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Wolfram Liebermeister

Publications and source records attributed to Wolfram Liebermeister.

14 recordsLinked to original sources
arXiv2025

A compact model of Escherichia coli core and biosynthetic metabolism

Metabolic models condense biochemical knowledge about organisms in a structured and standardised way. As large-scale network reconstructions are readily available for many organisms, genome-scale models are being widely used among modellers and engineers. However, these large models can be difficult to analyse and visualise and occasionally generate predictions that are hard to interpret or even biologically unrealistic. Of the thousands of enzymatic reactions in a typical bacterial metabolism, only a few hundred form the metabolic pathways essential to produce energy carriers and biosynthetic precursors. These pathways carry relatively high flux, are central to maintaining and reproducing the cell, and provide precursors and energy to engineered metabolic pathways. Focusing on these central metabolic subsystems, we present iCH360, a manually curated medium-scale model of energy and biosynthesis metabolism for the well-studied bacterium Escherichia coli K-12 MG1655. The model is a sub-network of the most recent genome-scale reconstruction, iML1515, and comes with an updated layer of database annotations and with a range of metabolic maps for visualisation. We enriched the stoichiometric network with extensive biological information and quantitative data, enhancing the scope and applicability of the model. In addition, we assess the properties of this model in comparison to its genome-scale parent and demonstrate the use of the network and supporting data in various scenarios, including enzyme-constrained flux balance analysis, elementary flux mode analysis, and thermodynamic analysis. Overall, we believe this model holds the potential to become a reference medium-scale metabolic model for E. coli.

q-bio.MN↗
arXiv2025

Complexity reduction by symmetry: uncovering the minimal regulatory network for logical computation in bacteria

Symmetry principles play an important role in geometry, and physics, allowing for the reduction of complicated systems to simpler, more comprehensible models that preserve the system's features of interest. Biological systems are often highly complex and may consist of a large number of interacting parts. Using symmetry fibrations, the relevant symmetries for biological "message-passing" networks, we introduce a scheme, called Complexity Reduction by Symmetry or ComSym, to reduce the gene regulatory networks of Escherichia coli and Bacillus subtilis bacteria to core networks in a way that preserves the dynamics and uncovers the computational capabilities of the network. Gene nodes in the original network that share isomorphic input trees are collapsed by the fibration into equivalence classes called fibers, whereby nodes that receive signals with the same "history" belong to one fiber and synchronize. Then we reduce the networks to its minimal computational core via k-core decomposition. This computational core consists of a few strongly connected components or "signal vortices", in which signals can cycle through. While between them, these "signal vortices" transmit signals in a feedforward manner. These connected components perform signal processing and decision making in the bacterial cell by employing a series of genetic toggle-switch circuits that store memory, plus oscillator circuits. These circuits act as the central computation device of the network, whose output signals then spread to the rest of the network. Our reduction method opens the door to narrow the vast complexity of biological systems to their minimal parts in a systematic way by using fundamental theoretical principles of symmetry.

q-bio.CB↗
arXiv2022

Metabolic fluxes and value production

Metabolic fluxes in cells are governed by physical, physiological, and economic principles. Here I assume an optimal allocation of enzyme resources and postulate a general principle for metabolism: each enzyme must convert less valuable into more valuable metabolites to justify its own cost. The "values", called economic potentials, describe the individual contributions of metabolites to cell fitness. Local value production implies that the cost of an enzyme must be balanced by a benefit, given by the economic potential difference the catalysed reaction multiplied by the flux. Flux profiles that satisfy this principle - i.e. for which consistent potentials can be found - are called economical. Economical fluxes must lead from lower to higher economic potentials, so certain flux cycles are incompatible with any choice of economic potentials and can be excluded. To obtain economical flux profiles, non-beneficial local patterns, called futile motifs, can be systematically removed from a given flux distribution. The principle of local value production resembles thermodynamic principles and complements them in models. Here I describe a modelling framework called Value Balance Analysis (VBA) that uses the two principles and yields the same solution as enzyme cost minimisation (in kinetic models) and flux cost minimisation (in FBA). Given an economical flux distribution, kinetic models in enzyme-optimal states and with these fluxes can be constructed systematically. VBA justifies the principle of minimal fluxes and the exclusion of futile cycles, predicts enzymes that could be plausible targets for regulation, provides criteria for the usage of enzymes and pathways, and explains the choice between high-yield and low-yield flux modes.

q-bio.MN↗
arXiv2022

Enzyme economy and metabolic control

The metabolic state of a cell, comprising fluxes, metabolite concentrations and enzyme levels, is shaped by a compromise between metabolic benefit and enzyme cost. This hypothesis and its consequences can be studied by computational models and using a theory of metabolic value. In optimal metabolic states, any increase of an enzyme level must improve the metabolic performance to justify its own cost, so each active enzyme must contribute to the cell's benefit by producing valuable products. This principle of value production leads to variation rules that relate metabolic fluxes and reaction elasticities to enzyme costs. Metabolic value theory provides a language to describe this. It postulates a balance of local values, which I derive here from concepts of metabolic control theory. Economic state variables, called economic potentials and loads, describe how metabolites, reactions, and enzymes contribute to metabolic performance. Economic potentials describe the indirect value of metabolite production, while economic loads describe the indirect value of metabolite concentrations. These economic variables, and others, are linked by local balance equations. These laws for optimal metabolic states define conditions for metabolic fluxes that hold for a wide range of rate laws. To produce metabolic value, fluxes run from lower to higher economic potentials, must be free of futile cycles, and satisfy a principle of minimal weighted fluxes. Given an economical flux mode, one can systematically construct kinetic models in which all enzymes have positive effects on metabolic performance.

q-bio.MN↗
arXiv2022

Optimal enzyme rhythms in cells

Cells can use periodic enzyme activities to adapt to periodic environments or existing internal rhythms and to establish metabolic cycles that schedule biochemical processes in time. A periodically changing allocation of the protein budget between reactions or pathways may increase the overall metabolic efficiency. To study this hypothesis, I quantify the possible benefits of small-amplitude enzyme rhythms in kinetic models. Starting from an enzyme-optimised steady state, I score the effects of possible enzyme rhythms on a metabolic objective and optimise their amplitudes and phase shifts. Assuming small-amplitude rhythms around an optimal reference state, optimal phases and amplitudes can be computed by solving a quadratic optimality problem. In models without amplitude constraints, general periodic enzyme profiles can be obtained by Fourier synthesis. The theory of optimal enzyme rhythms combines the dynamics and economics of metabolic systems and explains how optimal small-amplitude enzyme profiles are shaped by network structure, kinetics, external rhythms, and the metabolic objective. The formulae show how orchestrated enzyme rhythms can exploit synergy effects to improve metabolic performance and that optimal enzyme profiles are not simply adapted to existing metabolic rhythms, but that they actively shape these rhythms to improve their own (and other enzymes') efficiency. The resulting optimal enzyme profiles "portray" the enzymes' dynamic effects in the network: for example, enzymes that act synergistically may be coexpressed, periodically and with some optimal phase shifts. The theory yields optimality conditions for enzyme rhythms in metabolic cycles, with static enzyme adaptation as a special case, and predicts how cells should combine transcriptional and posttranslational regulation to realise enzyme rhythms at different frequencies.

q-bio.MN↗
arXiv2022

Flux cost functions and optimal metabolic states

The metabolic fluxes in cells follow physical, biochemical, and economic principles. Some flux balance analysis (FBA) methods trade flux benefit against flux cost. However, if flux cost functions are linear and meant to describe underlying enzyme costs, this entails that enzyme efficiencies are constant and ignores the interplay between fluxes, metabolite concentrations and enzyme levels in cells. Here I introduce realistic flux cost functions that describe an "overhead cost", namely the minimum enzyme and metabolite cost associated with the fluxes in a kinetic model. These flux cost functions have general mathematical properties. Enzymatic flux cost functions, which represent enzyme costs, scale proportionally with the flux profile and are concave on the flux polytope. Kinetic flux cost functions represent the sum of enzyme and metabolite costs. If two flux profiles are superimposed, their different demands for metabolite concentrations cause an extra compromise cost, which makes flux cost functions strictly concave in almost all cases. When fluxes change their direction, the enzymatic cost jumps abruptly. Here I propose two methods for flux modelling: Flux Cost Minimisation, a nonlinear variant of FBA with flux minimisation, and Flux Benefit Optimisation, a nonlinear variant of FBA with molecular crowding. The optimal flux profiles, at a given flux benefit, are vertices of the flux polytope. Linear approximations of enzymatic flux cost can be used in FBA. In contrast to flux costs chosen ad hoc, these functions reflect the enzyme kinetics and extracellular concentrations in realistic kinetic models. Based on enzymatic flux costs, we can describe the cell growth rate as a convex function on the flux polytope and derive growth-optimal metabolic states and statistical distributions for the fluxes in cell populations.

q-bio.MN↗
arXiv2022

BioSimulators: a central registry of simulation engines and services for recommending specific tools

Computational models have great potential to accelerate bioscience, bioengineering, and medicine. However, it remains challenging to reproduce and reuse simulations, in part, because the numerous formats and methods for simulating various subsystems and scales remain siloed by different software tools. For example, each tool must be executed through a distinct interface. To help investigators find and use simulation tools, we developed BioSimulators (https://biosimulators.org), a central registry of the capabilities of simulation tools and consistent Python, command-line, and containerized interfaces to each version of each tool. The foundation of BioSimulators is standards, such as CellML, SBML, SED-ML, and the COMBINE archive format, and validation tools for simulation projects and simulation tools that ensure these standards are used consistently. To help modelers find tools for particular projects, we have also used the registry to develop recommendation services. We anticipate that BioSimulators will help modelers exchange, reproduce, and combine simulations.

q-bio.QM↗
arXiv2022

Structural thermokinetic modelling

Translating metabolic networks into dynamic models is difficult if kinetic constants are unknown. Structural Kinetic Modelling (SKM) replaces reaction elasticities by independent random numbers. Here I propose a variant that accounts for reversible reactions and thermodynamics: in Structural Thermokinetic Modelling (STM), correlated elasticities are computed from enzyme saturation values and thermodynamic forces, which are physically independent. STM relies on a dependency schema in which basic variables can be sampled, fitted to data, or optimised, while all other variables are computed from them. Probability distributions in the dependency schema define a model ensemble, which leads to probabilistic predictions even if data are scarce. STM highlights the importance of variabilities, dependencies and covariances of biological variables. By choosing or sampling the basic variables, we can convert metabolic networks into kinetic models with consistent reversible rate laws. Metabolic control coefficients obtained from these models can tell us about metabolic dynamics, including responses and optimal adaptations to perturbations as well as enzyme synergies, metabolite correlations, and metabolic fluctuations arising from chemical noise. By comparing model variants with different network structures, fluxes, thermodynamic forces, regulation, or types of rate laws, we can quantify the effects of these model features. To showcase STM, I study metabolic control, metabolic fluctuations, and enzyme synergies, and how they are shaped by thermodynamic forces. Thermodynamics can be used to obtain more precise predictions of flux control, enzyme synergies, correlated flux and metabolite variations, and of the emergence and propagation of metabolic noise.

q-bio.MN↗
arXiv2020

ObjTables: structured spreadsheets that promote data quality, reuse, and integration

A central challenge in science is to understand how systems behaviors emerge from complex networks. This often requires aggregating, reusing, and integrating heterogeneous information. Supplementary spreadsheets to articles are a key data source. Spreadsheets are popular because they are easy to read and write. However, spreadsheets are often difficult to reanalyze because they capture data ad hoc without schemas that define the objects, relationships, and attributes that they represent. To help researchers reuse and compose spreadsheets, we developed ObjTables, a toolkit that makes spreadsheets human- and machine-readable by combining spreadsheets with schemas and an object-relational mapping system. ObjTables includes a format for schemas; markup for indicating the class and attribute represented by each spreadsheet and column; numerous data types for scientific information; and high-level software for using schemas to read, write, validate, compare, merge, revision, and analyze spreadsheets. By making spreadsheets easier to reuse, ObjTables could enable unprecedented secondary meta-analyses. By making it easy to build new formats and associated software for new types of data, ObjTables can also accelerate emerging scientific fields.

cs.DB↗
arXiv2019

Automated generation of bacterial resource allocation models

Resource Balance Analysis (RBA) is a computational method based on resource allocation, which performs accurate quantitative predictions of whole-cell states (i.e. growth rate, meta-bolic fluxes, abundances of molecular machines including enzymes) across growth conditions. We present an integrated workflow of RBA together with the Python package RBApy. RBApy builds bacterial RBA models from annotated genome-scale metabolic models by add-ing descriptions of cellular processes relevant for growth and maintenance. The package in-cludes functions for model simulation and calibration and for interfacing to Escher maps and Proteomaps for visualization. We demonstrate that RBApy faithfully reproduces results ob-tained by a hand-curated and experimentally validated RBA model for Bacillus subtilis. We also present a calibrated RBA model of Escherichia coli generated from scratch, which ob-tained excellent fits to measured flux values and enzyme abundances. RBApy makes whole-cell modeling accessible for a wide range of bacterial wild-type and engineered strains, as il-lustrated with a CO2-fixing Escherichia coli strain.

q-bio.QM↗
arXiv2016

The protein cost of metabolic fluxes: prediction from enzymatic rate laws and cost minimization

Bacterial growth depends crucially on metabolic fluxes, which are limited by the cell's capacity to maintain metabolic enzymes. The necessary enzyme amount per unit flux is a major determinant of metabolic strategies both in evolution and bioengineering. It depends on enzyme parameters (such as kcat and KM constants), but also on metabolite concentrations. Moreover, similar amounts of different enzymes might incur different costs for the cell, depending on enzyme-specific properties such as protein size and half-life. Here, we developed enzyme cost minimization (ECM), a scalable method for computing enzyme amounts that support a given metabolic flux at a minimal protein cost. The complex interplay of enzyme and metabolite concentrations, e.g. through thermodynamic driving forces and enzyme saturation, would make it hard to solve this optimization problem directly. By treating enzyme cost as a function of metabolite levels, we formulated ECM as a numerically tractable, convex optimization problem. Its tiered approach allows for building models at different levels of detail, depending on the amount of available data. Validating our method with measured metabolite and protein levels in E. coli central metabolism, we found typical prediction fold errors of 3.8 and 2.7, respectively, for the two kinds of data. ECM can be used to predict enzyme levels and protein cost in natural and engineered pathways, establishes a direct connection between protein cost and thermodynamics, and provides a physically plausible and computationally tractable way to include enzyme kinetics into constraint-based metabolic models, where kinetics have usually been ignored or oversimplified.

q-bio.MN↗
arXiv2015

SBtab - Conventions for structured data tables in Systems Biology

Data tables in the form of spreadsheets or delimited text files are the most utilised data format in Systems Biology. However, they are often not sufficiently structured and lack clear naming conventions that would be required for modelling. We propose the SBtab format as an attempt to establish an easy-to-use table format that is both flexible and clearly structured. It comprises defined table types for different kinds of data; syntax rules for usage of names, shortnames, and database identifiers used for annotation; and standardised formulae for reaction stoichiometries. Predefined table types can be used to define biochemical network models and the biochemical constants therein. The user can also define own table types, adjusting SBtab to other types of data. Software code, tools, and further information can be found at www.sbtab.net.

q-bio.MN↗
arXiv2015

The enzyme cost of given metabolic flux distributions, as a function of logarithmic metabolite levels, is convex

Enzyme costs play a major role in the choice of metabolic routes, both in evolution and bioengineering. Given desired fluxes, necessary enzyme levels can be estimated based on known rate laws and on a principle of minimal enzyme cost. With logarithmic metabolite levels as free variables, enzyme cost functions and constraints in optimality and sampling problems can be handled easily. The set of feasible metabolite profiles forms a polytope in log-concentration space, whose points represent all possible steady states of a kinetic model. We show that enzyme cost is a convex function on this polytope. This makes enzyme cost minimization - finding optimal enzyme profiles and corresponding metabolite profiles that realize a desired flux at a minimal cost - a convex optimization problem.

q-bio.MN↗