Since changing oxygen levels affect the growth rate, but not the yield, points move vertically between the two conditions. The oxygen level directly affects the catalytic rate of oxidative phosphorylation reactions oxphos and sdh : lower oxygen levels require higher enzyme levels for compensation, to keep the fluxes unchanged.
The non-respiring EFM ana-lac shows an oxygen-independent growth rate. In all other focal EFMs, the growth rate increases with the oxygen level and saturates around 10 mM. The corresponding changes in enzyme allocation are shown in Figure 18 in S1 Text. For a closed approximation formula, see Section 4. The effect of external glucose levels can be studied similarly Figures 12 and 16 in S1 Text : at lower external glucose concentrations, the PTS transporter becomes less efficient and cells must increase its expression in order to maintain the flux.
This increases the total enzyme cost and slows down growth. Since the PTS transporter is the only glucose transporter in our model, it is used by all EFMs, leading to a universal monotonic relationship between glucose concentration and growth rate. The y-axis shows relative protein demands normalized to a sum of 1. The dashed line indicates the reference glucose level mM corresponding to the pie chart in panel a.
By varying the glucose and oxygen levels, we can screen a range of environmental conditions and obtain a two-dimensional Monod surface plot. The winning strategies, i.
More than 20 different EFMs achieve a maximal growth rate in at least one of the conditions scanned. To simplify the picture, we can focus on EFM features such as uptake rates and plot them on the Monod surface Fig 4 c —4 f. As expected, oxygen uptake Fig 4 d decreases when oxygen levels are low.
This pattern occurs across the entire range of glucose levels, but the transition—from full respiration to acetate overflow Fig 4 e and further to anaerobic lactate fermentation EFMs Fig 4 f —is shifted at lower glucose levels. Interestingly, this transition disappears at extremely low glucose concentrations 0. While glucose levels are relatively easy to adjust in experiments, it is difficult to measure oxygen levels in the local environment of exponentially growing cells.
This has resulted in a long-standing debate about the exact conditions that E. Our model predicts that at a constant level of [O 2 ], E. A similar shift from pure respiration to a mixture of respiration and acetate secretion has been observed in chemostat cultures [ 49 ], where higher glucose levels result from higher dilution rates. The choice of metabolic strategies does not only depend on external conditions, but also on enzyme parameters.
Not surprisingly, slowing down the enzyme decreases the growth rate see Figure 20 in S1 Text. But to what extent? Two of our focal EFMs max-gr and pareto are not affected at all, since they do not use the tpi reaction. All other focal EFMs show strongly reduced growth rates.
To study this systematically, we predicted the growth effects of all enzyme parameters in the model equilibrium constants, catalytic constants, Michaelis-Menten constants by computing the growth sensitivities, i. A sensitivity analysis between all model parameters and the growth rates of all EFMs or alternatively, their biomass-specific enzyme cost can be performed without running any additional optimizations Sections 4.
Growth sensitivities are informative for several reasons. On the one hand, parameters with a large impact on growth will be under strong selection where positive or negative sensitivities indicate a selection for larger or smaller parameter values, respectively. On the other hand, these are also the parameters that need to be known precisely for reliable growth predictions.
The parameters of a reaction can have very different effects on the growth rate. For example, the sensitivities of the k cat and K M values of pgi are low, but the growth rate is very sensitive to the K eq value. To study the effects of a gene deletion, we can simply discard all EFMs that use the affected reaction: based on a precalculated EFCM analysis of the full network, we can easily analyze the restricted network without any new optimization runs.
By switching off pathways, we can easily quantify the growth advantage they convey. Instead of studying pathways in isolation as in Flamholz et al. Fig 6 shows an analysis for two common variants of glycolysis, the high ATP yield, high enzyme demand EMP and the low ATP yield, low enzyme demand ED pathway, across different external glucose and oxygen levels see Section 3.
Same data as in Fig 4 c , but shown as a heatmap. The heatmap shows the relative growth advantage of the wild-type strain i. The ED pathway provides its highest advantage at low oxygen and medium to low glucose levels. Blue areas indicate conditions where ED is more favorable, and red areas indicate conditions where EMP would be favored.
The dark blue region at low oxygen and medium glucose levels may correspond to the environment of bacteria such as Z. The same data are shown as Monod surface plots in Figure 21 in S1 Text. Our case study on E. At high oxygen levels, growth-maximizing flux modes have an almost maximal yield and the Pareto front is very narrow. In contrast, under low-oxygen conditions the highest growth rates are obtained by low-yield strategies and a long Pareto front emerges Fig 4 a.
As shown in [ 9 ], wild-type cell populations might be far from the Pareto front, and a selection for fast growth may push the populations and individuals closer to it. It would be interesting to study whether these results are in fact dependent on oxygen availability. EFCM predicts which flux modes are likely to be used by well-adapted cells. We expected that the EFM with the highest growth rate max-gr , in the standard conditions chosen in this study would coincide with the experimentally determined flux mode exp in the same conditions.
Our model predicts a much higher maximal biomass yield than the yield measured in batch cultures However, for the experimentally determined flux mode exp , we overestimate the yield The overestimation of yield which depends on network structure, not on kinetics may be caused by the fact that our model misses some waste products or additional processes that dissipate energy, or that our high-yield EFMs are kinetically unfavorable in reality.
The underestimated growth rates may result from our simplistic conversion of enzyme costs into growth rates. However, we hope that these over- and underestimations occur consistently across EFMs and do not affect the qualitative results of this study. In contrast to the much simpler model by Basan et al. In our standard aerobic conditions see Fig 2 and Figure 14 h in S1 Text , the winning mode, max-gr , is completely respiratory and produces no fermentation products.
This misprediction may depend on several factors:. First, we may have underestimated the effective cost of oxidative phosphorylation oxphos , which becomes costly at lower oxygen levels, or we may have overestimated the oxygen availability. Moreover, the affinity of the reactions to oxygen is not precisley known, so even a precise value of the oxygen concentration would not suffice.
Second, the experimentally observed acetate production may result from additional, growth-rate dependent flux constraints like those employed by Basan et al. In our model, we did not impose any bounds on fluxes aside from normalizing the flux modes to unit per biomass production , and thus metabolic efficiency is maximized by an EFM. The growth rate does not even appear in the optimization. We account for it only later, when metabolic efficiency is translated into an achievable growth rate.
Thus, it is possible that we miss some physiological constraints such as membrane real-estate [ 52 ], changing biomass composition, or extracellular oxygen diffusion rates. Even without flux constraints, some EFMs mix respiration and acetate production, e. However, none of them corresponds exactly to the fluxes observed experimentally. Moreover, the measured relative rate of acetate production increases continuously with the growth rate, which cannot be captured by a single constant EFM.
A usage of flux constraints in EFCM would be possible and would allow us, for example, to limit certain fluxes or to enforce some minimal flux, e.
To screen all vertices of the flux polytope, one may build on the concept of elementary flux vectors [ 53 , 54 ]. However, the number of these vertices may become very large, and whenever flux bounds are changing e. Third, it is also possible that the experimentally observed acetate secretion is simply not optimal. In adaptive laboratory evolution experiments [ 36 , 37 ], the evolved strains grew about 1. Apparently, if acetate secretion is due to a glucose uptake constraint, this constraint can be bypassed by mutations and cells may be able to decrease acetate secretion while growing faster.
In a recent comparison of seven E. Two of these fully respiring strains grew just as fast as the evolved strains from the adaptive evolution studies about 1. Some variants of FBA manage to predict flux distributions with a suboptimal biomass yield by putting bounds on enzyme investments. However, these methods are insensitive to environmental conditions: the crowding coefficients assigned to reactions are constants, and metabolite concentrations are not considered at all. In this approximation, the constraints are exactly like in FBAwMC, except that the crowding coefficients of exchange reactions are divided by saturation values.
The saturation values, numbers between 0 and 1, account for the concentrations of external metabolites such as glucose and oxygen. However, satFBA assumes that transport reactions are the only reactions affected by metabolite levels, whereas EFCM models the interplay between metabolite levels, enzyme efficiencies, and enzyme investments in all enzymatic reactions. Constraint-based whole-cell models such as Resource Balance Analysis RBA [ 56 , 57 ] or ME-models [ 58 ] treat protein production as a part of the cellular network and couple metabolic rates to production rates of the catalyzing enzymes.
These methods differ from EFCM in three main ways: in the modeling of protein production, of catalytic rates, and of biomass composition and enzyme cost weights. This capacity utilization lower than 1 depends on metabolite levels and is quantified by the efficiency factors of ECM [ 34 ].
These values, for different enzymes, span almost the entire range between 0 and 1 see Figure 11 in S1 Text. In a linearized variant of EFCM that assumes full capacity utilization, the growth rate would be overestimated and the growth differences between EFMs would be distorted.
In fact, our predicted enzyme cost is between 1. RBA avoids this problem by replacing the k cat values by empirically determined, growth-rate dependent apparent catalytic rates. Again, these options would be hard to implement in EFCM because biomass composition is a defining part of the stoichiometric model, and any growth-rate dependent changes in biomass composition would also change the set of EFMs.
Although efficient protein allocation may be important for fast growth [ 63 ], there is empirical evidence that cells do not always minimize enzyme cost. Lactococcus lactis , for example, can undergo a metabolic switch that leads to big changes in growth rate, but involves no changes in protein levels [ 64 ]. These cells could, in theory, save enzyme resources while maintaining the same metabolic fluxes, but do not do so—possibly because their enzyme levels provide other benefits, e.
By considering secondary objectives, e. Our study has demonstrated that enzyme kinetics is a useful addition to constraint-based flux prediction see Section 1. As long as in vivo kinetic constants are not precisely known, this harbours the risk of mispredictions. Curiously, for example, the EFMs with the highest predicted growth rates bypass upper glycolysis and use the pentose phosphate pathway instead.
On the contrary, an ab initio approach allows modelers to recover empirical laws directly from cell biological knowledge, for example, the shape of Monod curves and Monod surfaces see Figure 15 and Section 4. It allows us to compute quantitative effects of allosteric regulation or mutated enzymes see Figure 2 in S1 Text , the residual glucose concentration in chemostats see Figure 15 in S1 Text , and the trade-offs between metabolic strategies at different glucose levels see Figure 19 in S1 Text.
The decomposition into EFMs also greatly facilitates calculating the epistatic interactions between reaction knockouts see Figure 2 f in S1 Text. Although yield-related epistatic interactions were previously computed using FBA see Section 3. EFCM could be applied to larger models and models with flux constraints, and other cost functions could be implemented see Section 1. As a fully mechanistic method, it puts existing biochemical models and ideas about resource allocation to test and enables us to address fundamental issues of unicellular growth and cell metabolism, such as the trade-off between growth rate and biomass yield.
A metabolic state is characterized by cellular enzyme levels, metabolite levels, and fluxes. All these variables are coupled by rate laws, which depend on external conditions and enzyme kinetics. The EFCM algorithm finds optimal metabolic states in the following way. First, we enumerate the elementary flux modes of a network, which constitute the set of potentially growth-optimal flux modes. Then we consider a specific simulation scenario, defined by kinetic constants and external metabolite levels, and compute the growth rates for all EFMs.
To determine the optimal metabolic state—a state expected to evolve in a selection for fast growth—we choose the EFM with the highest growth rate. The optimal state v , c , E can be found efficiently by a nested screening procedure Fig 1 b and 1 c. ECM has recently been applied to a similar model of E. It assumes a given flux distribution in our case, an EFM and treats the enzyme concentrations as explicit functions of substrate and product levels and fluxes.
Given a flux mode v , we consider all feasible possible metabolite profiles ln c , consistent with the flux directions and respecting predefined bounds on metabolite levels. As a function of the logarithmic metabolite levels, E met is convex; this allows us to find the global minimum efficiently.
In the model, we use common modular rate laws [ 39 ], for which the enzymatic cost in log-metabolite space is strictly convex Joost Hulshof, personal communication. The optimized enzyme cost is a concave function in flux space [ 30 — 32 ]. This combination of convexity and concavity allows for a fast optimization of enzyme levels and fluxes for each condition and set of kinetic parameters.
The NEOS Server is available free of charge and offers a variety of interfaces for accessing the solvers, which run on distributed high-performance machines enabled by the HTCondor software. Using our online service, users can run EFCM for their own models, using different rate laws.
With our E. Details can be found in Section 1. Following the approach of Scott et al. The link between biomass production, total enzyme mass concentration, and growth rate can also be understood through the cell doubling time. We first define the enzyme doubling time , the doubling time of a hypothetical cell consisting only of core metabolism enzymes. Since E. Furthermore, this fraction decreases with the doubling time, as seen in experiments [ 67 ] and as expected from trade-offs between metabolic enzymes and ribosome investment [ 66 ].
This leads to a constant offset in the final cell doubling time formula: 3. The calculation of sensitivities between enzyme parameters and growth rate is based on the following reasoning. If a parameter change slows down a reaction rate, this change can be compensated by increasing the enzyme level in the same reaction while keeping all metabolite levels and fluxes unchanged. For example, when a catalytic constant changes by a factor of 0. Instead of adapting only one enzyme, the cell may save some costs by adjusting all enzyme and metabolite levels in a coordinated fashion.
These markers help separate whether or not the injury is to the liver parenchyma liver cells or to the biliary system. For the purposes of this article, the important tests are the liver aminotransferases: alanine aminotransferase ALT and aspartate aminotransferase AST.
ALT is primarily produced by the liver, while AST can be from the liver, cardiac muscle, skeletal muscle, kidney, and brain. These reference ranges vary from hospital to hospital. The test is a routine blood test that takes place in a laboratory. No fasting or special preparation is necessary. But tell your doctor before the test about all prescription and OTC medications and supplements you take. Your arm may be sore at the puncture site, and you might have some mild bruising or brief throbbing.
Most people have no serious or lasting side effects from a blood test. Rare complications include:. Abnormal test results can indicate a variety of problems from disease to a simple muscle strain because enzymes are present in every cell of your body.
The CPK isoenzymes test is a way to measure the levels of the enzyme creatine phosphokinase in your bloodstream. This enzyme is important for muscle…. If your doctor suspects that you've recently had a heart attack, you may be given a cardiac enzyme test.
Find out what it measures, what it means, and…. The protein troponin is released in the blood after you have a heart attack. Learn about the troponin test, other causes of high troponin levels, and…. If you have ascites, you have fluid in the space between the abdominal lining and the organs. An alkaline phosphatase level test can help identify health concerns in your liver, gallbladder, and more.
The liver is a powerhouse organ, performing a variety of tasks that are essential to maintaining good health. Eat these 11 foods for optimal liver…. Lifestyle changes can help reduce your risk for fatty liver disease and damage. Learn what 10 foods you should eat and what 6 foods to avoid. Edelmann , and Matthew K. Biochemistry , 52 43 , Little , Heather Griffiths , P. Lynne Howell , and Mark Nitz.
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