Biology subjects

Planque, R.

Publications and source records attributed to Planque, R..

14 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↗

bioRxiv2025

On the conditions for shifts in metabolic strategies

AO_SCPLOWBSTRACTC_SCPLOWMany heterotrophic microorganisms gradually replace an energetically-efficient mode of metabolism by an inefficient, more-wasteful overflow metabolism above a critical growth rate, even though the energy demand continues to rise with growth rate. For instance, complete respiration of a sugar is replaced by its fermentation. We derive the conditions for this to happen, using a core model of metabolism and growth that is qualitatively in agreement with experimental data. Assuming a fixed cellular protein content, the model shows that protein expression of efficient metabolism and anabolism rises as function of growth rate until a critical value is reached. This growth-associated protein expression is at the expense of proteins associated with future adaptation. At the critical growth rate, this preparatory pool is reduced to zero. Beyond the critical growth rate, the anabolic protein pool and the energy demand continue to rise and therefore less protein remains for catabolism. In this regime, the inefficient metabolism gradually takes over ATP synthesis from the efficient mode. It can do so if it requires less protein per unit of ATP flux. The catabolic protein pool then decreases while the anabolic pool increases. This continues until all catabolic protein is allocated to the inefficient strategy and to anabolism. We show that this can occur only if the maximal growth rate of the inefficient mode is higher than the critical growth rate. We show that this condition is precisely the requirement for the second mode to be more proteome-efficient than the first mode. Finally, we reduce a genome-scale model of protein expression in the yeast Saccharomyces cerevisiae to a variant of our core model and show that it is still qualitatively in agreement with the experimental data used to validate the original model.

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

Sensing cellular growth rate facilitates its robust optimal adaptation to changing conditions

AO_SCPLOWBSTRACTC_SCPLOWThe determinants of growth rate and the associated metabolism has been at center stage in microbial physiology for over seventy years. In this paper we show that a cell sensing its own growth rate is in principle capable of maximising it using a gene regulatory circuit responsible for adapting metabolic enzyme concentrations in dynamic conditions. This is remarkable, since any state of (close-to) optimal growth depends on nutrient conditions, and is thus not a fixed target. We derive the properties of such gene regulatory networks, and prove that such circuits allow the growth rate to be a Lyapunov function. We derive this from a general stoichiometric and kinetic description of cellular metabolism. Interestingly, our finding is in agreement with our current understanding of how E. coli controls its growth rate. It uses ppGpp to tune the growth rate by balancing metabolic and ribosomal protein expression. Since ppGpp covaries 1-to-1 with the protein translation rate, an excellent proxy for growth rate, on a timescale of seconds, this suggests that direct sensing of the growth rate underlies growth rate optimisation in E. coli.

systems biology↗

bioRxiv2022

Lysosomal calcium loading promotes arrhythmias by potentiating ryanodine receptor release

Spontaneous calcium release by ryanodine receptors (RyRs) due to intracellular calcium overload results in delayed afterdepolarisations, closely associated with life-threatening arrhythmias. In this regard, inhibiting lysosomal calcium release by two-pore channel 2 (TPC2) knockout has been shown to reduce the incidence of ventricular arrhythmias under {beta}-adrenergic stimulation. However, mechanistic investigations into the role of lysosomal function on RyR spontaneous release remain missing. We investigate the calcium handling mechanisms by which lysosome function modulates RyR spontaneous release, and determine how lysosomes are able to mediate arrhythmias by its influence on calcium loading. Mechanistic studies were conducted using a population of biophysically-detailed mouse ventricular models including for the first time modelling of lysosomal function, and calibrated by experimental calcium transients modulated by TPC2. We demonstrate that lysosomal calcium uptake and release can synergistically provide a buffering pathway of fast calcium transport, by which lysosomal calcium release primarily modulates sarcoplasmic reticulum (SR) calcium reuptake and RyR release. Enhancement of this lysosomal transport pathway promoted RyR spontaneous release by elevating the SR-junction calcium gradient. In contrast, blocking either lysosomal calcium uptake or release revealed an antiarrhythmic impact. Under conditions of calcium overload, our results indicate that these responses are strongly modulated by intercellular variability in L-type calcium current, RyR release, and SERCA reuptake. Altogether, our investigations identify that lysosomal calcium handling directly influences RyR spontaneous release by regulating the SR-junction calcium gradient, suggesting antiarrhythmic strategies and identifying key modulators of lysosomal proarrhythmic action. Statement of SignificanceDelayed afterdepolarisations arising from spontaneous RyR calcium release are an important risk factor for arrhythmogenesis. Inhibiting lysosomal calcium release by TPC2-KO reduces the propensity for ventricular arrhythmias. However, understanding downstream effects of lysosomal calcium release on spontaneous RyR release is lacking. Understanding lysosomes as arrhythmia sources requires alternative approaches to controlled laboratory techniques: these restrain variability experimentally and statistically. Our study presents two methodological novelties by focusing on calibration with experimental findings using a population of biophysically-detailed models and incorporating lysosomal mechanisms. Lysosomal calcium handling promotes RyR spontaneous release by elevating the SR-junction calcium gradient. Blocking lysosomal function uncovers an antiarrhythmic strategy. Lysosome-release proarrhythmic risk is determined by synergistic enhancements of lysosomal uptake with RyR release or L-type calcium current.

biophysics↗

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

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

Elementary Growth Modes provide a molecular description of cellular self-fabrication

A major aim of biology is to predict phenotype from genotype. Here we ask if we can describe all possible molecular states (phenotypes) for a cell that fabricates itself at a constant rate, given its enzyme kinetics and the stoichiometry of all reactions (the genotype). For this, we must understand the autocatalytic process of cellular growth which is inherently nonlinear: steady-state self-fabrication requires a cell to synthesize all of its components, including metabolites, enzymes and ribosomes, in the proportions that exactly match its own composition - the growth demand thus depends on the cellular composition. Simultaneously, the concentrations of these components should be tuned to accomplish this synthesis task - the cellular composition thus depends on the growth demand. We here derive a theory that describes all phenotypes that solve this circular problem; the basic equations show how the concentrations of all cellular components and reaction rates must be balanced to get a constant self-fabrication rate. All phenotypes can be described as a combination of one or more minimal building blocks, which we call Elementary Growth Modes (EGMs). EGMs can be used as the theoretical basis for all models that explicitly model self-fabrication, such as the currently popular Metabolism and Expression models. We then used our theory to make concrete biological predictions: we find that natural selection for maximal growth rate drives microorganisms to states of minimal phenotypic complexity: only one EGM will be active when cellular growth rate is maximised. The phenotype of a cell is only extended with one more EGM whenever growth becomes limited by an additional biophysical constraint, such as a limited solvent capacity of a cellular compartment. Our theory starts from basic biochemical and evolutionary considerations, and describes unicellular life, both in growth-promoting and in stress-inducing environments, in terms of EGMs, the universal building blocks of self-fabrication and a cells phenotype.

systems biology↗

bioRxiv2019

Stability of an adaptively controlled pathway maximising specific flux under varying conditions

Microbial cells need to adapt to changing environmental conditions to survive. There is an evolutionary advantage to grow fast; this requires high metabolic rates, and an efficient allocation of enzymatic resources. Here we study a general control theory called qORAC, developed previously, which allows cells to adaptively control their enzyme allocations to achieve maximal steady state flux. The control is robust to perturbations in the environment, but those perturbations themselves do not feature in the control. In this paper we focus on the archetypical pathway, the linear chain with reversible Michaelis-Menten kinetics, together with qORAC control. First we assume that the metabolic pathway is in quasi-steady state with respect to enzyme synthesis. Then we show that the map between steady state metabolite and enzyme concentrations is a smooth bijection. Using this information, we finally show that the unique (and hence flux-maximising) steady state of this system is locally stable. We provide further evidence that it may in fact be globally stable.

systems biology↗

bioRxiv2018

The winner takes it all: how semelparous insects can become periodical

The aim of this short note is to give a simple explanation for the remarkable periodicity of Magicicada species, which appear as adults only every 13 or 17 years, depending on the region. We show that a combination of two types of density dependence may drive, for large classes of initial conditions, all but one year class to extinction. Competition for food leads to negative density dependence in the form of a uniform (i.e., affecting all age classes in the same way) reduction of the survival probability. Satiation of predators leads to positive density dependence within the reproducing age class. The analysis focuses on the full life cycle map derived by iteration of a semelparous Leslie matrix.

ecology↗

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↗

bioRxiv2017

Maintaining maximal metabolic flux by gene expression control

Many evolutionarily successful bacteria attain high growth rates across growth-permissive conditions. They express metabolic networks that synthesise all cellular components at a high rate. Metabolic reaction rates are bounded by the concentration of the catalysing enzymes and cells have finite resources available for enzyme synthesis. Therefore, bacteria that grow fast should express needed metabolic enzymes at precisely tuned concentrations. To maintain fast growth in a dynamic environment, cells should adjust gene expression of metabolic enzymes. The activity of many of the associated transcription factors is regulated by their binding to intracellular metabolites. We study optimal metabolite-mediated regulation of metabolic-gene expression that preserves maximisation of metabolic fluxes across varying conditions. We logically derive the underlying control logic of this type of optimal regulation, which we term Specific Flux (q) Optimization by Robust Adaptive Control (qORAC), and illustrate it with several examples. We show that optimal metabolic flux can be maintained in the face of K changing parameters only if the number of transcription-factor-binding metabolites is at least equal to K. qORAC-regulation of metabolism can generally be achieved with basic biochemical interactions, indicating that metabolism can operate close to optimality. The theory that we present is directly applicable to synthetic biology, biotechnology and fundamental studies of the regulation of metabolism.

systems biology↗