Section: New Results

Fields of applications

Bioenergy

Modelling microalgae production

Participants : Olivier Bernard, Antoine Sciandra, Frédéric Grognard, Ghjuvan Grimaud, Quentin Béchet, David Demory, Anaïs Bacquet, Jean-Philippe Steyer, Francis Mairet.

Experimental developments

Experiments have been carried out to study the effects of nitrogen limitation on the lipid production in microalgae and support model development. These experiments have been carried out in the Lagrangian simulator, under constant or periodic light and temperature, varying the total amount of light dose in the day [11]. The response in terms of storage carbon (triglycerides and carbohydrates) has been measured and correlated to the environment fluctuations.

Other experiments were carried out to reproduce the light signal percept by a cell in a raceway pond [71], derived from hydrodynamical studies [79]. An electronic platform was developed to reproduce this high frequency light signal. The experiments show that the microalgae adapt their pigments to the average light that they have received [70]. Experiments with coloured light demonstrated that the growth rate results from the absorbed light, whatever its wavelength.

A new methodology to measure cell viability has been set up. This approach is very promising to distinguish between net and gross growth rate [66]. It was used in the models to assess the impact of temperature on growth and mortality [20], [30].

On top of this, we carried out pilot experiments with solar light. We tested the impact of coloured film mimicking possible photovoltaic material. The collected data were used to calibrate models integrating the light spectrum in Ambre Veisseix's master thesis.

These works have been carried out in collaboration with A. Talec, S. Rabouille, and E. Pruvost (CNRS/UPMC -Oceanographic Laboratory of Villefranche-sur-Mer LOV).

Metabolism of carbon storage and lipid production

A macroscopic model for lipid production by oleaginous microalgae [7] has been previously proposed. This model describes the accumulation of neutral lipids (which can be turned into biofuel), carbohydrates and structural carbon [57], [56][16]. A metabolic model has been set up and validated for the microalgae Isochrysis luthea. A model was developed to represent heterotrophic growth on a mixture of acetate and butyrate [95]. A metabolic model was set up, on the basis of the DRUM framework [1], in order to simulate autotophic, heterotropic and mixotrophic growth, and to determine how to reduce substrate inhibition. The model was extended for other substrates such as glucose or glycerol in Anais Bacquet's master thesis.

Modelling the coupling between hydrodynamics and biology

The evolution of the biomass of microalgae in a raceway may be analyzed through an advection-diffusion-reaction Partial Differential Equations (PDE). First, the advection part corresponds to the transportation of the biomass through the raceway. Second, the diffusion coefficient allows to consider a Brownian motion for each particular trajectory of the particle. Finally, the reaction term corresponds to the biological dynamics. The optimization of the raceway was carried out by a vertical discretization of the raceway and an adjoint-based approach. In a similar way, the shape optimization was considered with the steady solutions of the Saint-Venant equations.

In collaboration with the Inria ANGE team, a model coupling the hydrodynamics of the raceway (based on a new multilayer discretisation of Navier-Stokes equations) with microalgae growth was developed [63]. This model is supported by the work of ANGE aiming at improving the discretization scheme to more finely represent the hydrodynamics of the raceway and more accurately reconstruct Lagrangian trajectories.

Modelling the photosynthesis response to fast fluctuating light

The impact of hydrodynamics on the light perceived by a single cell was studied thanks to fluid dynamics simulations of a raceway pond [78]. The light signals that a cell experiences at the Lagrangian scale, depending on the fluid velocity, were then estimated. A Droop-Han model was used to assess the impact of light fluctuation on photosynthesis. A new model accounting for photoacclimation was also proposed [28]. Single cell trajectories were simulated, and the effect on photosynthesis efficiency was assessed using models of photosynthesis. These results were compared to experimental measurements where the high frequency light was reproduced.

Modelling photosynthetic biofilms

Several models have been developed to represent the growth of microalgae within a biofilm. A first structured physiological model uses mixture theory to represent the microalgae growth, based on the consideration of intracellular reserves triggering the processes of growth, respiration and excretion. We consider separately the intracellular storage carbon (lipids and carbohydrates) and the functional part of microalgae. A simpler model was developed and used to identify the optimal working mode of a process based on photosynthetic biofilm growing on a conveyer belt, in Jérome Grenier's internship.

Modeling microalgae production processes

The integration of different models developed within BIOCORE [61], [65], [7] was performed to represent the dynamics of microalgae growth and lipid production in raceway systems, on the basis of the dynamical model developed to describe microalgal growth under light and nitrogen limitations.

Using these approaches, we have developed a model which predicts lipid production in raceway systems under varying light, nutrients and temperature [36]. This model is used to predict lipid production in the perspective of large scale biofuel production [61].

In the framework of the ANR project Purple Sun, we developed a thermic model of a raceway pond within a greenhouse in order to estimate the culture temperature. We also included in the microalgae model the effect of light wavelength. This model has been calibrated on experimental data from LOV and has been used to support lighting strategy in order to optimize microalgal productivity (a patent on this process has been submitted). Modelling thermal adaptation in microalgae

An extended statistical analysis was carried out on a database representing the temperature response of more than 200 microalgal species [12]. First the model proposed by [62] turned out to properly reproduce the temperature response. A model was then extracted to predict the observed link between the cardinal temperatures.

We have used Adaptive Dynamics theory to understand how temperature drives evolution in microalgae. For a constant temperature, we have shown that the optimal temperature trait tends to equal the environment temperature [12]. We now use this method at the scale of the global ocean, validating our approach with experimental data sets from 194 species [75], [76].

Modelling viral infection in microalgae

Experiments have been carried out in collaboration with A.-C. Baudoux (Biological Station of Roscoff) in order to study the impact of viral infections on the development of populations of Micromonas at different temperatures. This work revealed a qualitative change in viral infection when temperature increases. A model was developed to account for the infection of a Micromonas population, with population of susceptible, infected and also free viruses. The model turned out to accurately reproduce the infection experiments at various temperatures, and the reduction of virus production above a certain temperature.

Control and Optimization of microalgae production

On-line monitoring

Interval observers give an interval estimation of the state variables, provided that intervals for the unknown quantities (initial conditions, parameters, inputs) are known [73], [86]. Interval observers were designed for the estimation of the microalgae growth and lipid production within a production process [61] and validated experimentally [83].

Optimization of the bioenergy production systems

Based on simple microalgae models, analytical optimization strategies were proposed. We assessed strategies for optimal operation in continuous mode using the detailed model for raceways [88]. We first solved numerically an optimal control problem on a finite time horizon. Then, we re-analysed the optimization problem and derived a simplified sub-optimal strategy. These approaches were extended to outdoor cultivation, considering a possible variable culture depth. Assuming known weather forecasts considerably improved the control efficiency [21].

We also propose a nonlinear adaptive controller for light-limited microalgae culture, which regulates the light absorption factor (defined by the ratio between the incident light and the light at the bottom of the reactor).

Interactions between species

We had formerly proposed an adaptive controller which regulates the light at the bottom of the reactor [84]. When applied for a culture with $n$ species, the control law allows the selection of the strain with the maximum growth rate for a given range of light intensity. This is of particular interest for optimizing biomass production as species adapted to high light levels (with low photoinhibition) can be selected. We have also proposed a strategy based on light stresses in order to penalize the strains with a high pigment content and finally select microalgae with a low Chlorophyll content [64][39]. This characteristic is of particular interest for maximizing biomass production in dense culture. The strategy has been carried out at the LOV and eventually the productivity of Tisochrysis lutea was improved by 75%. A patent on this strategy has been submitted.

Strategies to improve the temperature response have also been proposed. First we modelled the adaptive dynamics for a population submitted to a variable temperature [12]. This was used at the LOV to design experiments with periodic temperature stresses during 200 days aiming at enlarging the thermal niche of Tisochrysis lutea. It resulted in an increase by 2 degrees of the thermal niche [64].

Finally, in a more theoretical framework, we studied how to select as fast as possible a given species in a chemostat with two species at the initial instant. Using the Pontryagin maximum principle, we have shown that the optimal strategy is to maintain the substrate concentration to the value maximizing the difference between the growth rates of two species [58]. We now try to extend this result for $n$ species with mutations.

Biological depollution

Control and optimization of bioprocesses for depollution

Participants : Olivier Bernard, Francis Mairet, Jean-Luc Gouzé.

We have considered the problem of global stabilization of an unstable bioreactor model (e.g. for anaerobic digestion), when the measurements are discrete and in finite number ("quantized"). These measurements define regions in the state space, wherein a constant dilution rate is applied We show that this quantized control may lead to global stabilization: trajectories have to follow some transitions between the regions, until the final region where they converge toward the reference equilibrium [82].

Although bioprocesses involve an important biodiversity, the design of bioprocess control laws are generally based on single-species models. In [26], we have proposed to define and study the multispecies robustness of bioprocess control laws: given a control law designed for one species, what happens when two or more species are present? We have illustrated our approach with a control law which regulates substrate concentration using measurement of growth activity. Depending on the properties of the additional species, the control law can lead to the correct objective, but also to an undesired monospecies equilibrium point, coexistence, or even a failure point. Finally, we have shown that, for this case, the robustness can be improved by a saturation of the control.

Coupling microalgae to anaerobic digestion

Participants : Olivier Bernard, Antoine Sciandra, Jean-Philippe Steyer, Frédéric Grognard, Francis Mairet.

The coupling between a microalgal pond and an anaerobic digester is a promising alternative for sustainable energy production and wastewater treatment by transforming carbon dioxide into methane using light energy. The ANR Phycover project is aiming at evaluating the potential of this process [93], [92].

We have proposed and analysed a three dimensional model which represent the coupling of a culture of microalgae limited by light and an anaerobic digester. We first prove the existence and attraction of periodic solutions. Applying Pontryagin's Maximum Principle, we have characterized optimal controls, including the computation of singular controls, in order to maximize methane production. Finally, we have determined numerically optimal trajectories by direct and indirect methods [59].

Life Cycle Assessment

Participants : Olivier Bernard, Jean-Philippe Steyer, Marjorie Alejandra Morales Arancibia.

In the sequel of the pioneering life cycle assessment (LCA) work of [80], we continued to identify the obstacles and limitations which should receive specific research efforts to make microalgae production environmentally sustainable.

The improvements due to technological breakthrough (leading to higher productivities) have been compared to the source of electricity. It turns out that the overall environmental balance can much more easily be improved when renewable electricity is produced on the plant [90]. As a consequence, a new paradigm to transform solar energy (in the large) into transportation biofuel is proposed, including a simultaneous energy production stage. This motivated the design of the purple sun ANR-project where electricity is produced by semi transparent photovoltaic panels [60] under which microalgae are growing. The LCA of such innovative processes where microalgae are grown under greenhouses has been carried out.

Finally, some work are aiming at normalising LCA for microalgae and proposing guidelines to make the LCA more easily comparable [69].

This work is the result of a collaboration with Arnaud Helias of INRA-LBE (Laboratory of Environmental Biotechnology, Narbonne) and Pierre Collet (IFPEN).

Design of ecologically friendly plant production systems

Controlling plant pests

Participants : Frédéric Grognard, Ludovic Mailleret, Suzanne Touzeau, Nicolas Bajeux.

Optimization of biological control agent introductions

The question of how many and how frequently natural enemies should be introduced into crops to most efficiently fight a pest species is an important issue of integrated pest management. The topic of optimization of natural enemies introductions has been investigated for several years [6] [89], unveiling the crucial influence of within-predator density dependent processes. Since some natural enemies may be more prone to exhibit positive density dependent dynamics rather than negative ones, we studied the impact of positive predator-predator interactions on the optimal biological control introduction strategies (PhD of Nicolas Bajeux, [15]). Current research aims to understand the influence of different forms of stochasticity in the introduction process or the population dynamics on the efficacy of the introduction program [43], [33]. This last part of N. Bajeux's PhD si performed in collaboration with Vincent Calcagno (ISA).

Characteristics of space and the behavior and population dynamics of parasitoids

We tested the influence of the spatial heterogeneity of resource (hosts) distribution on the movements and fitness of individual parasitoids on a laboratory and a wild strain of the same species of Trichogramma. We showed that the level of resource aggregation has not the same influence on the different strains of the parasitoid, pointing out a behavioral adaptation of the laboratory strain [44]. This work is part of Victor Burte PhD Thesis (ISA, 2015-) and is done in close collaboration with V. Calcagno (ISA).

Connected research on the influence of space on the establishment of biological control agents is also being pursued both through computer simulations and laboratory experiments on Trichogramma [50]. This was the topic of the PhD thesis of Thibaut Morel Journel (ISA, defended in December 2015) [87] and is the present topic of Marjorie Haond (ISA, 2015-). In particular, we showed both theoretically and experimentally how landscape connectivity [27] or habitat richness [45], [37], [46] shape the spatio-temporal dynamics of populations in spatially structured environments. This work is being performed in collaboration with Elodie Vercken (ISA) and Lionel Roques (BioSP, Avignon).

Controlling plant pathogens

Participants : Frédéric Grognard, Ludovic Mailleret, Suzanne Touzeau, Elsa Rousseau.

Sustainable management of plant resistance

We studied other plant protection methods dedicated to fight plant pathogens. One such method is the introduction of plant strains that are resistant to one pathogen. This often leads to the appearance of virulent pathogenic strains that are capable of infecting the resistant plants.

Experiments were also conducted in INRA Avignon, followed by high-throughput sequencing (HTS) to identify the dynamics of virus strains competing within host plants. Different plant genotypes were chosen for their contrasted effects on genetic drift and selection they induce on virus populations. Those two evolutionary forces can play a substantial role on the durability of plant resistance. Therefore we fitted a mechanistic-statistical model to these HTS data in order to disentangle the relative role of genetic drift and selection during within-host virus evolution [41], [42]. A stochastic model was also produced to simulate the effect of drift on the virus epidemiological dynamics and on the durability of qualitative resistances [32], [40]. This was the topic of Elsa Rousseau's PhD thesis [14], and was done in collaboration with Frédéric Fabre (INRA Bordeaux) and Benoît Moury (INRA Avignon).

We also developed an epidemiological model describing the dynamics of root-knot nematodes in a protected vegetable cropping system, to design optimal management strategies of crop resistance. The model was fitted to experimental and field data. Preliminary results show that alternating susceptible and resistant crops not only increased the resistance durability, but reduced the disease intensity over time [47]. This research is the main topic of Samuel Nilusmas PhD thesis (ISA, 2016- ).

We extended the epidemiological model describing the phoma stem canker of oilseed rape, which aims at assessing the durability of crop resistance in the field and design efficient deployment strategies. We introduced a spatial structure based on real landscapes, as well as plant rotation strategies based on surveys conducted among farmers and cooperatives. We also performed a sensitivity analysis, to guide the model calibration. This ongoing work is part of (i) the K-Masstec project, which also incorporates experimental and field studies in collaboration with BIOGER (INRA Grignon); (ii) the GESTER project, with close collaborations with various INRA partners. It benefits from the resources and support of NEF computation cluster.

Eco-evolutionary dynamics of plant pathogens in seasonal environments

Understanding better pathogen evolution also requires to understand how closely related plant parasites may coexist. Such coexistence is widespread and is hardly explained through resource specialization. We showed that, in agricultural systems in temperate environments, the seasonal character of agrosystems is an important force promoting evolutionary diversification of plant pathogens [77]. The plant parasites reproduction mode may also strongly interact with seasonality. In this context, we investigated the special case of oak powdery mildew, an oak disease which is actually caused by a complex of two different species, combining original plant epidemic data with the semi-discrete seasonal plant epidemic model we introduced a few years ago [24]. This work has been done in collaboration with Frédéric Hamelin (Agrocampus Ouest), Marie Laure Desprez Loustau and Frederic Fabre (INRA Bordeaux).

Optimality/games in population dynamics

Participants : Frédéric Grognard, Ludovic Mailleret, Pierre Bernhard, Ivan Egorov.

Optimal resource allocation

Mycelium growth and sporulation is considered for phytopathogenic fungi. For biotrophic fungi, a flow of resource is uptaken by the fungus without killing its host; in that case, the life history traits (latence-sporulation strategy) have been computed based on a simple model considering a single spore initiating the mycelium, several spores in competition and applying optimal resource allocation, and several spores in competition through a dynamic game. This work, in the framework of the ANR Funfit project, is done with Fabien Halkett of INRA Nancy.

Optimal foraging and residence times variations

We also investigated the problem in foraging theory of evaluating the expected harvest of an animal when conspecifics may arrive on the same patch of resource in a stochastic fashion, specificaly according to a Poisson process or a Bernoulli process [18].

With Marc Deschamps, similar questions were studied in theoretical economy in the context of a Cournot competition on a single market [17].