Mathematical modelling of microbes: metabolism, gene expression and growth

Modeling of astaxanthin biosynthesis via machine learning, mathematical and metabolic network modeling

Natural astaxanthin is synthesized by diverse organisms including: bacteria, fungi, microalgae, and plants involving complex cellular processes, which depend on numerous interrelated parameters. Nonetheless, existing knowledge regarding astaxanthin biosynthesis and the conditions influencing astaxanthin accumulation is fairly limited. Thus, manipulation of the growth conditions to achieve desired biomass and astaxanthin yields can be a complicated process requiring cost-intensive and time-consuming experiment-based research. As a potential solution, modeling and simulation of biological systems have recently emerged, allowing researchers to predict/estimate astaxanthin production dynamics in selected organisms. Moreover, mathematical modeling techniques would enable further optimization of astaxanthin synthesis in a shorter period of time, ultimately contributing to a notable reduction in production costs. Thus, the present review comprehensively discusses existing mathematical modeling techniques which simulate the bioaccumulation of astaxanthin in diverse organisms. Associated challenges, solutions, and future perspectives are critically analyzed and presented.

Bioactive exometabolites drive maintenance competition in simple bacterial communities

During prolonged resource limitation, bacterial cells can persist in metabolically active states of non-growth. These maintenance periods, such as those experienced in stationary phase, can include upregulation of secondary metabolism and release of exometabolites into the local environment. As resource limitation is common in many environmental microbial habitats, we hypothesized that neighboring bacterial populations employ exometabolites to compete or cooperate during maintenance and that these exometabolite-facilitated interactions can drive community outcomes. Here, we evaluated the consequences of exometabolite interactions over the stationary phase among three environmental strains: Burkholderia thailandensis E264, Chromobacterium subtsugae ATCC 31532, and Pseudomonas syringae pv. tomato DC3000. We assembled them into synthetic communities that only permitted chemical interactions. We compared the responses (transcripts) and outputs (exometabolites) of each member with and without neighbors. We found that transcriptional dynamics were changed with different neighbors and that some of these changes were coordinated between members. The dominant competitor B. thailandensis consistently upregulated biosynthetic gene clusters to produce bioactive exometabolites for both exploitative and interference competition. These results demonstrate that competition strategies during maintenance can contribute to community-level outcomes. It also suggests that the traditional concept of defining competitiveness by growth outcomes may be narrow and that maintenance competition could be an additional or alternative measure.

IMPORTANCE

Free-living microbial populations often persist and engage in environments that offer few or inconsistently available resources. Thus, it is important to investigate microbial interactions in this common and ecologically relevant condition of non-growth. This work investigates the consequences of resource limitation for community metabolic output and for population interactions in simple synthetic bacterial communities. Despite non-growth, we observed active, exometabolite-mediated competition among the bacterial populations. Many of these interactions and produced exometabolites were dependent on the community composition but we also observed that one dominant competitor consistently produced interfering exometabolites regardless. These results are important for predicting and understanding microbial interactions in resource-limited environments.

Predictions of rhizosphere microbiome dynamics with a genome-informed and trait-based energy budget model

Soil microbiomes are highly diverse, and to improve their representation in biogeochemical models, microbial genome data can be leveraged to infer key functional traits. By integrating genome-inferred traits into a theory-based hierarchical framework, emergent behaviour arising from interactions of individual traits can be predicted. Here we combine theory-driven predictions of substrate uptake kinetics with a genome-informed trait-based dynamic energy budget model to predict emergent life-history traits and trade-offs in soil bacteria. When applied to a plant microbiome system, the model accurately predicted distinct substrate-acquisition strategies that aligned with observations, uncovering resource-dependent trade-offs between microbial growth rate and efficiency. For instance, inherently slower-growing microorganisms, favoured by organic acid exudation at later plant growth stages, exhibited enhanced carbon use efficiency (yield) without sacrificing growth rate (power). This insight has implications for retaining plant root-derived carbon in soils and highlights the power of data-driven, trait-based approaches for improving microbial representation in biogeochemical models.

A coarse-grained resource allocation model of carbon and nitrogen metabolism in unicellular microbes

Coarse-grained resource allocation models (C-GRAMs) are simple mathematical models of cell physiology, where large components of the macromolecular composition are abstracted into single entities. The dynamics and steady-state behaviour of such models provides insights on optimal allocation of cellular resources and have explained experimentally observed cellular growth laws, but current models do not account for the uptake of compound sources of carbon and nitrogen. Here, we formulate a C-GRAM with nitrogen and carbon pathways converging on biomass production, with parametrizations accounting for respirofermentative and purely respiratory growth. The model describes the effects of the uptake of sugars, ammonium and/or compound nutrients such as amino acids on the translational resource allocation towards proteome sectors that maximized the growth rate. It robustly recovers cellular growth laws including the Monod law and the ribosomal growth law. Furthermore, we show how the growth-maximizing balance between carbon uptake, recycling, and excretion depends on the nutrient environment. Lastly, we find a robust linear correlation between the ribosome fraction and the abundance of amino acid equivalents in the optimal cell, which supports the view that simple regulation of translational gene expression can enable cells to achieve an approximately optimal growth state.

Understanding and application of Bacillus nitrogen regulation: A synthetic biology perspective

BACKGROUND

Nitrogen sources play an essential role in maintaining the physiological and biochemical activity of bacteria. Nitrogen metabolism, which is the core of microorganism metabolism, makes bacteria able to autonomously respond to different external nitrogen environments by exercising complex internal regulatory networks to help them stay in an ideal state. Although various studies have been put forth to better understand this regulation in Bacillus, and many valuable viewpoints have been obtained, these views need to be presented systematically and their possible applications need to be specified.

AIM OF REVIEW

The intention is to provide a deep and comprehensive understanding of nitrogen metabolism in Bacillus, an important industrial microorganism, and thereby apply this regulatory logic to synthetic biology to improve biosynthesis competitiveness. In addition, the potential researches in the future are also discussed.

KEY SCIENTIFIC CONCEPT OF REVIEW

Understanding the meticulous regulation process of nitrogen metabolism in Bacillus not only could facilitate research on metabolic engineering but also could provide constructive insights and inspiration for studies of other microorganisms.

Complex and unexpected outcomes of antibiotic therapy against a polymicrobial infection

Antibiotics are our primary approach to treating complex infections, yet we have a poor understanding of how these drugs affect microbial communities. To better understand antimicrobial effects on host-associated microbial communities we treated cultured sputum microbiomes from people with cystic fibrosis (pwCF, n = 24) with 11 different antibiotics, supported by theoretical and mathematical modeling-based predictions in a mucus-plugged bronchiole microcosm. Treatment outcomes we identified in vitro that were predicted in silico were: 1) community death, 2) community resistance, 3) pathogen killing, and 4) fermenter killing. However, two outcomes that were not predicted when antibiotics were applied were 5) community profile shifts with little change in total bacterial load (TBL), and 6) increases in TBL. The latter outcome was observed in 17.8% of samples with a TBL increase of greater than 20% and 6.8% of samples with an increase greater than 40%, demonstrating significant increases in community carrying capacity in the presence of an antibiotic. An iteration of the mathematical model showed that TBL increase was due to antibiotic-mediated release of pH-dependent inhibition of pathogens by anaerobe fermentation. These dynamics were verified in vitro when killing of fermenters resulted in a higher community carrying capacity compared to a no antibiotic control. Metagenomic sequencing of sputum samples during antibiotic therapy revealed similar dynamics in clinical samples. This study shows that the complex microbial ecology dictates the outcomes of antibiotic therapy against a polymicrobial infection.

Elementary vectors and autocatalytic sets for resource allocation in next-generation models of cellular growth

Traditional (genome-scale) metabolic models of cellular growth involve an approximate biomass “reaction”, which specifies biomass composition in terms of precursor metabolites (such as amino acids and nucleotides). On the one hand, biomass composition is often not known exactly and may vary drastically between conditions and strains. On the other hand, the predictions of computational models crucially depend on biomass. Also elementary flux modes (EFMs), which generate the flux cone, depend on the biomass reaction. To better understand cellular phenotypes across growth conditions, we introduce and analyze new classes of elementary vectors for comprehensive (next-generation) metabolic models, involving explicit synthesis reactions for all macromolecules. Elementary growth modes (EGMs) are given by stoichiometry and generate the growth cone. Unlike EFMs, they are not support-minimal, in general, but cannot be decomposed “without cancellations”. In models with additional (capacity) constraints, elementary growth vectors (EGVs) generate a growth polyhedron and depend also on growth rate. However, EGMs/EGVs do not depend on the biomass composition. In fact, they cover all possible biomass compositions and can be seen as unbiased versions of elementary flux modes/vectors (EFMs/EFVs) used in traditional models. To relate the new concepts to other branches of theory, we consider autocatalytic sets of reactions. Further, we illustrate our results in a small model of a self-fabricating cell, involving glucose and ammonium uptake, amino acid and lipid synthesis, and the expression of all enzymes and the ribosome itself. In particular, we study the variation of biomass composition as a function of growth rate. In agreement with experimental data, low nitrogen uptake correlates with high carbon (lipid) storage.

Next-generation, genome-scale metabolic models allow to study the reallocation of cellular resources upon changing environmental conditions, by not only modeling flux distributions, but also expression profiles of the catalyzing proteome. In particular, they do no longer assume a fixed biomass composition. Methods to identify optimal solutions in such comprehensive models exist, however, an unbiased understanding of all feasible allocations is missing so far. Here we develop new concepts, called elementary growth modes and vectors, that provide a generalized definition of minimal pathways, thereby extending classical elementary flux modes (used in traditional models with a fixed biomass composition). The new concepts provide an understanding of all possible flux distributions and of all possible biomass compositions. In other words, elementary growth modes and vectors are the unique functional units in any comprehensive model of cellular growth. As an example, we show that lipid accumulation upon nitrogen starvation is a consequence of resource allocation and does not require active regulation. Our work puts current approaches on a theoretical basis and allows to seamlessly transfer existing workflows (e.g. for the design of cell factories) to next-generation metabolic models.

Dimensionless parameter predicts bacterial prodrug success

Understanding mechanisms of antibiotic failure is foundational to combating the growing threat of multidrug-resistant bacteria. Prodrugs-which are converted into a pharmacologically active compound after administration-represent a growing class of therapeutics for treating bacterial infections but are understudied in the context of antibiotic failure. We hypothesize that strategies that rely on pathogen-specific pathways for prodrug conversion are susceptible to competing rates of prodrug activation and bacterial replication, which could lead to treatment escape and failure. Here, we construct a mathematical model of prodrug kinetics to predict rate-dependent conditions under which bacteria escape prodrug treatment. From this model, we derive a dimensionless parameter we call the Bacterial Advantage Heuristic (BAH) that predicts the transition between prodrug escape and successful treatment across a range of time scales (1-104  h), bacterial carrying capacities (5 × 104 -105  CFU/µl), and Michaelis constants (KM  = 0.747-7.47 mM). To verify these predictions in vitro, we use two models of bacteria-prodrug competition: (i) an antimicrobial peptide hairpin that is enzymatically activated by bacterial surface proteases and (ii) a thiomaltose-conjugated trimethoprim that is internalized by bacterial maltodextrin transporters and hydrolyzed by free thiols. We observe that prodrug failure occurs at BAH values above the same critical threshold predicted by the model. Furthermore, we demonstrate two examples of how failing prodrugs can be rescued by decreasing the BAH below the critical threshold via (i) substrate design and (ii) nutrient control. We envision such dimensionless parameters serving as supportive pharmacokinetic quantities that guide the design and administration of prodrug therapeutics.

Genome-Scale Reconstruction of Microbial Dynamic Phenotype: Successes and Challenges

This review is a part of the SI 'Genome-Scale Modeling of Microorganisms in the Real World'. The goal of GEM is the accurate prediction of the phenotype from its respective genotype under specified environmental conditions. This review focuses on the dynamic phenotype; prediction of the real-life behaviors of microorganisms, such as cell proliferation, dormancy, and mortality; balanced and unbalanced growth; steady-state and transient processes; primary and secondary metabolism; stress responses; etc. Constraint-based metabolic reconstructions were successfully started two decades ago as FBA, followed by more advanced models, but this review starts from the earlier nongenomic predecessors to show that some GEMs inherited the outdated biokinetic frameworks compromising their performances. The most essential deficiencies are: (i) an inadequate account of environmental conditions, such as various degrees of nutrients limitation and other factors shaping phenotypes; (ii) a failure to simulate the adaptive changes of MMCC (MacroMolecular Cell Composition) in response to the fluctuating environment; (iii) the misinterpretation of the SGR (Specific Growth Rate) as either a fixed constant parameter of the model or independent factor affecting the conditional expression of macromolecules; (iv) neglecting stress resistance as an important objective function; and (v) inefficient experimental verification of GEM against simple growth (constant MMCC and SGR) data. Finally, we propose several ways to improve GEMs, such as replacing the outdated Monod equation with the SCM (Synthetic Chemostat Model) that establishes the quantitative relationships between primary and secondary metabolism, growth rate and stress resistance, process kinetics, and cell composition.

The effect of natural selection on the propagation of protein expression noise to bacterial growth

In bacterial cells, protein expression is a highly stochastic process. Gene expression noise moreover propagates through the cell and adds to fluctuations in the cellular growth rate. A common intuition is that, due to their relatively high noise amplitudes, proteins with a low mean expression level are the most important drivers of fluctuations in physiological variables. In this work, we challenge this intuition by considering the effect of natural selection on noise propagation. Mathematically, the contribution of each protein species to the noise in the growth rate depends on two factors: the noise amplitude of the protein’s expression level, and the sensitivity of the growth rate to fluctuations in that protein’s concentration. We argue that natural selection, while shaping mean abundances to increase the mean growth rate, also affects cellular sensitivities. In the limit in which cells grow optimally fast, the growth rate becomes most sensitive to fluctuations in highly abundant proteins. This causes abundant proteins to overall contribute strongly to the noise in the growth rate, despite their low noise levels. We further explore this result in an experimental data set of protein abundances, and test key assumptions in an evolving, stochastic toy model of cellular growth.

Gene expression in bacterial cells is intrinsically stochastic: copy numbers of all proteins vary between genetically identical cells, even in a homogeneous environment. Such noise in gene expression affects metabolic fluxes and even propagates to the cellular level. Indeed, also the growth rate of individual cells, an important proxy for fitness, fluctuates strongly. This beckons the question as to which protein species contribute most to the noise in the cell’s growth rate. We here derive general mathematical predictions stating that if cells have been optimised by evolution to grow fast, abundant protein species contribute most to the noise in the growth rate. This result is counter-intuitive, because the noise levels in the expression of those highly expressed proteins are small.

Systematic variation in the temperature dependence of bacterial carbon use efficiency

Carbon use efficiency (CUE) is a key characteristic of microbial physiology and underlies community-level responses to changing environments. Yet, we currently lack general empirical insights into variation in microbial CUE at the level of individual taxa. Here, through experiments with 29 strains of environmentally isolated bacteria, we find that bacterial CUE typically responds either positively to temperature, or has no discernible response, within biologically meaningful temperature ranges. Using a global data synthesis, we show that these results are generalisable across most culturable groups of bacteria. This variation in the thermal responses of bacterial CUE is taxonomically structured, and stems from the fact that relative to respiration rates, bacterial population growth rates typically respond more strongly to temperature, and are also subject to weaker evolutionary constraints. Our results provide new insights into microbial physiology, and a basis for more accurately modelling the effects of thermal fluctuations on complex microbial communities.

Gene Expression Space Shapes the Bioprocess Trade-Offs among Titer, Yield and Productivity

Optimal gene expression is central for the development of both bacterial expression systems for heterologous protein production, and microbial cell factories for industrial metabolite production. Our goal is to fulfill industry-level overproduction demands optimally, as measured by the following key performance metrics: titer, productivity rate, and yield (TRY). Here we use a multiscale model incorporating the dynamics of (i) the cell population in the bioreactor, (ii) the substrate uptake and (iii) the interaction between the cell host and expression of the protein of interest. Our model predicts cell growth rate and cell mass distribution between enzymes of interest and host enzymes as a function of substrate uptake and the following main lab-accessible gene expression-related characteristics: promoter strength, gene copy number and ribosome binding site strength. We evaluated the differential roles of gene transcription and translation in shaping TRY trade-offs for a wide range of expression levels and the sensitivity of the TRY space to variations in substrate availability. Our results show that, at low expression levels, gene transcription mainly defined TRY, and gene translation had a limited effect; whereas, at high expression levels, TRY depended on the product of both, in agreement with experiments in the literature.

gapseq: informed prediction of bacterial metabolic pathways and reconstruction of accurate metabolic models

Genome-scale metabolic models of microorganisms are powerful frameworks to predict phenotypes from an organism's genotype. While manual reconstructions are laborious, automated reconstructions often fail to recapitulate known metabolic processes. Here we present gapseq ( https://github.com/jotech/gapseq ), a new tool to predict metabolic pathways and automatically reconstruct microbial metabolic models using a curated reaction database and a novel gap-filling algorithm. On the basis of scientific literature and experimental data for 14,931 bacterial phenotypes, we demonstrate that gapseq outperforms state-of-the-art tools in predicting enzyme activity, carbon source utilisation, fermentation products, and metabolic interactions within microbial communities.

Searching for principles of microbial physiology

Why do evolutionarily distinct microorganisms display similar physiological behaviours? Why are transitions from high-ATP yield to low(er)-ATP yield metabolisms so widespread across species? Why is fast growth generally accompanied with low stress tolerance? Do these regularities occur because most microbial species are subject to the same selective pressures and physicochemical constraints? If so, a broadly-applicable theory might be developed that predicts common microbiological behaviours. Microbial systems biologists have been working out the contours of this theory for the last two decades, guided by experimental data. At its foundations lie basic principles from evolutionary biology, enzyme biochemistry, metabolism, cell composition and steady-state growth. The theory makes predictions about fitness costs and benefits of protein expression, physicochemical constraints on cell growth and characteristics of optimal metabolisms that maximise growth rate. Comparisons of the theory with experimental data indicates that microorganisms often aim for maximisation of growth rate, also in the presence of stresses; they often express optimal metabolisms and metabolic proteins at optimal concentrations. This review explains the current status of the theory for microbiologists; its roots, predictions, experimental evidence and future directions.

Flapjack: Data Management and Analysis for Genetic Circuit Characterization

Characterization is fundamental to the design, build, test, learn (DBTL) cycle for engineering synthetic genetic circuits. Components must be described in such a way as to account for their behavior in a range of contexts. Measurements and associated metadata, including part composition, constitute the test phase of the DBTL cycle. These data may consist of measurements of thousands of circuits, measured in hundreds of conditions, in multiple assays potentially performed in different laboratories and using different techniques. In order to inform the learn phase this large volume of data must be filtered, collated, and analyzed. Characterization consists of using this data to parametrize models of component function in different contexts, and combining them to predict behaviors of novel circuits. Tools to store, organize, share, and analyze large volumes of measurement and metadata are therefore essential to linking the test phase to the build and learn phases, closing the loop of the DBTL cycle. Here we present such a system, implemented as a web app with a backend data registry and analysis engine. An interactive frontend provides powerful querying, plotting, and analysis tools, and we provide a REST API and Python package for full integration with external build and learn software. All measurements are associated with circuit part composition via SBOL (Synthetic Biology Open Language). We demonstrate our tool by characterizing a range of genetic components and circuits according to composition and context.

Automated engineering of synthetic metabolic pathways for efficient biomanufacturing

Metabolic engineering involves the engineering and optimization of processes from single-cell to fermentation in order to increase production of valuable chemicals for health, food, energy, materials and others. A systems approach to metabolic engineering has gained traction in recent years thanks to advances in strain engineering, leading to an accelerated scaling from rapid prototyping to industrial production. Metabolic engineering is nowadays on track towards a truly manufacturing technology, with reduced times from conception to production enabled by automated protocols for DNA assembly of metabolic pathways in engineered producer strains. In this review, we discuss how the success of the metabolic engineering pipeline often relies on retrobiosynthetic protocols able to identify promising production routes and dynamic regulation strategies through automated biodesign algorithms, which are subsequently assembled as embedded integrated genetic circuits in the host strain. Those approaches are orchestrated by an experimental design strategy that provides optimal scheduling planning of the DNA assembly, rapid prototyping and, ultimately, brings forward an accelerated Design-Build-Test-Learn cycle and the overall optimization of the biomanufacturing process. Achieving such a vision will address the increasingly compelling demand in our society for delivering valuable biomolecules in an affordable, inclusive and sustainable bioeconomy.

Genome-scale metabolic modeling of Acetobacter pasteurianus 386B reveals its metabolic adaptation to cocoa fermentation conditions

Acetobacter pasteurianus 386B has been selected as a candidate functional starter culture to better control the cocoa fermentation process. Previously, its genome has been sequenced and a genome-scale metabolic model (GEM) has been reconstructed. To understand its metabolic adaptation to cocoa fermentation conditions, different flux balance analysis (FBA) simulations were performed and compared with experimental data. In particular, metabolic flux distributions were simulated for two phases that characterize the growth of A. pasteurianus 386B under cocoa fermentation conditions, predicting a switch in respiratory chain usage in between these phases. The possible influence on the resulting energy production was shown using a reduced version of the GEM. FBA simulations revealed the importance of the compartmentalization of the ethanol oxidation reactions, namely in the periplasm or in the cytoplasm, and highlighted the potential role of ethanol as a source of carbon, energy, and NADPH. Regarding the latter, the physiological function of a proton-translocating NAD(P)⁺ transhydrogenase was further investigated in silico. This study revealed the potential of using a GEM to simulate the metabolism of A. pasteurianus 386B, and may provide a general framework toward a better physiological understanding of functional starter cultures in food fermentation processes.

A mechanism-aware and multiomic machine-learning pipeline characterizes yeast cell growth

Metabolic modeling and machine learning are key components in the emerging next generation of systems and synthetic biology tools, targeting the genotype-phenotype-environment relationship. Rather than being used in isolation, it is becoming clear that their value is maximized when they are combined. However, the potential of integrating these two frameworks for omic data augmentation and integration is largely unexplored. We propose, rigorously assess, and compare machine-learning-based data integration techniques, combining gene expression profiles with computationally generated metabolic flux data to predict yeast cell growth. To this end, we create strain-specific metabolic models for 1,143 Saccharomyces cerevisiae mutants and we test 27 machine-learning methods, incorporating state-of-the-art feature selection and multiview learning approaches. We propose a multiview neural network using fluxomic and transcriptomic data, showing that the former increases the predictive accuracy of the latter and reveals functional patterns that are not directly deducible from gene expression alone. We test the proposed neural network on a further 86 strains generated in a different experiment, therefore verifying its robustness to an additional independent dataset. Finally, we show that introducing mechanistic flux features improves the predictions also for knockout strains whose genes were not modeled in the metabolic reconstruction. Our results thus demonstrate that fusing experimental cues with in silico models, based on known biochemistry, can contribute with disjoint information toward biologically informed and interpretable machine learning. Overall, this study provides tools for understanding and manipulating complex phenotypes, increasing both the prediction accuracy and the extent of discernible mechanistic biological insights.

Flux Balance Analysis for Media Optimization and Genetic Targets to Improve Heterologous Siderophore Production

Siderophores are small molecule metal chelators secreted in sparse quantities by their native microbial hosts but can be engineered for enhanced production from heterologous hosts like Escherichia coli. These molecules have been proved to be capable of binding heavy metals of commercial and/or environmental interest. In this work, we incorporated, as needed, the appropriate pathways required to produce several siderophores (anguibactin, vibriobactin, bacillibactin, pyoverdine, and enterobactin) into the base E. coli K-12 MG1655 metabolic network model to computationally predict, via flux balance analysis methodologies, gene knockout targets, gene over-expression targets, and media modifications capable of improving siderophore reaction flux. E. coli metabolism proved supportive for the underlying production mechanisms of various siderophores. Within such a framework, the gene deletion and over-expression targets identified, coupled with complementary insights from medium optimization predictions, portend experimental implementation to both enable and improve heterologous siderophore production. Successful production of siderophores would then spur novel metal-binding applications.

An analytical theory of balanced cellular growth

The biological fitness of microbes is largely determined by the rate with which they replicate their biomass composition. Mathematical models that maximize this balanced growth rate while accounting for mass conservation, reaction kinetics, and limits on dry mass per volume are inevitably non-linear. Here, we develop a general theory for such models, termed Growth Balance Analysis (GBA), which provides explicit expressions for protein concentrations, fluxes, and growth rates. These variables are functions of the concentrations of cellular components, for which we calculate marginal fitness costs and benefits that are related to metabolic control coefficients. At maximal growth rate, the net benefits of all concentrations are equal. Based solely on physicochemical constraints, GBA unveils fundamental quantitative principles of cellular resource allocation and growth; it accurately predicts the relationship between growth rates and ribosome concentrations in E. coli and yeast and between growth rate and dry mass density in E. coli.

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

In this paper we try to 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. For this, we must understand the process of cellular growth: steady-state self-fabrication requires a cell to synthesize all of its components, including metabolites, enzymes and ribosomes, in proportions that match its own composition. Simultaneously, the concentrations of these components affect the rates of metabolism and biosynthesis, and hence the growth rate. We here derive a theory that describes all phenotypes that solve this circular problem. All phenotypes can be described as a combination of 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 use 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 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. The theory presented here extends recent results on Elementary Flux Modes: the minimal building blocks of cellular growth models that lack the self-fabrication aspect. 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.

Modelling microbial communities using biochemical resource allocation analysis

To understand the functioning and dynamics of microbial communities is a fundamental challenge in current biology. To tackle this challenge, the construction of computational models of interacting microbes is an indispensable tool. There is, however, a large chasm between ecologically motivated descriptions of microbial growth used in many current ecosystems simulations, and detailed metabolic pathway and genome-based descriptions developed in the context of systems and synthetic biology. Here, we seek to demonstrate how resource allocation models of microbial growth offer the potential to advance ecosystem simulations and their parametrization. In particular, recent work on quantitative resource allocation allow us to formulate mechanistic models of microbial growth that are physiologically meaningful while remaining computationally tractable. These models go beyond Michaelis-Menten and Monod-type growth models, and are capable of accounting for emergent properties that underlie the remarkable plasticity of microbial growth. We outline the utility and advantages of using biochemical resource allocation models by considering a coarse-grained model of cyanobacterial growth and demonstrate how the model allows us to address specific questions of relevance for the simulation of marine microbial ecosystems, including the physiological acclimation of protein expression to different environments, the description of co-limitation by several nutrients and the differential use of alternative nutrient sources, as well as the description of metabolic diversity based on our increasing knowledge about quantitative cell physiology.

Computational Modelling of Metabolic Burden and Substrate Toxicity in Escherichia coli Carrying a Synthetic Metabolic Pathway

In our previous work, we designed and implemented a synthetic metabolic pathway for 1,2,3-trichloropropane (TCP) biodegradation in Escherichia coli. Significant effects of metabolic burden and toxicity exacerbation were observed on single cell and population levels. Deeper understanding of mechanisms underlying these effects is extremely important for metabolic engineering of efficient microbial cell factories for biotechnological processes. In this paper, we present a novel mathematical model of the pathway. The model addresses for the first time the combined effects of toxicity exacerbation and metabolic burden in the context of bacterial population growth. The model is calibrated with respect to the real data obtained with our original synthetically modified E. coli strain. Using the model, we explore the dynamics of the population growth along with the outcome of the TCP biodegradation pathway considering the toxicity exacerbation and metabolic burden. On the methodological side, we introduce a unique computational workflow utilising algorithmic methods of computer science for the particular modelling problem.

Optimal proteome allocation strategies for phototrophic growth in a light-limited chemostat

BACKGROUND

Cyanobacteria and other phototrophic microorganisms allow to couple the light-driven assimilation of atmospheric [Formula: see text] directly to the synthesis of carbon-based products, and are therefore attractive platforms for microbial cell factories. While most current engineering efforts are performed using small-scale laboratory cultivation, the economic viability of phototrophic cultivation also crucially depends on photobioreactor design and culture parameters, such as the maximal areal and volumetric productivities. Based on recent insights into the cyanobacterial cell physiology and the resulting computational models of cyanobacterial growth, the aim of this study is to investigate the limits of cyanobacterial productivity in continuous culture with light as the limiting nutrient.

RESULTS

We integrate a coarse-grained model of cyanobacterial growth into a light-limited chemostat and its heterogeneous light gradient induced by self-shading of cells. We show that phototrophic growth in the light-limited chemostat can be described using the concept of an average light intensity. Different from previous models based on phenomenological growth equations, our model provides a mechanistic link between intracellular protein allocation, population growth and the resulting reactor productivity. Our computational framework thereby provides a novel approach to investigate and predict the maximal productivity of phototrophic cultivation, and identifies optimal proteome allocation strategies for developing maximally productive strains.

CONCLUSIONS

Our results have implications for efficient phototrophic cultivation and the design of maximally productive phototrophic cell factories. The model predicts that the use of dense cultures in well-mixed photobioreactors with short light-paths acts as an effective light dilution mechanism and alleviates the detrimental effects of photoinhibition even under very high light intensities. We recover the well-known trade-offs between a reduced light-harvesting apparatus and increased population density. Our results are discussed in the context of recent experimental efforts to increase the yield of phototrophic cultivation.

Optimal control of bacterial growth for the maximization of metabolite production

Microorganisms have evolved complex strategies for controlling the distribution of available resources over cellular functions. Biotechnology aims at interfering with these strategies, so as to optimize the production of metabolites and other compounds of interest, by (re)engineering the underlying regulatory networks of the cell. The resulting reallocation of resources can be described by simple so-called self-replicator models and the maximization of the synthesis of a product of interest formulated as a dynamic optimal control problem. Motivated by recent experimental work, we are specifically interested in the maximization of metabolite production in cases where growth can be switched off through an external control signal. We study various optimal control problems for the corresponding self-replicator models by means of a combination of analytical and computational techniques. We show that the optimal solutions for biomass maximization and product maximization are very similar in the case of unlimited nutrient supply, but diverge when nutrients are limited. Moreover, external growth control overrides natural feedback growth control and leads to an optimal scheme consisting of a first phase of growth maximization followed by a second phase of product maximization. This two-phase scheme agrees with strategies that have been proposed in metabolic engineering. More generally, our work shows the potential of optimal control theory for better understanding and improving biotechnological production processes.

Noise propagation in an integrated model of bacterial gene expression and growth

In bacterial cells, gene expression, metabolism, and growth are highly interdependent and tightly coordinated. As a result, stochastic fluctuations in expression levels and instantaneous growth rate show intricate cross-correlations. These correlations are shaped by feedback loops, trade-offs and constraints acting at the cellular level; therefore a quantitative understanding requires an integrated approach. To that end, we here present a mathematical model describing a cell that contains multiple proteins that are each expressed stochastically and jointly limit the growth rate. Conversely, metabolism and growth affect protein synthesis and dilution. Thus, expression noise originating in one gene propagates to metabolism, growth, and the expression of all other genes. Nevertheless, under a small-noise approximation many statistical quantities can be calculated analytically. We identify several routes of noise propagation, illustrate their origins and scaling, and establish important connections between noise propagation and the field of metabolic control analysis. We then present a many-protein model containing >1000 proteins parameterized by previously measured abundance data and demonstrate that the predicted cross-correlations between gene expression and growth rate are in broad agreement with published measurements.