Universal Transitions between Growth and Dormancy via Intermediate Complex Formation.

A simple cell model consisting of a catalytic reaction network with intermediate complex formation is numerically studied. As nutrients are depleted, the transition from the exponential growth phase to the growth-arrested dormant phase occurs along with hysteresis and a lag time for growth recovery. This transition is caused by the accumulation of intermediate complexes, leading to the jamming of reactions and the diversification of components. These properties are generic in random reaction networks, as supported by dynamical systems analyses of corresponding mean-field models.

Linear Response Theory of Evolved Metabolic Systems.

Predicting cellular metabolic states is a central problem in biophysics. Conventional approaches, however, sensitively depend on the microscopic details of individual metabolic systems. In this Letter, we derived a universal linear relationship between the metabolic responses against nutrient conditions and metabolic inhibition, with the aid of a microeconomic theory. The relationship holds in arbitrary metabolic systems as long as the law of mass conservation stands, as supported by extensive numerical calculations. It offers quantitative predictions without prior knowledge of systems.

Microeconomics of Metabolism: The Warburg Effect as Giffen Behaviour.

Metabolic behaviours of proliferating cells are often explained as a consequence of rational optimization of cellular growth rate, whereas microeconomics formulates consumption behaviours as optimization problems. Here, we pushed beyond the analogy to precisely map metabolism onto the theory of consumer choice. We thereby revealed the correspondence between long-standing mysteries in both fields: the Warburg effect, a seemingly wasteful but ubiquitous strategy where cells favour aerobic glycolysis over more energetically efficient oxidative phosphorylation, and Giffen behaviour, the unexpected consumer behaviour where a good is demanded more as its price rises. We identified the minimal, universal requirements for the Warburg effect: a trade-off between oxidative phosphorylation and aerobic glycolysis and complementarity, i.e. impossibility of substitution for different metabolites. Thus, various hypotheses for the Warburg effect are integrated into an identical optimization problem with the same universal structure. Besides, the correspondence between the Warburg effect and Giffen behaviour implies that oxidative phosphorylation is counter-intuitively stimulated when its efficiency is decreased by metabolic perturbations such as drug administration or mitochondrial dysfunction; the concept of Giffen behaviour bridges the Warburg effect and the reverse Warburg effect. This highlights that the application of microeconomics to metabolism can offer new predictions and paradigms for both biology and economics.

Adaptation of metabolite leakiness leads to symbiotic chemical exchange and to a resilient microbial ecosystem.

Microbial communities display remarkable diversity, facilitated by the secretion of chemicals that can create new niches. However, it is unclear why cells often secrete even essential metabolites after evolution. Based on theoretical results indicating that cells can enhance their own growth rate by leaking even essential metabolites, we show that such "leaker" cells can establish an asymmetric form of mutualism with "consumer" cells that consume the leaked chemicals: the consumer cells benefit from the uptake of the secreted metabolites, while the leaker cells also benefit from such consumption, as it reduces the metabolite accumulation in the environment and thereby enables further secretion, resulting in frequency-dependent coexistence of multiple microbial species. As supported by extensive simulations, such symbiotic relationships generally evolve when each species has a complex reaction network and adapts its leakiness to optimize its own growth rate under crowded conditions and nutrient limitations. Accordingly, symbiotic ecosystems with diverse cell species that leak and exchange many metabolites with each other are shaped by cell-level adaptation of leakiness of metabolites. Moreover, the resultant ecosystems with entangled metabolite exchange are resilient against structural and environmental perturbations. Thus, we present a theory for the origin of resilient ecosystems with diverse microbes mediated by secretion and exchange of essential chemicals.

Advantage of Leakage of Essential Metabolites for Cells.

Microbial cells generally leak various metabolites including those necessary to grow. Why cells secrete even essential chemicals so often is, however, still unclear. Based on analytical and numerical calculations, we show that if the intracellular metabolism includes multibody (e.g., catalytic) reactions, leakage of essential metabolites can promote the leaking cell's growth. This advantage is typical for most metabolic networks via "flux control" and "growth-dilution" mechanisms, as a general consequence of the balance between synthesis and growth-induced dilution with autocatalytic reactions. We further argue that this advantage may lead to a novel form of symbiosis among diverse cells.

Symbiotic Cell Differentiation and Cooperative Growth in Multicellular Aggregates.

As cells grow and divide under a given environment, they become crowded and resources are limited, as seen in bacterial biofilms and multicellular aggregates. These cells often show strong interactions through exchanging chemicals, as evident in quorum sensing, to achieve mutualism and division of labor. Here, to achieve stable division of labor, three characteristics are required. First, isogenous cells differentiate into several types. Second, this aggregate of distinct cell types shows better growth than that of isolated cells without interaction and differentiation, by achieving division of labor. Third, this cell aggregate is robust with respect to the number distribution of differentiated cell types. Indeed, theoretical studies have thus far considered how such cooperation is achieved when the ability of cell differentiation is presumed. Here, we address how cells acquire the ability of cell differentiation and division of labor simultaneously, which is also connected with the robustness of a cell society. For this purpose, we developed a dynamical-systems model of cells consisting of chemical components with intracellular catalytic reaction dynamics. The reactions convert external nutrients into internal components for cellular growth, and the divided cells interact through chemical diffusion. We found that cells sharing an identical catalytic network spontaneously differentiate via induction from cell-cell interactions, and then achieve division of labor, enabling a higher growth rate than that in the unicellular case. This symbiotic differentiation emerged for a class of reaction networks under the condition of nutrient limitation and strong cell-cell interactions. Then, robustness in the cell type distribution was achieved, while instability of collective growth could emerge even among the cooperative cells when the internal reserves of products were dominant. The present mechanism is simple and general as a natural consequence of interacting cells with limited resources, and is consistent with the observed behaviors and forms of several aggregates of unicellular organisms.