Optimal protein production by a synthetic microbial consortium: coexistence, distribution of labor, and syntrophy.

The bacterium E. coli is widely used to produce recombinant proteins such as growth hormone and insulin. One inconvenience with E.

Resource allocation accounts for the large variability of rate-yield phenotypes across bacterial strains.

Different strains of a microorganism growing in the same environment display a wide variety of growth rates and growth yields. We developed a coarse-grained model to test the hypothesis that different resource allocation strategies, corresponding to different compositions of the proteome, can account for the observed rate-yield variability. The model predictions were verified by means of a database of hundreds of published rate-yield and uptake-secretion phenotypes of strains grown in standard laboratory conditions.

Optimal proteome allocation and the temperature dependence of microbial growth laws.

Although the effect of temperature on microbial growth has been widely studied, the role of proteome allocation in bringing about temperature-induced changes remains elusive. To tackle this problem, we propose a coarse-grained model of microbial growth, including the processes of temperature-sensitive protein unfolding and chaperone-assisted (re)folding. We determine the proteome sector allocation that maximizes balanced growth rate as a function of nutrient limitation and temperature.

Global dynamics of the chemostat with overflow metabolism.

Fast growing E. coli cells, in glucose-aerobic conditions, excrete fermentation by-products such as acetate. This phenomenon is known as overflow metabolism and has been observed in a diverse range of microorganisms.

Optimal bacterial resource allocation: metabolite production in continuous bioreactors.

We show novel results addressing the problem of synthesizing a metabolite of interest in continuous bioreactors through resource allocation control. Our approach is based on a coarse-grained self-replicator dynamical model that accounts for microbial culture growth inside the bioreactor, and incorporates a synthetic growth switch that allows to externally modify the RNA polymerase concentration of the bacterial population, thus disrupting the natural process of allocation of available resources in bacteria. Further on, we study its asymptotic behavior using dynamical systems theory, and we provide conditions for the persistence of the bacterial population.

Enhanced production of heterologous proteins by a synthetic microbial community: Conditions and trade-offs.

Synthetic microbial consortia have been increasingly utilized in biotechnology and experimental evidence shows that suitably engineered consortia can outperform individual species in the synthesis of valuable products. Despite significant achievements, though, a quantitative understanding of the conditions that make this possible, and of the trade-offs due to the concurrent growth of multiple species, is still limited. In this work, we contribute to filling this gap by the investigation of a known prototypical synthetic consortium.

Reducing a model of sugar metabolism in peach to catch different patterns among genotypes.

Several studies have been conducted to understand the dynamic of primary metabolisms in fruit by translating them into mathematics models. An ODE kinetic model of sugar metabolism has been developed by Desnoues et al. (2018) to simulate the accumulation of different sugars during peach fruit development.

Modeling the bioconversion of polysaccharides in a continuous reactor: A case study of the production of oligogalacturonates by .

In the quest for a sustainable economy of the Earth's resources and for renewable sources of energy, a promising avenue is to exploit the vast quantity of polysaccharide molecules contained in green wastes. To that end, the decomposition of pectin appears to be an interesting target because this polymeric carbohydrate is abundant in many fruit pulps and soft vegetables. To quantitatively study this degradation process, here we designed a bioreactor that is continuously fed with de-esterified pectin (PGA).

Analysis of a genetic-metabolic oscillator with piecewise linear models.

Interactions between gene regulatory networks and metabolism produce a diversity of dynamics, including multistability and oscillations. Here, we characterize a regulatory mechanism that drives the emergence of periodic oscillations in metabolic networks subject to genetic feedback regulation by pathway intermediates. We employ a qualitative formalism based on piecewise linear models to systematically analyze the behavior of gene-regulated metabolic pathways.

Optimal control of bacterial growth for the maximization of metabolite production.

Microorganisms have evolved complex strategies for controlling the distribution of available resources over cellular functions. Biotechnology aims at interfering with these strategies, so as to optimize the production of metabolites and other compounds of interest, by (re)engineering the underlying regulatory networks of the cell. The resulting reallocation of resources can be described by simple so-called self-replicator models and the maximization of the synthesis of a product of interest formulated as a dynamic optimal control problem.

Principal process analysis of biological models.

Background: Understanding the dynamical behaviour of biological systems is challenged by their large number of components and interactions. While efforts have been made in this direction to reduce model complexity, they often prove insufficient to grasp which and when model processes play a crucial role. Answering these questions is fundamental to unravel the functioning of living organisms.

Reduction and Stability Analysis of a Transcription-Translation Model of RNA Polymerase.

The aim of this paper is to analyze the dynamical behavior of biological models of gene transcription and translation. We focus on a particular positive feedback loop governing the synthesis of RNA polymerase, needed for transcribing its own gene. We write a high-dimension model based on mass action laws and reduce it to a two-variable model (RNA polymerase and its mRNA) by means of monotone system theory and timescale arguments.

Mathematical modelling of microbes: metabolism, gene expression and growth.

The growth of microorganisms involves the conversion of nutrients in the environment into biomass, mostly proteins and other macromolecules. This conversion is accomplished by networks of biochemical reactions cutting across cellular functions, such as metabolism, gene expression, transport and signalling. Mathematical modelling is a powerful tool for gaining an understanding of the functioning of this large and complex system and the role played by individual constituents and mechanisms.

Dynamical Allocation of Cellular Resources as an Optimal Control Problem: Novel Insights into Microbial Growth Strategies.

Microbial physiology exhibits growth laws that relate the macromolecular composition of the cell to the growth rate. Recent work has shown that these empirical regularities can be derived from coarse-grained models of resource allocation. While these studies focus on steady-state growth, such conditions are rarely found in natural habitats, where microorganisms are continually challenged by environmental fluctuations.

Links between topology of the transition graph and limit cycles in a two-dimensional piecewise affine biological model.

A class of piecewise affine differential (PWA) models, initially proposed by Glass and Kauffman (in J Theor Biol 39:103-129, 1973), has been widely used for the modelling and the analysis of biological switch-like systems, such as genetic or neural networks. Its mathematical tractability facilitates the qualitative analysis of dynamical behaviors, in particular periodic phenomena which are of prime importance in biology. Notably, a discrete qualitative description of the dynamics, called the transition graph, can be directly associated to this class of PWA systems.

Global stability of enzymatic chains of full reversible Michaelis-Menten reactions.

We consider a chain of metabolic reactions catalyzed by enzymes, of reversible Michaelis-Menten type with full dynamics, i.e. not reduced with any quasi-steady state approximations.

Global stability of reversible enzymatic metabolic chains.

We consider metabolic networks with reversible enzymatic reactions. The model is written as a system of ordinary differential equations, possibly with inputs and outputs. We prove the global stability of the equilibrium (if it exists), using techniques of monotone systems and compartmental matrices.

Stabilizing effect of cannibalism in a two stages population model.

In this paper we build a prey-predator model with discrete weight structure for the predator. This model will conserve the number of individuals and the biomass and both growth and reproduction of the predator will depend on the food ingested. Moreover the model allows cannibalism which means that the predator can eat the prey but also other predators.

Probabilistic approach for predicting periodic orbits in piecewise affine differential models.

Piecewise affine models provide a qualitative description of the dynamics of a system, and are often used to study genetic regulatory networks. The state space of a piecewise affine system is partitioned into hyperrectangles, which can be represented as nodes in a directed graph, so that the system's trajectories follow a path in a transition graph. This paper proposes and compares two definitions of probability of transition between two nodes A and B of the graph, based on the volume of the initial conditions on the hyperrectangle A whose trajectories cross to B.

A theoretical exploration of birhythmicity in the p53-Mdm2 network.

Experimental observations performed in the p53-Mdm2 network, one of the key protein modules involved in the control of proliferation of abnormal cells in mammals, revealed the existence of two frequencies of oscillations of p53 and Mdm2 in irradiated cells depending on the irradiation dose. These observations raised the question of the existence of birhythmicity, i.e.

Comparing Boolean and piecewise affine differential models for genetic networks.

Multi-level discrete models of genetic networks, or the more general piecewise affine differential models, provide qualitative information on the dynamics of the system, based on a small number of parameters (such as synthesis and degradation rates). Boolean models also provide qualitative information, but are based simply on the structure of interconnections. To explore the relationship between the two formalisms, a piecewise affine differential model and a Boolean model are compared, for the carbon starvation response network in E.

Periodic solutions of piecewise affine gene network models with non uniform decay rates: the case of a negative feedback loop.

This paper concerns periodic solutions of a class of equations that model gene regulatory networks. Unlike the vast majority of previous studies, it is not assumed that all decay rates are identical. To handle this more general situation, we rely on monotonicity properties of these systems.

Hierarchical analysis of piecewise affine models of gene regulatory networks.

A key point in the analysis of dynamical models of biological systems is to handle systems of relatively high dimensions. In the present paper we propose a method to hierarchically organize a certain type of piecewise affine (PWA) differential systems. This specific class of systems has been extensively studied for the past few years, as it provides a good framework to model gene regulatory networks.

Piecewise-linear models of genetic regulatory networks: equilibria and their stability.

A formalism based on piecewise-linear (PL) differential equations, originally due to Glass and Kauffman, has been shown to be well-suited to modelling genetic regulatory networks. However, the discontinuous vector field inherent in the PL models raises some mathematical problems in defining solutions on the surfaces of discontinuity. To overcome these difficulties we use the approach of Filippov, which extends the vector field to a differential inclusion.