Understanding and computational design of genetic circuits of metabolic networks.

The expression of metabolic proteins is controlled by genetic circuits, matching metabolic demands and changing environmental conditions. Ideally, this regulation brings about a competitive level of metabolic fitness. Understanding how cells can achieve a robust (close-to-optimal) functioning of metabolism by appropriate control of gene expression aids synthetic biology by providing design criteria of synthetic circuits for biotechnological purposes. It also extends our understanding of the designs of genetic circuitry found in nature such as metabolite control of transcription factor activity, promoter architectures and transcription factor dependencies, and operon composition (in bacteria). Here, we review, explain and illustrate an approach that allows for the inference and design of genetic circuitry that steers metabolic networks to achieve a maximal flux per unit invested protein across dynamic conditions. We discuss how this approach and its understanding can be used to rationalize Escherichia coli's strategy to regulate the expression of its ribosomes and infer the design of circuitry controlling gene expression of amino-acid biosynthesis enzymes. The inferred regulation indeed resembles E. coli's circuits, suggesting that these have evolved to maximize amino-acid production fluxes per unit invested protein. We end by an outlook of the use of this approach in metabolic engineering applications.

Lysosomal calcium loading promotes spontaneous calcium release by potentiating ryanodine receptors.

Spontaneous calcium release by ryanodine receptors (RyRs) due to intracellular calcium overload results in delayed afterdepolarizations, closely associated with life-threatening arrhythmias. In this regard, inhibiting lysosomal calcium release by two-pore channel 2 (TPC2) knockout has been shown to reduce the incidence of ventricular arrhythmias under ß-adrenergic stimulation. However, mechanistic investigations into the role of lysosomal function on RyR spontaneous release remain missing. We investigate the calcium handling mechanisms by which lysosome function modulates RyR spontaneous release, and determine how lysosomes are able to mediate arrhythmias by its influence on calcium loading. Mechanistic studies were conducted using a population of biophysically detailed mouse ventricular models including for the first time modeling of lysosomal function, and calibrated by experimental calcium transients modulated by TPC2. We demonstrate that lysosomal calcium uptake and release can synergistically provide a pathway for fast calcium transport, by which lysosomal calcium release primarily modulates sarcoplasmic reticulum calcium reuptake and RyR release. Enhancement of this lysosomal transport pathway promoted RyR spontaneous release by elevating RyR open probability. In contrast, blocking either lysosomal calcium uptake or release revealed an antiarrhythmic impact. Under conditions of calcium overload, our results indicate that these responses are strongly modulated by intercellular variability in L-type calcium current, RyR release, and sarcoplasmic reticulum calcium-ATPase reuptake. Altogether, our investigations identify that lysosomal calcium handling directly influences RyR spontaneous release by regulating RyR open probability, suggesting antiarrhythmic strategies and identifying key modulators of lysosomal proarrhythmic action.

The discrete-time Kermack-McKendrick model: A versatile and computationally attractive framework for modeling epidemics.

The COVID-19 pandemic has led to numerous mathematical models for the spread of infection, the majority of which are large compartmental models that implicitly constrain the generation-time distribution. On the other hand, the continuous-time Kermack-McKendrick epidemic model of 1927 (KM27) allows an arbitrary generation-time distribution, but it suffers from the drawback that its numerical implementation is rather cumbersome. Here, we introduce a discrete-time version of KM27 that is as general and flexible, and yet is very easy to implement computationally. Thus, it promises to become a very powerful tool for exploring control scenarios for specific infectious diseases such as COVID-19. To demonstrate this potential, we investigate numerically how the incidence-peak size depends on model ingredients. We find that, with the same reproduction number and the same initial growth rate, compartmental models systematically predict lower peak sizes than models in which the latent and the infectious period have fixed duration.

Unlocking Elementary Conversion Modes: ecmtool Unveils All Capabilities of Metabolic Networks.

The metabolic capabilities of cells determine their biotechnological potential, fitness in ecosystems, pathogenic threat levels, and function in multicellular organisms. Their comprehensive experimental characterization is generally not feasible, particularly for unculturable organisms. In principle, the full range of metabolic capabilities can be computed from an organism's annotated genome using metabolic network reconstruction. However, current computational methods cannot deal with genome-scale metabolic networks. Part of the problem is that these methods aim to enumerate all metabolic pathways, while computation of all (elementally balanced) conversions between nutrients and products would suffice. Indeed, the elementary conversion modes (ECMs, defined by Urbanczik and Wagner) capture the full metabolic capabilities of a network, but the use of ECMs has not been accessible until now. We explain and extend the theory of ECMs, implement their enumeration in ecmtool, and illustrate their applicability. This work contributes to the elucidation of the full metabolic footprint of any cell.

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.

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.

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

The aim of this short note is to give a simple explanation for the remarkable periodicity of Magicicada species, which appear as adults only every 13 or 17 years, depending on the region. We show that a combination of two types of density dependence may drive, for large classes of initial conditions, all but 1 year class to extinction. Competition for food leads to negative density dependence in the form of a uniform (i.e., affecting all age classes in the same way) reduction of the survival probability. Satiation of predators leads to positive density dependence within the reproducing age class. The analysis focuses on the full life cycle map derived by iteration of a semelparous Leslie matrix.

The common message of constraint-based optimization approaches: overflow metabolism is caused by two growth-limiting constraints.

Living cells can express different metabolic pathways that support growth. The criteria that determine which pathways are selected in which environment remain unclear. One recurrent selection is overflow metabolism: the simultaneous usage of an ATP-efficient and -inefficient pathway, shown for example in Escherichia coli, Saccharomyces cerevisiae and cancer cells. Many models, based on different assumptions, can reproduce this observation. Therefore, they provide no conclusive evidence which mechanism is causing overflow metabolism. We compare the mathematical structure of these models. Although ranging from flux balance analyses to self-fabricating metabolism and expression models, we can rewrite all models into one standard form. We conclude that all models predict overflow metabolism when two, model-specific, growth-limiting constraints are hit. This is consistent with recent theory. Thus, identifying these two constraints is essential for understanding overflow metabolism. We list all imposed constraints by these models, so that they can hopefully be tested in future experiments.

The number of active metabolic pathways is bounded by the number of cellular constraints at maximal metabolic rates.

Growth rate is a near-universal selective pressure across microbial species. High growth rates require hundreds of metabolic enzymes, each with different nonlinear kinetics, to be precisely tuned within the bounds set by physicochemical constraints. Yet, the metabolic behaviour of many species is characterized by simple relations between growth rate, enzyme expression levels and metabolic rates. We asked if this simplicity could be the outcome of optimisation by evolution. Indeed, when the growth rate is maximized-in a static environment under mass-conservation and enzyme expression constraints-we prove mathematically that the resulting optimal metabolic flux distribution is described by a limited number of subnetworks, known as Elementary Flux Modes (EFMs). We show that, because EFMs are the minimal subnetworks leading to growth, a small active number automatically leads to the simple relations that are measured. We find that the maximal number of flux-carrying EFMs is determined only by the number of imposed constraints on enzyme expression, not by the size, kinetics or topology of the network. This minimal-EFM extremum principle is illustrated in a graphical framework, which explains qualitative changes in microbial behaviours, such as overflow metabolism and co-consumption, and provides a method for identification of the enzyme expression constraints that limit growth under the prevalent conditions. The extremum principle applies to all microorganisms that are selected for maximal growth rates under protein concentration constraints, for example the solvent capacities of cytosol, membrane or periplasmic space.

Maintaining maximal metabolic flux by gene expression control.

One of the marvels of biology is the phenotypic plasticity of microorganisms. It allows them to maintain high growth rates across conditions. Studies suggest that cells can express metabolic enzymes at tuned concentrations through adjustment of gene expression. The associated transcription factors are often regulated by intracellular metabolites. Here we study metabolite-mediated regulation of metabolic-gene expression that maximises metabolic fluxes across conditions. We developed an adaptive control theory, qORAC (for 'Specific Flux (q) Optimization by Robust Adaptive Control'), and illustrate it with several examples of metabolic pathways. The key feature of the theory is that it does not require knowledge of the regulatory network, only of the metabolic part. We derive that maximal metabolic flux can be maintained in the face of varying N environmental parameters only if the number of transcription-factor binding metabolites is at least equal to N. The controlling circuits appear to require simple biochemical kinetics. We conclude that microorganisms likely can achieve maximal rates in metabolic pathways, in the face of environmental changes.

Understanding start-up problems in yeast glycolysis.

Yeast glycolysis has been the focus of research for decades, yet a number of dynamical aspects of yeast glycolysis remain poorly understood at present. If nutrients are scarce, yeast will provide its catabolic and energetic needs with other pathways, but the enzymes catalysing upper glycolytic fluxes are still expressed. We conjecture that this overexpression facilitates the rapid transition to glycolysis in case of a sudden increase in nutrient concentration. However, if starved yeast is presented with abundant glucose, it can enter into an imbalanced state where glycolytic intermediates keep accumulating, leading to arrested growth and cell death. The bistability between regularly functioning and imbalanced phenotypes has been shown to depend on redox balance. We shed new light on these phenomena with a mathematical analysis of an ordinary differential equation model, including NADH to account for the redox balance. In order to gain qualitative insight, most of the analysis is parameter-free, i.e., without assigning a numerical value to any of the parameters. The model has a subtle bifurcation at the switch between an inviable equilibrium state and stable flux through glycolysis. This switch occurs if the ratio between the flux through upper glycolysis and ATP consumption rate of the cell exceeds a fixed threshold. If the enzymes of upper glycolysis would be barely expressed, our model predicts that there will be no glycolytic flux, even if external glucose would be at growth-permissable levels. The existence of the imbalanced state can be found for certain parameter conditions independent of the mentioned bifurcation. The parameter-free analysis proved too complex to directly gain insight into the imbalanced states, but the starting point of a branch of imbalanced states can be shown to exist in detail. Moreover, the analysis offers the key ingredients necessary for successful numerical continuation, which highlight the existence of this bistability and the influence of the redox balance.

Understanding bistability in yeast glycolysis using general properties of metabolic pathways.

UNLABELLED: Glycolysis is the central pathway in energy metabolism in the majority of organisms. In a recent paper, van Heerden et al. showed experimentally and computationally that glycolysis can exist in two states, a global steady state and a so-called imbalanced state. In the imbalanced state, intermediary metabolites accumulate at low levels of ATP and inorganic phosphate. It was shown that Baker's yeast uses a peculiar regulatory mechanism--via trehalose metabolism--to ensure that most yeast cells reach the steady state and not the imbalanced state. RESULTS: Here we explore the apparent bistable behaviour in a core model of glycolysis that is based on a well-established detailed model, and study in great detail the bifurcation behaviour of solutions, without using any numerical information on parameter values. CONCLUSION: We uncover a rich suite of solutions, including so-called imbalanced states, bistability, and oscillatory behaviour. The techniques employed are generic, directly suitable for a wide class of biochemical pathways, and could lead to better analytical treatments of more detailed models.

Species interactions and the structure of complex communication networks.

A universal challenge faced by animal species is the need to communicate effectively against a backdrop of heterospecific signals. It is often assumed that this need results in signal divergence to minimize interference among community members, yet previous support for this idea is mixed, and few studies have tested the opposing hypothesis that interactions among competing species promote widespread convergence in signaling regimes. Using a null model approach to analyze acoustic signaling in 307 species of Amazonian birds, we show that closely related lineages signal together in time and space and that acoustic signals given in temporal or spatial proximity are more similar in design than expected by chance. These results challenge the view that multispecies choruses are structured by temporal, spatial, or acoustic partitioning and instead suggest that social communication between competing species can fundamentally organize signaling assemblages, leading to the opposite pattern of clustering in signals and signaling behavior.

Lost in transition: start-up of glycolysis yields subpopulations of nongrowing cells.

Cells need to adapt to dynamic environments. Yeast that fail to cope with dynamic changes in the abundance of glucose can undergo growth arrest. We show that this failure is caused by imbalanced reactions in glycolysis, the essential pathway in energy metabolism in most organisms. The imbalance arises largely from the fundamental design of glycolysis, making this state of glycolysis a generic risk. Cells with unbalanced glycolysis coexisted with vital cells. Spontaneous, nongenetic metabolic variability among individual cells determines which state is reached and, consequently, which cells survive. Transient ATP (adenosine 5'-triphosphate) hydrolysis through futile cycling reduces the probability of reaching the imbalanced state. Our results reveal dynamic behavior of glycolysis and indicate that cell fate can be determined by heterogeneity purely at the metabolic level.

Fatal attraction in glycolysis: how Saccharomyces cerevisiae manages sudden transitions to high glucose.

In the model eukaryote Saccharomyces cerevisiae, it has long been known that a functional trehalose pathway is indispensable for transitions to high glucose conditions. Upon addition of glucose, cells with a defect in trehalose 6-phosphate synthase (Tps1), the first committed step in the trehalose pathway, display what we have termed an imbalanced glycolytic state; in this state the flux through the upper part of glycolysis outpaces that through the lower part of glycolysis. As a consequence, the intermediate fructose 1,6-bisphosphate (FBP) accumulates at low concentrations of ATP and inorganic phosphate (Pi). Despite significant research efforts, a satisfactory understanding of the regulatory role that trehalose metabolism plays during such transitions has remained infamously unresolved. In a recent study, we demonstrate that the startup of glycolysis exhibits two dynamic fates: a proper, functional, steady state or the imbalanced state described above. Both states are stable, attracting states, and the probability distribution of initial states determines the fate of a yeast cell exposed to glucose. Trehalose metabolism steers the dynamics of glycolysis towards the proper functional state through its ATP hydrolysis activity; a mechanism that ensures that the demand and supply of ATP is balanced with Pi availability under dynamic conditions. [van Heerden et al. Science (2014), DOI: 10.1126/science.1245114.].

On the maintenance of bird song dialects.

Many bird species, especially song birds but also for instance some hummingbirds and parrots, have noted dialects. By this we mean that locally a particular song is sung by the majority of the birds, but that neighbouring patches may feature different song types. Behavioural ecologists have been interested in how such dialects come about and how they are maintained for over 45 years. As a result, a great deal is known about different mechanisms at play, such as dispersal, assortative mating and learning of songs, and there are several competing hypotheses to explain the dialect patterns known in nature. There is, however, surprisingly little theoretical work testing these different hypotheses at present. We analyse the simplest kind of model that takes into account the most important biological mechanisms, and in which one may speak of dialects: a model in which there are but two patches, and two song types. It teaches us that a combination of little dispersal and strong assortative mating ensures dialects are maintained. Assuming a simple, linear frequency-dependent learning rule has little effect on the maintenance of dialects. A nonlinear learning rule, however, has dramatic consequences and greatly facilitates dialect maintenance. Adding fitness benefits for singing particular songs in a given patch also has a great impact. Now rare song types may invade and remain in the population.

The interplay between scent trails and group-mass recruitment systems in ants.

Large ant colonies invariably use effective scent trails to guide copious ant numbers to food sources. The success of mass recruitment hinges on the involvement of many colony members to lay powerful trails. However, many ant colonies start off as single queens. How do these same colonies forage efficiently when small, thereby overcoming the hurdles to grow large? In this paper, we study the case of combined group and mass recruitment displayed by some ant species. Using mathematical models, we explore to what extent early group recruitment may aid deployment of scent trails, making such trails available at much smaller colony sizes. We show that a competition between group and mass recruitment may cause oscillatory behaviour mediated by scent trails. This results in a further reduction of colony size to establish trails successfully.

Recruitment strategies and colony size in ants.

Ants use a great variety of recruitment methods to forage for food or find new nests, including tandem running, group recruitment and scent trails. It has been known for some time that there is a loose correlation across many taxa between species-specific mature colony size and recruitment method. Very small colonies tend to use solitary foraging; small to medium sized colonies use tandem running or group recruitment whereas larger colonies use pheromone recruitment trails. Until now, explanations for this correlation have focused on the ants' ecology, such as food resource distribution. However, many species have colonies with a single queen and workforces that grow over several orders of magnitude, and little is known about how a colony's organization, including recruitment methods, may change during its growth. After all, recruitment involves interactions between ants, and hence the size of the colony itself may influence which recruitment method is used--even if the ants' behavioural repertoire remains unchanged. Here we show using mathematical models that the observed correlation can also be explained by recognizing that failure rates in recruitment depend differently on colony size in various recruitment strategies. Our models focus on the build up of recruiter numbers inside colonies and are not based on optimality arguments, such as maximizing food yield. We predict that ant colonies of a certain size should use only one recruitment method (and always the same one) rather than a mix of two or more. These results highlight the importance of the organization of recruitment and how it is affected by colony size. Hence these results should also expand our understanding of ant ecology.

Objective determination of the oncolytic potency of conditionally-replicating adenoviruses using mathematical modeling.

BACKGROUND: Conditionally-replicating adenoviruses (CRAds) infect and replicate in tumor cells, releasing viral progeny upon lysis of the cell. This is a dynamic and inherently exponential process and, thus, the assessment of CRAds should incorporate these dynamics. In vitro experiments are therefore prone to subjective assessment because no validated assay exists that truly appreciates the dynamics of the process. An objective assay could simplify experiments and reduce the number of CRAd variants required to enter a full preclinical evaluation. METHODS: We developed a simple and practical mathematical model incorporating easily obtainable parameters of the interaction between replicating viruses and growing tumor cells in vitro and, in the present study, validate this model by fitting the predicted values to experimentally-derived values. RESULTS: From the exponential curves of cellular growth and the viral propagation rate in glioma cells, we derive the four parameters needed in this model and show a robust fit to experimental data. Because the initial infection conditions appear to significantly influence the final outcome of CRAd experiments, these conditions are determined using the same cells and correlated with the expression of the primary adenovirus receptor CAR (coxsackie and adenovirus receptor). CONCLUSIONS: The results obtained shed light upon the method of action of CRAds and provide an objective and practical model and assay for determining and predicting CRAd activity in tumor cells.

On optimal decision-making in brains and social insect colonies.

The problem of how to compromise between speed and accuracy in decision-making faces organisms at many levels of biological complexity. Striking parallels are evident between decision-making in primate brains and collective decision-making in social insect colonies: in both systems, separate populations accumulate evidence for alternative choices; when one population reaches a threshold, a decision is made for the corresponding alternative, and this threshold may be varied to compromise between the speed and the accuracy of decision-making. In primate decision-making, simple models of these processes have been shown, under certain parametrizations, to implement the statistically optimal procedure that minimizes decision time for any given error rate. In this paper, we adapt these same analysis techniques and apply them to new models of collective decision-making in social insect colonies. We show that social insect colonies may also be able to achieve statistically optimal collective decision-making in a very similar way to primate brains, via direct competition between evidence-accumulating populations. This optimality result makes testable predictions for how collective decision-making in social insects should be organized. Our approach also represents the first attempt to identify a common theoretical framework for the study of decision-making in diverse biological systems.