Flux coupling analysis (FCA) is a useful method for finding dependencies between fluxes of a metabolic network at steady-state. FCA classifies reactions into subsets  in which activity of one reaction implies activity of another reaction. Several approaches for FCA have been proposed in the literature.We introduce a new FCA algorithm, FFCA , which is based on checking the feasibility of a system of linear inequalities. We show on a set of benchmarks that for genome-scale networks FFCA is faster than other existing FCA methods.http://www.bioinformatics.org/ffca/.We present FFCA as a new method for flux coupling analysis and prove it to be faster than existing approaches. A corresponding software tool is freely available for non-commercial use at  Constraint-based analysis of metabolic networks has become increasingly important for describing and predicting the behavior of living organisms ,2. WhileFlux coupling analysis (FCA)  is a useIn the rest of this section, we first recall some basic definitions. Then we briefly review the previously proposed FCA methods.m  metabolites and n reactions, the stoichiometric matrix S is an m × n matrix, where element ij Sis the stoichiometric coefficient of metabolite i in reaction j. We denote by R = {1, ..., n} the set of reactions and by M = {1, ..., m} the set of metabolites.For a metabolic network with Irr is the set of irreversible reactions which are assumed to always have non-negative flux values. Rev is the set of reversible reactions which are allowed to have positive, negative or zero flux values. If a reversible reaction has a positive (resp. negative) flux, we say that it is working in forward (resp. backward) direction. Splitting a reversible reaction i means making reaction i irreversible and adding one more irreversible reaction i + n to the network, which works in the backward direction. Without loss of generality, we assume that in the numbering of reactions, the first |Rev| reactions are the reversible ones.There are two types of reactions in a metabolic network. v is the vector of metabolic fluxes through all the reactions, the steady-state condition holds for v if S · v = 0. The steady-state flux cone is defined as C = {v ∈ ℝn | S · v = 0, i ≥v0, for all i ∈ Irr}. The lineality space of C is given by lin.space(C) = {v ∈ ℝn | S · v = 0, i v= 0, for all i ∈ Irr}.If r ∈ R, r v= 0 for all v ∈ C, then r is called blocked, otherwise r is unblocked. The set of blocked reactions will be denoted by Blk. The set of unblocked reactions can be further partitioned based on the reversibility type of reactions [Irev as the set of all reactions that can work only in one direction, i.e., those reactions that take only non-negative or only non-positive flux values at steady-state. If i ∈ Irev and i v≤ 0 for all v ∈ C, one can multiply by -1 the i-th column of the stoichiometric matrix, such that in the modified network, we have i v≥ 0 for all v ∈ C. Without loss of generality, we assume that all reactions in Irev are operating in the forward direction.If for some reaction eactions . We defia) Prev, the set of pseudo-irreversible reactions, and (b) Frev, the set of fully reversible reactions. A reaction i is in Prev if it can work in both directions, and additionally, for all flux vectors v in the lineality space of the flux cone, we have i v= 0. Accordingly, we define Frev as the set of those reactions, which can work in both directions, and additionally, can have a non-zero flux value if fluxes through all irreversible reactions are set to zero.The set of reactions that can work in both directions at steady-state is further partitioned into two subsets:  = {i ∈ R | i v≠ 0} of reactions active in v is called the support of v. Suppose v ∈ C is a flux vector and A ⊆ R is a subnetwork. The flux pattern of v for A is defined as A ∩ supp(v), which is the set of those reactions in A which have non-zero values in v[elementary flux pattern (EFP) if it cannot be written as the union of other flux patterns. For studying EFPs, Kaleta et al. [The set lues in v. A flux a et al.  assume tIn this subsection, we briefly recall existing approaches to flux coupling analysis. For additional information and the technical details on the implementation of these algorithms, we refer to Additional file i and j, two LPs are solved. Depending on the optimal values obtained, the coupling relation between i and j is determined. There is a post-processing step in FCF. Since the reversible reactions have been split, flux coupling relations for these reactions have to be obtained from the coupling relations of the corresponding irreversible forward and backward reactions.The most widely used method for FCA is the Flux Coupling Finder (FCF) algorithm . This apThe FCF algorithm has been successfully used for finding coupling relations in a number of metabolic networks -13,16. HLarhlimi and Bockmayr ,17 have i and j. If each of these reactions can have a non-zero flux independently of the other  that i is directionally coupled to j, then the EFPs of this subnetwork are {i, j} and {j}. Finally, if the reactions are partially coupled, we will have only one EFP, which is {i, j}. With this method, it is not possible to distinguish between partial and full coupling, since flux patterns only contain the information about the activity or inactivity of the fluxes, but not the flux values.Recently, Kaleta et al.  introducIn FCF, and some other FCA approaches, every reversible reaction is split into a forward and a backward reaction. This splitting procedure results in an increase in the number of LPs and also in the size of each LP to be solved. Moreover, a complicated postprocessing step is required to infer the flux coupling relations of the original reversible reactions. For all these reasons, it might be better to perform flux coupling analysis without splitting the reversible reactions. An implementation of FCF without splitting is presented in Additional file i and j can be coupled only if one of the following 4 cases holds  would be possible):Additionally, Larhlimi and Bockmayr  show thai, j ∈ Irev: In this case, i and j can be directionally, partially or fully coupled.1. i ∈ Irev and j ∈ Prev: The only possibility is j → i.2. i, j ∈ Prev: In this case, we can only have i ⇔ j.3. i, j ∈ Frev: In this case, we can only have i ⇔ j.4. i and j, and then check if the corresponding coupling relation holds. This will be referred to as "Reversibility-Type prunings" . RT-prunings were originally used in MMB-FCA as presented in [Therefore, it is enough to determine the reversibility types of ented in .S, the columns corresponding to the blocked reactions have been removed. According to Proposition 6.13 in [i and j such that i, j ∈ Prev or i, j ∈ Frev, the following two statements are equivalent:After RT-prunings, a further improvement can be applied to LP-based FCA methods. Assume that in the stoichiomtric matrix  6.13 in , for two• i ⇔ j• For all v such that Sv = 0, i v= 0 implies j v= 0.This means that it is sufficient to solve only one LP:i and j will be fully coupled if and only if in the above LP Prev/Frev-based improvement .The two reactions An improved version of FCF, which takes into account all of the above-mentioned improvements, has been suggested in . Here weFCA is a promising tool for metabolic network analysis. However, to perform FCA most authors seem to use their personal implementation of the FCF algorithm ,13. Onlymaximize(T x c| Ax ≤ b) can be solved by enumerating a sequence of feasible solutions, i.e., solutions of the system of linear inequalities Ax ≤ b such that at each solution x the objective function value T x cimproves. Accordingly, finding one feasible solution could be faster than computing an optimal solution . If (P1) and (P2) are both infeasible, then i and j are partially (and maybe fully) coupled. To check whether they are fully coupled, one has to use other methods, e.g. computing enzyme subsets [If (P1) and (P2) are both feasible, then  subsets  or solvi subsets .i ∈ Irev and j ∈ Prev: The only possible coupling relation is j → i (but not i → j). Hence, (P1) will always be feasible, because feasibility of (P1) means that i → j does not hold. However, we need to check the feasibility of (P2). Additionally, since j can take negative values, one more system should be checked for feasibility:2. j → i. Otherwise, i and j are uncoupled.It can be easily shown that if (P2) and (P3) are both infeasible, then i, j ∈ Prev or i, j ∈ Frev: In this case, the following system of linear inequalities should be checked for feasibility:3. i ⇔ j (because feasibility of (P4) implies j → i, which in turn implies i ⇔ j based on Proposition 2 in [i and j are uncoupled.If (P4) is infeasible, then ion 2 in ). If , one can solve the following LP:i vis constant, the optimal value exists if and only if this problem is feasible. Similar LPs can be solved to check the feasibility of (P2) and (P3).Since In Table H. pylori network and especially for the large networks of S. cerevisiae and E. coli, FFCA proves to be faster than MMB-FCA. The computation time required for MMB-FCA rapidly grows when the number of reactions increases. This is due to the possibly exponential size of the set of generating vectors which has to be computed before finding the coupled reactions . EFP-FCBoth the FCF algorithm and the current implementation of FFCA solve LPs for flux coupling analysis. One might ask why FFCA is faster than the classical FCF method. There are at least five major differences between FCF and FFCA:• When an LP is solved in FFCA, finding the first feasible solution is sufficient, while the LPs should be solved to optimality in case of the FCF algorithm.• In the FCF method, in contrast to FFCA, every reversible reaction is split into two (forward and backward) irreversible reactions. This step slows down the procedure and increases the size of the LPs to be solved.• For computing the flux coupling relation between any pair of reactions, we always need two LPs in FFCA, while in FCF sometimes more LPs have to be solved. For example, for computing the coupling relation between an irreversible and a reversible reaction (after splitting), four LPs are solved  FCF was re-implemented without splitting reactions (W-FCF); (ii) FCF was re-implemented without splitting reactions and with the RT-prunings (WR-FCF); and (iii) FCF was re-implemented without splitting reactions and with the RT-prunings and the PF-improvement (WRP-FCF), as suggested in [One can think of implementing FCF without splitting reversible reactions and/or with the RT-prunings and/or PF-improvement. In order to assess the importance of these issues, three improved versions of FCF were implemented  FCA hasE. coli [E. coli [Since FFCA includes the RT-prunings and PF-improvement, it might be interesting to see how the number of coupling relations  depends on the number of reversible reactions in a network. This problem is studied in Additional file E. coli , for the[E. coli   genome-scale metabolic network [E. coli (iJR904) [E. coli (iAF1260) [Nine metabolic networks were used in this study: (i) ork from ; (ii) RBood cell ; (iii) E E. coli ; (iv) H. network ; (v) yea network ; (vi) th(iJR904) ; (vii) tiAF1260) ; (viii) iAF1260) ; and (ixiAF1260) .For FCA, all uptake reactions were assumed to be able to carry non-zero fluxes.Unless indicated otherwise, all tools were implemented in Matlab v7.4. Details about the implementation of the different FCA approaches, together with the corresponding pseudo-codes are presented in Additional file All computations were performed on a 64-bit Debian Linux system with Intel Xeon 3.0 GHz processor. The running times include the CPU time for preprocessing, computation of flux coupling relations, and post-processing (where necessary).Prev/Frev-based improvement.FCA: Flux Coupling Analysis; FFCA: Feasibility-based Flux Coupling Analysis; FCF: Flux Coupling Finder; MMB-FCA: Flux Coupling Analysis based on Minimal Metabolic Behaviors; EFP-FCA: Flux Coupling Analysis based on Elementary Flux Patterns; LP: Linear Program; MILP: Mixed-Integer Linear Program; RT-prunings: Reversibility-Type prunings; PF-improvement: The authors declare that they have no competing interests.SAM, LD and AB presented the original idea of the work and designed the study. AL and LD introduced the improved versions of FCF. BM and LD implemented the tools and carried out the experiments. The manuscript was first drafted by SAM. The final manuscript was approved by all authors.Different approaches to flux coupling analysis and implementation details. In this file, pseudocodes and implementation details of different FCA methods are presented.Click here for fileDependence of flux coupling analysis on the number of reversible reactions. In this file, we show how flux coupling relations depend on the number of reversible reactions in the E. coli metabolic network.Click here for file


Results of extensive experiments on different genome-scale metabolic networks show that optGpSampler is up to 40 times faster than gpSampler. Application of existing convergence diagnostics on small network reconstructions indicate that optGpSampler converges roughly ten times faster than gpSampler towards similar sampling distributions. For networks of higher dimension (i.e. containing more than 500 reactions), we observed significantly better convergence of optGpSampler and a large deviation between the samples generated by the two algorithms. Availability:optGpSampler for Matlab and Python is available for non-commercial use at: http://cs.ru.nl/~wmegchel/optGpSampler/.Constraint-based models of metabolic networks are typically underdetermined, because they contain more reactions than metabolites. Therefore the solutions to this system do not consist of unique flux rates for each reaction, but rather a space of possible flux rates. By uniformly sampling this space, an estimated probability distribution for each reaction’s flux in the network can be obtained. However, sampling a high dimensional network is time-consuming. Furthermore, the constraints imposed on the network give rise to an irregularly shaped solution space. Therefore more tailored, efficient sampling methods are needed. We propose an efficient sampling algorithm (called  Modelling metabolic networks helps to unravel the complex machinery of metabolism within the cell. A classic approach is to model the reaction pathways in a dynamic fashion, using detailed kinetic data. For genome-scale models, often involving hundreds or thousands of reactions and metabolites, it is experimentally prohibitive to obtain the kinetic parameters involved. A constraint-based approach has successfully been applied to model and address a wide range of biological questions in the absence of detailed kinetic data where Many constraint-based methods have been proposed to find flux distributions that are of biological interest. A successful approach is Flux Balance Analysis (FBA) hit-and-run (HR) gpSampler is often used to sample metabolic networks and implemented in the COnstrained Based Reconstruction and Analysis (COBRA) Toolbox In order to obtain an estimated probability distribution of attainable flux values for each reaction in the network, methods based on uniform sampling are used. A fast algorithm for this task is called gpSampler; (2) we propose a new measure to quantify the deviation between samples obtained from two independent sampling runs; (3) we perform a thorough analysis on five metabolic network models.Therefore in this paper we investigate uniform random sampling in the context of metabolic networks. Our contributions are threefold: (1) we introduce an efficient and effective random sampling algorithm which combines the advantages of ACHR and rejection sampling technique One of the first attempts to sample the flux states in a metabolic network used a hit-and-run (HR) algorithm The In general, the constraints in metabolic network models lead to a convex space of irregular shape which is elongated for reactions whose flux rates are loosely constrained, and is narrow for tightly constrained fluxes. A consequence of this phenomenon is that many sample points are close to the boundary of the solution space. Since HR chooses a direction warm-up phase an arbitrary initial point sampling phase starts from warm-up and the main sampling phase of ACHR.ACHR The sequence of ACHR iterates is not a Markov chain, due to the dependence of directions on prior iterates. Thus the sequence of iterates is not guaranteed to converge to a uniform distribution gpSamplergpSampler works. The highly irregular shape of the solution space of metabolic networks makes a uniform direction choice on gpSampler’s warm-up phase uses linear programming in a two parts procedure. In part (1) gpSampler uses a linear transformation to ‘pull’ the warm-up points more into the interior of the solution space. Then, each moved warm-up point is used in the main sampling phase to generate step count parameter ACHR is at the core of gpSampler and ACHR. The resulting algorithm is called optGpSampler  and inequality (2) often lead to the same or a similar optimal solution. This could bias the starting points and directions choice of our sampler.We propose to combine a part of the warm-up phase of optGpSampler is similar to that of ACHR , producing For each reaction Compute the mean chain of the Our assumption is that chains generated by sampler Our choice to use a mean deviation over the standard deviation is motivated by the fact that the mean deviation is more efficient than the standard deviation in the realistic situation where some of the measurements are in error, and more efficient for distributions other than perfect normal xy-deviation over Then the xy-deviation indicate convergence of gpSampler implementation in the COBRA Toolbox. Results of extensive experiments are given in supplementary material. Tables S1–S5 in We used the gpSampler and optGpSampler were executed in parallel mode on an AMD desktop computer using optGpSampler is roughly 6 to 40 times faster than gpSampler.We sampled all networks four times using To asses the quality of the results, we performed four independent runs with each sampler. Each run collected gpSampler and optGpSampler was assessed by applying the Wilcoxon signed-rank test to the corresponding vectors. The results for the Gelman and Rubin test indicated convergence for all experiments, in disagreement with results of the Geweke and HW tests.We ran all convergence diagnostics with the default settings in the CODA package. The convergence tests results were averaged over the four runs. A univariate test for a sampler outputs a vector of length The obtained chains were also used to compute the E. coli central metabolism network, the Geweke test returned relatively low z-values for both gpSampler and optGpSampler . We compared the runtimes with those of gpSampler, and showed its superior efficiency. We investigated empirical convergence using different diagnostics and showed faster convergence of optGpSampler on the two smaller networks studied. Moreover, by using the here introduced optGpSampler using a small step count are close to those obtained with a high step count by both optGpSampler and gpSampler.We proposed a new algorithm for uniform sampling of the steady-state solution space of metabolic networks. Our algorithm also implements ACHR, but in a different manner than the state-of-the-art sampling method for metabolic networks Click here for additional data file.


One of the challenging tasks in systems biology is to understand how molecular networks give rise to emergent functionality and whether universal design principles apply to molecular networks. To achieve this, the biophysical, evolutionary and physiological constraints that act on those networks need to be identified in addition to the characterisation of the molecular components and interactions. Then, the cellular “task” of the network—its function—should be identified. A network contributes to organismal fitness through its function. The premise is that the same functions are often implemented in different organisms by the same type of network; hence, the concept of design principles. In biology, due to the strong forces of selective pressure and natural selection, network functions can often be understood as the outcome of fitness optimisation. The hypothesis of fitness optimisation to understand the design of a network has proven to be a powerful strategy. Here, we outline the use of several optimisation principles applied to biological networks, with an emphasis on metabolic regulatory networks. We discuss the different objective functions and constraints that are considered and the kind of understanding that they provide.  The availability of genome-wide datasets is increasing rapidly. Surprisingly, more data does not, per se, lead to better understanding. In other words, a mechanistic understanding of biological networks that are used to generate these datasets is lacking behind. One reason for being so is the emergent behaviour that arises from the interactions within these networks. Consequently, the systemic consequences of molecular perturbations cannot be predicted, nor does it lay bare the molecular mechanisms leading to cellular behaviour. Systems biology develops methodology to overcome these limitations and supplements molecular cell biology. Systems biology aims to understand the (dys-) function of living organisms by studying the dynamics of molecular networks; effectively by answering how molecular interactions give rise to cellular behaviour ,2,3. i.e., how they are regulated and why, is less well understood [To achieve understanding of the function of a molecular network and how this results from molecular interactions requires the identification of the molecular make-up as an obvious first (and important) step. This often involves whole-genome sequencing, additional biochemical knowledge (“legacy data”) and experiments. Such approaches have led to the determination of the topology of metabolic networks for a great number of organisms ,5. Yet, derstood . This prhow activities or components are affected by environments. Yet, a very different question is why this particular behaviour is there in the first place. Is it possible to understand the design principles of MRNs? We think we can, and we think that such understanding will help in finding the generic biological structures underlying the piles of data that are being gathered with todays technologies. The activity of metabolic networks results in a complex manner from internal constraints  and the interplay between environment and the impact of the associated signalling and gene network. Together these networks form, what we will call, the metabolic regulatory network MRN, . This coetc. When one studies a biological design, the reverse approach is required. The function—arising from the “specs”—and the relevant constraints need to be identified. When a similar function occurs across organisms or networks and when those are achieved by similar networks, a design principle is found. In other words, a design principle can be seen as the mechanism for network functions that have proven to be successful in evolution. Such principles likely have emerged as the outcome of similar selective pressures. Thus, in biology, it makes sense to identify design principles as the result of an optimisation process of (a determinant of) fitness. The outcome of an optimisation of a given fitness measure and/or a given set of constraints is then taken as a hypothesis that can either be falsified or verified [Figuring out the design principles of a MRN compares to a reverse engineering strategy. In order to design a certain device, an engineer needs a system specification saying what the system should do—what its function is—and all the relevant constraints should be considered, e.g. the production costs, life-time of the device, verified . This prWe thus start from the fact that adaptations are an inherent property of all living organisms, which is to be explained by natural selection. However, that does not mean that the adaptations are always perfect, nor that fitness is always optimal, only that fitness changes in a direction of increase. Thus, we try to gain insight by studying specific examples of adaptation, in the light of natural selection and historical interactions and constraints , which is in the end achieved through adaptations . Robustness is a fundamental property of biological systems ,34,35,36Escherichia coli. The signalling network in bacteria responsible for chemotaxis has served as a classical example for understanding how functions at the network level emerge from interactions between constituent molecular components. In this network, as shown in et al. [x represents the methylation state of the receptors. The difference between output (y1) and a reference value (y0) represents the error. Integral control arises through the feedback loop in which the integrated error is fed back into the system, leading to perfect adaptation. A recent computational search of all possible three-node networks which are able to perform perfect adaptation confirmed this observation [Cells often achieve robustness through feedback circuitry or the activity of a signalling network, which sense environmental changes and induce compensatory or adaptive responses. Many characteristics of signalling modules have been studied by analysing their input-output relationship. A feature displayed by several signalling modules is perfect adaptation. Arguably the best studied module for perfect adaptation is bacterial chemotaxis in n et al. . In an en et al. ,42,43. Tervation . Perfect adaptation was also experimentally demonstrated in the regulation of osmotic shock in yeast . By meanIn contrast to perfect adaptation, another observed adaptive response is fold change detection (FCD) ,49,50. IWhat are the advantages of FCD? It is postulated that having a FCD (i) ensures an adequate response towards an activator that is known to naturally vary up to many folds and (ii) the ability to maintain sensitive despite noise in the input signal  see als. The latgal operon in E. coli: external galactose is transported into the cell by a permease . Internal galactose  binds to gal isorepressor , which negatively regulates the gal operon. External glucose inhibits production of cAMP which, when bound to protein Crp, acts as an activator of the gal operon. I1-FFL speeds up a response (indicated by the red dots) and generates a pulse upon stimulation compared to simple regulation  that are integrated by Z. Upon an increase in X, Z is rapidly increased, but after some time, Y builds up and starts to decrease Z again. As a result, initially Z rises rapidly, and then its concentration drops again, leading to pulse-like dynamics. An example of this motif can be found in the gulation B. The acdynamics . The molecules that make up biological networks are continuously synthesised and degraded, where the latter process results from intrinsic degradation and/or via dilution due to cell growth. Synthesis and degradation rates should be balanced to maintain a molecular species at a constant level over time. Due to the inevitable asynchrony in the individual synthesis and degradation events, fluctuations in molecule numbers are such that transient deviations from the steady state level occur. Those fluctuations occur in single cells and remain invisible when populations of cells are studied. When single cells were studied it became clear that molecular species, which occur in small numbers, such as transcription factors, can display large fluctuations—“noise”; the coefficient of variation (defined as the ratio of the standard deviation to the mean) ranges in 25%–40%. Even though such fluctuations are transient, they do cause alterations in network function because they induce variable protein expression levels. In this manner, fluctuations in molecular species can lead to phenotypic differences between genetically identical cells living in a homogeneous environment ,54. In det al. [In many cases, molecular regulatory networks are inevitably distorted by noise—although it remains to be shown how much of a reduction in fitness it actually causes. One situation where noise can cause a reduction in cellular performance is when it occurs in signalling networks. Such systems respond to environmental changes and show changes in their output, e.g., a transcription factor, upon a change in external signal level. But, if the components of the signalling network spontaneously fluctuate in their level and their activation state, these systems can show changes in their output even at a constant signal level: this is when they make an error. This effectively reduces the capacity of cells to distinguish alternative environmental states. The number of distinguishable states can be related to the characteristic size of the change in the output level due to changes in the signal level divided by the size of the output change induced by spontaneous fluctuations at a fixed signal level. This measure thus compares the level of desired signal to the level of background noise and is called the signal-to-noise ratio; a central concept in information theory . Recentlet al.  determinet al.  show simBacillus subtilis upon sudden stress conditions [B. subtilis but also in other cells. The design principle here is that a bistable network is used that can switch between states due to spontaneous fluctuations in the levels of its molecular components  supplied directly into the medium. One might predict that, under such conditions, the trait of excreting the protease will be selected for; after all, excretion of the protease lead to more free peptides that are needed for cellular growth. However, since the proteases are excreted extracellularly, the peptides produced do not merely benefit the cell secreting the protease, but in part also diffuse away from it, becoming accessible to neighbouring cells. Imagine the scenario where one cell does not excrete the protease. This “cheater” cell does not have the burden of production and excretion, but is still able to take up free peptides. On the long term, this cheater can thus, on average, generate more offspring leading to an increase in the protease-negative trait. Ultimately, the trait can completely disappear in a population, as was shown experimentally [Optimisation of organismal fitness is not always as straightforward as discussed so far. This has to do with the fact that optimal biological traits or designs should also be evolutionary stable. Excretion of extracellular proteins is such an intriguing trait. Let us take the excretion of extracellular protease by the lactic acid bacterium, mentally . Similarmentally . These tmentally . In concet al. to propose a self-replicating model of a cell that is composed of a minimal set of required modules, such as a module for the ribosomes, metabolic pathways, substrate transporters and lipid biosynthesis [Cellular behaviour is governed by interacting networks. How is it possible to explain a global cellular property, such as the growth rate, if one studies only a sub-part of the network? This question inspired Molenaar ynthesis . The essE. coli is maximal at the wild type level of ATPase expression, indicating that in E. coli—for the enzymes considered—protein levels are fine-tuned to result in the highest growth rate. Similar results have been described for glycolytic enzymes in L. lactis [las operon [Experiments in which enzyme levels were titrated using inducible promoters provide indirect but compelling evidence that microorganisms optimally tune enzyme levels ,73,74. I. lactis ,76 as wes operon . In addis operon , by means operon , also cos operon ,18,19. Dlac operon in E. coli, these authors were able to experimentally measure the cost and benefit of protein expression of β-galactosidase (LacZ), which hydrolyses lactose into glucose. While increasing the expression level of this enzyme will increase the cost, the benefit of its activity will increase with increasing lactose concentrations. Cost and benefit were measured by the effect of different protein expression levels on the growth rate at different lactose concentrations. The optimal expression level—that is, where the difference between benefit and cost is maximal—was measured for different lactose concentrations. Interestingly, a serial propagation evolution experiment, at different lactose concentrations, revealed that cells adapt their protein expression level to the predicted optimal level (within a few hundred generations) [Above examples show that mutations affecting the amount of protein expressed are an adaptive mechanism to deal with changing environments and thus a target for selective pressure to act on. However, these observations do not provide an explanation in terms of the underlying design principle. This was provided by Dekel and Alon, who proposed a quantitative model in terms of the underlying costs and benefit of protein expression . Using trations) . This inE. coli strains, and showed that the lac permease (LacY) activity is a major physiological source of expression costs in the lac operon [lac operon. In light of the regulatory network of the operon, these results signify mechanisms that minimise the physiological costs of LacY activity, such as the direct inactivation of LacY function in the presence of glucose and other carbon sources, known as inducer exclusion. Additionally, Eames and Kortemme recently presented an approach to perturb the production, function and folding efficiency in redesigned c operon . The coslac operon [E. coli, the authors were able to explain the shape of the gene regulation function in terms of underlying regulatory mechanisms. For example, the steep shape of the regulation function at intermediate lactose levels is suggested to optimally minimise the effects of noise in an environment with a bimodal distribution of lactose concentrations. The concept of a cost-benefit optimisation has also been applied to explain gene regulation functions  of the c operon . Startinlac operon kinetics for E. coli. In order to make such an analysis applicable to metabolic pathways, we recently presented generalised definitions for cost and benefit . We propose quantitative and intuitive concepts for cost and benefit of enzymes in a metabolic pathway, and calculate these from kinetic and biochemical data, under the assumption that fitness increases with pathway flux. To test our predictions, a laboratory evolution experiment with Saccharomyces cerevisiae, propagated on galactose, under growth rate selection, was performed. Interestingly, the experimental data agree with the model predictions by showing that a high increase of growth rate is attained by increasing phosphoglucomutase levels, as observed previously as well [The definitions for cost and benefit as initially coined by Dekel and Alon  were exp as well ,82. The why and how questions might be a step towards obtaining a better understanding of the regulation of MRNs. Recently we have proposed such a method: feasibility analysis [The regulation of metabolic networks is the net result of the interplay between modulation of enzyme levels   and a (sub-) set of these samples is selected according to an objective function or multiple objective functions. Thus, feasibility analysis allows for  discrimination between different modes of metabolic regulation, and evaluates conditions where multiple objective functions have to be traded-off by cells. Using experimental data from long-term carbon limited chemostat cultivation of yeast cells , with fe13C-flux experiments in different bacteria, it was recently shown that metabolism indeed operates close to the optimal surface defined by multiple objective functions: maximum ATP yield, maximum biomass yield and minimal sum of absolute fluxes [E. coli on alternating carbon sources, it was proposed that the location in the flux state space (the feasible space constrained by the three objective functions) can be understood from an underlying trade-off between (near-) optimality under a given condition and minimal adjustment to alternative conditions. Based on e fluxes . Using fin vitro conditions which do not always resemble in vivo environments [An advantage of feasibility analysis is that the analysis is based on a kinetic model, therefore a more extensive set of objective functions can be implemented. An example is the objective functions that involve dynamics, which cannot be studied within FBA. Simultaneously, it limits feasibility analysis, due to the number of kinetic models available. Although a kinetic model of the entire metabolic network of an organism will be extremely useful to characterise fully the mechanics of each enzymatic reaction, and to combine such knowledge to ultimately predict system-behaviour, we are far from that. Besides some first attempts towards this goal ,89, the ronments ,91,92. Fronments  and Biomronments . Note ththe requirement to understand biological function (and ultimately to cure diseases). It turned out, however, that due to elaborate regulatory networks these promises could only be partially achieved. Nevertheless, these studies have facilitated the acceleration of the development of other experimental techniques (for instance ChIP-and RNAseq) as well as the development of an active field of research that develops genome-scale in silico models. These models are used to explore all flux distributions within the network which results in optimisation of an objective function. The arrival of whole-genome sequencing techniques has provided a comprehensive description of the genetic content (the “parts-list”) that makes up an organism. The reconstruction of all (metabolic) reactions within an organism requires the identification of all enzymes encoded by the genome and the chemical transitions that they participate in. A complete description of the entire genome was long thought to be Flux balance analysis (FBA), inspired by the premise that during evolution natural selection prompts biological systems towards optimality, assumes that cells perform optimally with respect to a given objective function. The optimisation of such an objective function is used to find a (sub-) set of optimal states from the large solution space that is defined by the constraints. The optimisation of the production of biomass or ATP are examples of commonly used objective functions. Does the optimality assumption within FBA help in understanding biological systems? Yes and no. Let us take the optimisation of specific growth rate  as an e−1),  is the biomass yield with respect to the substrate  and Vsubstrate is the specific uptake rate of the growth substrate (unit mmol h−1 gDW−1). With the uptake rate fixed as an environment-dependent capacity constraint, in order to find the highest µ, FBA just finds the flux distribution with the highest yield. Thus, it should be realised that the maximisation of growth rate is essentially done by finding a flux distribution that maximises  . Hence,see also ; however[E. coli  as well lantarum  achieve oduction ; similar glucose . i.e.,a whole solution space of flux distributions that is consistent with the prediction of the objective function). In addition, point (ii) can be addressed by, for instance, flux variability analysis (FVA) [Due to the still growing number of genome-scale models across all kingdoms, FBA is a powerful tool to explore systemic properties of genome-scale metabolic networks for applications in biotechnology and medicine ,99. Neveis (FVA) . FVA is E. coli that, within the FBA formalism, different objective functions were needed to predict optimal flux states for different conditions [The above examples point to an important aspect that obviously applies not only to FBA alone but also to all analyses that assume some kind of optimality criteria: the predictive power critically depends on the correspondence between the chosen objective function with the real biological objective. Indeed, it was shown for nditions . The remMethylobacterium extorquens the fluxes predicted by the method were in good agreement with those calculated on the basis of a kinetic model [The surmise that protein expression and maintenance is a costly process has also penetrated the field of FBA. One way of implementing this is the minimisation of overall fluxes as the objective function. The rationale for this approach is the assumption that the magnitude of fluxes is related to the amount of protein required as catalyst of that flux. When applied to metabolic schemes of erythrocytes and ic model ,103. UnfThe optimality assumption underlying FBA may be valid for wild type organisms that have been evolved over many thousands of generations. It is less likely that this will also hold for engineered or mutant-strains. To overcome this, extensions of FBA that use different objective functions are proposed, such as ROOM  and MoMaE. coli, S. cerevisiae and L. lactis) which differ in their metabolic strategies. With this extension, FBA was able to predict experimental findings and it was reported that different metabolic strategies could be attributed to the design principle of maintaining a redox balance within these organisms [In order to further improve the predictive power of FBA, there are options that do not act on the objective function, but on the constraints that limit the ways in which the objective can be reached. An example of an additional constraint is a molecular-crowding constraint. The rationale for this constraint comes from the limited amount of space inside cells available for metabolic enzymes . As argurganisms . et al. proposed an extension to FBA using regulatory information  [In the FBA formalism, constraints always act on the potential fluxes through reactions. First, one tries to include additional data that can be used to constrain the fluxes, particularly for cases where regulatory effects have a dominant influence on the behaviour of the organism’s metabolic fluxes. Covert A, rFBA) . This waA, rFBA) . This apA, rFBA) . et al. [et al. suggested applying changes in gene expression as soft constraints on changes in fluxes, i.e., it is to be expected that if the expression of a gene is increased, its corresponding flux will also increase [There have been a number of other approaches to augment regular FBA with regulatory constraints. Shlomi et al.  proposedincrease . In theiE. coli, they were able to simulate respiro-fermentation [E. coli [Other examples, originating from biophysical limitations, that are used as additional constraints are competition for membrane space  and grouentation . The sec[E. coli . E. coli the authors found a significant improvement over the individual rFBA and kinetic model. Such approaches have the potential to combine the best of two worlds: generating simulations which are more globally accurate and informative than the kinetic-based model, and more accurate in their details than the rFBA model alone. FBA would greatly benefit from kinetic information of metabolic reactions. For some subnetworks, such as glycolysis, these kinetic models are available, and they have been integrated with FBA (iFBA) . FocusinAll approaches mentioned above, although coherent, still require further validation by datasets of steady-state flux distributions and microarray data, and so at this stage it is difficult to assess which of these methods is to be preferred. Finally, we would like to stress that predictions, true or false, are useful either way because these predictions are testable and therefore able to confirm or rule out hypotheses. i.e., the ability to generate offspring), but generally the link between fitness and molecular network properties is rather vague or indirect. However, for several networks, especially under the standard laboratory conditions, we have quite a good understanding of which underlying principles and mechanisms are responsible for optimising fitness; many examples have been discussed in this review. For other networks it remains to be shown whether the lack of understanding is due to (i) an incomplete topology of the network , (ii) a lack in experimental data, or (iii) finding the right objective functions and constraints. As argued throughout, we believe that focusing on points (i) and (iii) will shed most light on understanding biological behaviour. Furthermore, care should be taken that biological networks cannot be optimal at multiple objective functions at the same time. Multiple objectives have then to be traded-off, which can be studied by means of a Pareto front [The overwhelming speed at which experimental data is currently generated has led to the recognition that the complexity of the underlying networks is enormous. In order to make sense of this data, systems biology is a scientific tool that can help in extracting design principles from it. In this review we have presented experimental and theoretical examples of this extraction procedure based on the premise that evolution has moulded biological networks to perform optimally. This assumption immediately raises the question: “optimised for what?”. This is an intriguing and difficult question to answer. Optimisation of an objective function is strongly related to cellular fitness (to front . In our


It has been difficult to correlate the quality of CD8 Vaccination is one of the most successful medical achievements of the last century. Due to our limited understanding of the correlates of protection, most vaccines have been developed by a trial and error approach, and we have yet failed to deliver vaccines for important diseases like AIDS or malaria. It is generally believed that most of the currently used vaccines provide protection by inducing high titers of pathogen-neutralizing antibodies in vitro. There is very little quantitative data on the control of pathogen growth in tissues by T cell immunity in vivo one can transfer target cells that are pulsed with viral peptides into mice harboring virus-specific effector or memory CD8Our limited understanding of the level of protection provided by memory T cells is partly due to the fact that the functionality of effector and memory T cells is typically measured per capita killing efficacy of CD8Even though the total number of LCMV-specific CD8We analyze published data on killing of peptide-pulsed splenocytes by LCMV-specific effector and memory CD8lculated .In the second set of experiments (“adoptive transfer”), cipients . The numDetails of the mathematical model proposed to describe migration of injected targets from the blood to the spleen and killing of peptide-pulsed targets in the spleen are given elsewhere We have shown previously that the rate of recruitment of target cells from the blood to the spleen depends on the size of the spleen To fit the data on recruitment of targets into the spleen and on killing of peptide-pulsed targets in the spleen simultaneously, we To describe the effect of the initial number of virus-specific CD8in vivo cytotoxicity assay To quantify the rates at which effector and memory CD8ling see .To further investigate the relationship between the death rate of peptide-pulsed targets and the frequency (or the number) of epitope-specific CD8e spleen . Transfet ratios . Two houe points .To estimate the average death rate of GP33-pulsed targets due to the killing by GP33-specific effector or memory CD8ese data . The mod targets .per capita killing efficacy of CD8From these two types of experiments, we have in total 11 estimates for the average death rate of target cells elicited by LCMV-specific CD8requency , or the requency , of epitOur result on mass-action killing allows for a simple estimate of the level of virus-specific memory CD8response . Howevernfection . In the  per day , we woulrmstrong . The majFor viruses infecting other organs  predicting the number of CD8Our results confirm and extend recent findings on killing of peptide-pulsed targets by effector CD8ssay see . Our curssay see  providinRecent interest in T cell based vaccines against several chronic infections of humans requires the development of experimental and theoretical tools to access the efficacy of such vaccines in vivo efficacy of effector and memory CD8in vivo data we found that the death rate of targets due to killing by LCMV-specific CD8in vitro experiments that the death rate of targets in vitro bound by 2 CTL is not dramatically different from death rate of targets bound by 3 or 4 CTLs in vitro experiments involving the in vivo the death rate of targets remains simply proportional to the density of killers. Possible explanations for the lack of a saturation in the death rate with CD8in vivo data vary from experimental artifacts to biological reality.Quantitative approaches aimed at estimating the e spleen . This isFirst, the observed high densities of epitope-specific CD8in vivo encounter between the target cell and its specific killer cell, may give the targets ample time to die after a brief, and perhaps marginal exposure, to a specific CD8in vivo cytotoxicity assay largely measures the initial rate of encounter between target cells and CD8a priori be expected to follow mass-action kinetics. Our estimated half-life of NP396 pulsed target cells is about three minutes in vitro or in vivoin vivo, but their subsequent experimental manipulation in vitro could lead to cell death at the time the cell suspensions are produced. If this is true, we are overestimating the death rate, and if prolonged contacts between effectors and targets are required for cell death in vivo, we may be underestimating the saturation effects.Second, the mass-action could be an artifact of the experimental procedure because the loss rate of target cells was only measured after making a single cell suspension from the spleen, and sorting the cells by their CFSE fluorescence. This experimental procedure, and the time delay between the The possibility that preparation of cell suspensions could lead to an early death of peptide-pulsed targets is corroborated by recent work demonstrating that granzymes A and B are dispensable for the killing of peptide-pulsed targets by CD8per capita killing efficacy of NP396-specific CD8per capita killing efficacy of CD8Finally, it is possible that our results arise due to the fact that we combine data on the killing by CD82–5 fold , while tA recent study re-analyzing the same published data suggested that killing of targets saturates when the frequency of LCMV-specific CD8It remains unclear whether the killing of targets depends on the frequency or on the total number of epitope-specific CD8quencies . In contquencies . UnderstSupporting Information S1Here we show a mathematical model for the in vivo cytotoxicity assay, estimates of the death rate of targets pulsed with NP396 and GP276 peptides following acute LCMV infection and the correlations between the fraction of target cells killed and the frequency of epitope-specific CD8(PDF)Click here for additional data file.


N-linked glycosylation of recombinant proteins.The glycosylation of recombinant proteins can be altered by a range of parameters including cellular metabolism, metabolic flux and the efficiency of the glycosylation process. We present an experimental set-up that allows determination of these key processes associated with the control of N-linked glycosylation of recombinant human chorionic gonadotrophin (HCG) was also altered under these conditions; the sialylation, fucosylation and antennarity decreased, while the proportion of neutral structures increased. A continuous culture set-up was subsequently used to understand the control of HCG glycosylation in the presence of varied glutamine concentrations; when glycolytic flux was reduced in the absence of glutamine, the glycosylation changes that were observed in shake flask culture were similarly detected. The intracellular content of UDP-GlcNAc was also reduced, which correlated with a decrease in sialylation and antennarity of the N-linked glycans attached to HCG.Chinese hamster ovary cells (CHO) were cultivated in shake flasks at 0 mM glutamine and displayed a reduced growth rate, glucose metabolism and a slower decrease in pH, when compared to other glutamine-supplemented cultures. The The use of metabolic flux analysis illustrated a case of steady state multiplicity, where use of the same operating conditions at each steady state resulted in altered flux through glycolysis and the TCA cycle. This study clearly demonstrated that the control of glycoprotein microheterogeneity may be examined by use of a continuous culture system, metabolic flux analysis and assay of intracellular nucleotides. This system advances our knowledge of the relationship between metabolic flux and the glycosylation of biotherapeutics in CHO cells and will be of benefit to the bioprocessing industry. N-linked glycans [The conformation, solubility, antigenicity, activity and recognition properties of any given glycoprotein may be influenced by the structure of its  glycans . Control glycans  In anoth glycans .N-linked glycosylation due to the stability of the culture mode. After a defined period of time, the viable cell number, productivity and concentrations and rates of consumption and production of metabolites stabilize in this set-up, and a steady state is attained. This is achieved with the continuous flow of fresh medium into a culture inoculated in a bioreactor, and this is coupled with outflow of harvest culture at the same rate. Additionally, the pH, temperature, pO2, pCO2 are controlled by the bioreactor set-up. The set-up for these experiments is based on previous literature where the effect of a range of pCO2 values on the glycosylation of IgG was firstly screened in a batch culture, and then scaled up to a more controlled culture environment [Use of continuous cultivation, metabolic flux analysis and assay of intracellular sugar nucleotide levels is an ideal method to study the control of ironment . A diffeN-linked glycans attached to HCG were determined on days 1, 3 and 5 of culture. The same cell line was subsequently inoculated in a continuous culture system, and the glutamine concentration in the culture medium was altered between 8 mM and 0 mM to study four steady states in total. Metabolic flux analysis was carried out at each steady state, and the intracellular content of nucleotides and sugar nucleotides and structure of N-linked glycans attached to HCG were also determined. With use of both of these cultivation systems, decreased glycolytic flux and intracellular concentration of UDP-GlcNAc was found to correlate with a reduction in the sialylation and antennarity of the N-linked glycans attached to HCG under glutamine-limited conditions.This study aims to investigate the mechanisms of changing glycan microheterogeneity by coupling metabolic flux analysis to assay of intracellular sugar nucleotides. A CHO cell line recombinantly expressing HCG was initially cultivated in batch shake flasks since it presents an ideal small-scale method to test the effect of many parameters on the subsequent glycosylation of recombinant proteins. In this case, 0 mM, 4 mM or 8 mM glutamine was supplied in the culture medium and the structures of the 2 and 80% RH.A CHOK1 (Chinese hamster ovary) cell line recombinantly expressing HCG (human chorionic gonadotrophin) was a kind gift of Merck, Sharp & Dohme, Oss, Netherlands. The cells were routinely maintained in CD-CHO medium (GIBCO) supplemented with 8 mM glutamine and HT supplement . Cells were precultured in shake flasks in a Kuhner ClimoShaker ISF1-X incubator at 150 rpm, 5% CO6 cells/ml in a volume of 150 ml in 500 ml shake flasks. The cultures were inoculated to result in a final concentration of 0 mM, 4 mM and 8 mM glutamine (gln). Six shake flasks per condition were incubated, and duplicate cultures were harvested on days 1, 3 and 5 of culture.Cells were inoculated at 0.5 × 106 cells/ml and cultured for three days in batch mode. At this point, the harvest pump (Watson Marlow 101 U/R) was switched on in order to set the medium flow rate at 0.4/d. The culture level was maintained at 1.7 L with use of a level controller (AppliSens APS501 level controller), which activated the delivery of fresh medium to the bioreactor via the feed pump when necessary. Fresh, sterile medium was stored at 4°C, while harvest cell suspension was collected into a reservoir stored at room temperature. (At each steady state the cell suspension was harvested at 4°C via a clean harvest line). A theoretical steady state is attained 5 volume changes after the last perturbation, and if there were minimal changes in the mean value of each cell culture parameter at this point, a steady state was defined. The glutamine concentration was altered between values of 8 mM and 0 mM to study four steady states in total, defined as follows; days 30-33 , days 45-48 , days 72-75  and days 88-91 .Duplicate continuous cultures were carried out in 2L bioreactors (Applikon) with a working volume of 1.7L. Culture pH and dissolved oxygen were controlled at 7.20 and 50% of air saturation, respectively, with the use of an ADI 1030 bioprocessor (Applikon). The temperature was maintained at 37°C and agitation rate was set at 325 rpm. The bioreactors were inoculated at an initial cell density of 0.3 × 1020 (Roche Innovatis AG), the extracellular concentrations of ammonium, glucose, glutamate, glutamine and lactate were assayed with use of the Nova Bioprofile 100 plus  and BGA parameters  were determined with the Bayer Rapidlab 248 . Cell-free supernatants were stored at -20°C before analysis of HCG content by ELISA at key time points.Viable cell number and cell viability was determined using the CEDEX ASave):The specific rate of substrate consumption (qS) and product formation (qP) and was calculated as described below , i.e. the rate of change in substrate or product concentration  per unit time (dt) per viable cell number  and ammonium production (equation 4) .andk, was determined for CD-CHO medium in both a shake flask and bioreactor system by incubating glutamine-supplemented medium under experimental conditions. The glutamine concentration was determined daily and a plot of the percentage glutamine remaining as a function of time was constructed, and fitted to the exponential function y = ek.x-. A value of k = 0.078/d and 0.069/d was determined for bioreactors and shake flasks, respectively.The value for the first order degradation rate constant, On three consecutive days during each steady state, cell culture supernatant was harvested and stored at -20°C from each bioreactor. The concentration of extracellular amino acids was subsequently determined by HPLC (SAFC Biosciences). Specific rates of production of amino acids, Nova metabolites, product titer and biomass were combined with material balances of carbon and nitrogen via a reaction network to estimate the metabolic fluxes at each steady state. The excel algorithm version of a metabolic flux analysis model developed by Mr. Jongchan Lee in the University of Minnesota was used . The oxyet al [Cells were harvested for analysis on two consecutive days during each steady state by adaptation of the technique of Kochanowski et al . FirstlyN-linked glycans attached to 5 μg of purified HCG were determined according to the method of Royle et al [HCG was purified from culture supernatant harvested on two consecutive days during a steady state by affinity chromatography. The structure of the le et al . Brieflyle et al . The folOne-way ANOVA with Bonferroni's post-test was performed using GraphPad Prism version 4.0a for Macintosh . Statistical significance was illustrated as follows; * = p < 0.05, ** = p < 0.01, *** = p < 0.001.On days 1 through 3 of shake flask cultivation at 0 mM glutamine, the number of viable cells was significantly lower than the glutamine supplemented cultures , the concentration of glutamate increased at state 3 only (p < 0.001), while the concentration of ammonium was significantly different at each steady state , and the continuous culture method ensures that the metabolism of the cells stabilized after a defined period of time (e.g. qGluc, qLac, qGln, qGlu, qNH4+, Figure A simple illustration of the increased stability of this culture system is seen when comparing the culture pH in batch and continuous culture Figure , 3C. WitN-linked glycosylation of HCG during shake flask cultivation at 0 mM glutamine were also present at steady state 4 of continuous culture (Figure After an initial period of adaptation, the cells settled into four steady states. The changes in the e Figure . The rate Figure , 7. Addie Figure .N-linked glycans is altered by varying the intracellular content of the UDP-GNAc sugars i.e. UDP-GlcNAc and UDP-GalNAc [The antennarity and sialylation of P-GalNAc -17. UndeP-GalNAc .N-linked glycan found in shake flask and continuous cultivation was largely similar, though the amount of underprocessed glycans was reduced in shake flasks (peaks 2, 6 and 7, Tables Therefore, the reduction in sialylation and antennarity of HCG may be related to the decreased intracellular content of UDP-GlcNAc caused by a lack of glutamine coupled with low glycolytic flux. The reasons for the decrease in fucosylation were not examined, but it is possible that the reduction in glycolytic flux has an impact, since fructose-6-phosphate is interconverted to fucose-1-phosphate, a precursor for the formation of the GDP-fucose sugar donor. Glutamine limitation has previously been shown to induce an increase in nucleotide levels , observeThe results of the metabolic flux analysis illustrate the mechanisms by which these cells adapt to the lack of glutamine, since this amino acid is necessary for the synthesis of nucleotides and nicotinamide co-enzymes, in addition to the previously described role in the formation of activated sugars. Under conditions of excess glucose, there was no net flux from glutamine to the TCA cycle, suggesting that glutamine was primarily used in these other pathways (Jgln-glu, steady state 1, Figure A distinct set of changes to the fluxes around the TCA cycle was seen at steady state 3 Figure . FirstlyThis indicates that the aim to replicate data by the sequential cultivation method was unsuccessful, however, these results suggest a case of steady state multiplicity - a difference in cell metabolism despite the use of identical dilution rate and medium composition in a continuous culture ,21,22. IThe productivity of HCG was significantly increased on day 5 of batch shake flask culture with 0 mM glutamine supplementation Figure . The groDespite the lack of significance in the trend of changing productivity during the continuous culture, there was a statistical decrease in the flux from amino acids towards the synthesis of HCG Figures , 7. A reN-linked glycans attached to HCG. By its nature, batch cultivation resulted in variations in metabolism during the culture time, such as growth rate, the rate of consumption and production of key metabolites and recombinant protein, and, also in some important culture conditions such as pH. With use of a continuous culture set up, growth rate and culture pH were controlled while the glutamine concentration in culture medium was altered between 8 mM and 0 mM. Additionally, a metabolic steady state was attained; the consumption and production rates of key metabolites stabilized after a key length of time. By determining the intracellular content of nucleotides and sugar nucleotides, the mechanisms for these changes were explored. It was demonstrated that lack of glutamine coupled with reduced glycolytic flux caused a reduction in the sialylation and antennarity of the N-linked glycans attached to HCG, an event mediated by the decrease in the intracellular pool of UDP-GlcNAc. The use of metabolic flux analysis at each steady state illustrated the metabolic diversions that occurred in the presence of varying glutamine concentrations, and highlighted a case of steady state multiplicity. The occurrence of multiple steady states under the same culture conditions suggests the potential to guide cells into key metabolic states that may improve the characteristics of recombinant proteins. Consequently, this method of coupling use of continuous culture with analytical techniques to probe the mechanisms of changing N-linked glycosylation is effective, and lends itself towards a range of other applications.This work has illustrated that reducing glutamine concentrations to 0 mM in a batch shake flask resulted in reduced sialylation, fucosylation and antennarity, and, increased proportions of neutral Aa: Amino acid; 2AB: 2-Aminobenzamide; AcCoA: Acetyl coenzyme; akg: α-Ketoglutarate; CHO: Chinese hamster ovary cells; CMP-NeuAc: CMP-N-acetylneuraminic acid; Fuc: Fucose; Fum: Fumarate; Gal: Galactose; GDP: Guanosine diphosphate; GDP-Man: GDP-mannose; Glc: Glucose; Gln: Glutamine; Glu: Glutamate; HCG: Human chorionic gonadotrophin; Lac: Lactate; Mal: Malate; Neu5Ac: N-acetylneuraminic acid; OAA: Oxaloacetate; Pyr: Pyruvate qX: Rate of consumption or production of X; SuccCoA: Succinyl-Co-A; tPA: Tissue plasminogen activator; UDP-Gal: UDP-galactose; UDP-GalNAc: UDP-N-acetylgalactosamine; UDP-Glc: UDP-glucose; UDP-GlcNAc: UDP-N-acetylglucosamine; UDP-GNAc: UDP-GlcNAc/UDP-GalNAc.The authors declare that they have no competing interests.SCB carried out the studies and drafted the manuscript. TVDL CJMS, WMJVG and GPD conceived of the study, and participated in its design and coordination. GPD oversaw the project. NOD and PMR assisted in the interpretation of glycan analysis results. All authors read and approved the final manuscript.


In silico variations of those maximal capacities allow for a global view of the consortium responses to various metabolic and environmental constraints. Secondly, cFBA is very useful for comparing the performance of different metabolic cross-feeding strategies to either find one that agrees with experimental data or one that is most efficient for the community of microorganisms.A central focus in studies of microbial communities is the elucidation of the relationships between genotype, phenotype, and dynamic community structure. Here, we present a new computational method called community flux balance analysis (cFBA) to study the metabolic behavior of microbial communities. cFBA integrates the comprehensive metabolic capacities of individual microorganisms in terms of  stoichiometric models of metabolism, and the metabolic interactions between species in the community and abiotic processes. In addition, cFBA considers constraints deriving from reaction stoichiometry, reaction thermodynamics, and the ecosystem. cFBA predicts for communities at balanced growth the maximal community growth rate, the required rates of metabolic reactions within and between microbes and the relative species abundances. In order to predict species abundances and metabolic activities at the optimal community growth rate, a nonlinear optimization problem needs to be solved. We outline the methodology of cFBA and illustrate the approach with two examples of microbial communities. These examples illustrate two useful applications of cFBA. Firstly, cFBA can be used to study how specific biochemical limitations in reaction capacities cause different types of metabolic limitations that microbial consortia can encounter.  In nature, microbes generally occur in communities. These microbial communities play important roles: they are essential for global nitrogen, carbon and energy cycling Today, advanced molecular methods (meta-omics) facilitate the detailed characterization of microbial communities, providing information at an unprecedented level of molecular detail. These methods catalogue the active molecular processes, the ecotypes present, and report the identity and abundances of specific microbial species Constraint-based stoichiometric modeling of genome-scale metabolic networks is a set of computational methods developed in systems biology for studying the comprehensive metabolic capacities of organisms In microbial communities, a new level of complexity is added on top of microbial metabolism that complicates the application of constraint-based stoichiometric modeling to microbial communities. Besides the presence of all metabolic reactions in each of the microorganisms, the exchange of metabolites between species and biomass abundances of each of the microbial species has to be considered. In addition, each of these microorganisms has specific nutrient requirements for growth, which it can meet through metabolic cross-feeding, nutrient-competition or by uptake from the environment. On top of that, selective pressures at the level of single species change the metabolic interactions between species through mutations, which leads to accumulation of genetic variants and co-evolution of metabolic partnerships. These forces together shape the structure of microbial communities. In such systems, the actions of individual species are constrained by their own biochemical processes and by their interactions with other species. Computational methods are essential to address those complex aspects of biological systems Considerable effort has been invested in recent years to develop suitable computational approaches that, in principle, can consider all the metabolic reactions occurring in a microbial community The reason why constraint-based stoichiometric modeling of microbial communities is much more complicated than for single organisms originates from the interdependencies between the metabolic objectives of microorganisms in the community. Generally, in constraint-based stoichiometric modeling, a single metabolic objective is postulated for the organism, such as optimization of biomass yield, to give rise to a manageable solution space of flux distributions Balanced growth occurs when internal metabolism is at steady state while the cells grow exponentially at a fixed growth rate. Here, we extend this definition to microbial ecosystems and, hence, require all metabolites (intra- and extracellular) to attain a steady state level. Under those growth conditions, our computational method, community flux balance analysis (cFBA), predicts the fractional biomass abundances of all the participating microorganisms in the community as well as the intra- and extracellular flux distributions and metabolic exchanges. cFBA predicts the complete state of the microbial community engaging in balanced growth and postulates only a single objective. cFBA applies to microbial ecosystems that function in a fairly constant environment, such as specific microbial communities involved in bioremediation, waste water treatment or in laboratory settings, e.g. chemostats.E. coli consortium with genome-scale models.The community flux balance analysis (cFBA) that we will present in this paper is a direct translation of FBA for single organisms to microbial communities and requires only a few community-specific constraints. It is based on the concept of balanced growth of microorganisms and the corresponding metabolic network states. It is therefore a fundamental description of the microbial community structure resulting from basic concepts of microbiology. It directly applies to the study of stable microbial communities under laboratory conditions in controlled bioreactors, either resulting from laboratory evolutionary experiments or from direct samples from the environment, or for microbial communities in nature that are exposed to prolonged stable environmental conditions. cFBA predicts the optimal flux distribution, growth rate, and abundance of all species in the consortium as well as the exchange fluxes between species and the community environment. As a proof of concept, we first investigate a simple microbial community in which species are mutually dependent for their growth. Next, we study an evolved syntrophic Constraint-based stoichiometric modeling of a microbial consortia requires the coupling of the metabolic networks of the interacting species. To highlight the essential steps, we illustrate our methodology first by considering interacting microorganisms described by highly simplified stoichiometric models consisting of lumped metabolic processes: anabolism, catabolism, respiration and product formation. In all cases, the reaction networks are balanced with respect to elemental composition, charge and degree of reduction In Besides the stoichiometric aspects of model merger, we also consider the biomass abundances of each of the participating microorganisms; a feature, which is not explicitly addressed in many existing multi-species FBA approaches, except for OptCom −1•h−1mol•g) for reaction −1h) for organism −1mol•h. The mass balances for the variable metabolites in the community, occurring either intracellularly or extracellularly, will then have the following structure (we omit abiotic conversions between variable metabolites in the environment but those can be added straightforwardly):We distinguish three types of reactions: an intracellular, enzyme catalyzed reaction occurring at a specific rate −1mol•h. Metabolite −1h). The resulting unit of −1mol•h. Finally, metabolite −1mol•h with Here, In our approach, the entire consortium is considered at steady state such that all the mass balances for the metabolites equal zero and the reaction rates remain constant. In that condition, for microorganisms growing at the same specific  growth rate Here, time Division of −1•h−1mol•g),This relationship now holds for the entire period of exponential growth,  is important to assess the types of limitations that microbial consortia encounter and that scanning of those bounds allows for a global view of systemic consortium responses to metabolic and environmental constraints. This scanning of flux bounds is common practice in FBA applied to single species and is normally referred to as phase plane analysis Escherichia coli culture that was grown for 765 generations in a glucose-limited continuous culture. In a follow-up experiment, Rosenzweig et al E. coli strains from these polymorphic populations. It turned out that one strain had evolved to become a specialized acetate consumer ‘E. coli cell Escherichia coli K-12 strain Helling & Vargas  acetate . The gluInstead of parameterizing fractional biomass abundance of one organism of a community , here weNext, we asked what the acetate cross-feeding flux values should be to give rise to the measured biomass ratio; the corresponding curve we denote as the below CF curve. Though the acetate cross-feeding fluxes were not measured during the experiment, our approach predicts a probable range of flux values that gives rise to the measured biomass ratio, glucose-uptake rate, and the specific-growth rate of both of the strains. This illustrates how cFBA can be used to predict cross-feeding fluxes in a microbial community using a genome-scale metabolic model of the community.E. coli is known to excrete many other metabolites that can readily pass biological membranes, such as the weak acids occurring in central metabolism. To explore this question of alternative cross-feeding metabolites, we performed a series of simulations where we allowed the two strains to cross-feed via a set of metabolites (one-at-a-time) and minimized the glucose uptake flux to achieve the experimental growth rate with unlimited cross-feeding flux capacities. We fixed the specific growth rate at the set dilution rate and then minimized the glucose uptake rate. We then searched for single alternative cross-feeding metabolites that would give rise to the same or lower glucose uptake rate than experimentally found. In We also tested whether cFBA predicts alternative cross-feeding metabolites that can explain the experimental data equally well as acetate does, to illustrate one useful application of cFBA. It was concluded in Helling et al. retation .To construct the community stoichiometric matrix, the reactions of individual microorganisms involved in cross-feeding reactions and communication with the environment need to be identified. The reactions of individual species can typically be derived from genome-scale stoichiometric models that already exist but can, in principle, also be derived from reduced stoichiometric models of species that are less well characterized. Three types of metabolites and four types of reactions can be distinguished at the level of the metabolism of every microorganism. Collecting these metabolites and reactions leads to a rearranged stoichiometric matrix  stoichiometric models of the participating species and constraints derived from biochemistry, thermodynamics, microbial physiology, and ecology. We derived the cFBA method from the microbiological principles of balanced growth and mass flow in microbial communities. We thus extended the concept of balanced growth of a single organism in microbiology to microbial ecology.At present, cFBA is limited to microbial communities at balanced growth, such that all microorganisms grow equally fast and have an intracellular metabolism operating at steady state. The resulting condition of equal specific growth rate can be directly used as the objective function that is to be maximized computationally. The optimization leads to the identification of an optimal community structure. This structure encompasses the rates of all the metabolic fluxes in the community and fractional biomass abundances. cFBA applies to microbial communities where the environmental changes are slow enough for the entire community to settle to a steady state. Communities involved in wastewater treatment or bioremediation can attain steady state levels when done in specific bioreactors Constraint-based stoichiometric modeling approaches for the metabolic networks of microbial communities, such as cFBA or other methods The constraint-based stoichiometric modeling of microbial communities is still largely in its infancy. Much is still to be learnt from studies where the predictions of these modeling approaches are critically compared to experimental data. How can we study microbial communities in a sensible fashion by using an optimization approach? Do we need to consider multi-objective nonlinear optimization approaches? If so, the computational approaches will quickly run into problems related to computational speed and uniqueness of solutions. However, even if not all the assumptions hold, as is also often the case for single-species FBA, these models will be useful to explore the metabolic potential of microbial communities. We thus expect approaches such as cFBA to be already sufficiently informative to become a vital component of the workflow of studying communities with modern “omics” approaches.http://cbmpy.sourceforge.net/) package and IBM ILOG CPLEX Optimizer by IBM. CBMPy has been developed based on the principles of Python Simulator of Cellular Systems (PySCes) Mathematica® 8, python scripts and data for analyses depicted in This cFBA framework has been coded using Python™ programming language and requires CBMPy  or extra-cellular metabolite names, followed by species name (i or j ) separated by underscore. And, metabolites are classified on the basis of the compartments they exist in i.e. intracellular (denoted with species name as subscript), extracellular (subscript ‘ext’) and fixed environmental (underlined) metabolites. These specific fluxes have as their unit: mass flow per gram biomass, i.e. −1•h−1mol•g; and every reaction considered in these models should be elementally and charge balanced. All reactions can conveniently be expressed in terms of a stoichiometric matrix for each organism, denoted by N and the species name as subscript, as shown in ix and jx.(TIF)Click here for additional data file.Information S1Detailed mathematical descriptions of the optimization problem, two-species community and structure of the C matrix of a three-species microbial consortium.(PDF)Click here for additional data file.Scripts S2Programming scripts for reproducing data shown in  of the manuscript.(ZIP)Click here for additional data file.Scripts S3Programming scripts for reproducing data shown in  of the manuscript.(ZIP)Click here for additional data file.