplasm. Fasting either produced no change or a fall in enzyme levels in rats fasted after feeding HSF or chow continuously. 3. If animals fed on RSF were changed to HSF and either fed or fasted for 24 h up to the time of killing there was an increase in amylase (EC 3.2.1.1), trypsin (EC 3.4.21.4), lipase (triacylglycerol lipase; EC 3.1.1.3) and protein 1 d after the change, followed by a fall over the next 6 d to levels similar to those seen in rats fed on HSF continuously. 4. Animals changed from RSF to chow showed similar effects as far as trypsin, lipase and protein were concerned, but amylase rose, to reach the level seen in rats fed on chow continuously (about ten times that seen in soya-bean-fed rats), after 2 d. 5. These results suggest that in the rats fed on RSF, pancreatic enzyme synthesis is rapid but secretion is equally rapid and intracellular enzyme levels are low. When these animals are fasted or changed to a diet free of trypsin inhibitor the rate of secretion falls but the high rate of synthesis continues for at least 24 h and enzymes accumulate in the pancreas. In studies of pancreatic enzyme levels in rats fed on trypsin inhibitor the extent of fasting before killing the animal is therefore an important variable. Such animals should probably not be fasted before study.
- Peer Review Report
- 10.7554/elife.84379.sa0
- Dec 12, 2022
Article Figures and data Abstract Editor's evaluation eLife digest Introduction Results Discussion Materials and methods Appendix 1 Appendix 2 Appendix 3 Appendix 4 Appendix 5 Appendix 6 Appendix 7 Appendix 8 Appendix 9 Appendix 10 Appendix 11 Data availability References Decision letter Author response Article and author information Metrics Abstract Cycling of co-substrates, whereby a metabolite is converted among alternate forms via different reactions, is ubiquitous in metabolism. Several cycled co-substrates are well known as energy and electron carriers (e.g. ATP and NAD(P)H), but there are also other metabolites that act as cycled co-substrates in different parts of central metabolism. Here, we develop a mathematical framework to analyse the effect of co-substrate cycling on metabolic flux. In the cases of a single reaction and linear pathways, we find that co-substrate cycling imposes an additional flux limit on a reaction, distinct to the limit imposed by the kinetics of the primary enzyme catalysing that reaction. Using analytical methods, we show that this additional limit is a function of the total pool size and turnover rate of the cycled co-substrate. Expanding from this insight and using simulations, we show that regulation of these two parameters can allow regulation of flux dynamics in branched and coupled pathways. To support these theoretical insights, we analysed existing flux measurements and enzyme levels from the central carbon metabolism and identified several reactions that could be limited by the dynamics of co-substrate cycling. We discuss how the limitations imposed by co-substrate cycling provide experimentally testable hypotheses on specific metabolic phenotypes. We conclude that measuring and controlling co-substrate dynamics is crucial for understanding and engineering metabolic fluxes in cells. Editor's evaluation This manuscript presents an important mathematical analysis of metabolic "co-substrates" and how their cycling can affect metabolic fluxes. Through mathematical analysis of simple network motifs, it shows the impact of co-substrate cycling on constraining metabolic fluxes. The combination of mathematical modeling and comparisons with existing data from previous studies offers convincing support for the potential biological relevance of co-substrate cycling. The work will be of interest to researchers who study microbial metabolism and metabolic engineering. https://doi.org/10.7554/eLife.84379.sa0 Decision letter Reviews on Sciety eLife's review process eLife digest Metabolism powers individual cells and ultimately the body. It comprises a sequence of chemical reactions that cells use to break down substances and generate energy. These reactions are catalyzed by enzymes, which are proteins that speed up the rate of the reaction. Many reactions also involve co-substrates, which are themselves transformed by individual reactions but are eventually converted back into their original form in a series of steps. This process is known as co-substrate cycling. Scientists have long been interested in understanding what controls the rate at which metabolic reactions and metabolic pathways convert a substance into a final product. This is a difficult subject to study because of the complexity of the metabolic pathways, with their branched, linear or coupled structures. In the past, researchers have looked at the influence of enzymes on the rate of a metabolic pathway, but less has been known about the effect of co-substrate cycling. To find out more, West, Delattre et al. developed a series of mathematical models to describe different types of metabolic pathways in terms of the number of metabolites that enter and leave it, including the influence of co-substrates. They found that co-substrate cycling, when involved in a metabolic reaction, limits the speed with which the reaction happens. This is distinct from the limit that enzymes impose on the speed of the reaction. It depends on the total amount of co-substrates in the cell: changing the number of co-substrates in the cell influences the speed at which the metabolic reaction takes place. This study has increased our understanding of how metabolic pathways work, and what controls the speed at which reactions take place. It opens up a new potential method for explaining how cells control metabolic reaction rates and how metabolic substrates can be directed across different pathways. This research is likely to inspire future research into the influence of co-substrates in different cell types and conditions. Introduction Dynamics of cell metabolism directly influences individual and population-level cellular responses. Examples include metabolic oscillations underpinning the cell cycle (Papagiannakis et al., 2017; Murray et al., 2007) and metabolic shifts from respiration to fermentation, as observed in cancer phenotypes (Warburg, 1956; Diaz-Ruiz et al., 2009; Carmona-Fontaine et al., 2013) and cell-to-cell cross-feeding (Ponomarova et al., 2017; Campbell et al., 2015; Großkopf et al., 2016). Predicting or conceptualising these physiological responses using dynamical models is difficult due to the large size and high connectivity of cellular metabolism. Despite this complexity, however, it is possible that cellular metabolism features certain 'design principles' that determine the overall dynamics. There is ongoing interest in finding such simplifying principles. A key concept for understanding the dynamics of any metabolic system is that of 'reaction flux', which is a measure of the rate of biochemical conversion in a given reaction. To identify possible limitations on reaction fluxes, early studies focused on linear pathways involving ATP production and studied their dynamics under the optimality assumption of maximisation of overall pathway flux under limited enzyme levels available to the pathway (Heinrich et al., 1991). The resulting theory predicted a trade-off between pathway flux vs. yield (i.e. rate of ATP generation vs. amount of ATP generated per metabolite consumed by the pathway) in linear pathways (Heinrich and Hoffmann, 1991). This theory is subsequently used to explain the emergence of different metabolic phenotypes (Pfeiffer et al., 2001). In related studies, models pertaining to flux optimisation and enzyme levels being a key limitation are used to explain the structure of different metabolic pathways (Flamholz et al., 2013), and the metabolic shifting from respiration to fermentative pathways under increasing glycolysis rates (Großkopf et al., 2016; Basan et al., 2015; Majewski and Domach, 1990). There are, however, increasing number of studies suggesting that enzyme levels alone might not be sufficient to explain observed flux levels. For example, it was shown that the maximal value of the apparent activities (kappmax) of an enzyme, derived using measured enzyme levels and fluxes under different conditions, was a good estimate for the specific activity of that enzyme in vitro (kcat) (Davidi et al., 2016). However, individual estimates from each condition (i.e. individual kapp values) were commonly lower than the specific activity – suggesting that the flux is limited by something other than enzyme levels under those conditions. Other studies have shown that metabolic flux changes, caused by perturbations in media conditions, are not explained solely by changes in expression levels of enzymes (Chubukov et al., 2013; Gerosa et al., 2015). Another conceptual framework emphasized the importance of cyclic reaction motifs, particularly those involving so-called co-substrate pairs, such as ATP / ADP or NAD(P)H / NAD(P)+, as a key to understanding metabolic system dynamics (Reich and Sel'kov, 1981). This framework is linked to the idea of considering the supply and demand structures around specific metabolites as regulatory blocks within metabolism (Hofmeyr and Cornish-Bowden, 2000). For example, the total pool of ATP and its derivates (the 'energy charge') is suggested as a key determinant of physiological cell states (Atkinson, 1968). Inspired by these ideas, theoretical studies have shown that metabolic systems featuring metabolite cycling together with allosteric regulation can introduce switch-like and bistable dynamics (Okamoto and Hayashi, 1983; Hervagault and Cimino, 1989), and that metabolite cycling motifs introduce total co-substrate level as an additional control element in metabolic control analysis (Hofmeyr et al., 1986; Sauro, 1994). Specific analyses of ATP cycling in the glycolysis pathway, sometimes referred to as a 'turbo-design', and metabolite cycling with autocatalysis, as seen for example in the glyoxylate cycle, have shown that these features constrain pathway fluxes (Koebmann et al., 2002; Teusink et al., 1998; van Heerden et al., 2014; Hatakeyama and Furusawa, 2017; Barenholz et al., 2017; Kurata, 2019). Taken together, these studies indicate that metabolite cycling, in general, and co-substrate cycling specifically, could provide a key 'design feature' in cell metabolism, imposing certain constraints or dynamical properties to it. Towards better understanding the role of co-substrate cycling in cell metabolism dynamics, we undertook here an analytical and simulation-based mathematical study together with analyses of measured fluxes. We created models of enzymatic reaction systems featuring co-substrate cycling, abstracted from real metabolic systems such as glycolysis, nitrogen-assimilation, and central carbon metabolism. We found that co-substrate cycling introduces a fundamental constraint on reaction flux. In the case of single reaction and short linear pathways, we were able to derive a mathematical expression of the constraint, showing that it relates to the pool size and turnover rate of the co-substrate. Analysing measured fluxes, we find that several of the co-substrate featuring reactions in central carbon metabolism carry lower fluxes than expected from the kinetics of their primary enzymes, suggesting that these reactions might be limited by co-substrate cycling. In addition to its possible constraining role, we show that co-substrate cycling can also act as a regulatory element, where control of co-substrate pool size can allow control of flux dynamics across connected or branching pathways. Together, these findings show that co-substrate cycling can act both as a constraint and a regulatory element in cellular metabolism. The resulting theory provides testable hypotheses on how to manipulate metabolic fluxes and cell physiology through the control of co-substrate pool sizes and turnover dynamics, and can be expanded to explain dynamic measurements of metabolite concentrations in different perturbation experiments. Results Co-substrate cycling represents a ubiquitous motif in metabolism with co-substrate pools acting as 'conserved moieties' Certain pairs of metabolites can be interconverted via different reactions in the cell, thereby resulting in their 'cycling'. This cycling creates interconnections within metabolism, spanning either multiple reactions in a single, linear pathway, or multiple pathways that are independent or are branching from common metabolites. For example, in glycolysis, ATP is consumed in reactions mediated by the enzymes glucose hexokinase and phosphofructokinase, and is produced by the downstream reactions mediated by phosphoglycerate and pyruvate kinase (Appendix 1—figure 1A). In the nitrogen assimilation pathway, the NAD+ / NADH pair is cycled by the enzymes glutamine oxoglutarate aminotransferase and glutamate dehydrogenase (Appendix Dynamics of co-substrate pools can constrain and regulate metabolic fluxes - Appendix 1—figure 1B). Many other cycling motifs can be identified, involving either metabolites from the central carbon metabolism or metabolites that are usually referred to as co-substrates. Examples for the latter include NADPH, FADH2, GTP, and Acetyl-CoA and their corresponding alternate forms, while examples for the former include the tetrahydrofolate (THF) / 5,10-Methylene-THF and glutamate / α-ketoglutarate (akg) pairs involved in one-carbon transfer and in amino acid biosynthesis pathways, respectively (Appendix 1—figure 1C and D). For some of these metabolites, their cycling can connect many reactions in the metabolic network. Taking ATP (NADH) as an example, there are 265 (118) and 833 (601) reactions linked to the cycling of this metabolite in the genome-scale metabolic models of Escherichia coli and human respectively models iJO1366 (Orth et al., 2011) and Recon3d (Brunk et al., 2018). We notice here that many of the co-substrate involving cycling reactions can be abstracted as a simplified motif as shown in (Figure 1A). This abstract representation highlights the fact that the total pool-size involving all the different forms of a cycled metabolite can become a conserved quantity. This would be the case even when we consider biosynthesis or environmental uptake of co-substrates, as the total concentration of a cycled metabolite across its different forms at steady state would then be given by a constant defined by the ratio of the influx and outflux rates (see Appendices 2 and 3). In other words, the cycled metabolite would become a 'conserved moiety' for the rest of the metabolic system and can have a constant 'pool size'. Supporting this, temporal measurement of specific co-substrate pool sizes shows that ATP and GTP pools are constant under stable metabolic conditions, but can rapidly change in response to external perturbations, possibly through inter-conversions among pools rather than through biosynthesis (Walther et al., 2010). Figure 1 Download asset Open asset Motif, time-series and threshold in a single co-substrate involving reaction. (A) Cartoon representation of a single irreversible reaction with co-substrate cycling (see Appendices for other reaction schemes). The co-substrate is considered to have two forms A0 and A1. (B) Concentrations of the metabolites M0 (red) and M1 (green), and the A0/A1 ratio (blue) are shown as a function of time. At t=500, the parameters are switched from the white dot in panel (C) (where a steady state exists) to the black dot (where we see continual build-up of M0 and decline of A0 without steady state). (C & D) Heatmap of the steady state concentration of M0 as a function of the total co-substrate pool size (Atot) and inflow flux (kin). White area shows the region where there is no steady state. On both panels, the dashed line indicates the limitation from the primary enzyme, kin<Vmax,E0, and the solid line indicates the limitation from co-substrate cycling, kin<AtotVmax,Ea/(KM,Ea+Atot). In panel (C), there is a range of Atot values for which the first limitation is more severe than the second. In contrast, in panel (D), the second limitation is always more severe than the first. In (B & C) the parameters used for the primary enzyme (for the reaction converting M0 into M1) are picked from within a physiological range (see Supplementary file 1) and are set to: Etot=0.01 mM, kcat=100/s, KM,E0=KM,Ea=50μM, while kout is set to 0.1/s. The Etot and kcat for the co-substrate cycling enzyme are 1.2 times those for the primary enzyme. In panel (D) the parameters are the same except for the Etot and kcat of the co-substrate cycling enzyme, which are set to 0.7 times those for the primary enzyme. Co-substrate cycling introduces a limitation on reaction flux To explore the effect of co-substrate cycling on pathway fluxes, we first consider a didactic case of a single reaction. This reaction converts an arbitrary metabolite M0 to M1 and involves co-substrate cycling (Figure 1A). For co-substrate cycling, we consider additional 'background' enzymatic reactions that are independent of M0 and can also convert the co-substrate (denoted Ea on Figure 1A). We use either irreversible or reversible enzyme dynamics to build an ordinary differential equation (ODE) kinetic model for this reaction system and solve for its steady states analytically (see Methods and Appendix 3). In the case of using irreversible enzyme kinetics, we obtain that the steady state concentration of the two metabolites, M0 and M1 (denoted as m0 and m1) are given by: (1) m0=α kinKM,E0(Vmax,E0−kin)(Vmax,EaAtot−kin(KM,Ea+Atot))m1=kinkout where kin and kout denote the rate of in-flux of M0, and out-flux of M1, either in-and-out of the cell or from other pathways, and Atot denotes the total pool size of the cycled metabolite (with the different forms of the cycled metabolite indicated as A0 and A1 in Figure 1A). The parameters Vmax,E0 and Vmax,Ea are the maximal rates (i.e. Vmax=kcatEtot) for the enzymes catalysing the conversion of A0 and M0 into A1 and M1 (enzyme E0), and the turnover of A1 into A0 (enzyme Ea), respectively, while the parameters KM,E0 and KM,Ea are the individual or combined Michaelis-Menten coefficients for these enzymes' substrates (i.e. for A0 and M0 and A1, respectively). The term α is (in this case where all reactions are irreversible) equal to Vmax,Ea-kin, and in general is a positive expression comprising kin, and the Michaelis-Menten coefficients and the Vmax parameters of the background enzymes in the model (see Appendix 3, Equations 7; 9; 11). The steady states for the model with all enzymatic conversions being reversible, and for a model with degradation and synthesis of A0 and A1, are given in Appendix 3. The steady state solutions of these alternative models are structurally akin to (1), and do not alter the qualitative conclusions we make in what follows. A key property of (1) is that it contains terms in the denominator that involve a subtraction. The presence of these terms introduces a limit on the parameter values for the system to attain a positive steady state. Specifically, we obtain the following conditions for positive steady states to exist: (2) kin<Vmax,E0andkin<AtotVmax,EaKM,Ea+Atot. Additionally, the 'shape' of (1) indicates a 'threshold effect' on the steady state value of m0, where it would rise towards infinity as kin increases towards the lower one among the limits given in (2) (see Figure 1B). Why does (1) show this specific form, leading to these limits? We find that this is a direct consequence of the steady state condition, where metabolite production and consumption rates need to be the same at steady state. In the case of co-substrate cycling, the production rate of M0 is given by kin, while its consumption rate is a function of the Vmax,E0 and the concentration of A0. In turn, the concentration of A0 is determined by its re-generation rate (which is a function of KM,Ea and Vmax,Ea) and the pool size (Atot). This explains the inequalities given in (2) and shows that a cycled co-substrate creates the same type of limitation (mathematically speaking) on the flux of a reaction it is involved in, as that imposed by the enzyme catalysing that reaction (E0 in this example) (see Figure 1C & D). We also show that considering the system shown in Figure 1A as an enzymatic reaction without co-substrate cycling leads to only the constraint kin<Vmax,E0, while considering it as a non-enzymatic reaction with co-substrate cycling only, leads to only the constraint kin<AtotVmax,Ea/(KM,Ea+Atot) becoming the sole limitation on the system (see Appendix 3). In other words, the two limitations act independently. To conclude this section, we re-iterate its main result. The flux of a reaction involving co-substrate cycling is limited either by the kinetics of the primary enzyme mediating that reaction, or by the turnover rate of the co-substrate. The latter is determined by the co-substrate pool size and the kinetics of the enzyme(s) mediating its turnover. Co-substrate cycling causes a flux limit on linear metabolic pathways We next considered a generalised, linear pathway model with n+1 metabolites and arbitrary locations of reactions for co-substrate cycling, for example as seen in upper glycolysis (Appendix 1—figure 1A). In this model, we only consider intra-pathway metabolite cycling, i.e. the co-substrate is consumed and re-generated solely by the reactions of the pathway. Here, we show results for this model with 5 metabolites as an illustration (Figure 2A), while the general case is presented in Appendix 4. Figure 2 Download asset Open asset Motif, time-series and thresholds for the linear pathway model with n=4. (A) Cartoon representation of a of reversible reactions with co-substrate cycling solely The co-substrate is considered to have two forms A0 and A1. (B) Heatmap of the steady state concentration of M0 as a function of the total metabolite pool size (Atot) and inflow rate constant (kin). White area shows the region where there is no steady state. The dashed and solid indicate the limitations from primary enzyme in this and co-substrate cycling, respectively, as in Figure (C) Concentrations of and A0/A1 ratio as a function of (with as indicated in the At the parameters are switched from the white dot in panel (B) (where a steady state exists) to the black dot (where we see build-up of all substrates that are produced the first co-substrate cycling reaction, and decline of The parameters used are picked from within a physiological range (see Supplementary file 1) and are set to: Etot=0.01 mM, kcat=100/s, for all reactions, and We find the same of threshold dynamics as in the single reaction kin is a threshold the metabolite M0 towards infinity and the system does not have a steady state (Figure A as well as our analytical that the of metabolites to all metabolites of the first reaction with co-substrate cycling (Figure and Appendix Additionally, metabolites downstream of the cycling reaction to a steady state level that does not on kin (Figure and Appendix In other words, pathway be increased by increasing kin the as kin the cycled metabolite pool shifts towards one form and the ratio of the two forms (Figure analytical expression for the threshold for kin, shown in could not be derived for linear pathways with but our analytical study indicates that the threshold is always linked to Atot and enzyme kinetic and the concentration of all metabolites to the reaction coupled to metabolite cycling will towards infinity as kin the threshold (see Appendix In Figure we these dynamics with for a system with n=4. We also considered several of this linear pathway model, corresponding to cases as shown in Appendix 1—figure These intra-pathway cycling of two different metabolites, as seen with ATP and NADH in combined upper glycolysis and pathways (Appendix different for consumption and re-generation reactions of the cycled as seen in upper glycolysis (Appendix and cycling of one metabolite with that of as seen in nitrogen assimilation (Appendix The results in the Appendices that all these cases threshold dynamics, where the threshold is a function of the co-substrate pool size and the enzyme metabolite related limit could be for specific reactions from central metabolism on flux values that are either experimentally measured or predicted by flux analysis many reactions from the central carbon metabolism of the model Escherichia coli are shown to have lower flux than expected from the kinetics of their enzymes (i.e. (Davidi et al., 2016). This finding is on Vmax from in vitro measured kcat values of specific enzymes and their in levels on studies in coli (see Materials and The flux and enzyme concentration data were from other studies which measured the in coli on media with carbon et al., 2016; Gerosa et al., 2015). we consider measured fluxes for each reaction as a for kin that these two would be equal at steady we can conclude from the fact that there were no observed in these reactions, as an for the analysed reactions fluxes the first limit identified in There could be several for this of measured fluxes being lower than the limit set by measured enzyme kinetics and simple could be that there is a between in vitro measured enzyme kinetics and in this can be but the lower flux could be because there are additional other than the enzymes mediating the main reaction. such additional limitation and are shown to explain observed lower fluxes in some reactions (Davidi et al., 2016; see also Here, we that the presented theory shows that an additional possible limitation could be the co-substrate pool size and turnover dynamics. To explore this we the flux values (Davidi et al., 2016; Gerosa et al., and focused solely on reactions that are linked to or pools (see Materials and methods and Supplementary file The resulting fluxes, and enzyme levels for different reactions determined under 7 different conditions with turnover and kinetic of the corresponding In we of values with data and with only flux We the flux values that would be expected from the primary enzyme limit identified under all conditions analysed (Figure and in addition the effect of the primary could explain the (Appendix We found that in both about of these reactions carry flux lower than what is expected from enzyme kinetics (Appendix suggesting that the limits imposed by dynamics might be constraining the flux The number of the cases where the flux the limit might be due to in measurement of enzyme or Figure 3 Download asset Open asset and flux values are lower than the primary enzyme (A) and flux values et al., 2016; Gerosa et al., the primary enzyme kinetic threshold of that there are 7 for each reaction, corresponding to the different conditions under which measurements or was (see Supplementary file 1 for with reaction and metabolites flux values under different conditions Gerosa et al., for reactions the corresponding co-substrate pool to show reactions for phosphoglycerate kinase dehydrogenase and dehydrogenase on these is a flux measurement under a different environmental condition, where the co-substrate pool size is also of flux and metabolite measurements as in the from Gerosa et al. co-substrate type and are as shown in the to panel show the linear with the corresponding shown in the panel It is also possible that observed lower fluxes are due to This is difficult to analyse without more as reaction of concentrations for all substrates and as well as enzyme Michaelis-Menten in both and This information is not available except for of the reactions among the we to as insight as possible on the we analysed the physiological energy (the is that all are at 1 and the flux – (Appendix 3). This shows that in such as dehydrogenase the flux to be by the the general is that there is between reaction flux and We have also the between fluxes and co-substrate pool Co-substrate pool sizes do change between different conditions, and we that such changes be due to flux changes in co-substrate on the other changes in pool size can affect flux in those reactions, where co-substrate dynamics is predicted by the For both measured and fluxes, we find that several reactions show between flux and co-substrate pool size (see Figure see also Appendix 1 and Appendix
- Peer Review Report
- 10.7554/elife.84379.sa1
- Dec 12, 2022
Article Figures and data Abstract Editor's evaluation eLife digest Introduction Results Discussion Materials and methods Appendix 1 Appendix 2 Appendix 3 Appendix 4 Appendix 5 Appendix 6 Appendix 7 Appendix 8 Appendix 9 Appendix 10 Appendix 11 Data availability References Decision letter Author response Article and author information Metrics Abstract Cycling of co-substrates, whereby a metabolite is converted among alternate forms via different reactions, is ubiquitous in metabolism. Several cycled co-substrates are well known as energy and electron carriers (e.g. ATP and NAD(P)H), but there are also other metabolites that act as cycled co-substrates in different parts of central metabolism. Here, we develop a mathematical framework to analyse the effect of co-substrate cycling on metabolic flux. In the cases of a single reaction and linear pathways, we find that co-substrate cycling imposes an additional flux limit on a reaction, distinct to the limit imposed by the kinetics of the primary enzyme catalysing that reaction. Using analytical methods, we show that this additional limit is a function of the total pool size and turnover rate of the cycled co-substrate. Expanding from this insight and using simulations, we show that regulation of these two parameters can allow regulation of flux dynamics in branched and coupled pathways. To support these theoretical insights, we analysed existing flux measurements and enzyme levels from the central carbon metabolism and identified several reactions that could be limited by the dynamics of co-substrate cycling. We discuss how the limitations imposed by co-substrate cycling provide experimentally testable hypotheses on specific metabolic phenotypes. We conclude that measuring and controlling co-substrate dynamics is crucial for understanding and engineering metabolic fluxes in cells. Editor's evaluation This manuscript presents an important mathematical analysis of metabolic "co-substrates" and how their cycling can affect metabolic fluxes. Through mathematical analysis of simple network motifs, it shows the impact of co-substrate cycling on constraining metabolic fluxes. The combination of mathematical modeling and comparisons with existing data from previous studies offers convincing support for the potential biological relevance of co-substrate cycling. The work will be of interest to researchers who study microbial metabolism and metabolic engineering. https://doi.org/10.7554/eLife.84379.sa0 Decision letter Reviews on Sciety eLife's review process eLife digest Metabolism powers individual cells and ultimately the body. It comprises a sequence of chemical reactions that cells use to break down substances and generate energy. These reactions are catalyzed by enzymes, which are proteins that speed up the rate of the reaction. Many reactions also involve co-substrates, which are themselves transformed by individual reactions but are eventually converted back into their original form in a series of steps. This process is known as co-substrate cycling. Scientists have long been interested in understanding what controls the rate at which metabolic reactions and metabolic pathways convert a substance into a final product. This is a difficult subject to study because of the complexity of the metabolic pathways, with their branched, linear or coupled structures. In the past, researchers have looked at the influence of enzymes on the rate of a metabolic pathway, but less has been known about the effect of co-substrate cycling. To find out more, West, Delattre et al. developed a series of mathematical models to describe different types of metabolic pathways in terms of the number of metabolites that enter and leave it, including the influence of co-substrates. They found that co-substrate cycling, when involved in a metabolic reaction, limits the speed with which the reaction happens. This is distinct from the limit that enzymes impose on the speed of the reaction. It depends on the total amount of co-substrates in the cell: changing the number of co-substrates in the cell influences the speed at which the metabolic reaction takes place. This study has increased our understanding of how metabolic pathways work, and what controls the speed at which reactions take place. It opens up a new potential method for explaining how cells control metabolic reaction rates and how metabolic substrates can be directed across different pathways. This research is likely to inspire future research into the influence of co-substrates in different cell types and conditions. Introduction Dynamics of cell metabolism directly influences individual and population-level cellular responses. Examples include metabolic oscillations underpinning the cell cycle (Papagiannakis et al., 2017; Murray et al., 2007) and metabolic shifts from respiration to fermentation, as observed in cancer phenotypes (Warburg, 1956; Diaz-Ruiz et al., 2009; Carmona-Fontaine et al., 2013) and cell-to-cell cross-feeding (Ponomarova et al., 2017; Campbell et al., 2015; Großkopf et al., 2016). Predicting or conceptualising these physiological responses using dynamical models is difficult due to the large size and high connectivity of cellular metabolism. Despite this complexity, however, it is possible that cellular metabolism features certain ‘design principles’ that determine the overall dynamics. There is ongoing interest in finding such simplifying principles. A key concept for understanding the dynamics of any metabolic system is that of ‘reaction flux’, which is a measure of the rate of biochemical conversion in a given reaction. To identify possible limitations on reaction fluxes, early studies focused on linear pathways involving ATP production and studied their dynamics under the optimality assumption of maximisation of overall pathway flux under limited enzyme levels available to the pathway (Heinrich et al., 1991). The resulting theory predicted a trade-off between pathway flux vs. yield (i.e. rate of ATP generation vs. amount of ATP generated per metabolite consumed by the pathway) in linear pathways (Heinrich and Hoffmann, 1991). This theory is subsequently used to explain the emergence of different metabolic phenotypes (Pfeiffer et al., 2001). In related studies, models pertaining to flux optimisation and enzyme levels being a key limitation are used to explain the structure of different metabolic pathways (Flamholz et al., 2013), and the metabolic shifting from respiration to fermentative pathways under increasing glycolysis rates (Großkopf et al., 2016; Basan et al., 2015; Majewski and Domach, 1990). There are, however, increasing number of studies suggesting that enzyme levels alone might not be sufficient to explain observed flux levels. For example, it was shown that the maximal value of the apparent activities (kappmax) of an enzyme, derived using measured enzyme levels and fluxes under different conditions, was a good estimate for the specific activity of that enzyme in vitro (kcat) (Davidi et al., 2016). However, individual estimates from each condition (i.e. individual kapp values) were commonly lower than the specific activity – suggesting that the flux is limited by something other than enzyme levels under those conditions. Other studies have shown that metabolic flux changes, caused by perturbations in media conditions, are not explained solely by changes in expression levels of enzymes (Chubukov et al., 2013; Gerosa et al., 2015). Another conceptual framework emphasized the importance of cyclic reaction motifs, particularly those involving so-called co-substrate pairs, such as ATP / ADP or NAD(P)H / NAD(P)+, as a key to understanding metabolic system dynamics (Reich and Sel‘kov, 1981). This framework is linked to the idea of considering the supply and demand structures around specific metabolites as regulatory blocks within metabolism (Hofmeyr and Cornish-Bowden, 2000). For example, the total pool of ATP and its derivates (the ‘energy charge’) is suggested as a key determinant of physiological cell states (Atkinson, 1968). Inspired by these ideas, theoretical studies have shown that metabolic systems featuring metabolite cycling together with allosteric regulation can introduce switch-like and bistable dynamics (Okamoto and Hayashi, 1983; Hervagault and Cimino, 1989), and that metabolite cycling motifs introduce total co-substrate level as an additional control element in metabolic control analysis (Hofmeyr et al., 1986; Sauro, 1994). Specific analyses of ATP cycling in the glycolysis pathway, sometimes referred to as a ‘turbo-design’, and metabolite cycling with autocatalysis, as seen for example in the glyoxylate cycle, have shown that these features constrain pathway fluxes (Koebmann et al., 2002; Teusink et al., 1998; van Heerden et al., 2014; Hatakeyama and Furusawa, 2017; Barenholz et al., 2017; Kurata, 2019). Taken together, these studies indicate that metabolite cycling, in general, and co-substrate cycling specifically, could provide a key ‘design feature’ in cell metabolism, imposing certain constraints or dynamical properties to it. Towards better understanding the role of co-substrate cycling in cell metabolism dynamics, we undertook here an analytical and simulation-based mathematical study together with analyses of measured fluxes. We created models of enzymatic reaction systems featuring co-substrate cycling, abstracted from real metabolic systems such as glycolysis, nitrogen-assimilation, and central carbon metabolism. We found that co-substrate cycling introduces a fundamental constraint on reaction flux. In the case of single reaction and short linear pathways, we were able to derive a mathematical expression of the constraint, showing that it relates to the pool size and turnover rate of the co-substrate. Analysing measured fluxes, we find that several of the co-substrate featuring reactions in central carbon metabolism carry lower fluxes than expected from the kinetics of their primary enzymes, suggesting that these reactions might be limited by co-substrate cycling. In addition to its possible constraining role, we show that co-substrate cycling can also act as a regulatory element, where control of co-substrate pool size can allow control of flux dynamics across connected or branching pathways. Together, these findings show that co-substrate cycling can act both as a constraint and a regulatory element in cellular metabolism. The resulting theory provides testable hypotheses on how to manipulate metabolic fluxes and cell physiology through the control of co-substrate pool sizes and turnover dynamics, and can be expanded to explain dynamic measurements of metabolite concentrations in different perturbation experiments. Results Co-substrate cycling represents a ubiquitous motif in metabolism with co-substrate pools acting as ‘conserved moieties’ Certain pairs of metabolites can be interconverted via different reactions in the cell, thereby resulting in their ‘cycling’. This cycling creates interconnections within metabolism, spanning either multiple reactions in a single, linear pathway, or multiple pathways that are independent or are branching from common metabolites. For example, in glycolysis, ATP is consumed in reactions mediated by the enzymes glucose hexokinase and phosphofructokinase, and is produced by the downstream reactions mediated by phosphoglycerate and pyruvate kinase (Appendix 1—figure 1A). In the nitrogen assimilation pathway, the NAD+ / NADH pair is cycled by the enzymes glutamine oxoglutarate aminotransferase and glutamate dehydrogenase (Appendix Dynamics of co-substrate pools can constrain and regulate metabolic fluxes - Appendix 1—figure 1B). Many other cycling motifs can be identified, involving either metabolites from the central carbon metabolism or metabolites that are usually referred to as co-substrates. Examples for the latter include NADPH, FADH2, GTP, and Acetyl-CoA and their corresponding alternate forms, while examples for the former include the tetrahydrofolate (THF) / 5,10-Methylene-THF and glutamate / α-ketoglutarate (akg) pairs involved in one-carbon transfer and in amino acid biosynthesis pathways, respectively (Appendix 1—figure 1C and D). For some of these metabolites, their cycling can connect many reactions in the metabolic network. Taking ATP (NADH) as an example, there are 265 (118) and 833 (601) reactions linked to the cycling of this metabolite in the genome-scale metabolic models of Escherichia coli and human respectively models iJO1366 (Orth et al., 2011) and Recon3d (Brunk et al., 2018). We notice here that many of the co-substrate involving cycling reactions can be abstracted as a simplified motif as shown in (Figure 1A). This abstract representation highlights the fact that the total pool-size involving all the different forms of a cycled metabolite can become a conserved quantity. This would be the case even when we consider biosynthesis or environmental uptake of co-substrates, as the total concentration of a cycled metabolite across its different forms at steady state would then be given by a constant defined by the ratio of the influx and outflux rates (see Appendices 2 and 3). In other words, the cycled metabolite would become a ‘conserved moiety’ for the rest of the metabolic system and can have a constant ‘pool size’. Supporting this, temporal measurement of specific co-substrate pool sizes shows that ATP and GTP pools are constant under stable metabolic conditions, but can rapidly change in response to external perturbations, possibly through inter-conversions among pools rather than through biosynthesis (Walther et al., 2010). Figure 1 Download asset Open asset Motif, time-series and threshold in a single co-substrate involving reaction. (A) Cartoon representation of a single irreversible reaction with co-substrate cycling (see Appendices for other reaction schemes). The co-substrate is considered to have two forms A0 and A1. (B) Concentrations of the metabolites M0 (red) and M1 (green), and the A0/A1 ratio (blue) are shown as a function of time. At t=500, the parameters are switched from the white dot in panel (C) (where a steady state exists) to the black dot (where we see continual build-up of M0 and decline of A0 without steady state). (C & D) Heatmap of the steady state concentration of M0 as a function of the total co-substrate pool size (Atot) and inflow flux (kin). White area shows the region where there is no steady state. On both panels, the dashed line indicates the limitation from the primary enzyme, kin<Vmax,E0, and the solid line indicates the limitation from co-substrate cycling, kin<AtotVmax,Ea/(KM,Ea+Atot). In panel (C), there is a range of Atot values for which the first limitation is more severe than the second. In contrast, in panel (D), the second limitation is always more severe than the first. In (B & C) the parameters used for the primary enzyme (for the reaction converting M0 into M1) are picked from within a physiological range (see Supplementary file 1) and are set to: Etot=0.01 mM, kcat=100/s, KM,E0=KM,Ea=50μM, while kout is set to 0.1/s. The Etot and kcat for the co-substrate cycling enzyme are 1.2 times those for the primary enzyme. In panel (D) the parameters are the same except for the Etot and kcat of the co-substrate cycling enzyme, which are set to 0.7 times those for the primary enzyme. Co-substrate cycling introduces a limitation on reaction flux To explore the effect of co-substrate cycling on pathway fluxes, we first consider a didactic case of a single reaction. This reaction converts an arbitrary metabolite M0 to M1 and involves co-substrate cycling (Figure 1A). For co-substrate cycling, we consider additional ‘background’ enzymatic reactions that are independent of M0 and can also convert the co-substrate (denoted Ea on Figure 1A). We use either irreversible or reversible enzyme dynamics to build an ordinary differential equation (ODE) kinetic model for this reaction system and solve for its steady states analytically (see Methods and Appendix 3). In the case of using irreversible enzyme kinetics, we obtain that the steady state concentration of the two metabolites, M0 and M1 (denoted as m0 and m1) are given by: (1) m0=α kinKM,E0(Vmax,E0−kin)(Vmax,EaAtot−kin(KM,Ea+Atot))m1=kinkout where kin and kout denote the rate of in-flux of M0, and out-flux of M1, either in-and-out of the cell or from other pathways, and Atot denotes the total pool size of the cycled metabolite (with the different forms of the cycled metabolite indicated as A0 and A1 in Figure 1A). The parameters Vmax,E0 and Vmax,Ea are the maximal rates (i.e. Vmax=kcatEtot) for the enzymes catalysing the conversion of A0 and M0 into A1 and M1 (enzyme E0), and the turnover of A1 into A0 (enzyme Ea), respectively, while the parameters KM,E0 and KM,Ea are the individual or combined Michaelis-Menten coefficients for these enzymes’ substrates (i.e. for A0 and M0 and A1, respectively). The term α is (in this case where all reactions are irreversible) equal to Vmax,Ea-kin, and in general is a positive expression comprising kin, and the Michaelis-Menten coefficients and the Vmax parameters of the background enzymes in the model (see Appendix 3, Equations 7; 9; 11). The steady states for the model with all enzymatic conversions being reversible, and for a model with degradation and synthesis of A0 and A1, are given in Appendix 3. The steady state solutions of these alternative models are structurally akin to (1), and do not alter the qualitative conclusions we make in what follows. A key property of (1) is that it contains terms in the denominator that involve a subtraction. The presence of these terms introduces a limit on the parameter values for the system to attain a positive steady state. Specifically, we obtain the following conditions for positive steady states to exist: (2) kin<Vmax,E0andkin<AtotVmax,EaKM,Ea+Atot. Additionally, the ‘shape’ of (1) indicates a ‘threshold effect’ on the steady state value of m0, where it would rise towards infinity as kin increases towards the lower one among the limits given in (2) (see Figure 1B). Why does (1) show this specific form, leading to these limits? We find that this is a direct consequence of the steady state condition, where metabolite production and consumption rates need to be the same at steady state. In the case of co-substrate cycling, the production rate of M0 is given by kin, while its consumption rate is a function of the Vmax,E0 and the concentration of A0. In turn, the concentration of A0 is determined by its re-generation rate (which is a function of KM,Ea and Vmax,Ea) and the pool size (Atot). This explains the inequalities given in (2) and shows that a cycled co-substrate creates the same type of limitation (mathematically speaking) on the flux of a reaction it is involved in, as that imposed by the enzyme catalysing that reaction (E0 in this example) (see Figure 1C & D). We also show that considering the system shown in Figure 1A as an enzymatic reaction without co-substrate cycling leads to only the constraint kin<Vmax,E0, while considering it as a non-enzymatic reaction with co-substrate cycling only, leads to only the constraint kin<AtotVmax,Ea/(KM,Ea+Atot) becoming the sole limitation on the system (see Appendix 3). In other words, the two limitations act independently. To conclude this section, we re-iterate its main result. The flux of a reaction involving co-substrate cycling is limited either by the kinetics of the primary enzyme mediating that reaction, or by the turnover rate of the co-substrate. The latter is determined by the co-substrate pool size and the kinetics of the enzyme(s) mediating its turnover. Co-substrate cycling causes a flux limit on linear metabolic pathways We next considered a generalised, linear pathway model with n+1 metabolites and arbitrary locations of reactions for co-substrate cycling, for example as seen in upper glycolysis (Appendix 1—figure 1A). In this model, we only consider intra-pathway metabolite cycling, i.e. the co-substrate is consumed and re-generated solely by the reactions of the pathway. Here, we show results for this model with 5 metabolites as an illustration (Figure 2A), while the general case is presented in Appendix Figure 2 Download asset Open asset Motif, time-series and for the linear pathway model with (A) Cartoon representation of a of reversible reactions with co-substrate cycling solely The co-substrate is considered to have two forms A0 and A1. (B) Heatmap of the steady state concentration of M0 as a function of the total metabolite pool size (Atot) and inflow rate constant (kin). White area shows the region where there is no steady state. The dashed and solid indicate the limitations from primary enzyme in this and co-substrate cycling, respectively, as in Figure (C) Concentrations of and A0/A1 ratio as a function of (with as indicated in the At the parameters are switched from the white dot in panel (B) (where a steady state exists) to the black dot (where we see build-up of all substrates that are produced the first co-substrate cycling reaction, and decline of The parameters used are picked from within a physiological range (see Supplementary file 1) and are set to: Etot=0.01 mM, kcat=100/s, for all reactions, and We find the same of threshold dynamics as in the single reaction kin is a threshold the metabolite M0 towards infinity and the system does not have a steady state (Figure A as well as our analytical that the of metabolites to all metabolites of the first reaction with co-substrate cycling (Figure and Appendix Additionally, metabolites downstream of the cycling reaction to a steady state level that does not on kin (Figure and Appendix In other words, pathway be increased by increasing kin the as kin the cycled metabolite pool shifts towards one form and the ratio of the two forms (Figure analytical expression for the threshold for kin, shown in could not be derived for linear pathways with but our analytical study indicates that the threshold is always linked to Atot and enzyme kinetic and the concentration of all metabolites to the reaction coupled to metabolite cycling will towards infinity as kin the threshold (see Appendix In Figure we these dynamics with for a system with We also considered several of this linear pathway model, corresponding to cases as shown in Appendix 1—figure These intra-pathway cycling of two different metabolites, as seen with ATP and NADH in combined upper glycolysis and pathways (Appendix different for consumption and re-generation reactions of the cycled as seen in upper glycolysis (Appendix and cycling of one metabolite with that of as seen in nitrogen assimilation (Appendix The results in the Appendices that all these cases threshold dynamics, where the threshold is a function of the co-substrate pool size and the enzyme metabolite related limit could be for specific reactions from central metabolism on flux values that are either experimentally measured or predicted by flux analysis many reactions from the central carbon metabolism of the model Escherichia coli are shown to have lower flux than expected from the kinetics of their enzymes (i.e. (Davidi et al., 2016). This finding is on Vmax from in vitro measured kcat values of specific enzymes and their in levels on studies in coli (see Materials and The flux and enzyme concentration data were from other studies which measured the in coli on media with carbon et al., 2016; Gerosa et al., 2015). we consider measured fluxes for each reaction as a for kin that these two would be equal at steady we can conclude from the fact that there were no observed in these reactions, as an for the analysed reactions fluxes the first limit identified in There could be several for this of measured fluxes being lower than the limit set by measured enzyme kinetics and simple could be that there is a between in vitro measured enzyme kinetics and in this can be but the lower flux could be because there are additional other than the enzymes mediating the main reaction. such additional limitation and are shown to explain observed lower fluxes in some reactions (Davidi et al., 2016; see also Here, we that the presented theory shows that an additional possible limitation could be the co-substrate pool size and turnover dynamics. To explore this we the flux values (Davidi et al., 2016; Gerosa et al., and focused solely on reactions that are linked to or pools (see Materials and methods and Supplementary file The resulting fluxes, and enzyme levels for different reactions determined under 7 different conditions with turnover and kinetic of the corresponding In we of values with data and with only flux We the flux values that would be expected from the primary enzyme limit identified under all conditions analysed (Figure and in addition the effect of the primary could explain the (Appendix We found that in both about of these reactions carry flux lower than what is expected from enzyme kinetics (Appendix suggesting that the limits imposed by dynamics might be constraining the flux The number of the cases where the flux the limit might be due to in measurement of enzyme or Figure 3 Download asset Open asset and flux values are lower than the primary enzyme (A) and flux values et al., 2016; Gerosa et al., the primary enzyme kinetic threshold of that there are 7 for each reaction, corresponding to the different conditions under which measurements or was (see Supplementary file 1 for with reaction and metabolites flux values under different conditions Gerosa et al., for reactions the corresponding co-substrate pool to show reactions for phosphoglycerate kinase dehydrogenase and dehydrogenase on these is a flux measurement under a different environmental condition, where the co-substrate pool size is also of flux and metabolite measurements as in the from Gerosa et al. co-substrate type and are as shown in the to panel show the linear with the corresponding shown in the panel It is also possible that observed lower fluxes are due to This is difficult to analyse without more as reaction of concentrations for all substrates and as well as enzyme Michaelis-Menten in both and This information is not available except for of the reactions among the we to as insight as possible on the we analysed the physiological energy (the is that all are at 1 and the flux – (Appendix 3). This shows that in such as dehydrogenase the flux to be by the the general is that there is between reaction flux and We have also the between fluxes and co-substrate pool Co-substrate pool sizes do change between different conditions, and we that such changes be due to flux changes in co-substrate on the other changes in pool size can affect flux in those reactions, where co-substrate dynamics is predicted by the For both measured and fluxes, we find that several reactions show between flux and co-substrate pool size (see Figure see also Appendix 1 and Appendix
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