Understanding and controlling dynamics are at the core of major challenges in biology and ecology central to human and environmental health. With the increasing availability of experimental data time-series in these fields and better comprehension of the fundamental biological mechanisms, building models is required to fully grasp these dynamics. The objective of MACBES is to apply and develop methodologies of control theory and computational biology to specific applications in biology and ecology: the ecologically friendly protection and management of ecosystems, such as agroecosystems, and the characterization and deciphering of mammalian cell responses to their environment, in particular the effect of network interactions and developments in synthetic biology. MACBES has privileged access to biological data generated by the partners within the Common Project Team which allows for the development of the most relevant models related to its applications.
Control theory provides answers to questions related to identify parameters, reconstruct non measured quantities of interest, regulate and control the system towards a desired state and optimize the yield of a given product. In computational biology, the tools of theoretical ecology and evolutionary biology provide answers on what a system will become.
The development of dynamical models representing mechanisms and interactions within our systems of interest is a first step in our approach. We develop models built in continuous ordinary differential equations, impulsive models, discrete models, or hybrid models, to better represent the variety of biological processes. In their diversity, these models are often built on representations of simplified biological processes, which yield systems that have particular structures that can be exploited: their variables are positive, some interactions can be modeled as mass transfers, they can be monotonic,… Such models allow for analytical and numerical developments that help explaining the dynamics and the functioning of biological processes. These models are the cornerstones on which we can apply the comprehensive toolbox of control theory.
The link of our models to data depends on the context. On the one hand, we are at a turning point where the availability of “omics” and cell level data exceeds our capacity of interpretation, while on the other hand it may still be difficult to obtain reliable and useful data time series to understand ecosystem dynamics, though that could soon change too with the development, reliability and increasing affordability of remote sensing data through drones. Therefore, apprehending the complexity of these processes and interactions through this abundance of data or despite data scarcity, requires the construction of specific mathematical models with specific calibration approaches, that face the large uncertainties and variability that are intrinsic to biological systems. In addition, to limit the impact of uncertainties and callibration errors on our results, we also develop models and control theoretic approaches relying on qualitatively described functions, through which generic answers can be sought that are valid over a wide range of situations and parameter values.
MACBES is a common project-team between Inria, INRAE, CNRS and Université Côte d’Azur, associating researchers of Inria d'Université Côte d'Azur, Institut Sophia Agrobiotech (ISA - UMR INRAE CNRS and Université Côte d'Azur, Models and Methods for Plant Protection team), and Institut de Pharmacologie Moléculaire et Cellulaire (IPMC - UMR CNRS and Université Côte d'Azur). MACBES was created on July 1st, 2023 and is one of the two project-teams following the Biocore project-team.
The research program is organized around four axes inolving common tools from control theory and computational biology, with models built in continuous ordinary differential equations, impulsive models, discrete models, or hybrid models. Control theory provides answers to questions related to the need to identify parameters, reconstruct non measured quantities of interest, regulate and control the system towards a desired state and optimize the yield of a given product. In computational biology, we use the tools of theoretical ecology and evolutionary biology to provide answers on what a system will become. The fours research axes of MACBES are:
Cells have evolved highly sophisticated intracellular communication pathways to enable their development and growth, under multiple environmental stresses and stimuli (growth factors, hormones, different types of drugs, temperature or light changes, etc.). In a modular view of a biological organism, each task is executed by a specific network, or module. These modules often interact with each other, one task triggering the next in a chain of events or cyclic phenomena: cascades of signaling networks, genetic-metabolic interactions, oscillatory behavior. One of the greatest challenges at the interface between biology and mathematics is to decipher and reproduce the complex behavior arising from the interconnection of two or more modules. The ability to reproduce the complexity of cellular responses will lead to a better capacity for regulation and balancing of factors towards healthy behaviors.
Synthetic biology aims at joining elements from both biology and engineering to construct cellular circuits that perform a desired function or induce a particular type of response. It is also a complementary approach to (traditional) molecular biology: newly creating and assembling synthetic cellular circuits from basic biological components (such as DNA, proteins, or metabolites) to form a “whole organism”, serves as a proof of principle towards understanding the mechanisms of biological networks. One of the main bottlenecks in synthetic biology is how to integrate the new circuit into the cell’s machinery, without upsetting the cellular resource allocation balance. To tackle this problem, understanding resource allocation in the cell and the interconnection of cellular oscillators is a crucial challenge.
Plants are involved in a wide range of biotic interactions. Some are beneficial to plant health, as for pollinators or symbiotic organisms, whereas others are detrimental, as in the case of pathogens or herbivores. The dynamics and outcome of these interactions depend on the ecological conditions, including the phenotypes of the interacting species, their physiology and the abiotic environment in which the interactions take place. Our aim is to develop models relevant to several biotic interactions involving plants and other organisms, from the ecophysiological scale and the intimate interaction between plants and their partners, to the ecological interactions between populations and communities inhabiting crop fields.
In several contexts, such as bioreactors in industry or cropping systems in agriculture, it might be desirable to create an ecosystem that does not exist as is in nature. Putting together species that have mutualistic behaviors, whose synergy allows for the production of some desired output, or that protect one another, can enhance the functioning of the resulting ecosystem. Without going as far as designing an ecosystem de novo, it might also be necessary to take control actions to improve the functioning of an existing ecosystem or to restore a degraded ecosystem to a previous, desirable, state. The exploitation of natural or synthetic microbial communities for the accomplishment of processes of interest is being pursued in a vast range of scenarios, from established applications in the biotechnology and pharmaceutical industries, to innovative applications in medicine and environmental sciences. Larger scale managed ecosystems can simply be natural ecosystems into which one wants to re-introduce or maintain endangered species, but they can also be exploited ecosystems such as forests, agricultural fields, fish farms… A special focus is put in MACBES on the development of pest/pathogen control methods in agroecosystems.
As highlighted in the research program, in MACBES, we tackle real-life problems and contemporary challenges with respect to safe food, food security, human and environmental health. We develop mathematical techniques to characterize and decipher cell responses to their environment in research axes 3.1 and 3.2, and we deal with ecologically friendly methods for the protection and management of ecosystems, in particular of agroecosystems, in research axes 3.3 and 3.4.
The application of MACBES research for the development of ecologically friendly methods for crop protection aim at sustainable agroecosystems. Central to our work is the reduction of chemical pesticide usage, whose deleterious impact on health and the environment is well-documented. The applications concerning cell dynamics may impact the development of new anti-cancer drugs and in general aim at a better understanding of mechanisms affecting human health.
A workhop on mathematical modelling in tropical agriculture was organised in Dschang, Cameroon, 1-4 November 2023. Its aims were twofold: bring together people involved in the EPITAG associate team to present scientific achievements and discuss planned work, so as to capitalise on the experience gained; present EPITAG and foster interest in its approaches, in particular among young researchers. The workshop was a success: there were 18 presentations and more than 30 participants from the universities of Dschang, Douala, Yaoundé, and from France (hybrid meeting), among which a majority of young scientists. Most participants were applied mathematicians, but biologists also attended the workshop.
More details on the EPITAG website.
The MACBES project-team was created on July 1st, 2023. However, in order to present a sufficient body of work covering all the aspects of our activity, we decided to present works covering the whole 2023 year.
To analyze the considerable amount of data from fate-seq 58, we proposed an ODE model of the molecular pathways involved in cell death triggered by Tumor necrosis factor (TNF)-related apoptosis-inducing ligand (TRAIL) calibrated on single-cell time-trajectories of a Förster resonance energy transfer (FRET) reporter measuring apoptosis signaling dynamics in clonal HeLa cells 60. With this model, we constructed a timeline for the different steps in the regulation of apoptosis and located an initial cell fate decision just after TRAIL binding 62. Furthermore, we identified three specific parameter combinations that can distinguish between drug resistant or sensitive phenotypes. The next step was to combine the ODE model's mechanistic features with predictive values for cell decision with machine-learning classification models, to determine the drug response of each cell before it commits to an irreversible decision. Our mechanistic-informed approach, combining an ODE system with machine learning classifiers, outperformed classic machine learning approaches and enabled the accurate cell response prediction of otherwise unpredictable cells 61. This part of the work was in collaboration with Diego Oyarzún (University of Edinburgh). This methodology is part of Marielle Péré PhD thesis 37, who won a STIC Doctoral School prize.
In addition, based on her thesis work, Marielle participated to the start-up project CellEmax, which goal is to propose rational identification of new targets for anticancer combination treatments, for which she was awarded an i-PhD Concours d'Innovation grand prize.
Another line of research involves the application of optimal control to Lotka-Volterra models of competition between cancerous and healthy cells. The aim is to control cancer progression while reducing the harmful effects of chemotherapy. This strategy aims to strike a balance between eliminating cancer cells while preserving healthy tissues, providing a more refined method to manage the impact of cancer treatments. This is the subject of the PhD thesis of Pauline Mazel.
The intercellular interactions between peripheral circadian clocks, located in tissues and organs other than the suprachiasmatic nuclei of the hypothalamus, are still very poorly understood. To investigate this question, we performed a theoretical and computational study of the coupling between two or more clocks, using a reduced model of the mammalian circadian clock previously developed in 1.
Based on a piecewise linearization of the dynamics of the mutual CLOCK:BMAL1 / PER:CRY inactivation term, we proposed a segmentation of the circadian cycle into six stages, to help analyze different types of synchronization between two clocks, including single stage duration, total period, and maximal amplitudes. Our model reproduces some recent experimental results on the effects of different regimes of fasting/feeding alternance in liver circadian clocks of mice 52. This method helps to further characterize the synchronization steps between two clocks of distinct (but close) periods. This work was presented by
Microbial growth consists of the conversion of nutrients from the environment into biomass and small energy cofactors (ATP, NADH, NADPH, ...) driving biomass synthesis forward. Two macroscopic criteria for characterizing microbial growth are growth rate and growth yield. The former refers to the rate of conversion of substrate into biomass, and the latter to the efficiency of the process, that is, the fraction of substrate taken up by the cells that is converted into biomass.
In the framework of the ANR Maximic project (collab. H. de Jong, MICROCOSME team, and T. Gedeon, Montana State University), we developed a coarse-grained model of coupled energy and mass fluxes in microorganisms, based on minimal assumptions,
and used it to explore the variability of rate-yield phenotypes obtained by change in proteome allocation strategy 11. The model predictions were verified by means of a database of hundreds of published rate-yield and uptake-secretion phenotypes of Escherichia coli strains grown in standard laboratory conditions.
We found a very good quantitative agreement between the range of predicted and observed growth rates, growth yields, and glucose uptake and acetate secretion rates. These results support the hypothesis that resource allocation is a major explanatory factor of the observed variability of growth rates and growth yields across different bacterial strains.
One of the main outcomes of our model, supported by the experimental data, is that high growth rates are not necessarily accompanied by low growth yields.
The resource allocation strategies enabling high-rate, high-yield growth of E. coli lead to a higher saturation of enzymes and ribosomes, and thus to a more efficient utilization of proteomic resources.
The model is currently used to investigate the set of adaptation strategies that microbial cells can use to increase their growth rate or their growth yield in a given environment. Preliminary results suggest that multiple allocation choices are possible, depending on the initial allocation state of the cell and its biomass composition.
We consider a general model of genetic networks and examine two forms of interconnection, either homogeneous or heterogeneous coupling, corresponding to coupling functions that are either equal or different from those governing the individual dynamics. In the case of individual subsystems having unique but different steady states, we prove that the homogeneous coupled system has a unique globally asymptotically stable steady state. Moreover, in the case of large coupling strength, we show that under suitable assumptions the network achieves weak synchronization since the individual steady states become arbitrarily close 10. We apply the results to the synchronization of damped oscillators and to the control of multistable systems.
To study coupling and synchronization of two clock oscillator models, we have used Lyapunov function techniques to bound the difference between the two oscillators in terms of the difference between their oscillating periods. We have also analyzed the form of the periodic solutions as a function of some of the parameters, in particular one of the major degradation rates. This is part of
We study by techniques of optimal control the optimal allocation between
metabolism and gene expression during growth of bacteria, in
collaboration with Inria IBIS and MCTAO project-teams. We developed different versions of the
problem, and considered problems where
the aim is to optimize the production of a product in a batch or fedbatch bioreactor; the input of substrate may also be fluctuating
21, (ANR project Maximic, PhD thesis of Agustin Yabo, internship then ongoing PhD of
Root-knot nematodes (RKN) are microscopic root parasites that cause considerable yield losses in numerous crops worldwide. We are particularly interested in understanding the mechanisms that underlie plant tolerance, that is the ability of certains plants to sustain RKN infestation with limited damages. To address this, we built an ecophysiological model of plant growth, including both the vegetative and the reproductive phases, coupled with a model of nematode population dynamics. Briefly, the plant is divided into shoots, which provide carbon, and roots, which provide water for plant growth. During the reproductive phase, fruit onset marks the addition of a new carbon sink for the plant. Nematodes are explicitly considered as feeding on plant resources, so that any change in the plant physiological status or plant composition will in turn affect pest growth and multiplication, and vice versa. The apparition of fruits, in particular, can substantially modify the ressource allocation pattern of the plant, with important consequences on plant susceptibility to pest attack. The model was calibrated for two plant species using experimental data collected in the framework of INRAE ArchiNem project (2020-2021). A dedicated calibration pipeline was developed in order to combine heterogeneous data at different time-scales. Eventually, the model will be used to explore the dynamical behaviour of the system and to gain insight into the relative role of plant development and phenotypic traits (including physiological and architectural features), pest development and environmental factors in the progression of the infection.
This work is part of the PhD thesis of Joseph Penlap Tamagoua (Inria-INRAE funding 2022-2025) and was presented at several international conferences 49, 33, 34. Two publications are currently in preparation, focusing respectively on the experimental results and on model development and calibration.
Semi-discrete models have shown their relevance in modeling biological phenomena whose nature presents abrupt changes over time 56. In plant epidemiology, they can represent seasonality or external perturbations of natural systems, such as harvest. We developed and analyzed such models in the context of biological control applied to coffee leaf rust 16 or coffee berry borers 42, and of the sterile insect technique 32. Semi-discrete models were central in Frédéric Grognard's HDR defense 36 and Clotilde Djuikem's PhD thesis 35.
In this framework, we studied how recurrent migration events (“pulsed migration”) between different spatial locations influence the evolution of populations through a population genetics approach 9. We evidenced that migration pulsedness affects allele fixation rates in interaction with their selective value, generally reducing the level of local adaptation as compared to continuous migration. This research was part of Flora Aubree's PhD thesis (defended in 2022), and has been performed in collaboration with Vincent Calcagno (ISA).
We developed and analyzed dynamical systems describing plant-parasite interactions, in order to better understand, predict and control the evolution of damages in crops, with applications in tropical agriculture, in the framework of the EPITAG associate team with Cameroon (section 10.1.1). We considered several pathosystems.
We have been involved for several years in a mixed modeling-experimental approach to explore the spatio-temporal dynamics of populations, with special interest to micro-wasp parasitoids 59, 55. With such an approach, we explored how positive density-dependence in growth or dispersal interact with spatial heterogeneity to impact population spread 19. In this context, we showed that the expansion rate is not only determined by the current environmental conditions at the edge of the population, but is also strongly influenced by the conditions encountered at previous times and locations by the moving front of the population. This research has been performed in collaboration with Elodie Vercken (ISA).
Concurrently, we are exploring the correlation between biological control agents movement characteristics at different scales, from laboratory experimental characterization to semi-field dispersal on parasitoids belonging to the genus Trichogramma. A specific mid-scale laboratory device to study insect dispersal over several meters has been designed 15 and used to understand how insect movements shape group dispersal in such parasitoïds 13. This research was part of the PhD theses of Victor Burte (defended 2018) and Melina Cointe (defended 2023, 53) and was performed in collaboration with
In the framework of ANR project Ctrl-AB, we considered
a synthetic algal-bacterial consortium. The
co-culture of E. coli with Chlorella could lead to higher biomass and lipid productivity. We developed a model, studied its dynamical behaviour and built observers to try to optimize some output 26. Moreover, we studied the effects of control on the system (PhD thesis of Rand Aswad, Grenoble, in collaboration with E. Cinquemani (Microcosme )).
In the framework of IPL Cosy (led by E. Cinquemani), we studied the coexistence of two strains of bacteria E. Coli in a bioreactor. The strains had been modified synthetically. The aim was to obtain a better productivity in the consortium than in a single strain, by control methods 57. We obtained optimization results for the optimal production or yield 18.
The sterile insect technique (SIT) consists in releasing irradiated sterile individuals, usually males, that can mate but produce no offspring. SIT is used to reduce pest populations in an agricultural context. However, a small fraction of irradiated insects may escape sterilization and remain fertile. We showed that when residual fertility is below a threshold value, wild populations can be driven to extinction by flooding the landscape with sterile males. Nevertheless, even if the residual fertility exceeds the aforementioned threshold value, substantial decreases in outbreak levels can be achieved 48, 29, 47. In the framework of Taha Belkayate's internship, we extended these results to take remating into account. This work pertains to
Biological control was added to the multi-seasonal impulsive model describing coffee leaf rust spread in a plantation (section 8.3.2), using predators through one or more discrete introduction events over the year. Analytical and semi-numerical studies were performed to identify how much and how frequently predators needed to be introduced. We showed that the best strategy to efficiently control the disease depends on the predator mortality: low mortality parasites can be released only once a year, while high mortality parasites should be released more frequently to ensure their persistence in the plantation 16. This work pertains to
Controling coffee berry borers is particularly challenging, as the insects spend most of their life cycle inside berries. Pest control was introduced in the model describing the interactions between borers and coffee berries (section 8.3.2), based on the combination of a biopesticide (entomopathogenic fungus such as Beauveria bassiana), that is sprayed and persist on the berries, and traps. Using optimal control theory, we showed a synergy between the two controls for profit optimization 17. We also investigated how to optimize biopesticide spraying considering it as an impulsive control 42 (accepted in ARIMA).
This research pertains to Yves Fotso Fotso's PhD thesis 54.
We studied other plant protection methods dedicated to fight plant pathogens. One such method is the introduction of plant cultivars that are resistant to one pathogen. This often leads to the appearance of virulent pathogen strains that are capable of infecting the resistant plants.
We built a generic spatio-temporal epidemiological model representing (fungal) disease spread on annual field crops in a multi-pathogen context. This work benefits from data collected in INRAE projects COCODIV and DYNAMO on wheat diseases. It will pe pursued in the ENDURANCE and PAPEETE projects (section 10.4).
An epidemiological model of gene-for-gene interaction has been designed, considering increased defense to pathogen infections following previous exposure to a pathogen or an elicitor, namely priming. Priming provides a sort of immunity to virulent pathogens for resistant plants having undergone an infection attempt by an avirulent pathogen. We developed an epidemiological model to explore how mixing two distinct resistant varieties can reduce disease prevalence. We considered a pathogen population composed of three genotypes infecting either one or both varieties. We found that host mixtures should not contain an equal proportion of resistant plants, but a biased ratio to minimize disease prevalence, and that it should contain a lower proportion of the costliest resistance for the pathogen to break 14. This was done in collaboration with
We also participated in an opinion paper advocating that the theoretical framework of population genetics could bridge the gap existing between evolution/epidemiology approaches and molecular approaches to the durability of resistance problem 20. The ENDURANCE ANR project is built upon the findings presented in this paper (section 10.4).
CellEmax: is an ongoing project of start-up creation. The startup biotech will be a spin-off of our team and the experimental biology group led by
Exactcure: in the collaboration with the start-up Exactcure (Nice), the goal of the project is to study personalized pharmacokinetic models. We have regular contacts with Exactcure, which hired our PhD student Lucie Chambon.