Biology subjects

Liebermeister, W.

Publications and source records attributed to Liebermeister, W..

11 recordsLinked to original sources

bioRxiv2026

Model-based inference of enzyme inhibitions from perturbation-induced metabolic dynamics

In microbes, metabolism plays a key role in the first rapid adaptation to sudden challenges such as nutrient limitations or toxic compounds. While metabolomics enables the profiling of stimuli-induced metabolic changes, computational approaches that can interpret these data to mechanistically explain how perturbations propagate through metabolism to produce the observed changes are lagging behind. Here, we developed a computational framework, called Inference from Metabolic Fingerprints (IMF), to model the immediate dynamic response to a metabolic perturbation and systematically infer its entry point (i.e. enzymatic target). IMF assumes small perturbations and linearizes the nonlinear dynamics around a reference steady state. This allows IMF to scale with large metabolic networks and bypass missing kinetic parameters by allowing for fast and efficient ensemble sampling. We apply IMF to a model of central metabolism in Escherichia coli. Using in-silico and experimental data, we demonstrate the ability to infer the target of metabolic perturbations in spite of unknown kinetic parameters and incomplete metabolic data. Hence, we show that IMF is an effective approach for designing, analyzing and interpreting time-resolved metabolomics.

systems biology↗

bioRxiv2026

Growth costs of suboptimal protein allocation in nonlinear models of growing cells

Microbial growth depends on how cells allocate their limited proteome among competing functions. Although many proteins are expressed near levels that maximize growth, deviations from these optima are common and can impose substantial fitness costs. Modeling the growth costs of suboptimal protein allocation remains challenging because protein expression influences growth through multiple interacting mechanisms, including biosynthetic demands, enzyme kinetics, and limits on cellular density. Here we analyze these effects using growth balance analysis (GBA), a nonlinear framework that predicts steady-state growth and biomass composition of coarse-grained microbial models from basic cellular constraints. The optimal biomass compositions predicted for these models include not only protein concentrations but also the reactant concentrations required to saturate enzymes through nonlinear rate laws, thereby capturing more complex resource trade-offs than in conventional linear resource allocation models. Using these GBA models, we compute optimal biomass compositions with individual proteins fixed at suboptimal levels. The resulting relationships between suboptimal protein allocation and growth rate are consistent with qualitative experimental patterns in bacteria, with growth effects depending on protein function (including idle proteins), environmental conditions, toxic byproducts, and alternative reactions. These results indicate a practical and tractable approach for modeling growth costs arising from suboptimal protein allocation, and suggest a basis for predictive modeling in metabolic engineering and synthetic biology.

systems biology↗

bioRxiv2025

Growth Mechanics and the emergence of metabolic oscillations in growing cells

Unicellular organisms exhibit oscillations in metabolic activity and gene expression, even when growing in static media with no external dynamic stimuli. The cause and possible function of these endogenous oscillations are still not fully understood, with different hypotheses including its origin as a byproduct of misguided regulatory processes. To investigate whether such oscillations could be functional rather than incidental, we introduce Growth Mechanics (GM) as a general mathematical framework to study the dynamic resource allocation in models of whole self-replicating cells, built exclusively on the first principles of fitness maximization, mass conservation, nonlinear reaction kinetics, and constant cell density. Inspired by the physical theory of classical mechanics, we first find the simplest mathematical description the problem in terms of generalized coordinates, and then solve the optimal dynamical resource allocation for cells growing in any given medium using the Euler-Lagrange equation, resulting in analytical "equations of optimal motion" (EOM) that apply for growing cells in general. We then solve these equations numerically for simple growing cell models and show that, in general, oscillations are necessary to maximize cell fitness by getting more saturated reactions at the time they are most needed. We also show how the EOM predict the emergence of quasi-linear dependencies of the metabolic oscillation frequency and the ribosome protein allocation with the cell growth rate at different growth media, in line with the "growth laws" observed experimentally in microbes. This work contributes to the foundations of theoretical cell biology with general quantitative principles and a bridge to theoretical tools of physics.

biophysics↗

bioRxiv2023

Optimal enzyme profiles in unbranched metabolic pathways

How to optimize the allocation of enzymes in metabolic pathways has been a topic of study for many decades. Although the general problem is complex and non-linear, we have previously shown that it can be solved by convex optimization. In this paper, we focus on unbranched metabolic pathways with simplified enzymatic rate laws and derive analytic solutions to the optimization problem. We revisit existing solutions based on the limit of mass-action rate laws and present new solutions for other rate laws. Furthermore, we revisit a known relationship between flux control coefficients and enzyme abundances in optimal metabolic states. We generalize this relationship to models with density constrains on enzymes and metabolites, and present a new local relationship between optimal reaction elasticities and enzyme amounts. Finally, we apply our theory to derive simple kinetics-based formulae for protein allocation during bacterial growth.

systems biology↗

bioRxiv2022

RBAtools: a programming interface for Resource Balance Analysis modelling

MotivationEfficient resource allocation contributes to an organisms fitness and improves success in competition. The Resource Balance Analysis (RBA) computational framework enables the analysis of an organisms growth-optimal configurations in various environments, at genome-scale. The existing RBApy software enables the construction of RBA models on genome-scale and the calculation of medium-specific, growth-optimal cell states, including metabolic fluxes and the abundance of macromolecular machines. However, to address the needs of non-expert users, there is a need for a simple programming API, easy to use and interoperable with other software through convenient formats for models and data. ResultsThe RBAtools python package enables the convenient use of RBA models and addresses non-expert users. As a flexible programming interface, it enables the implementation of custom workflows and simplifies the modification of existing genome-scale RBA models and data export to various formats. The features comprise simulation, model fitting, parameter screens, sensitivity analysis, variability analysis, and the construction of Pareto fronts. Models and data are represented as structured tables, in HTML, and common formats for fluxomics and proteomics visualization. AvailabilityDetails about RBA can be found at rba.inrae.fr. RBAtools documentation, installation instructions, and tutorials are available at sysbioinra.github.io/rbatools. Contactwolfram.liebermeister@inrae.fr, anne.goelzer@inrae.fr

systems biology↗

bioRxiv2022

Growth Mechanics: General principles of optimal cellular resource allocation in balanced growth

The physiology of biological cells evolved under physical and chemical constraints such as mass conservation, nonlinear reaction kinetics, and limits on cell density. For unicellular organisms, the fitness that governs this evolution is mainly determined by the balanced cellular growth rate. We previously introduced Growth Balance Analysis (GBA) as a general framework to model such nonlinear systems, and we presented analytical conditions for optimal balanced growth in the special case that the active reactions are known. Here, we develop Growth Mechanics (GM) as a more general, succinct, and powerful analytical description of the growth optimization of GBA models, which we formulate in terms of a minimal number of dimensionless variables. GM uses Karush-Kuhn-Tucker (KKT) conditions in a Lagrangian formalism. It identifies fundamental principles of optimal resource allocation in GBA models of any size and complexity, including the analytical conditions that determine the set of active reactions at optimal growth. We identify from first principles the economic values of biochemical reactions, expressed as marginal changes in cellular growth rate; these economic values can be related to the costs and benefits of proteome allocation into the reactions catalysts. Our formulation also generalizes the concepts of Metabolic Control Analysis to models of growing cells. GM unifies and extends previous approaches of cellular modeling and analysis, putting forward a program to analyze cellular growth through the stationarity conditions of a Lagrangian function. GM thereby provides a general theoretical toolbox for the study of fundamental mathematical properties of balanced cellular growth.

biophysics↗

bioRxiv2022

Artificial Metabolic Networks: enabling neural computation with metabolic networks

Constraint-based metabolic models have been used for decades to predict the phenotype of microorganisms in different environments. However, quantitative predictions are limited unless labor-intensive measurements of media uptake fluxes are performed. We show how hybrid neural-mechanistic models can serve as an architecture for machine learning providing a way to improve phenotype predictions. We illustrate our hybrid models with growth rate predictions of Escherichia coli and Pseudomonas putida grown in different media and with phenotype predictions of gene knocked-out Escherichia coli mutants. Our neural-mechanistic models systematically outperform constraint-based models and require training set sizes orders of magnitude smaller than classical machine learning methods. Our hybrid approach opens a doorway to enhancing constraint-based modeling: instead of constraining mechanistic models with additional experimental measurements, our hybrid models grasp the power of machine learning while fulfilling mechanistic constrains, thus saving time and resources in typical systems biology or biological engineering projects.

systems biology↗

bioRxiv2019

Model balancing: consistent in-vivo kinetic constants and metabolic states obtained by convex optimisation

Enzyme kinetic constants in vivo are largely unknown, which limits the construction of large metabolic models. While model fitting, in principle, aims at fitting kinetic constants to measured metabolic fluxes, metabolite concentrations, and enzyme concentrations, the resulting estimation problems are typically non-convex and hard to solve, especially if models are large. Here we assume that metabolic fluxes are known and show how consistent kinetic constants, metabolite concentrations, and enzyme concentrations can be determined simultaneously from data. If one specific term is omitted - a term that penalises small enzyme concentrations - we obtain a convex optimality problem with a unique local optimum. The estimation method with or without this term, called model balancing, applies to models with a wide range of rate laws and accounts for thermodynamic constraints on kinetic constants and metabolite concentrations through thermodynamic forces. It can be used to estimate in-vivo kinetic constants from omics data, to complete and adjust available data, or to construct plausible metabolic states with a predefined flux distribution. As a demonstrative case, we balance a model of E. coli central metabolism with artificial or experimental data. The tests show what information about kinetic constants can be obtained from omics data, and reveal the practical limits of estimating in-vivo kinetic constants.

systems biology↗

bioRxiv2018

Optimal metabolic states in cells

Cells, in order to thrive, make efficient use of metabolites, proteins, energy, membrane space, and time. How, for example, should they allocate the available amount of protein to different metabolic pathways or cell functions? To model metabolic behaviour as an economic problem, some flux analysis model, kinetic models, and cell models apply optimality principles. However, due to their different assumptions these models are hard to compare and combine. Benefits and costs of metabolic pathways - e.g. favouring high production fluxes and low metabolite and enzyme cost - can be derived from general fitness objectives such as fast cell growth. To define pathway objectives, we may assume "optimistically" that, given a pathway state, any cell variables outside the pathway will be chosen for maximal fitness. The resulting fitness defines an effective pathway objective as a function of the pathway variables. Here I propose a unified theory that considers kinetic models, describes the set of feasible states as a state manifold and score each state by cost and benefit functions for fluxes, metabolite concentrations, and enzyme levels. To screen the state manifold and to find optimal states, the problem can be projected into flux, metabolite, or enzyme space, where effective cost and benefit functions are used. We reobtain existing modelling approaches such as enzyme cost minimisation or nonlinear versions of Flux Balance Analysis. Due to their common origin, the different approaches share mathematical optimality conditions of the same form. A general theory of optimal metabolic states, as proposed here, provides a logical link between existing modelling approaches and can help justify, interconvert, and combine metabolic optimality problems.

systems biology↗

bioRxiv2018

The value structure of metabolic states

To improve their metabolic performance, cells need to find compromises between high metabolic fluxes, low enzyme investments, and well-adapted metabolite concentrations. In mathematical models, such compromises can be described by optimality problems that trade metabolic benefit against enzyme cost. While many such modelling frameworks exist, they are often hard to compare and combine. To unify these modelling approaches, I propose a theory that characterises metabolic systems by a value structure, that is, a pattern of local costs and benefits assigned to all elements in the network. The economic values of metabolites, fluxes, and enzymes are interlinked by local balance equations. Formally defined as shadow values, the economic variables serve as local proxies for benefits that arise anywhere in the network, but are represented as local costs or benefits in the reaction of interest. Here I derive economic variables and their balance equations for kinetic, stoichiometric, and cell models. Metabolic value theory provides a new perspective on biochemical networks, defines concepts for comparing and combining metabolic optimality problems, and is useful for semi-automatic, layered, and modular modelling.

systems biology↗

bioRxiv2017

Profiling metabolic flux modes by enzyme cost reveals variable trade-offs between growth and yield in Escherichia coli.

Microbes may maximize the number of daughter cells per time or per amount of nutrients consumed. These two strategies correspond, respectively, to the use of enzyme-efficient or substrate-efficient metabolic pathways. In reality, fast growth is often associated with wasteful, yield-inefficient metabolism, and a general thermodynamic trade-off between growth rate and biomass yield has been proposed to explain this. We studied growth rate/yield trade-offs by using a novel modeling framework, Enzyme-Flux Cost Minimization (EFCM) and by assuming that the growth rate depends directly on the enzyme investment per rate of biomass production. In a comprehensive mathematical model of core metabolism in E. coli, we screened all elementary flux modes leading to cell synthesis, characterized them by the growth rates and yields they provide, and studied the shape of the resulting rate/yield Pareto front. By varying the model parameters, we found that the rate/yield trade-off is not universal, but depends on metabolic kinetics and environmental conditions. A prominent trade-off emerges under oxygen-limited growth, where yield-inefficient pathways support a 2-to-3 times higher growth rate than yield-efficient pathways. EFCM can be widely used to predict optimal metabolic states and growth rates under varying nutrient levels, perturbations of enzyme parameters, and single or multiple gene knockouts.\n\nAuthor SummaryWhen cells compete for nutrients, those that grow faster and produce more offspring per time are favored by natural selection. In contrast, when cells need to maximize the cell number at a limited nutrient supply, fast growth does not matter and an efficient use of nutrients (i.e. high biomass yield) is essential. This raises a basic question about metabolism: can cells achieve high growth rates and yields simultaneously, or is there a conflict between the two goals? Using a new modeling method called Enzymatic Flux Cost Minimization (EFCM), we predict cellular growth rates and find that growth rate/yield trade-offs and the ensuing preference for enzyme-efficient or substrate-efficient metabolic pathways are not universal, but depend on growth conditions such as external glucose and oxygen concentrations.

systems biology↗