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.

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.

Metabolic states with maximal specific rate carry flux through an elementary flux mode.

Specific product formation rates and cellular growth rates are important maximization targets in biotechnology and microbial evolution. Maximization of a specific rate (i.e. a rate expressed per unit biomass amount) requires the expression of particular metabolic pathways at optimal enzyme concentrations. In contrast to the prediction of maximal product yields, any prediction of optimal specific rates at the genome scale is currently computationally intractable, even if the kinetic properties of all enzymes are available. In the present study, we characterize maximal-specific-rate states of metabolic networks of arbitrary size and complexity, including genome-scale kinetic models. We report that optimal states are elementary flux modes, which are minimal metabolic networks operating at a thermodynamically-feasible steady state with one independent flux. Remarkably, elementary flux modes rely only on reaction stoichiometry, yet they function as the optimal states of mathematical models incorporating enzyme kinetics. Our results pave the way for the optimization of genome-scale kinetic models because they offer huge simplifications to overcome the concomitant computational problems.

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.].