Multiomics in the central Arctic Ocean for benchmarking biodiversity change.

Multiomics approaches need to be applied in the central Arctic Ocean to benchmark biodiversity change and to identify novel species and their genes. As part of MOSAiC, EcoOmics will therefore be essential for conservation and sustainable bioprospecting in one of the least explored ecosystems on Earth.

Shifts in carbon partitioning by photosynthetic activity increase terpenoid synthesis in glandular trichomes.

Several commercially important secondary metabolites are produced and accumulated in high amounts by glandular trichomes, giving the prospect of using them as metabolic cell factories. Due to extremely high metabolic fluxes through glandular trichomes, previous research focused on how such flows are achieved. The question regarding their bioenergetics became even more interesting with the discovery of photosynthetic activity in some glandular trichomes. Despite recent advances, how primary metabolism contributes to the high metabolic fluxes in glandular trichomes is still not fully elucidated. Using computational methods and available multi-omics data, we first developed a quantitative framework to investigate the possible role of photosynthetic energy supply in terpenoid production and next tested experimentally the simulation-driven hypothesis. With this work, we provide the first reconstruction of specialised metabolism in Type-VI photosynthetic glandular trichomes of Solanum lycopersicum. Our model predicted that increasing light intensities results in a shift of carbon partitioning from catabolic to anabolic reactions driven by the energy availability of the cell. Moreover, we show the benefit of shifting between isoprenoid pathways under different light regimes, leading to a production of different classes of terpenes. Our computational predictions were confirmed in vivo, demonstrating a significant increase in production of monoterpenoids while the sesquiterpenes remained unchanged under higher light intensities. The outcomes of this research provide quantitative measures to assess the beneficial role of chloroplast in glandular trichomes for enhanced production of secondary metabolites and can guide the design of new experiments that aim at modulating terpenoid production.

Stochastic modelling of a three-dimensional glycogen granule synthesis and impact of the branching enzyme.

In humans, glycogen storage diseases result from metabolic inborn errors, and can lead to severe phenotypes and lethal conditions. Besides these rare diseases, glycogen is also associated to widely spread societal burdens such as diabetes. Glycogen is a branched glucose polymer synthesised and degraded by a complex set of enzymes. Over the past 50 years, the structure of glycogen has been intensively investigated. Yet, the interplay between the detailed three-dimensional glycogen structure and the related enzyme activity is only partially characterised and still to be fully understood. In this article, we develop a stochastic coarse-grained and spatially resolved model of branched polymer biosynthesis following a Gillespie algorithm. Our study largely focusses on the role of the branching enzyme, and first investigates the properties of the model with generic parameter values, before comparing it to in vivo experimental data in mice. It arises that the ratio of glycogen synthase over branching enzyme reaction rates drastically impacts the structure of the granule. We deeply investigate the mechanism of branching and parametrise it using distinct lengths. Not only do we consider various possible sets of values for these lengths, but also distinct rules to apply them. We show how combining various values for these lengths finely tunes glycogen macromolecular structure. Comparing the model with experimental data confirms that we can accurately reproduce glycogen chain length distributions in wild type mice. Additional granule properties obtained for this fit are also in good agreement with typically reported values in the experimental literature. Nonetheless, we find that the mechanism of branching must be more flexible than usually reported. Overall, our model provides a theoretical basis to quantify the effect that single enzymatic parameters, in particular of the branching enzyme, have on the chain length distribution. Our generic model and methods can be applied to any glycogen data set, and could in particular contribute to characterise the mechanisms responsible for glycogen storage disorders.

Mathematical properties of optimal fluxes in cellular reaction networks at balanced growth.

The physiology of biological cells evolved under physical and chemical constraints, such as mass conservation across the network of biochemical reactions, 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 and analyze such nonlinear systems, revealing important analytical properties of optimal balanced growth states. It has been shown that at optimality, only a minimal subset of reactions can have nonzero flux. However, no general principles have been established to determine if a specific reaction is active at optimality. Here, we extend the GBA framework to study the optimality of each biochemical reaction, and we identify the mathematical conditions determining whether a reaction is active or not at optimal growth in a given environment. We reformulate the mathematical problem in terms of a minimal number of dimensionless variables and use the Karush-Kuhn-Tucker (KKT) conditions to identify fundamental principles of optimal resource allocation in GBA models of any size and complexity. Our approach helps to 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. We show how the extended GBA framework 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. GBA thereby provides a general theoretical toolbox for the study of fundamental mathematical properties of balanced cellular growth.

Manipulation of topoisomerase expression inhibits cell division but not growth and reveals a distinctive promoter structure in Synechocystis.

In cyanobacteria DNA supercoiling varies over the diurnal cycle and is integrated with temporal programs of transcription and replication. We manipulated DNA supercoiling in Synechocystis sp. PCC 6803 by CRISPRi-based knockdown of gyrase subunits and overexpression of topoisomerase I (TopoI). Cell division was blocked but cell growth continued in all strains. The small endogenous plasmids were only transiently relaxed, then became strongly supercoiled in the TopoI overexpression strain. Transcript abundances showed a pronounced 5'/3' gradient along transcription units, incl. the rRNA genes, in the gyrase knockdown strains. These observations are consistent with the basic tenets of the homeostasis and twin-domain models of supercoiling in bacteria. TopoI induction initially led to downregulation of G+C-rich and upregulation of A+T-rich genes. The transcriptional response quickly bifurcated into six groups which overlap with diurnally co-expressed gene groups. Each group shows distinct deviations from a common core promoter structure, where helically phased A-tracts are in phase with the transcription start site. Together, our data show that major co-expression groups (regulons) in Synechocystis all respond differentially to DNA supercoiling, and suggest to re-evaluate the long-standing question of the role of A-tracts in bacterial promoters.

COBREXA.jl: constraint-based reconstruction and exascale analysis.

SUMMARY: COBREXA.jl is a Julia package for scalable, high-performance constraint-based reconstruction and analysis of very large-scale biological models. Its primary purpose is to facilitate the integration of modern high performance computing environments with the processing and analysis of large-scale metabolic models of challenging complexity. We report the architecture of the package, and demonstrate how the design promotes analysis scalability on several use-cases with multi-organism community models. AVAILABILITY AND IMPLEMENTATION: https://doi.org/10.17881/ZKCR-BT30. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Interrogating the effect of enzyme kinetics on metabolism using differentiable constraint-based models.

Metabolic models are typically characterized by a large number of parameters. Traditionally, metabolic control analysis is applied to differential equation-based models to investigate the sensitivity of predictions to parameters. A corresponding theory for constraint-based models is lacking, due to their formulation as optimization problems. Here, we show that optimal solutions of optimization problems can be efficiently differentiated using constrained optimization duality and implicit differentiation. We use this to calculate the sensitivities of predicted reaction fluxes and enzyme concentrations to turnover numbers in an enzyme-constrained metabolic model of Escherichia coli. The sensitivities quantitatively identify rate limiting enzymes and are mathematically precise, unlike current finite difference based approaches used for sensitivity analysis. Further, efficient differentiation of constraint-based models unlocks the ability to use gradient information for parameter estimation. We demonstrate this by improving, genome-wide, the state-of-the-art turnover number estimates for E. coli. Finally, we show that this technique can be generalized to arbitrarily complex models. By differentiating the optimal solution of a model incorporating both thermodynamic and kinetic rate equations, the effect of metabolite concentrations on biomass growth can be elucidated. We benchmark these metabolite sensitivities against a large experimental gene knockdown study, and find good alignment between the predicted sensitivities and in vivo metabolome changes. In sum, we demonstrate several applications of differentiating optimal solutions of constraint-based metabolic models, and show how it connects to classic metabolic control analysis.

Constructing and analysing dynamic models with modelbase v1.2.3: a software update.

BACKGROUND: Computational mathematical models of biological and biomedical systems have been successfully applied to advance our understanding of various regulatory processes, metabolic fluxes, effects of drug therapies, and disease evolution and transmission. Unfortunately, despite community efforts leading to the development of SBML and the BioModels database, many published models have not been fully exploited, largely due to a lack of proper documentation or the dependence on proprietary software. To facilitate the reuse and further development of systems biology and systems medicine models, an open-source toolbox that makes the overall process of model construction more consistent, understandable, transparent, and reproducible is desired. RESULTS AND DISCUSSION: We provide an update on the development of modelbase, a free, expandable Python package for constructing and analysing ordinary differential equation-based mathematical models of dynamic systems. It provides intuitive and unified methods to construct and solve these systems. Significantly expanded visualisation methods allow for convenient analysis of the structural and dynamic properties of models. After specifying reaction stoichiometries and rate equations modelbase can automatically assemble the associated system of differential equations. A newly provided library of common kinetic rate laws reduces the repetitiveness of the computer programming code. modelbase is also fully compatible with SBML. Previous versions provided functions for the automatic construction of networks for isotope labelling studies. Now, using user-provided label maps, modelbase v1.2.3 streamlines the expansion of classic models to their isotope-specific versions. Finally, the library of previously published models implemented in modelbase is growing continuously. Ranging from photosynthesis to tumour cell growth to viral infection evolution, all these models are now available in a transparent, reusable and unified format through modelbase. CONCLUSION: With this new Python software package, which is written in currently one of the most popular programming languages, the user can develop new models and actively profit from the work of others. modelbase enables reproducing and replicating models in a consistent, tractable and expandable manner. Moreover, the expansion of models to their isotopic label-specific versions enables simulating label propagation, thus providing quantitative information regarding network topology and metabolic fluxes.

The view of microbes as energy converters illustrates the trade-off between growth rate and yield.

The application of thermodynamics to microbial growth has a long tradition that originated in the middle of the 20th century. This approach reflects the view that self-replication is a thermodynamic process that is not fundamentally different from mechanical thermodynamics. The key distinction is that a free energy gradient is not converted into mechanical (or any other form of) energy but rather into new biomass. As such, microbes can be viewed as energy converters that convert a part of the energy contained in environmental nutrients into chemical energy that drives self-replication. Before the advent of high-throughput sequencing technologies, only the most central metabolic pathways were known. However, precise measurement techniques allowed for the quantification of exchanged extracellular nutrients and heat of growing microbes with their environment. These data, together with the absence of knowledge of metabolic details, drove the development of so-called black-box models, which only consider the observable interactions of a cell with its environment and neglect all details of how exactly inputs are converted into outputs. Now, genome sequencing and genome-scale metabolic models (GEMs) provide us with unprecedented detail about metabolic processes inside the cell. However, mostly due to computational complexity issues, the derived modelling approaches make surprisingly little use of thermodynamic concepts. Here, we review classical black-box models and modern approaches that integrate thermodynamics into GEMs. We also illustrate how the description of microbial growth as an energy converter can help to understand and quantify the trade-off between microbial growth rate and yield.

A single-input binary counting module based on serine integrase site-specific recombination.

A device that counts and records the number of events experienced by an individual cell could have many uses in experimental biology and biotechnology. Here, we report a DNA-based 'latch' that switches between two states upon each exposure to a repeated stimulus. The key component of the latch is a DNA segment whose orientation is inverted by the actions of ϕC31 integrase and its recombination directionality factor (RDF). Integrase expression is regulated by an external input, while RDF expression is controlled by the state of the latch, such that the orientation of the invertible segment switches efficiently each time the device receives an input pulse. Recombination occurs over a time scale of minutes after initiation of integrase expression. The latch requires a delay circuit, implemented with a transcriptional repressor expressed in only one state, to ensure that each input pulse results in only one inversion of the DNA segment. Development and optimization of the latch in living cells was driven by mathematical modelling of the recombination reactions and gene expression regulated by the switch. We discuss how N latches built with orthogonal site-specific recombination systems could be chained together to form a binary ripple counter that could count to 2N - 1.

Theoretical and experimental approaches to understand the biosynthesis of starch granules in a physiological context.

Starch, a plant-derived insoluble carbohydrate composed of glucose polymers, is the principal carbohydrate in our diet and a valuable raw material for industry. The properties of starch depend on the arrangement of glucose units within the constituent polymers. However, key aspects of starch structure and the underlying biosynthetic processes are not well understood, limiting progress towards targeted improvement of our starch crops. In particular, the major component of starch, amylopectin, has a complex three-dimensional, branched architecture. This architecture stems from the combined actions of a multitude of enzymes, each having broad specificities that are difficult to capture experimentally. In this review, we reflect on experimental approaches and limitations to decipher the enzymes' specificities and explore possibilities for in silico simulations of these activities. We believe that the synergy between experimentation and simulation is needed for the correct interpretation of experimental data and holds the potential to greatly advance our understanding of the overall starch biosynthetic process. We furthermore propose that the formation of glucan secondary structures, concomitant with its synthesis, is a previously overlooked factor that directly affects amylopectin architecture through its impact on enzyme function.

Thermodynamic Limits and Optimality of Microbial Growth.

Understanding microbial growth with the use of mathematical models has a long history that dates back to the pioneering work of Jacques Monod in the 1940s. Monod's famous growth law expressed microbial growth rate as a simple function of the limiting nutrient concentration. However, to explain growth laws from underlying principles is extremely challenging. In the second half of the 20th century, numerous experimental approaches aimed at precisely measuring heat production during microbial growth to determine the entropy balance in a growing cell and to quantify the exported entropy. This has led to the development of thermodynamic theories of microbial growth, which have generated fundamental understanding and identified the principal limitations of the growth process. Although these approaches ignored metabolic details and instead considered microbial metabolism as a black box, modern theories heavily rely on genomic resources to describe and model metabolism in great detail to explain microbial growth. Interestingly, however, thermodynamic constraints are often included in modern modeling approaches only in a rather superficial fashion, and it appears that recent modeling approaches and classical theories are rather disconnected fields. To stimulate a closer interaction between these fields, we here review various theoretical approaches that aim at describing microbial growth based on thermodynamics and outline the resulting thermodynamic limits and optimality principles. We start with classical black box models of cellular growth, and continue with recent metabolic modeling approaches that include thermodynamics, before we place these models in the context of fundamental considerations based on non-equilibrium statistical mechanics. We conclude by identifying conceptual overlaps between the fields and suggest how the various types of theories and models can be integrated. We outline how concepts from one approach may help to inform or constrain another, and we demonstrate how genome-scale models can be used to infer key black box parameters, such as the energy of formation or the degree of reduction of biomass. Such integration will allow understanding to what extent microbes can be viewed as thermodynamic machines, and how close they operate to theoretical optima.

Balancing energy supply during photosynthesis - a theoretical perspective.

The photosynthetic electron transport chain (PETC) provides energy and redox equivalents for carbon fixation by the Calvin-Benson-Bassham (CBB) cycle. Both of these processes have been thoroughly investigated and the underlying molecular mechanisms are well known. However, it is far from understood by which mechanisms it is ensured that energy and redox supply by photosynthesis matches the demand of the downstream processes. Here, we deliver a theoretical analysis to quantitatively study the supply-demand regulation in photosynthesis. For this, we connect two previously developed models, one describing the PETC, originally developed to study non-photochemical quenching, and one providing a dynamic description of the photosynthetic carbon fixation in C3 plants, the CBB Cycle. The merged model explains how a tight regulation of supply and demand reactions leads to efficient carbon fixation. The model further illustrates that a stand-by mode is necessary in the dark to ensure that the carbon fixation cycle can be restarted after dark-light transitions, and it supports hypotheses, which reactions are responsible to generate such mode in vivo.

Review and perspective on mathematical modeling of microbial ecosystems.

Understanding microbial ecosystems means unlocking the path toward a deeper knowledge of the fundamental mechanisms of life. Engineered microbial communities are also extremely relevant to tackling some of today's grand societal challenges. Advanced meta-omics experimental techniques provide crucial insights into microbial communities, but have been so far mostly used for descriptive, exploratory approaches to answer the initial 'who is there?' QUESTION: An ecosystem is a complex network of dynamic spatio-temporal interactions among organisms as well as between organisms and the environment. Mathematical models with their abstraction capability are essential to capture the underlying phenomena and connect the different scales at which these systems act. Differential equation models and constraint-based stoichiometric models are deterministic approaches that can successfully provide a macroscopic description of the outcome from microscopic behaviors. In this mini-review, we present classical and recent applications of these modeling methods and illustrate the potential of their integration. Indeed, approaches that can capture multiple scales are needed in order to understand emergent patterns in ecosystems and their dynamics regulated by different spatio-temporal phenomena. We finally discuss promising examples of methods proposing the integration of differential equations with constraint-based stoichiometric models and argue that more work is needed in this direction.

The importance of the photosynthetic Gibbs effect in the elucidation of the Calvin-Benson-Bassham cycle.

The photosynthetic carbon reduction cycle, or Calvin-Benson-Bassham (CBB) cycle, is now contained in every standard biochemistry textbook. Although the cycle was already proposed in 1954, it is still the subject of intense research, and even the structure of the cycle, i.e. the exact series of reactions, is still under debate. The controversy about the cycle's structure was fuelled by the findings of Gibbs and Kandler in 1956 and 1957, when they observed that radioactive 14CO2 was dynamically incorporated in hexoses in a very atypical and asymmetrical way, a phenomenon later termed the 'photosynthetic Gibbs effect'. Now, it is widely accepted that the photosynthetic Gibbs effect is not in contradiction to the reaction scheme proposed by CBB, but the arguments given have been largely qualitative and hand-waving. To fully appreciate the controversy and to understand the difficulties in interpreting the Gibbs effect, it is illustrative to illuminate the history of the discovery of the CBB cycle. We here give an account of central scientific advances and discoveries, which were essential prerequisites for the elucidation of the cycle. Placing the historic discoveries in the context of the modern textbook pathway scheme illustrates the complexity of the cycle and demonstrates why especially dynamic labelling experiments are far from easy to interpret. We conclude by arguing that it requires sound theoretical approaches to resolve conflicting interpretations and to provide consistent quantitative explanations.

Modelling phosphorus uptake in microalgae.

Phosphorus (P) is an essential non-renewable nutrient that frequently limits plant growth. It is the foundation of modern agriculture and, to a large extent, demand for P is met from phosphate rock deposits which are limited and becoming increasingly scarce. Adding an extra stroke to this already desolate picture is the fact that a high percentage of P, through agricultural runoff and waste, makes its way into rivers and oceans leading to eutrophication and collapse of ecosystems. Therefore, there is a critical need to practise P recovery from waste and establish a circular economy applicable to P resources. The potential of microalgae to uptake large quantities of P and use of this P enriched algal biomass as biofertiliser has been regarded as a promising way to redirect P from wastewater to the field. This also makes the study of molecular mechanisms underlying P uptake and storage in microalgae of great interest. In the present paper, we review phosphate models, which express the growth rate as a function of intra- and extracellular phosphorus content for better understanding of phosphate uptake and dynamics of phosphate pools.

The mechanism of ϕC31 integrase directionality: experimental analysis and computational modelling.

Serine integrases, DNA site-specific recombinases used by bacteriophages for integration and excision of their DNA to and from their host genomes, are increasingly being used as tools for programmed rearrangements of DNA molecules for biotechnology and synthetic biology. A useful feature of serine integrases is the simple regulation and unidirectionality of their reactions. Recombination between the phage attP and host attB sites is promoted by the serine integrase alone, giving recombinant attL and attR sites, whereas the 'reverse' reaction (between attL and attR) requires an additional protein, the recombination directionality factor (RDF). Here, we present new experimental data on the kinetics and regulation of recombination reactions mediated by ϕC31 integrase and its RDF, and use these data as the basis for a mathematical model of the reactions. The model accounts for the unidirectionality of the attP × attB and attL × attR reactions by hypothesizing the formation of structurally distinct, kinetically stable integrase-DNA product complexes, dependent on the presence or absence of RDF. The model accounts for all the available experimental data, and predicts how mutations of the proteins or alterations of reaction conditions might increase the conversion efficiency of recombination.

A Diverse Community To Study Communities: Integration of Experiments and Mathematical Models To Study Microbial Consortia.

The last few years have seen the advancement of high-throughput experimental techniques that have produced an extraordinary amount of data. Bioinformatics and statistical analyses have become instrumental to interpreting the information coming from, e.g., sequencing data and often motivate further targeted experiments. The broad discipline of "computational biology" extends far beyond the well-established field of bioinformatics, but it is our impression that more theoretical methods such as the use of mathematical models are not yet as well integrated into the research studying microbial interactions. The empirical complexity of microbial communities presents challenges that are difficult to address with in vivo/in vitro approaches alone, and with microbiology developing from a qualitative to a quantitative science, we see stronger opportunities arising for interdisciplinary projects integrating theoretical approaches with experiments. Indeed, the addition of in silico experiments, i.e., computational simulations, has a discovery potential that is, unfortunately, still largely underutilized and unrecognized by the scientific community. This minireview provides an overview of mathematical models of natural ecosystems and emphasizes that one critical point in the development of a theoretical description of a microbial community is the choice of problem scale. Since this choice is mostly dictated by the biological question to be addressed, in order to employ theoretical models fully and successfully it is vital to implement an interdisciplinary view at the conceptual stages of the experimental design.

A mathematical model of non-photochemical quenching to study short-term light memory in plants.

Plants are permanently exposed to rapidly changing environments, therefore it is evident that they had to evolve mechanisms enabling them to dynamically adapt to such fluctuations. Here we study how plants can be trained to enhance their photoprotection and elaborate on the concept of the short-term illumination memory in Arabidopsis thaliana. By monitoring fluorescence emission dynamics we systematically observe the extent of non-photochemical quenching (NPQ) after previous light exposure to recognise and quantify the memory effect. We propose a simplified mathematical model of photosynthesis that includes the key components required for NPQ activation, which allows us to quantify the contribution to photoprotection by those components. Due to its reduced complexity, our model can be easily applied to study similar behavioural changes in other species, which we demonstrate by adapting it to the shadow-tolerant plant Epipremnum aureum. Our results indicate that a basic mechanism of short-term light memory is preserved. The slow component, accumulation of zeaxanthin, accounts for the amount of memory remaining after relaxation in darkness, while the fast one, antenna protonation, increases quenching efficiency. With our combined theoretical and experimental approach we provide a unifying framework describing common principles of key photoprotective mechanisms across species in general, mathematical terms.

Design starch: stochastic modeling of starch granule biogenesis.

Starch is the most widespread and abundant storage carbohydrate in plants and the main source of carbohydrate in the human diet. Owing to its remarkable properties and commercial applications, starch is still of growing interest. Its unique granular structure made of intercalated layers of amylopectin and amylose has been unraveled thanks to recent progress in microscopic imaging, but the origin of such periodicity is still under debate. Both amylose and amylopectin are made of linear chains of α-1,4-bound glucose residues, with branch points formed by α-1,6 linkages. The net difference in the distribution of chain lengths and the branching pattern of amylose (mainly linear), compared with amylopectin (racemose structure), leads to different physico-chemical properties. Amylose is an amorphous and soluble polysaccharide, whereas amylopectin is insoluble and exhibits a highly organized structure of densely packed double helices formed between neighboring linear chains. Contrarily to starch degradation that has been investigated since the early 20th century, starch production is still poorly understood. Most enzymes involved in starch growth (elongation, branching, debranching, and partial hydrolysis) are now identified. However, their specific action, their interplay (cooperative or competitive), and their kinetic properties are still largely unknown. After reviewing recent results on starch structure and starch growth and degradation enzymatic activity, we discuss recent results and current challenges for growing polysaccharides on granular surface. Finally, we highlight the importance of novel stochastic models to support the analysis of recent and complex experimental results, and to address how macroscopic properties emerge from enzymatic activity and structural rearrangements.