Origin of exponential growth in nonlinear reaction networks

Thermodynamics of Growth in Open Chemical Reaction Networks

We identify the thermodynamic conditions necessary to observe indefinite growth in homogeneous open chemical reaction networks (CRNs) satisfying mass action kinetics. We also characterize the thermodynamic efficiency of growth by considering the fraction of the chemical work supplied from the surroundings that is converted into CRN free energy. We find that indefinite growth cannot arise in CRNs chemostatted by fixing the concentration of some species at constant values, or in continuous-flow stirred tank reactors. Indefinite growth requires a constant net influx from the surroundings of at least one species. In this case, unimolecular CRNs always generate equilibrium linear growth, i.e., a continuous linear accumulation of species with equilibrium concentrations and efficiency one. Multimolecular CRNs are necessary to generate nonequilibrium growth, i.e., the continuous accumulation of species with nonequilibrium concentrations. Pseudounimolecular CRNs-a subclass of multimolecular CRNs-always generate asymptotic linear growth with zero efficiency. Our findings demonstrate the importance of the CRN topology and the chemostatting procedure in determining the dynamics and thermodynamics of growth.

Characterizing the conditions for indefinite growth in open chemical reaction networks

The thermodynamic and dynamical conditions necessary to observe indefinite growth in homogeneous open chemical reaction networks (CRNs) satisfying mass action kinetics are presented in Srinivas et al. [Phys. Rev. Lett. 132, 268001 (2024)10.1103/PhysRevLett.132.268001]. Unimolecular CRNs can accumulate only equilibrium concentrations of species while multimolecular CRNs are needed to produce indefinite growth with nonequilibrium concentrations. Within multimolecular CRNs, pseudo-unimolecular CRNs produce nonequilibrium concentrations with zero efficiencies. Nonequilibrium growth with efficiencies greater than zero requires dynamically nonlinear CRNs. In this paper, we provide a detailed analysis supporting these results. Mathematical proofs are provided for growth in unimolecular and pseudo-unimolecular CRNs. For multimolecular CRNs, four models displaying very distinctive topological properties are extensively studied, both numerically and partly analytically.

Biomolecular condensates tunes immune signaling at the Host-Pathogen interface

Membraneless organelles participate in diverse spatiotemporal regulation of cellular signal transduction by recruiting necessary signaling factors. During host-pathogen interactions, the plasma membrane (PM) at the interface between the plant and microbes serves as a central platform for forming multicomponent immune signaling hubs. The macromolecular condensation of the immune complex and regulators is important in regulating immune signaling outputs regarding strength, timing, and crosstalk between signaling pathways. This review discusses mechanisms that regulate specific and crosstalk of plant immune signal transduction pathways through macromolecular assembly and condensation.

Growth and depletion in linear stochastic reaction networks

This paper is about a class of stochastic reaction networks. Of interest are the dynamics of interconversion among a finite number of substances through reactions that consume some of the substances and produce others. The models we consider are continuous-time Markov jump processes, intended as idealizations of a broad class of biological networks. Reaction rates depend linearly on "enzymes," which are among the substances produced, and a reaction can occur only in the presence of sufficient upstream material. We present rigorous results for this class of stochastic dynamical systems, the mean-field behaviors of which are described by ordinary differential equations (ODEs). Under the assumption of exponential network growth, we identify certain ODE solutions as being potentially traceable and give conditions on network trajectories which, when rescaled, can with high probability be approximated by these ODE solutions. This leads to a complete characterization of the ω-limit sets of such network solutions (as points or random tori). Dimension reduction is noted depending on the number of enzymes. The second half of this paper is focused on depletion dynamics, i.e., dynamics subsequent to the "phase transition" that occurs when one of the substances becomes unavailable. The picture can be complex, for the depleted substance can be produced intermittently through other network reactions. Treating the model as a slow-fast system, we offer a mean-field description, a first step to understanding what we believe is one of the most natural bifurcations for reaction networks.

Connecting single-cell ATP dynamics to overflow metabolism, cell growth, and the cell cycle in Escherichia coli

Adenosine triphosphate (ATP) is an abundant and essential metabolite that cells consume and regenerate in large amounts to support growth. Although numerous studies have inferred the intracellular concentration of ATP in bacterial cultures, what happens in individual bacterial cells under stable growth conditions is less clear. Here, we use the QUEEN-2m biosensor to quantify ATP dynamics in single Escherichia coli cells in relation to their growth rate, metabolism, cell cycle, and cell lineage. We find that ATP dynamics are more complex than expected from population studies and are associated with growth-rate variability. Under stable nutrient-rich condition, cells can display large fluctuations in ATP level that are partially coordinated with the cell cycle. Abrogation of aerobic acetate fermentation (overflow metabolism) through genetic deletion considerably reduces both the amplitude of ATP level fluctuations and the cell-cycle trend. Similarly, growth in media in which acetate fermentation is lower or absent results in the reduction of ATP level fluctuation and cell-cycle trend. This suggests that overflow metabolism exhibits temporal dynamics, which contributes to fluctuating ATP levels during growth. Remarkably, at the single-cell level, growth rate negatively correlates with the amplitude of ATP fluctuation for each tested condition, linking ATP dynamics to growth-rate heterogeneity in clonal populations. Our work highlights the importance of single-cell analysis in studying metabolism and its implication to phenotypic diversity and cell growth.