Biology subjects

Bruggeman, F. J.

Publications and source records attributed to Bruggeman, F. J..

At least 19 recordsLinked to original sources

bioRxiv2026

Emergent metabolic cooperation in communities of microbes that maximise growth rate by optimal protein expression

Many microbial communities involve metabolic exchanges between their members. We present a mathematical modelling formalism for studying the adaptation of metabolic strategies by microbes to external metabolites produced by themselves and their community partners. Each microbial species is assumed to maximise its growth rate by optimal allocation of finite biosynthetic resources for protein synthesis in response to their current environment. Each species therefore acts as a selfish optimiser. Because the environment is shaped by all species, their strategies are interdependent. The optimal state of the community is the set of metabolic strategies of its members that outcompetes (outgrows) all other possible sets of metabolic strategies---including the ones in which some species may not be present at all. Our mathematical formalism compacts the coupled optimisations by the single species into one optimisation problem that also infers the optimal community composition. We show with simple examples how it can be used to study the emergence of positive species-species interactions such as commensalism, mutualism, syntrophy, and division of labour. The formalism is a direct generalisation of the well-known resource allocation models for single species, but includes reaction kinetics; we show that observed positive ecological interactions emerge from ecological feedback, in which producers are inhibited by the byproducts they excrete. This paper illustrates that (metabolism-dominated) microbial communities may be viewed as one coupled system in which the optimal pathway choice of each member depends on that of all others. It is directly generalisable to multiple species, and should pave the way for studies of larger communities.

systems biology↗

bioRxiv2026

A rapid HPLC-based method to determine NAD(P)(H) and NMN redox cofactor concentrations and ratios in microbes

Redox cofactors are a key part of cellular physiology as they are involved in most metabolic pathways, and their ratios are linked to cellular robustness. However, measuring their levels in cells remains a challenge. Here, we describe a novel method to rapidly measure NAD(H), NADP(H) and nicotinamide mononucleotide (NMN) levels and their oxidized/reduced ratios using an HPLC connected to a fluorescence detector. By extensively characterizing this method and benchmarking it against the classical iodonitrotetrazolium (INT) assay, we show that this method results in accurate and reproducible measurements of NAD+, NADP+ and NMN levels in bacteria. We further demonstrate that this method can be used to determine intracellular NADH and NADPH concentrations and ratios of nicotinamide nucleotide cofactors in engineered Escherichia coli strains, as well as other bacterial species such as Pseudomonas putida.

biochemistry↗

bioRxiv2025

Multiplexed imaging of G-proteins and ERK activity upon activation of CaSR

We have previously shown that the calcium sensing receptor (CaSR) activates different G proteins and second messengers in single cells, and that GPCR and G protein-mediated ERK activity can be highly dynamic and heterogeneous at the single cell level. Here, we attempted to investigate the CaSR-Gi-ERK signaling pathway in single cells with previously characterized biosensors. We developed a strategy to simultaneously track G-protein and ERK activities in a single cell, using FRET-based and translocation sensors, a novel large-Stokes-shift green fluorescent protein, and an imaging setup with a single detector and a single wavelength for excitation. Extensive characterization and optimization to unmix the signals showed that the differences in dynamic range and type of read-out obtained from these biosensors made it very challenging to obtain robust FRET-measurements in the developed setup. When focusing solely on ERK, we found signs of possible ERK activity in response to calcium stimulation via CaSR, as well as milder changes in the absence of calcium treatment. Further optimization of the model, probes, and image processing will be necessary to develop a setup to robustly measure FRET and translocation simultaneously in single cells. We present the challenges we encountered and discuss future developments that can overcome them.

cell biology↗

bioRxiv2025

Entangled stoichiometric objectives shape microbial catabolism

The search for fundamental relationships between energetic and biosynthetic parameters of catabolism and anabolism is a major goal in microbiology. This is complicated by the fact that ATP synthesis is required for some anabolic precursors, all building blocks, and their polymerization into macromolecules, while the synthesis of other anabolic precursors and catabolic products yields ATP. Yield parameters were classically predicted from approximate phenomenological relations between catabolic and anabolic stoichiometry. Here we compare the catabolisms of a diverse set of microbial species across conditions using genome-scale stoichiometric models. We focus on states of maximal energetic efficiency (maximal yield of biomass of the energy source) and present an unbiased method for calculating stoichiometric relations between catabolism and anabolism. We find that synthesis of charged energy-carriers and anabolic precursors by catabolism is strongly intertwined. Catabolic intermediates and reactions vary greatly, due to variation in the energy and carbon source for growth. We find that the ATP requirement for 1 gram biomass varies between 72.8 and 246.1 moles, precursor sets vary between 4 and 14 in size, and acetyl-CoA is the only common precursor across species. We conclude that the complex interplay between precursor synthesis and energy conservation of heterotrophic catabolism results from an optimal compromise between conflicting objectives. The state of maximal energetic efficiency is reached by minimizing the carbon source lost during energy catabolism due to catabolic-product formation. This choice is influenced by the need for an optimal precursor set that compromises between maximal ATP production during its formation from the carbon source and minimal ATP consumption when it is converted into building blocks. We find that the associated optimal catabolic pathways are diverse across species and conditions.

systems biology↗

bioRxiv2024

Thermodynamics of unicellular life: Entropy production rate as function of the balanced growth rate

AO_SCPLOWBSTRACTC_SCPLOWIn isothermal chemical reaction networks, reaction rates depend solely on the reactant concentrations setting their thermodynamic driving force. Living cells can, in addition, alter reaction rates in their enzyme-catalysed networks by changing enzyme concentrations. This gives them control over their metabolic activities, as function of conditions. Thermodynamics dictates that the steady-state entropy production rate (EPR) of an isothermal chemical reaction network rises with its reaction rates. Here we ask whether microbial cells that change their metabolism as function of growth rate can break this relation by shifting to a metabolism with a lower thermodynamic driving force at faster growth. We address this problem by focussing on balanced microbial growth in chemostats. Since the driving force can then be determined and the growth rate can be set, chemostats allow for the calculation of the (specific) EPR. First we prove that the EPR of a steady-state chemical reaction network rises with its driving force. Next, we study an example metabolic network with enzyme-catalysed reactions to illustrate that maximisation of specific flux can indeed lead to selection of a pathway with a lower driving force. Following this idea, we investigate microbes that change their metabolic network responsible for catabolism from an energetically-efficient mode to a less efficient mode as function of their growth rate. This happens for instance during a shift from complete degradation of glucose at slow growth to partial degradation at fast growth. If partial degradation liberates less free energy, fast growth can occur at a reduced driving force and possibly a reduced EPR. We analyse these metabolic shifts using three models for chemostat cultivation of the yeast Saccharomyces cerevisiae that are calibrated with experimental data. We also derive a criterion to predict when EPR drops after a metabolic switch that generalises to other organisms. Both analyses gave however inconclusive results, as current experimental evidence proved insufficient. We indicate which experiments are required to get a better understanding of the behaviour of the EPR during metabolic shifts in unicellular organisms.

systems biology↗

bioRxiv2024

Biosensor imaging of G protein mediated Signaling Pathways Activated Immediately Downstream of CaSR

Genetically encoded biosensors allow us to study events in single cells in real time. Here, we used biosensors with a read-out based on Forster resonance energy transfer (FRET) or intensity to investigate the main signaling pathways activated immediately downstream of the calcium sensing receptor (CaSR) in HEK-293 cells. CaSR responds to its endogenous ligand, calcium, to activate Gq and Gi protein dependent pathways. We demonstrate that CaSR activates Gq to promote intracellular calcium mobilization, and we monitored these two events simultaneously in the same cells. We also observed that CaSR activates the 3 Gi subtypes and decreases cAMP levels in a Gi-dependent manner. Moreover, the use of negative allosteric modulator NPS-2143 can inhibit these signaling events and also rapidly disrupts them if added after receptor activation by calcium stimulation. In addition, the increases in calcium and cAMP levels were respectively enhanced when activation of Gi or Gq proteins was prevented. Finally, we provide evidence that CaSR does not couple to G13 proteins, and that activation of RhoA by CaSR is solely dependent on Gq/G11 activity.

cell biology↗

bioRxiv2023

Growth consequences of the inhomogeneous organization of the bacterial cytoplasm

In many bacteria, translating ribosomes are excluded from the nucleoid, while amino-acid and energy-supplying metabolic enzymes spread evenly throughout the cytoplasm. Here we show with time-lapse fluorescence microscopy that this inhomogeneous organisation of the cytoplasm can cause single Escherichia coli cells to experience an imbalance between biosynthesis and metabolism when they divide, resulting in cell size-dependent growth rate perturbations. After division, specific growth rate and ribosome concentration correlates negatively with birthsize, and positively with each other. These deviations are compensated during the cell-cycle, but smaller-than-average cells do so with qualitatively different dynamics than larger-thanaverage cells. A mathematical model of cell growth, division and regulation of biosynthetic and metabolic resource allocation reproduces our experimental findings, suggesting a simple mechanism through which long-term growth rate homeostasis is maintained while heterogeneity is continuously generated. This work shows that the life of single bacterial cells is intrinsically out-of-steady-state, dynamic and reliant on cytoplasmic organization. Popular summaryClassical, population-level studies of the metabolism and growth of bacteria indicate that the average cell in a growing population operates at steady state and can be viewed as an homogeneous bag of enzymes. Here we show that this view does not capture the lives of single cells. At birth, they are perturbed from the steady state of their mother cell after which they need their entire cell cycle to return to this state by active regulation. Then they divide and their daughters are perturbed again; a never ending cycle that is inescapable and akin to a Sisyphean task. This behaviouremerges from the delicate interplay of the intrinsic randomness of (uneven) cell division, the inhomogeneous localisation of metabolic and ribosomal proteins in the cell, unbalanced metabolism, and compensatory steering of gene expression.

microbiology↗

bioRxiv2022

Coupling phenotype stability to growth rate overcomes limitations of bet-hedging strategies

Microbes in the wild face highly variable and unpredictable environments, and are naturally selected for their average growth rate across environments. Apart from using sensory-regulatory systems to adapt in a targeted manner to changing environments, microbes employ bet-hedging strategies where cells in an isogenic population switch stochastically between alternative phenotypes. Yet, bet-hedging suffers from a fundamental trade-off: increasing the phenotype switching rate increases the rate at which maladapted cells explore alternative phenotypes, but also increases the rate at which cells switch out of a well-adapted state. Consequently, it is currently believed that bet-hedging strategies are only effective when the number of possible phenotypes is limited and when environments last for sufficiently many generations. However, recent experimental results show that gene expression noise generally decreases with growth rate, suggesting that phenotype switching rates may systematically decrease with growth rate. We here show that such growth rate dependent stability (GRDS) can almost completely overcome the trade-off that limits bet-hedging, allowing for effective adaptation even when environments are diverse and change rapidly. GRDS allows cells to be more explorative when maladapted, and more phenotypically stable when well-adapted. We further show that even a small decrease in switching rates of faster growing phenotypes can substantially increase long-term fitness of bet-hedging strategies. Together, our results suggest that stochastic strategies may play an even bigger role for microbial adaptation than hitherto appreciated.

evolutionary biology↗

bioRxiv2021

Heterogeneity and dynamics of ERK and Akt activation by G protein-coupled receptors depend on the activated heterotrimeric G proteins

Kinases are fundamental regulators of cellular functions and play key roles in GPCR-mediated signaling pathways. Kinase activities are generally inferred from cell lysates, hiding the heterogeneity of the individual cellular responses to extracellular stimuli. Here, we study the dynamics and heterogeneity of ERK and Akt in genetically identical cells in response to activation of endogenously expressed GPCRs. We use kinase translocation reporters, high-content imaging, automated segmentation and clustering methods to assess cell-to-cell signaling heterogeneity. We observed ligand-concentration dependent response kinetics to histamine, a2-adrenergic, and S1P receptor stimulation that varied between cells. By using G protein inhibitors, we observed that Gq mediated the ERK and Akt responses to histamine. In contrast, Gi was necessary for ERK and Akt activation in response to 2-adrenergic receptor activation. ERK and Akt were also strongly activated by S1P, showing high heterogeneity at the single cell level, especially for ERK. In all cases, the cellular heterogeneity was not explained by distinct pre-stimulation levels or saturation of the measured response. Cluster analysis of time-series derived from 68,000 cells obtained under the different conditions revealed several distinct populations of cells that display similar response dynamics. The single-cell ERK responses to histamine and brimonidine showed remarkably similar dynamics, despite the activation of different heterotrimeric G proteins. In contrast, the ERK response dynamics to S1P showed high heterogeneity, which was reduced by the inhibition of Gi. To conclude, we have set up an imaging and analysis strategy that reveals substantial cell-to-cell heterogeneity in kinase activity driven by GPCRs. O_FIG_DISPLAY_L [Figure 1] M_FIG_DISPLAY C_FIG_DISPLAY

cell biology↗

bioRxiv2021

Whole-cell modeling in yeast predicts compartment-specific proteome constraints that drive metabolic strategies

When conditions change, unicellular organisms rewire their metabolism to sustain cell maintenance and cellular growth. Such rewiring may be understood as resource re-allocation under cellular constraints. Eukaryal cells contain metabolically active organelles such as mitochondria, competing for cytosolic space and resources, and the nature of the relevant cellular constraints remain to be determined for such cells. Here we developed a comprehensive metabolic model of the yeast cell, based on its full metabolic reaction network extended with protein synthesis and degradation reactions (16304 reactions in total). The model predicts metabolic fluxes and corresponding protein expression by constraining compartment-specific protein pools and maximising growth rate. Comparing model predictions with quantitative experimental data revealed that under glucose limitation, a mitochondrial constraint limits growth at the onset of ethanol formation - known as the Crabtree effect. Under sugar excess, however, a constraint on total cytosolic volume dictates overflow metabolism. Our comprehensive model thus identifies condition-dependent and compartment-specific constraints that can explain metabolic strategies and protein expression profiles from growth rate optimization, providing a framework to understand metabolic adaptation in eukaryal cells.

systems biology↗

bioRxiv2021

Escherichia coli robustly expresses ATP synthase at growth rate maximizing concentrations

Improved protein expression is an important evolutionary adaptation of bacteria. A key question is whether evolution has led to optimal protein expression that maximizes immediate growth rate (short-term fitness) across conditions. Alternatively, fitter genetic variants could display suboptimal short-term fitness, because they cannot do better or because they strive for long-term fitness maximization by, for instance, anticipating future conditions. To answer this question, we focus on the ATP-producing enzyme F1F0 H+-ATPase, which is an abundant enzyme and ubiquitously expressed across conditions. We tested the optimality of H+-ATPase expression in Escherichia coli across 27 different nutrient conditions. In all tested conditions, wild-type E. coli expresses its H+- ATPase remarkably close to optimal concentrations that maximize immediate growth rate. This work indicates that bacteria can achieve robust optimal protein expression for immediate growth- rate.

systems biology↗

bioRxiv2020

Elementary Conversion Modes enable exploration of all metabolic capabilities of any organism

The metabolic capabilities of cells determine their biotechnological potential, fitness in ecosystems, pathogenic threat levels, and function in multicellular organisms. Their comprehensive experimental characterisation is generally not feasible, particularly for unculturable organisms. In principle, the full range of metabolic capabilities can be computed from an organisms annotated genome using metabolic network reconstruction. However, current computational methods cannot deal with genome-scale metabolic networks. Part of the problem is that these methods aim to enumerate all metabolic pathways, while computation of all (elementally balanced) conversions between nutrients and products would suffice. Indeed, the elementary conversion modes (ECMs, defined by Urbanczik and Wagner) capture the full metabolic capabilities of a network, but the use of ECMs has not been accessible, until now. We extend and explain the theory of ECMs, implement their enumeration in ecmtool, and illustrate their applicability. This work contributes to the elucidation of the full metabolic footprint of any cell.

systems biology↗

bioRxiv2019

Latent information about optimal behaviour forces evolution of noisy signal transduction

An open problem in biology is to understand when particular adaptation strategies of microorganisms are selected during evolution. They range from random, bet-hedging strategies to deterministic, responsive strategies, relying on signalling circuits. We present an evolutionary model that integrates basic statistical physics of molecular circuits with fitness maximisation and information theory. This model provides an explanation for a puzzling observation on responsive strategies: the accuracy with which signalling networks track external signals seems remarkably low. Single cells often distinguish only between 2 to 4 concentration ranges, corresponding to 1 or 2 bits of mutual information between signal and response. Why did evolution lead to such low-fidelity signalling systems? Our theory offers an explanation by taking a novel perspective. It considers the fitness benefit of all signals, including those that are not sensed. We introduce a new concept, latent information, which captures the mutual information between all non-sensed signals and the optimal response. The theory predicts that it is often evolutionarily optimal to transduce sensed signals noisily when latent information is present. It indicates that fitness can indeed be maximal when the mutual information extracted from sensed signals is not maximal, but rather has a low value of about 1 or 2 bits. Cells likely do not sense all signals because of the fitness cost of expressing idle signalling systems that consume limited biosynthetic resources. Our theory illustrates that as the total available information about the optimal behaviour decreases, the cell should trust the available information less, and gamble more. Significance StatementSurprisingly, microorganisms appear to sense only very few environmental signals (such as nutrients and stresses) compared to the number of conditions they can encounter. Even worse, the signals they do sense are transduced at low fidelity. We study the accuracy of sensing in the situation where multiple signals determine the optimal response, but only few signals are actually sensed. We show that it is in fact to be expected that sensing in the presence of latent information should be imprecise, and that signalling circuits should underperform.

evolutionary biology↗

bioRxiv2019

The common message of constraint-based optimization approaches: overflow metabolism is caused by two growth-limiting constraints

Living cells can express different metabolic pathways that support growth. The criteria that determine which pathways are selected in which environment remain unclear. One recurrent selection is overflow metabolism: the simultaneous usage of an ATP-efficient and -inefficient pathway, shown for example in Escherichia coli, Saccharomyces cerevisiae and cancer cells. Many models, based on different assumptions, can reproduce this observation. Therefore, they provide no conclusive evidence which mechanism is causing overflow metabolism. We compare the mathematical structure of these models. Although ranging from Flux Balance Analyses to self-fabricating Metabolism and Expression models, we can rewrite all models into one standard form. We conclude that all models predict overflow metabolism when two, model-specific, growth-limiting constraints are hit. This is consistent with recent theory. Thus, identifying these two constraints is essential for understanding overflow metabolism. We list all imposed constraints by these models, so that they can hopefully be tested in future experiments.

systems biology↗

bioRxiv2019

Cell fate determination by Lamarckian molecule-inheritance and chance

Single, isogenic cells can differ in their survival and adaptation capacity. This phenotypic diversity is generally due to stochastic molecular events. Since mother cells on average pass half of their molecular content on to their daughters, the states of progeny cells strongly correlate with that of mother cells (Lamarckian inheritance). Why a particular cell deviates qualitatively from others therefore requires consideration of chance events along its ancestral lineage. Here we develop theory to understand cellular heterogeneity in terms of stochastic ancestral events of molecule synthesis, molecule degradation and cell divisions. We find that cell growth stochasticity has profound consequences for molecular heterogeneity in isogenic populations of cells, especially for long-lived molecules such as proteins. For instance, the lower bound on noise in molecule copy numbers that has often been observed experimentally is shown to be solely determined by the probability distribution for the generation times of cells. Thus, copy-number noise is unavoidable, even in high-copy number circuits. Stochastic cell-fate and cell-differentiation decisions are therefore not necessarily due to noise in genetic circuits. We conclude that consideration of past chance events along cell lineages improves our understanding of how adaptive and mal-adaptive phenotypic heterogeneity arises in populations of isogenic cells.

biophysics↗

bioRxiv2019

Growth-rate and protein-synthesis dynamics of single Bacillus subtilis cells along their cell-cycle

The growth rate of single bacterial cells is continuously disturbed by random fluctuations in biosynthesis rates and by deterministic cell-cycle events, such as division, genome duplication, and septum formation. It is not understood whether, and how, bacteria reject these disturbances. Here we quantified growth and constitutive protein expression dynamics of single Bacillus subtilis cells, as a function of cell-cycle-progression. Variation in birth size and growth rate, resulting from unequal cell division, is largely compensated for when cells divide again. We analysed the cell-cycle-dynamics of these compensations and found that both growth and protein expression exhibited biphasic behaviour. During a first phase of variable duration, the absolute rates were approximately constant and cells behaved as sizers. In the second phase, rates increased and growth behaviour exhibited characteristics of a timer-strategy. This work shows how cell-cycle-dependent rate adjustments of biosynthesis and growth are integrated to compensate for physio-logical disturbances caused by cell division.\n\nIMPORTANCEUnder constant conditions, bacterial populations can maintain a fixed average cell size and constant exponential growth rate. At the single cell-level, however, cell-division can cause significant physiological perturbations, requiring compensatory mechanisms to restore the growth-related characteristics of individual cells toward that of the average cell. Currently, there is still a major gap in our understanding of the dynamics of these mechanisms, i.e. how adjustments in growth, metabolism and biosynthesis are integrated during the bacterial cell-cycle to compensate the disturbances caused by cell division. Here we quantify growth and constitutive protein expression in individual bacterial cells at sub-cell-cycle resolution. Significantly, both growth and protein production rates display structured and coordinated cell-cycle-dependent dynamics. These patterns reveal the dynamics of growth rate and size compensations during cell-cycle progression. Our findings provide a dynamic cell-cycle perspective that offers novel avenues for the interpretation of physiological processes that underlie cellular homeostasis in bacteria.

microbiology↗

bioRxiv2017

Maximal growth rate requires minimal metabolic complexity

Growth rate is a near-universal selective pressure across microbial species. High growth rates require hundreds of metabolic enzymes, each with different nonlinear kinetics, to be precisely tuned within the bounds set by physicochemical constraints. Yet, the metabolic behaviour of many species is characterized by simple relations between growth rate, enzyme expression levels and metabolic rates. We asked if this simplicity could be the outcome of optimisation by evolution. Indeed, when the growth rate is maximized -in a static environment under mass-conservation and enzyme expression constraints- we prove mathematically that the resulting optimal metabolic flux distribution is described by a limited number of subnetworks, known as Elementary Flux Modes (EFMs). We show that, because EFMs are the minimal subnetworks leading to growth, a small active number automatically leads to the simple relations that are measured. We find that the maximal number of flux-carrying EFMs is determined only by the number of imposed constraints on enzyme expression, not by the size, kinetics or topology of the network. This minimal-EFM extremum principle is illustrated in a graphical framework, which explains qualitative changes in microbial behaviours, such as overflow metabolism and co-consumption, and provides a method for identification of the enzyme expression constraints that limit growth under the prevalent conditions. The extremum principle applies to all microorganisms that are selected for maximal growth rates under protein concentration constraints, for example the solvent capacities of cytosol, membrane or periplasmic space.\n\nAuthor summaryThe microbial genome encodes for a large network of enzyme-catalyzed reactions. The reaction rates depend on concentrations of enzymes and metabolites, which in turn depend on those rates. Cells face a number of biophysical constraints on enzyme expression, for example due to a limited membrane area or cytosolic volume. Considering this complexity and nonlinearity of metabolism, how is it possible, that experimental data can often be described by simple linear models? We show that it is evolution itself that selects for simplicity. When reproductive rate is maximised, the number of active independent metabolic pathways is bounded by the number of growth-limiting enzyme constraints, which is typically small. A small number of pathways automatically generates the measured simple relations. We identify the importance of growth-limiting constraints in shaping microbial behaviour, by focussing on their mechanistic nature. We demonstrate that overflow metabolism - an important phenomenon in bacteria, yeasts, and cancer cells - is caused by two constraints on enzyme expression. We derive experimental guidelines for constraint identification in microorganisms. Knowing these constraints leads to increased understanding of metabolism, and thereby to better predictions and more effective manipulations.

systems biology↗

bioRxiv2017

Bifurcation analysis of metabolic pathways: an illustration from yeast glycolysis

In microorganisms such as bacteria or yeasts, metabolic rates are tightly coupled to growth rate, and therefore to fitness. Although the topology of central pathways are largely conserved across organisms, the enzyme kinetics and their parameters generally vary. This prevents us to understand and predict (changes in) metabolic dynamics. The analytical treatment of metabolic pathways is generally restricted to small models, containing maybe two to four equations. Since such small core models involve much coarse graining, their biological interpretation is often hampered. In this paper we aim to bridge the gap between analytical, more in-depth treatment of small core models and biologically more realistic and detailed models by developing new methods. We illustrate these methods for a model of glycolysis in Saccharo-myces cerevisiae yeast, arguably the best characterised metabolic pathway in the literature. The model is more involved than in previous studies, and involves both ATP/ADP and NADH/NAD householding.\n\nA detailed analysis of the steady state equations sheds new light on two recently studied biological phenomena in yeast glycolysis: whether it is to be expected that fructose-1,6-biphosphate (FBP) parameterises all steady states, and the occurrence of bistability between a regular steady state and imbalanced steady state in which glycolytic intermediates keep accumulating.\n\nThis work shows that the special structure of metabolic pathways does allow for more in-depth bifurcation analyses than is currently the norm. We especially emphasise which of the techniques developed here scale to larger pathways, and which do not.

systems biology↗