Origin of exponential growth in nonlinear reaction networks

Incoherent feedback from coupled amino acids and ribosome pools generates damped oscillations in growing E. coli

Current theories of bacterial growth physiology demonstrate impressive predictive power but are often phenomenological, lacking mechanistic detail. Incorporating such details would significantly enhance our ability to predict and control bacterial growth under varying environmental conditions. The "Flux Controlled Regulation" (FCR) model serves as a reference framework, linking ribosome allocation to translation efficiency through a steady-state assumption. However, it neglects ppGpp-mediated nutrient sensing and transcriptional regulation of ribosomal operons. Here, we propose a mechanistic model that extends the FCR framework by incorporating three key components: (i) the amino acid pool, (ii) ppGpp sensing of translation elongation rate, and (iii) transcriptional regulation of protein allocation by ppGpp-sensitive promoters. Our model aligns with observed steady-state growth laws and makes testable predictions for unobserved quantities. We show that during environmental changes, the incoherent feedback between sensing and regulation generates oscillatory relaxation dynamics, a behavior that we support by new and existing experimental data.

Nonequilibrium properties of autocatalytic networks

Autocatalysis, the ability of a chemical system to make more of itself, is a crucial feature in metabolism and is speculated to have played a decisive role in the origin of life. Nevertheless, how autocatalytic systems behave far from equilibrium remains unexplored. In this work, we elaborate on recent advances regarding the stoichiometric characterization of autocatalytic networks, particularly their absence of mass-like conservation laws, to study how this topological feature influences their nonequilibrium behavior. Building upon the peculiar topology of autocatalytic networks, we derive a decomposition of the chemical fluxes, which highlights the existence of productive modes in their dynamics. These modes produce the autocatalysts in net excess and require the presence of external fuel/waste species to operate. Relying solely on topology, the flux decomposition holds under broad conditions and, in particular, does not require steady state or elementary reactions. Additionally, we show that once externally controlled, the nonconservative forces brought by the external species do not act on these productive modes. This must be considered when one is interested in the thermodynamics of open autocatalytic networks. Specifically, we show that an additional term must be added to the semigrand free energy. Finally, from the thermodynamic potential, we derive the thermodynamic cost associated with the production of autocatalysts.

Free-energy transduction mechanisms shape the flux space of metabolic networks

The transduction of free energy in metabolic networks represents a thermodynamic mechanism by which the free energy derived from nutrients is converted to drive nonspontaneous, energy-requiring metabolic reactions. This transduction is typically observed in processes that generate energy-rich molecules such as ATP and NAD(P)H, which, in turn, power specific reactions, particularly biosynthetic reactions. This property establishes a pivotal connection between the intricate topology of metabolic networks and their ability to redirect energy for functional purposes. The present study proposes a dedicated framework aimed at exploring the relationship between free-energy dissipation, network topology, and metabolic objectives. The starting point is that, regardless of the network topology, nonequilibrium chemostatting conditions impose stringent thermodynamic constraints on the feasible flux steady states to satisfy energy and entropy balances. An analysis of randomly sampled reaction networks shows that the network topology imposes additional constraints that restrict the accessible flux solution space, depending on key structural features such as the reaction's molecularity, reaction cycles, and conservation laws. Notably, topologies featuring multimolecular reactions that implement free-energy transduction mechanisms tend to extend the accessible flux domains, facilitating the achievement of metabolic objectives such as anabolic flux maximization or flux rerouting capacity. This approach is applied to a coarse-grained model of carbohydrate metabolism, highlighting the structural requirements for optimal biomass yield.

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.