Convex Representation of Metabolic Networks with Michaelis-Menten Kinetics.

Polyhedral models of metabolic networks are computationally tractable and can predict some cellular functions. A longstanding challenge is incorporating metabolites without losing tractability. In this paper, we do so using a new second-order cone representation of the Michaelis-Menten kinetics. The resulting model consists of linear stoichiometric constraints alongside second-order cone constraints that couple the reaction fluxes to metabolite concentrations. We formulate several new problems around this model: conic flux balance analysis, which augments flux balance analysis with metabolite concentrations; dynamic conic flux balance analysis; and finding minimal cut sets of networks with both reactions and metabolites. Solving these problems yields information about both fluxes and metabolite concentrations. They are second-order cone or mixed-integer second-order cone programs, which, while not as tractable as their linear counterparts, can nonetheless be solved at practical scales using existing software.

The Role of Permanently Resident Populations in the Two-Patches SIR Model with Commuters.

We consider a two-patches SIR model where communication occurs through commuters, distinguishing explicitly permanently resident populations from commuters populations. We give an explicit formula of the reproduction number and show how the proportions of permanently resident populations impact it. We exhibit nonintuitive situations for which allowing commuting from a safe territory to another one where the transmission rate is higher can reduce the overall epidemic threshold and avoid an outbreak.

Equivalent Formulations of Optimal Control Problems with Maximum Cost and Applications.

We revisit the optimal control problem with maximum cost with the objective to provide different equivalent reformulations suitable to numerical methods. We propose two reformulations in terms of extended Mayer problems with state constraints, and another one in terms of a differential inclusion with upper-semi-continuous right member without state constraint. For the latter we also propose a scheme that approximates from below the optimal value. These approaches are illustrated and discussed in several examples.

Performance Study of Two Serial Interconnected Chemostats with Mortality.

The present work considers the model of two chemostats in series when a biomass mortality is considered in each vessel. We study the performance of the serial configuration for two different criteria which are the output substrate concentration and the biogas flow rate production, at steady state. A comparison is made with a single chemostat with the same total volume. Our techniques apply for a large class of growth functions and allow us to retrieve known results obtained when the mortality is not included in the model and the results obtained for specific growth functions in both the mathematical literature and the biological literature. In particular, we provide a complete characterization of operating conditions under which the serial configuration is more efficient than the single chemostat, i.e., the output substrate concentration of the serial configuration is smaller than that of the single chemostat or, equivalently, the biogas flow rate of the serial configuration is larger than that of the single chemostat. The study shows that the maximum biogas flow rate, relative to the dilution rate, of the series device is higher than that of the single chemostat provided that the volume of the first tank is large enough. This non-intuitive property does not occur for the model without mortality.

Consideration of Maintenance in Wine Fermentation Modeling.

We show that a simple model with a maintenance term can satisfactorily reproduce the simulations of several existing models of wine fermentation from the literature, as well as experimental data. The maintenance describes a consumption of the nitrogen that is not entirely converted into biomass. We show also that considering a maintenance term in the model is equivalent to writing a model with a variable yield that can be estimated from data.

Life cycle assessment as decision support tool for water reuse in agriculture irrigation.

This study presents a decision support tool that evaluates the environmental efficiency of water reclamation for agricultural irrigation, among other options. The developed tool is published as open source at https://doi.org/10.18167/DVN1/YLP1BA. The objective of this decision support tool is to facilitate the interpretation of the Life Cycle Assessment (LCA) results. This framework was applied to a representative case of reuse of reclaimed water for vine irrigation at the Murviel-Les-Montpellier experimental site (Hérault, France). It was then generalized through modeling assumptions to consider different reuse scenarios. To highlight situations in which the supply of recycled water for irrigation may or may not provide significant environmental benefits, three main parameters were varied: (i) tertiary treatment technologies, (ii) availability of conventional water sources, (iii) energy mix composition. The results show that the environmental impact of reclaimed water depends directly on the type of tertiary treatment technology and the location of the treatment plant in relation to the field and other water sources. The decision support tool has identified where wastewater reuse is clearly an environmentally beneficial source of irrigation among surface and groundwater sources (e.g., WWTP closer to field than river, groundwater too deep, tertiary treatment environmentally beneficial). However, there are many situations where the decision support process cannot distinguish between water reuse for agricultural irrigation and conventional water sources, especially when the nutrient content of treated municipal wastewater is insufficient to offset the negative effects of high energy requirements and chemicals of tertiary treatment.

Study of the chemostat model with non-monotonic growth under random disturbances on the removal rate.

We revisit the chemostat model with Haldane growth function, here subject to bounded random disturbances on the input flow rate, as often met in biotechnological or waste-water industry. We prove existence and uniqueness of global positive solution of the random dynamics and existence of absorbing and attracting sets that are independent of the realizations of the noise. We study the long-time behavior of the random dynamics in terms of attracting sets, and provide first conditions under which biomass extinction cannot be avoided. We prove conditions for weak and strong persistence of the microbial species and provide lower bounds for the biomass concentration, as a relevant information for practitioners. The theoretical results are illustrated with numerical simulations.

Study of performance criteria of serial configuration of two chemostats.

This paper deals with thorough analysis of serial configurations of two chemostats. We establish an in-depth mathematical study of all possible steady states, and we compare the performances of the two serial interconnected chemostats with the performances of a single one. The comparison is evaluated under three different criteria. We analyze, at steady state, the minimization of the output substrate concentration, the productivity of the biomass and the biogas flow rate. We determine specific conditions, which depend on the biological parameters, the operating parameters of the model and the distribution of the total volume. These necessary and sufficient conditions provide the most efficient serial configuration of two chemostats versus one. Complementarily, this mainly helps to discern when it is not advisable to use the serial configuration instead of a simple chemostat, depending on: the considered criterion, the operating parameters fixed by the operator and the distribution of the volumes into the two tanks.

Insights from Microbial Transition State Theory on Monod's Affinity Constant.

Microbial transition state theory (MTS) offers a theoretically explicit mathematical model for substrate limited microbial growth. By considering a first order approximation of the MTS equation one recovers the well-known Monod's expression for growth, which was regarded as a purely empirical function. The harvest volume of a cell as defined in MTS theory can then be related to the affinity concept, giving a new physical interpretation to it, and a new way to determine its value. Consequences of such a relationship are discussed.

Author Correction: Demonstration of facilitation between microalgae to face environmental stress.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Demonstration of facilitation between microalgae to face environmental stress.

Positive interactions such as facilitation play an important role during the biological colonization and species succession in harsh or changing environments. However, the direct evidence of such ecological interaction in microbial communities remains rare. Using common freshwater microalgae isolated from a High Rate Algal Pond HRAP treating wastewaters, we investigated with both experimental and modeling approaches the direct facilitation between two algal strains during the colonization phase. Our results demonstrate that the first colonization by microalgae under a severe chemical condition arose from the rapid growth of pioneer species such as Chlorella sorokiniana, which facilitated the subsequent colonization of low growth specialists such as Scenedesmus pectinatus. The pioneer species rapidly depleted the total available ammonia nitrogen favoring the specialist species initially inhibited by free ammonia toxicity. This latter species ultimately dominated the algal community through competitive exclusion under low nutrient conditions. We show that microbial successions are not only regulated by climatic conditions but also by interactions between species based on the ability to modify their growth conditions. We suggest that facilitation within the aquatic microbial communities is a widespread ecological interaction under a vast range of environmental stress.

Major changes in the composition of a Southern Ocean bacterial community in response to diatom-derived dissolved organic matter.

In the Southern Ocean, natural iron fertilization in the wake of islands leads to annually occurring spring phytoplankton blooms associated with enhanced heterotrophic activity through the release of labile dissolved organic matter (DOM). The aim of this study was to investigate experimentally how diatom-derived DOM affects the composition of Southern Ocean winter water bacterial communities and to identify the most responsive taxa. A bacterial community collected in the naturally iron-fertilized region off Kerguelen Island (KEOPS2 October-November 2011) was grown onboard in continuous cultures, on winter water alone or amended with diatom-derived DOM supplied at identical DOC concentrations. 454 sequencing of 16S amplicons revealed that the two DOM sources sustained strikingly different bacterial communities, with higher relative abundances of Sulfitobacter, Colwellia and Methylophaga operational taxonomic units (OTUs) and lower relative abundances of Polaribacter, Marinobacter, NAC11-7 and SAR11 OTUs in diatom-DOM compared to winter water conditions. Using a modeling approach, we obtained growth rates for phylogenetically diverse taxa varying between 0.12 and 0.49 d-1 under carbon-limited conditions. Our results identify diatom DOM as a key factor shaping Southern Ocean winter water bacterial communities and suggest a role for niche partitioning and microbial interactions in organic matter utilization.

Light-driven increase in carbon yield is linked to maintenance in the proteorhodopsin-containing Photobacterium angustum S14.

A type of photoheterotrophic bacteria contain a transmembrane light-driven proton pump called proteorhodopsins (PRs). Due to the prevalence of these organisms in the upper water column of the World's Ocean, and their potential for light-driven ATP generation, they have been suggested to significantly influence energy and matter flows in the biosphere. To date, evidence for the significance of the light-driven metabolism of PR-containing prokaryotes has been obtained by comparing growth in batch culture, under light versus dark conditions, and it appears that responses to light are linked to unfavorable conditions, which so far have not been well parameterized. We studied light responses to carbon yields of the PR-containing Photobacterium angustum S14 using continuous culture conditions and light-dark cycles. We observed significant effects of light-dark cycles compared to dark controls, as well as significant differences between samples after 12 h illumination versus 12 h darkness. However, these effects were only observed under higher cell counts and lower pH associated with higher substrate concentrations. Under these substrate levels Pirt's maintenance coefficient was higher when compared to lower substrate dark controls, and decreased under light-dark cycles. It appears that light responses by P. angustum S14 are induced by the energetic status of the cells rather than by low substrate concentrations.

Design, analysis and validation of a simple dynamic model of a submerged membrane bioreactor.

In this study, a simple dynamic model of a submerged membrane bioreactor (sMBR) is proposed, which would be suitable for process control. In order to validate the proposed model structure, informative data sets are generated using a detailed simulator built in a well-established environment, namely GPS-X. The model properties are studied, including equilibrium points, stability, and slow/fast dynamics (three different time scales). The existence of slow-fast dynamics is central to the development of a dedicated parameter estimation procedure. Finally, a nonlinear model predictive control is designed to illustrate the potential of the developed model within a model-based control structure. The problem of water treatment in a recirculating aquaculture system is considered as an application example.

Global dynamics of the buffered chemostat for a general class of response functions.

We study how a particular spatial structure with a buffer impacts the number of equilibria and their stability in the chemostat model. We show that the occurrence of a buffer can allow a species to persist or on the opposite to go extinct, depending on the characteristics of the buffer. For non-monotonic response functions, we characterize the buffered configurations that make the chemostat dynamics globally asymptotically stable, while this is not possible with single, serial or parallel vessels of the same total volume and input flow. These results are illustrated with the Haldane kinetic function.

A methodology for a quantitative interpretation of DGGE with the help of mathematical modelling: application in biohydrogen production.

Molecular biology techniques provide valuable insights in the investigation of microbial dynamics and evolution. Denaturing gradient gel electrophoresis (DGGE) analysis is one of the most popular methods which have been used in bioprocess assessment. Most of the anaerobic digestion models consider several microbial populations as state variables. However, the difficulty of measuring individual species concentrations may cause inaccurate model predictions. The integration of microbial data and ecosystem modelling is currently a challenging issue for improved system control. A novel procedure that combines common experimental measurements, DGGE, and image analysis is presented in this study in order to provide a preliminary estimation of the actual concentration of the dominant bacterial ribotypes in a bioreactor, for further use as a variable in mathematical modelling of the bioprocess. This approach was applied during the start-up of a continuous anaerobic bioreactor for hydrogen production. The experimental concentration data were used for determining the kinetic parameters of each species, by using a multi-species chemostat-model. The model was able to reproduce the global trend of substrate and biomass concentrations during the reactor start-up, and predicted in an acceptable way the evolution of each ribotype concentration, depicting properly specific ribotype selection and extinction.

Priming effect and microbial diversity in ecosystem functioning and response to global change: a modeling approach using the SYMPHONY model.

Integration of the priming effect (PE) in ecosystem models is crucial to better predict the consequences of global change on ecosystem carbon (C) dynamics and its feedbacks on climate. Over the last decade, many attempts have been made to model PE in soil. However, PE has not yet been incorporated into any ecosystem models. Here, we build plant/soil models to explore how PE and microbial diversity influence soil/plant interactions and ecosystem C and nitrogen (N) dynamics in response to global change (elevated CO2 and atmospheric N depositions). Our results show that plant persistence, soil organic matter (SOM) accumulation, and low N leaching in undisturbed ecosystems relies on a fine adjustment of microbial N mineralization to plant N uptake. This adjustment can be modeled in the SYMPHONY model by considering the destruction of SOM through PE, and the interactions between two microbial functional groups: SOM decomposers and SOM builders. After estimation of parameters, SYMPHONY provided realistic predictions on forage production, soil C storage and N leaching for a permanent grassland. Consistent with recent observations, SYMPHONY predicted a CO2 -induced modification of soil microbial communities leading to an intensification of SOM mineralization and a decrease in the soil C stock. SYMPHONY also indicated that atmospheric N deposition may promote SOM accumulation via changes in the structure and metabolic activities of microbial communities. Collectively, these results suggest that the PE and functional role of microbial diversity may be incorporated in ecosystem models with a few additional parameters, improving accuracy of predictions.

A method for the reconstruction of unknown non-monotonic growth functions in the chemostat.

We propose an adaptive control law that allows one to identify unstable steady states of the open-loop system in the single-species chemostat model without the knowledge of the growth function. We then show how one can use this control law to trace out (reconstruct) the whole graph of the growth function. The process of tracing out the graph can be performed either continuously or step-wise. We present and compare both approaches. Even in the case of two species in competition, which is not directly accessible with our approach due to lack of controllability, feedback control improves identifiability of the non-dominant growth rate.

Effects of spatial structure and diffusion on the performances of the chemostat.

Given hydric capacity and nutrient flow of a chemostat-like system, we analyse the influence of a spatial structure on the output concentrations at steady-state. Three configurations are compared: perfectly-mixed, serial and parallel with diffusion rate. We show the existence of a threshold on the input concentration of nutrient for which the benefits of the serial and parallel configurations over the perfectly-mixed one are reversed. In addition, we show that the dependency of the output concentrations on the diffusion rate can be non-monotonic, and give precise conditions for the diffusion effect to be advantageous. The study encompasses dead-zone models.