Melen Leclerc
email: melen.leclerc@inrae.fr

Stéphane Jumel

Frédéric M Hamelin

Rémi Treilhaud

Nicolas Parisey

Youcef Mammeri

Imaging with spatio-temporal modelling to characterize the dynamics of plant-pathogen lesions

Within-host spread of pathogens is an important process for the study of plant-pathogen interactions. However, the development of plant-pathogen lesions remains practically difficult to characterize beyond the common traits such as lesion area. Here, we address this question by combining image-based phenotyping with mathematical modelling. We consider the spread of Peyronellaea pinodes on pea stipules that were monitored daily with visible imaging. We assume that pathogen propagation on host-tissues can be described by the Fisher-KPP model where lesion spread depends on both a logistic growth and an homogeneous diffusion. Model parameters are estimated using a variational data assimilation approach on sets of registered images. This modelling framework is used to compare the spread of an aggressive isolate on two pea cultivars with contrasted levels of partial resistance. We show that the expected slower spread on the most resistant cultivar is actually due to a significantly lower diffusion coefficient. This study shows that combining imaging with spatial mechanistic models can offer a mean to disentangle some processes involved in host-pathogen interactions and further development may allow a better identification of quantitative traits thereafter used in genetics and ecological studies.

Introduction

Assessing quantitative life-history traits of pathogens on host plants, also called quantitative traits of pathogenicity or aggressiveness by plant pathologists, is central for the study of plant diseases. These quantitative traits describe the essential stages of pathogens life-cycle into their hosts and are used to understand the adaptation of pathogens to plant resistance and to identify quantitative trait loci for both host resistance and pathogen aggressiveness [START_REF] Lannou | Variation and selection of quantitative traits in plant pathogens[END_REF]. In the particular case of fungal plant pathogens, the most frequently measured traits are incubation and latency periods, spore production and lesion size [START_REF] Pariaud | Aggressiveness and its role in the adaptation of plant pathogens[END_REF]. In practice, they are often obtained after inoculating a host, monitoring the development of the lesions caused by the pathogen and finally estimating the traits of interest. However, phenotyping the dynamics of host-pathogen interactions remains challenging and is often performed through inaccurate traits that, though they already contrast phenotypes, poorly describe the processes and can hide or skew differences between individuals [START_REF] Leclerc | Assessing the effects of quantitative host resistance on the life-history traits of sporulating parasites with growing lesions[END_REF]. The lesion size is a good example to illustrate this as there is an infinity of spatial dynamics than can produce identical size at a given time. Considering the lesion growth rate is more informative but again, it ignores lesions shapes and depends on processes such as local growth and diffusion. Mechanistic models offer a mean to decipher the processes involved in host-pathogen interactions but are still seldom considered for analyzing plant disease phenotypic data [START_REF] Leclerc | Assessing the effects of quantitative host resistance on the life-history traits of sporulating parasites with growing lesions[END_REF][START_REF] Leonard | Methods for estimating epidemiological effects of quantitative resistance to plant diseases[END_REF]. In this case the model should remain parsimonious enough so that the parameters can be identified from the data.

The recent development of image-based phenotyping methods enables in vivo non-destructive longitudinal monitoring of infected tissues. Besides allowing precise and automated quantification of necrotic plant tissues, that already improved disease phenotyping (e.g. [START_REF] Karisto | Ranking quantitative resistance to Septoria tritici blotch in elite wheat cultivars using automated image analysis[END_REF][START_REF] Bousset | Automated image processing framework for analysis of the density of fruiting bodies of Leptosphaeria maculans on oilseed rape stems[END_REF][START_REF] Yates | Precision phenotyping reveals novel loci for quantitative resistance to septoria tritici blotch[END_REF]), imaging opens new possibilities to further investigate the spatial dimension of host-pathogen interactions. As illustrated by works on the development of human lesions, imaging data can be particularly interesting for fitting spatially explicit process-based models [START_REF] Hogea | An image-driven parameter estimation problem for a reaction-diffusion glioma growth model with mass effects[END_REF][START_REF] Mang | Integrated biophysical modeling and image analysis: application to neuro-oncology[END_REF]. It provides new insights into the main mechanisms involved in lesion development in relation with host immunity but also modelling tools for phenotyping. Perhaps surprisingly, although the main physiological mechanisms of plants and their parasites have been described by mathematical models (e.g. [START_REF] Boswell | Growth and function of fungal mycelia in heterogeneous environments[END_REF][START_REF] Sellier | Diurnal dynamics of phloem loading: theoretical consequences for transport efficiency and flow characteristics[END_REF]) the spread of lesions has received little attention by modellers [START_REF] Leclerc | Assessing the effects of quantitative host resistance on the life-history traits of sporulating parasites with growing lesions[END_REF][START_REF] Powell | Epidemic spread of a lesion-forming plant pathogen-Analysis of a mechanistic model with infinite age structure[END_REF][START_REF] Mammeri | Modelling of the airborne dispersal of a pathogen over a structured vegetal cover[END_REF][START_REF] Garin | A modelling framework to simulate foliar fungal epidemics using functional-structural plant models[END_REF] and is rarely validated against images [START_REF] Belin | Modèle stochastique et représentation par graphe pour le suivi spatio-temporel de pathogènes à la surface de feuilles par imagerie[END_REF].

In this study we consider the fungal pathogen Peyronellaea pinodes (formerly Mycosphaerella pinodes and Didymella pinodes) on pea as an example pathosystem to analyze its spread using modelling and imaging. With the two fungi Phoma medicaginis and Ascochyta pisi, P. pinodes belongs to the Ascochyta blight of pea disease complex that causes substantial yield losses worldwide [START_REF] Bretag | The epidemiology and control of ascochyta blight in field peas: a review[END_REF]. In Europe, P. pinodes is generally the predominant and the most destructive species, though P. medicaginis is also prevalent and tends to develop later in the growing season [START_REF] Dutt | Life history traits and trade-offs between two species of the ascochyta blight disease complex of pea[END_REF][START_REF] Dutt | Competition and facilitation among fungal plant parasites affect their life-history traits[END_REF]. P. pinodes is able to infect all aerial parts of its host plant and induces necrotic growing lesions. The development of resistant cultivars to P. pinodes has been central for the integrated management of this disease, but difficult as only quantitative (or partial) resistance was available [START_REF] Bretag | The epidemiology and control of ascochyta blight in field peas: a review[END_REF][START_REF] Prioul | Mapping of quantitative trait loci for partial resistance to Mycosphaerella pinodes in pea (Pisum sativum L.), at the seedling and adult plant stages[END_REF]. For most fungal pathogens, quantitative host resistance reduces pathogen fitness by altering spore production, infection and within-host growth [START_REF] Lannou | Variation and selection of quantitative traits in plant pathogens[END_REF][START_REF] Pariaud | Aggressiveness and its role in the adaptation of plant pathogens[END_REF][START_REF] Leclerc | Assessing the effects of quantitative host resistance on the life-history traits of sporulating parasites with growing lesions[END_REF][START_REF] Gilchrist | Identifying fitness and optimal life-history strategies for an asexual filamentous fungus[END_REF]. The evaluation of quantitative host resistance on pathogen life-history traits is often performed in controlled conditions with ad hoc protocols. In the case of P. pinodes partial resistance of pea can be assessed on inoculated detached leaflets, or stipules, by measuring necrotic lesions either manually [START_REF] Onfroy | Biotic factors affecting the expression of partial resistance in pea to ascochyta blight in a detached stipule assay[END_REF] or with imaging [START_REF] Dutt | Life history traits and trade-offs between two species of the ascochyta blight disease complex of pea[END_REF].

We begin by presenting the experiment, including the image acquisition protocol and the processing framework, that allowed the longitudinal monitoring of lesions on inoculated pea stipules. Then, we consider the Fisher-KPP reaction-diffusion model to describe the spread of necrotic lesions on host tissues which is fitted to image sequences (Fig 1). We show that combining imaging and spatially explicit models enables a finer description of within-host spread of pathogen, including lesions coalescence, and allows one to disentangle local growth and diffusion of the necrosis. The comparison of estimated parameters obtained on two cultivars provides new insights into how the partially resistant cultivar reduces pathogen development. It highlights the potential of combining image-based phenotyping with spatial mechanistic models to further improve our understanding of host-pathogen interactions.

Materials and methods

Host inoculation experiment

The aggressive isolate of P. pinodes named Mp 91.31.12 was inoculated on two pea cultivars previously tested in our laboratory: Solara, a common susceptible reference, and James, that reduces symptom development in controlled conditions [START_REF] Onfroy | Biotic factors affecting the expression of partial resistance in pea to ascochyta blight in a detached stipule assay[END_REF]. These two cultivars are semi-leafless without conventional leaves but extended pairs of hypertrophied stipules below each stem node. For each cultivar, leaf stipules were inoculated according to a standard biotest protocol developed in our laboratory [START_REF] Dutt | Life history traits and trade-offs between two species of the ascochyta blight disease complex of pea[END_REF][START_REF] Onfroy | Biotic factors affecting the expression of partial resistance in pea to ascochyta blight in a detached stipule assay[END_REF]. Plants were grown in a climate chamber, kept at 18 • C and with a 12h photoperiod, in 9cm diameter pots containing vermiculite and five pea seeds. When they reached the 6 leaf stage, stipules from nodes 3 and 4 were sampled and placed on tap water in a compartmented square Petri dish. The inoculum consisted in a pycnidiospore suspension whose concentration was determined with a haemocytometer and adjusted at 5 × 10 4 spores ml -1 following [START_REF] Onfroy | Biotic factors affecting the expression of partial resistance in pea to ascochyta blight in a detached stipule assay[END_REF] protocol. For both cultivar, 16 pairs of attached stipules were inoculated by placing a 10µl droplet at their center. Afterwards, the Petri dishes containing the inoculated stipules were placed into transparent plastic containers to avoid drop evaporation and incubated in a climatic chamber kept at 20

Image acquisition

The spread of lesions caused by the pathogen was assessed daily from 3 to 7 days after inoculation following a standardized acquisition protocol developed for plant disease phenotyping [START_REF] Bousset | Automated image processing framework for analysis of the density of fruiting bodies of Leptosphaeria maculans on oilseed rape stems[END_REF][START_REF] Dutt | Life history traits and trade-offs between two species of the ascochyta blight disease complex of pea[END_REF][START_REF] Bousset | Besides stem canker severity, oilseed rape host genotype matters for the production of Leptosphaeria maculans fruit bodies[END_REF]. Image acquisition was performed using two FotoQuantum LightPro 50 × 70 cm soft boxes, placed on both sides of the Petri dish with four daylight bulbs each (5400 K, 30 W). Pictures were taken with a Nikon D5300 digital camera equipped with an AF-S DX Micro Nikkor 40 mm 1:2.8G lens, on a Kaiser Repro stand, and with computer control using DigiCamControl software ver. 2.1.1.0.

Aperture was set at F22 for maximal depth of field, iso 125, daylight white balance. Initial pictures were saved as RGB images with a resolution of 6000 × 4000 pixels.

Image processing

As illustrated in Fig 1, several processing steps were required to enable model fitting to image sequences. First, stipules (i.e. our region of interest) were extracted from raw images using the Simple Interactive Object Extraction algorithm [START_REF] Friedland | Siox: Simple interactive object extraction in still images[END_REF] (Fig 1a). At this step we saved images with stipules on a white background instead of stipules masks (i.e. binary images). Second, images were registered (i.e. aligned to each other) using the Coherent Point Drift method [START_REF] Myronenko | Point set registration: Coherent point drift[END_REF], assuming rigid transformations and the first image (3 days after inoculation) as the reference (Fig 1b). Third, images were segmented by classifying pixels in either healthy, symptomatic or background states.

The prediction of each pixel-class was based on several nonlinear image features that captured local image characteristics. In particular we computed features for colours (e.g. Gaussian blur), edges (e.g. Laplacian), and textures (e.g. Hessian) at different scales using spherical filters with radii varying from 1 to 16 pixels. Based on these features, Random Forest classifiers were trained for each date of observation using the Trainable Waikato Environment for Knowledge Analysis (Weka) [START_REF] Arganda-Carreras | Trainable Weka Segmentation: a machine learning tool for microscopy pixel classification[END_REF]. They 4/14

were tested on ground truth images from an independent study [START_REF] Dutt | Life history traits and trade-offs between two species of the ascochyta blight disease complex of pea[END_REF] and showed good performances to classify pixels (i.e. balanced accuracies above 0.82, S2 Appendix), and thus separate background, healthy leaf and symptomatic areas. Afterwards, these classifiers were used to process the full dataset and to get three probability images giving the probabilities of each pixel to be in each state (e.g. Fig 1c and S3 Appendix for state symptomatic). The predicted state probabilities correspond to the mean predicted state probabilities of the trees in the forest. For each pixel the sum is 1 and the state (or class) obtained in the pixel-based segmentation is given by the class with the highest probability (soft voting). To finish with, we considered the Jaccard index (i.e. the intersection over the union of the two sets, that can vary between 0 and 1) as a measure of stipules deformation, that was computed for each date assuming the 3 rd day as the reference set. All the images and classifiers are available in an open dataverse [START_REF]Segmentation of ascochyta blight symptoms on pea stipules[END_REF][START_REF]Image sequences of growing lesions -Ascochyta blight of pea[END_REF].

Spatial lesion growth model

Most existing models for the spread of plant pathogens within host tissues are rather spatially implicit and generally assume a constant radial growth rate and a simplified geometry of the host organ [START_REF] Powell | Epidemic spread of a lesion-forming plant pathogen-Analysis of a mechanistic model with infinite age structure[END_REF][START_REF] Mammeri | Modelling of the airborne dispersal of a pathogen over a structured vegetal cover[END_REF][START_REF] Garin | A modelling framework to simulate foliar fungal epidemics using functional-structural plant models[END_REF]. Yet, these models were able to fit non-spatial lesion size data [START_REF] Leclerc | Assessing the effects of quantitative host resistance on the life-history traits of sporulating parasites with growing lesions[END_REF], including for the particular P. pinodes-pea pathosystem [START_REF] Dutt | Life history traits and trade-offs between two species of the ascochyta blight disease complex of pea[END_REF].

Here, we consider the Fisher-KPP equation as a model for the spatio-temporal dynamics of lesions. Because pathogen density cannot be directly inferred from common observations of symptoms in biotests, we describe the spread of the probability of infection, and thus the appearance of symptomatic host tissues, rather than pathogen load. The Fisher-KPP equation was introduced in 1937 by Fisher [START_REF] Fisher | The wave of advance of an advantageous gene[END_REF] and Kolmogorov-Petrovsky-Piskunov [START_REF] Kolmogorov | Etude de l'équation de la diffusion avec croissance de la quantité de la matière et son application à un problème biologique[END_REF] as a semilinear parabolic partial differential equation (PDE) combining Fick's diffusion with logistic growth. Let Ω ⊂ R 2 be the stipules area, the Fisher-KPP equation reads as the following reaction-diffusion equation, for the position x = (x, y) ∈ Ω and the time t > t 0

∂u ∂t (x, t) = D∆u(x, t) + au(x, t) (1 -u(x, t)) . (1)
where u(x, t) the probability that the host is infected at location x and time t, D > 0 is the diffusion coefficient, a ≥ 0 the growth rate. As P. pinodes is a necrotrophic pathogen, we can assume that the probability of being necrotic is similar to the probability of being infected. The initial conditions are given by an initial image u 0 as

u(x, t = t 0 ) = u 0 (x) in Ω.
Assuming the pathogen cannot move out of the leaf, homogeneous Neumann boundary conditions are imposed ∂u ∂n (x, t) = 0 on ∂Ω.

This model exhibits traveling waves with asymptotic speed 2 √ aD which is coherent with the assumption of a constant radial growth rate considered in several studies and supported by non-spatial lesion data [START_REF] Leclerc | Assessing the effects of quantitative host resistance on the life-history traits of sporulating parasites with growing lesions[END_REF][START_REF] Dutt | Life history traits and trade-offs between two species of the ascochyta blight disease complex of pea[END_REF].

Numerical solutions of the model are obtained by computing the spatial domain Ω with a level-set formalism so the boundaries ∂Ω match those of the leaves in the image [START_REF] Osher | Level Set Methods and Dynamic Implicit Surfaces[END_REF][START_REF] Sethian | Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry[END_REF], and solving the partial differential equations using explicit Euler finite differences in time and second order centered finite differences in space. More details on these numerical aspects are provided in S4 Appendix.

Parameters estimation from image sequences

For each inoculated stipule, the observations consisted in a set of registered images u reg (x, t) for times after inoculation t = {t 3 , t 4 , t 5 , t 6 , t 7 } (Fig 1). Parameters identification consisted in seeking estimates θ such that the output of the spatial model u(x, t, θ) matches these observations.

5/14

Depending on the estimation problem, inverse problems or statistical inference of reaction-diffusion can be addressed by several methods such as mathematical analysis, maximum likelihood or nonlinear least-squares [START_REF] Soubeyrand | Parameter estimation for reaction-diffusion models of biological invasions[END_REF]. When observations are image sequences, parameter estimation can be performed using some data assimilation methods used to fit models to image data, for instance in fluid dynamics [START_REF] Papadakis | Variational assimilation of fluid motion from image sequence[END_REF] or biomedical modelling [START_REF] Mang | Integrated biophysical modeling and image analysis: application to neuro-oncology[END_REF]. We consider a variational data assimilation approach based on optimal control theory [START_REF] Asch | Data assimilation: methods, algorithms, and applications[END_REF]. The estimation procedure is based on the nonlinear least-squares cost function:

J(θ) = 1 2 t∈t x∈Ω (u(x, t, θ) -u reg (x, t)) 2 . ( 2
)
Following the variational assimilation framework [START_REF] Asch | Data assimilation: methods, algorithms, and applications[END_REF], estimates θ are found by minimizing J(θ) thanks to the Lagrangian function L(θ) and a numerical procedure both detailed in S4 Appendix. This approach enables a more efficient numerical optimization and thus a faster parameter estimation.

In our case, the probability images (Fig 1 ) were considered as the observation u reg (x, t) in the cost function Eq (2) for parameters estimation [START_REF] Hogea | An image-driven parameter estimation problem for a reaction-diffusion glioma growth model with mass effects[END_REF]. For each image sequence, the image of the 3 rd day provides the initial conditions (t 0 = t 3 and u 0 (x) = u reg (x, t 3 )) while the remaining 4 images at times {t 4 , t 5 , t 6 , t 7 } enables stable estimation of parameters [START_REF] Cristofol | Stable estimation of two coefficients in a nonlinear Fisher-KPP equation[END_REF]. Even if pixel data are spatially and temporally correlated we did not consider any structure of the errors to fit the model to the image data. While accounting for correlated observation errors would improve parameters estimation it remains challenging in image data assimilation [START_REF] Chabot | Accounting for observation errors in image data assimilation[END_REF].

As the diffusion coefficient depends on image size, we rather consider the relative diffusion (in cm 2 .day -1 ) obtained from the raw diffusion coefficient and the stipules area previously extracted from the original images with dedicated landmarks used in the acquisition setup. The model was fitted to the 2 × 16 inoculated stipules and we compared the two cultivars through one-way ANOVAs on the estimated diffusion coefficient D and growth rate â. The adequacy of the Fisher-KPP model to the data was assessed by comparing observations against fitted models' predictions and by viewing the raw residuals for each date, i.e. [u reg (x, t i ) -u(x, t i , θ)] for t i ∈ t (S3 Appendix). In order to evaluate the ability of the model to capture lesions sizes rather than probabilities of infection, we estimated symptomatic surfaces for each image by counting the number of pixels with probabilities higher than 0.5 in probability maps and model outputs, and then compared the estimated values.

A Python code for fitting the Fisher-KPP on image sequences is available in an open repository [START_REF]Python Code for fitting the Fisher-KPP model on image sequences[END_REF].

Results

The Fisher-KPP model and its numerical resolution were able to describe the spread and the coalescence of lesions caused by P. pinodes on pea stipules as observed in standard biotests (Fig 2, S1 Movie and S2 Movie). The image processing framework associated with the data assimilation method allowed us to fit the reaction-diffusion model that captured the essential patterns of the spatio-temporal data (S3 Appendix). Except for one stipule (James N • 27), for which only one lesion was detected in the image at day 3, used for initial conditions, the model always described the joint spread of the two lesions. In detail, the comparison between the fitted models and the image data suggests that the model tends to underestimate the probability of infection, especially at days 5 and 6. The discrepancy between the reaction-diffusion model and the data may be mostly explained by patterns observed in the probability images (S3 Appendix). Even if the trained Random Forest classifiers showed good performances to classify pixels (S2 Appendix), classification became less certain over time with lower probabilities (Fig 1c). While this may not impact pixel classification through soft voting (the probability of the symptomatic class is still the highest), it can introduce some noise and residual errors in mechanistic model fitting. At days 5 and 6 the contours of the lesions are relatively easy to draw and the segmentation exhibits high probabilities in the symptomatic areas. On the contrary for the last two days the appearance of the lesions 6/14 changes and it becomes more difficult for an expert (or annotator), and for an algorithm, to separate healthy and symptomatic parts of the stipules. As a consequence, within lesions some pixels had lower probabilities of being symptomatic on the last dates than for the first ones which induced discrepancy with the Fisher-KPP model (S3 Appendix). Moreover, in this study we assumed a fixed (non-moving or deforming) domain for the reaction diffusion using the leaf contours in the first image (day 3). Although stipules deformation remained limited (S5 Appendix) with Jaccard indexes above 0.8 for all individuals (Fig 3 ), it occurred and could have induced some errors between the PDE model and images as illustrated in Fig 2b at day 7. To finish with, when looking at symptomatic surface instead of infection probability, the model exhibited a better adequacy with the image data (i.e. relationship close to the first bisector (Fig 4 )). Overall, despite some discrepancy between the model and the probability images, the Fisher-KPP model appeared to be relevant for describing the evolution of symptomatic areas. We successfully estimated the growth rate â and the diffusion coefficient D for the 32 monitored individuals (S6 Appendix). James cultivar was characterized by smaller stipules than Solara with average surfaces of 4.49 and 7.93 cm 2 respectively. The spread of the pathogen on James cultivar was characterized by mean growth rate â and diffusion coefficient D of respectively 0.55 and 1.33 against 1.26 and 1.54 on the more susceptible Solara. As suggested by the distributions of parameters estimates (Fig 5 ), analyses of variance pointed out a significant difference between cultivars for the diffusion coefficient D (p-values < 0.05, S6 Appendix) whereas the analysis does not support the hypothesis different growth rates â (p-values > 0.1, S6 Appendix). These results suggest that the partial resistance of James, previously observed in controlled conditions, may only due to mechanisms that slow down pathogen diffusion into host tissues. Therefore, for inoculated stipules with identical areas and shapes, lesions caused by P. pinodes will spread at a higher speed, and thus coalesce and reach edges earlier, on Solara than on James.

Discussion

In this study we combined image processing and mathematical modelling to investigate the dynamics of host-pathogen interactions. We showed that a longitudinal monitoring of inoculated leaves through visible imaging provides data to fit reaction-diffusion models that describe the spatio-temporal spread of pathogen on host tissues. While such methodological approaches are common in biomedical sciences (e.g. [START_REF] Mang | Integrated biophysical modeling and image analysis: application to neuro-oncology[END_REF][START_REF] Habbal | Assessing the ability of the 2D Fisher-KPP equation to model cell-sheet wound closure[END_REF]) they are original in plant pathology. Here, we considered the fungal pathogen P. pinodes on pea as an example pathosystem and used the Comparison of symptomatic surface predicted by the reaction-diffusion models against the surface obtained after pixel-based image segmentation for all images used to fit the model. For each cultivar, i.e. James (black points) and Solara (gray points), there are thus 16 stipules × 4 dates points. The black line is the first bisector that indicates a perfect agreement between values while the red line is the estimated linear relationship between prediction and observation considering all data (slope = 1.05, intercept = -3392.0). In detail, the relationship for James cultivar was better (slope = 1.01, intercept = -1418.7) than for James and (slope = 1.14, intercept = -6947.1). lesions. Using this PDE model with a variational data assimilation method we were able to capture the essential patterns of image-sequences data and disentangle growth and diffusion. These processes are actually two distinct life-history traits that both explain host colonization by the pathogen through lesions. They provide a finer description of the interaction but cannot be determined without the use of spatially-explicit models with spatial information, as provided by images, because different growth rates and diffusion coefficients can lead to identical lesion speed. Furthermore, while lesions coalescence, different leaves sizes, or lesion saturation at leaves boundaries can be problematic when comparing lesion sizes in common aggressiveness biotests, the inference of parameters in parsimonious PDE models can handle properly such situations. We assessed the development of an aggressive isolate on two cultivars with contrasted level of partial resistance using a standard protocol developed for screening both pathogen aggressiveness and host resistance [START_REF] Onfroy | Biotic factors affecting the expression of partial resistance in pea to ascochyta blight in a detached stipule assay[END_REF]. Our results were consistent with previous findings as the spread of lesions caused by P. pinodes was slower on James than Solara. Most interestingly, by combining image-based phenotyping and mechanistic modelling we found that the partial resistance of James were explained by a significant lower diffusion coefficient and not by a decreased growth rate. Although this finding may not be a posteriori surprising it remains impossible to demonstrate using usual measurements of lesions size without the use of spatial models and data. The diffusion coefficient and the local growth rate could be considered as hard traits that capture the function of interest but are difficult to measure [START_REF] Violle | Let the concept of trait be functional![END_REF]. On the opposite, lesion size (or lesion growth rate) are soft traits that are easier to measure and are surrogates of the hard traits [START_REF] Lannou | Variation and selection of quantitative traits in plant pathogens[END_REF]. Hard traits obtained with the use of mechanistic models provide a better description of processes involved in pathogen fitness [START_REF] Leclerc | Assessing the effects of quantitative host resistance on the life-history traits of sporulating parasites with growing lesions[END_REF][START_REF] Gilchrist | Identifying fitness and optimal life-history strategies for an asexual filamentous fungus[END_REF]. Although our results are obtained on only two cultivars, this study demonstrates the potential of combining imaging with mathematical models to improve the comparison of cultivars (or isolates) and gain new insights into plant resistance to disease. Optical sensors recently percolated in plant sciences and contributed to recent development of precision phenotyping for plant diseases [START_REF] Karisto | Ranking quantitative resistance to Septoria tritici blotch in elite wheat cultivars using automated image analysis[END_REF][START_REF] Yates | Precision phenotyping reveals novel loci for quantitative resistance to septoria tritici blotch[END_REF][START_REF] Mahlein | Plant disease detection by imaging sensors-parallels and specific demands for precision agriculture and plant phenotyping[END_REF]. On the other side the usefulness of mechanistic models for analyzing phenotypic data is recognized (e.g. [START_REF] Leclerc | Assessing the effects of quantitative host resistance on the life-history traits of sporulating parasites with growing lesions[END_REF][START_REF] Leonard | Methods for estimating epidemiological effects of quantitative resistance to plant diseases[END_REF]) but remains seldom considered. We think that the combination of these two approaches would be particularly relevant for investigating host-pathogen interactions in relation with quantitative or partial resistance.

Although our modelling framework was able to describe the overall visible spread of nectrotrophic lesions caused by P. pinodes it may be improved and extended on several points. Firstly, for the sake of simplicity we ignored stipules deformation. This change in the shape of host organs caused by parasitism frequently occurs in plants and would be worth considering using existing mathematical and numerical methods for explicit modelling of shapes [START_REF] Osher | Level Set Methods and Dynamic Implicit Surfaces[END_REF][START_REF] Bertalmio | Morphing active contours[END_REF][START_REF] Pineda | Leaf modeling and growth process simulation using the level set method[END_REF] or plant growth [START_REF] Bonneu | A minimal continuous model for simulating growth and development of plant root systems[END_REF]. While such improvement would increase the complexity of the model, it may contribute to decrease the discrepancy between the model and the data, and perhaps, help to identify genotypes that are less susceptible to disease-induced deformation. Secondly, the inoculated host leaves were digitalized through visible imaging and the reaction-diffusion model was fitted to probability images obtained with trained classifiers [START_REF] Hogea | An image-driven parameter estimation problem for a reaction-diffusion glioma growth model with mass effects[END_REF]. The appearance models, learned by experts, that transform raw image into an output which match with the state variable of the process model can have an influence on parameter estimation. In our case we could improve the classifiers to reduce the noise that occur in time by training more advanced algorithm for pixel-based segmentation [START_REF] Zhang | Modified U-Net for plant diseased leaf image segmentation[END_REF] or include some filtering after predictions (e.g. morphological closing). Comparing different appearance models or segmentation algorithms and assessing how they modify parameters estimation would be interesting, especially for pathosystems that cause unclear lesions that are difficult to annotate. For practical reasons we ignored any spatial and temporal correlation in pixel data for parameters estimation. As such a strong assumption can bias parameters estimates (mean and variance) it would be worth considering correlated errors in future works [START_REF] Chabot | Accounting for observation errors in image data assimilation[END_REF]. Yet, for comparing cultivars and isolates we believe that the bias introduced by the classifier might have a stronger impact on parameters than the assumption of uncorrelated data. Moreover, because there is no direct relationship between the appearance of symptoms and pathogen density in infected tissues we rather considered the spread of the probability of infection. Although this choice and the interpretation of some parameters 9/14 could be criticized, it seems to describe well enough the dynamics of infections. In our case, whereas the estimated diffusion coefficient may describe well enough within-host spread we believe that the growth rate should be taken with care. In further studies it would be very interesting to assess the spread of pathogen density using destructive sampling with real-time quantitative PCR [START_REF] Maciá-Vicente | Real-time PCR quantification and live-cell imaging of endophytic colonization of barley (Hordeum vulgare) roots by Fusarium equiseti and Pochonia chlamydosporia[END_REF][START_REF] Akimoto-Tomiyama | Real time live imaging of phytopathogenic bacteria Xanthomonas campestris pv. campestris MAFF106712 in 'plant sweet home[END_REF] and non-destructive monitoring, e.g. with bioluminescence imaging [START_REF] Xu | Bioluminescence imaging of Clavibacter michiganensis subsp. michiganensis infection of tomato seeds and plants[END_REF]. Thirdly, as lesions caused by P. pinodes appeared to spread at a constant speed with quite homogeneous patterns, we choose the Fisher-KPP equation. Although this first model already described the essential patterns of the data, it would be interesting to relax some of its assumptions to improve the description of the observed spatial dynamics. For instance, one could consider a heterogeneous diffusion to capture the acceleration that seems to occur at the end of the experiment. Moreover, the Fisher-KPP equation will not be appropriate to describe the spreading processes that occur in all pathosystems. The spatial dynamics of plant-pathogen lesions remains poorly addressed and further works could benefit from theoretical knowledge on PDE for propagating systems and existing models for the spread of invasive organisms [START_REF] Mammeri | How changes in the dynamic of crop susceptibility and cultural practices can be used to better control the spread of a fungal pathogen at the plot scale?[END_REF][START_REF] Roques | Modelling population dynamics in realistic landscapes with linear elements: A mechanistic-statistical reaction-diffusion approach[END_REF], microbial populations and fungal colonies [START_REF] Boswell | Growth and function of fungal mycelia in heterogeneous environments[END_REF], or human lesions [START_REF] Hogea | An image-driven parameter estimation problem for a reaction-diffusion glioma growth model with mass effects[END_REF][START_REF] Mang | Integrated biophysical modeling and image analysis: application to neuro-oncology[END_REF]. For example, the effect of leaf veins that can guide lesion spread in some pathosystems could be considered through advection terms or by considering hybrid reaction-diffusion models with different dynamics on host tissues (2D) and veins (1D) [START_REF] Roques | Modelling population dynamics in realistic landscapes with linear elements: A mechanistic-statistical reaction-diffusion approach[END_REF]. On the other side, like microbial populations in controlled media, plant-pathogen lesions can be an interesting experimental systems to test and feed some mathematical theories [START_REF] Müller | Genetic drift opposes mutualism during spatial population expansion[END_REF][START_REF] Gandhi | Range expansions transition from pulled to pushed waves as growth becomes more cooperative in an experimental microbial population[END_REF]. Fourthly, our model ignored any host response to infection and further development could take into account some key physiological and immune processes. For instance it would be worth including ontogenetic and disease-induced changes in host susceptibility, e.g. caused by senescence or hypersensitive responses, that are known to occur in several pathosystems and can be spatially localized on leaf tissues [START_REF] Dolatabadian | Virulence/avirulence patterns among Leptosphaeria maculans isolates determines expression of resistance, senescence and yellowing in cotyledons of Brassica napus[END_REF][START_REF] Richard | Influence of plant stage and organ age on the receptivity of Pisum sativum to Mycosphaerella pinodes[END_REF]. Such phenomena may be taken into account using age-structured PDE considering the age of infection [START_REF] Burie | Asymptotic behaviour of an age and infection age structured model for the propagation of fungal diseases in plants[END_REF] and the physiological age of host tissues.

From an epidemiological point of view the within-host dynamics of the pathogen is an important phase that can have strong impact on epidemics at the population level. Scaling-up the behaviour of epidemics from individuals to populations is still a challenging question for mathematical and computational epidemiology and, at least in the case of plant diseases, the within-host spread of pathogens is either ignored or extremely simplified compared to other epidemiological processes such as spores production [START_REF] Powell | Epidemic spread of a lesion-forming plant pathogen-Analysis of a mechanistic model with infinite age structure[END_REF][START_REF] Garin | A modelling framework to simulate foliar fungal epidemics using functional-structural plant models[END_REF][START_REF] Mammeri | How changes in the dynamic of crop susceptibility and cultural practices can be used to better control the spread of a fungal pathogen at the plot scale?[END_REF][START_REF] Segarra | Epidemic dynamics and patterns of plant diseases[END_REF]. This is mainly due to the challenges of multiscale and spatial modelling, but perhaps, also to the lack of spatial models for within-host pathogen development. Thus, we believe that besides providing new fundamental knowledge and phenotyping tools, spatial lesions models that describe observable spread of pathogen on host organs would also contribute to improve modelling works focused on higher scales. In addition, new insights into the effects of host resistance on within-host dynamics would also feed models for understanding the durability plant resistance to diseases [START_REF] Bourget | Sustainable deployment of QTLs conferring quantitative resistance to crops: first lessons from a stochastic model[END_REF][START_REF] Fabre | An epi-evolutionary model for predicting the adaptation of spore-producing pathogens to quantitative resistance in heterogeneous environments[END_REF][START_REF] Rimbaud | Models of Plant Resistance Deployment[END_REF]. For instance, the impact of partial resistance on either the diffusion coefficient or the local growth rate may affect differently pathogen fitness and have contrasted impacts on pathogen invasion, persistence and evolution.

1 Fig 1 .Fig 2 .

 112 Fig 1. Schematic representation of lesion growth monitoring through imaging. The initial RGB images (a) are first registered to align stipules in time (b). Afterwards, a supervised segmentation is performed to produce probability maps indicating the probability of each pixel to be in either healthy, symptomatic or background classes. Probability images of the symptomatic state (c) are used for fitting the Fisher-KPP model. Images of day 3 are used as initial conditions while the remaining 4 images are used to estimate the pathogen local growth rate â and diffusion coefficient D that are actually two distinct life-history traits of within-host pathogen spread.

Fig 3 .

 3 Fig 3. Visualization of stipules deformation in time. Change in the Jaccard index with time for cultivars James (a) and Solara (b). At each time after inoculation the Jaccard index was calculated in comparison with the image at day 3, also used as a reference for image registration.

  Fig 4.Comparison of symptomatic surface predicted by the reaction-diffusion models against the surface obtained after pixel-based image segmentation for all images used to fit the model. For each cultivar, i.e. James (black points) and Solara (gray points), there are thus 16 stipules × 4 dates points. The black line is the first bisector that indicates a perfect agreement between values while the red line is the estimated linear relationship between prediction and observation considering all data (slope = 1.05, intercept = -3392.0). In detail, the relationship for James cultivar was better (slope = 1.01, intercept = -1418.7) than for James and (slope = 1.14, intercept = -6947.1).

Fig 5 .

 5 Fig 5. Distributions of the estimated parameters. a) diffusion coefficient D with a mean values of 0.55 for James against 1.54 for the more susceptible cultivar Solara, b) local growth rate â with mean values of 1.33 and 1.26 for respectively James and Solara. The 32 estimated parameters (16 for each cultivar) are available in S6 Appendix.

Acknowledgments

We are grateful to Alain Baranger, Christophe Le May, Agathe Dutt, Lydia Bousset, Théo Fabien and Tristan Boureau for useful discussions, and Claudine Pasco and Amélie Morin for their help during the experiment.

Appendices


Jessica Ou

Béatrice Louis

Laure Balasse

Tom Roussel

Ling Peng

Benjamin Guillet

Philippe Garrigue

Florence Gattacceca

Physiologically-based pharmacokinetic modelling of dendrimer nanoparticles to unravel structure -PK parameters relationships

come   L'archive ouverte pluridisciplinaire

In vivo data [2] 𝑪𝒐𝒏𝒄𝒆𝒏𝒕𝒓𝒂𝒕𝒊𝒐𝒏 𝒊𝒏 𝒐𝒓𝒈𝒂𝒏𝒔, 𝒕𝒊𝒔𝒔𝒖𝒆𝒔 (%𝑰𝑫/𝒈) 𝑪𝒐𝒏𝒄𝒆𝒏𝒕𝒓𝒂𝒕𝒊𝒐𝒏 𝒊𝒏 𝒃𝒍𝒐𝒐𝒅 (%𝑰𝑫/𝒈) Physiology Brown et al. [3] Permeability (P) (mL/h)

Estimated

Renal clearance (CLr, mL/h)

In vivo data (popPK model) [2] Hepatic clearance (CLh, mL/h)

In vivo data (popPK model) [2] dA

Muscle

Individual plasmatic profiles after permeability fitting in organs

▪

  Collection of in vitro parameters to add NP-specific processes in the model (cellular uptake (endocytosis), opsonization) ▪ Expand the PBPK model to other types of NPs ▪ Apply this approach to design new optimal NPs ▪ Data: o Model: healthy Swiss mice o Administration: intravenous o mPET/CT imaging for 2h (n=6, except for (C 4 F 9 )-C11 n=5, and (C 4 F 9 )-C11 with RGD n=3) o gamma counting (blood) for 2h (n=6, except (C 4 F 9 )-C11 with RGD n=3) ▪ Software: R version 4.2.2 ▪ Ordinary Differential Equation (ODE) solver: deSolve ▪ Plots: ggplot and GraphPad Prism 9

  CERIMED, CNRS, Aix-Marseille University, Marseille, France (4) C2VN, INSERM 1263, INRAE 1260, Aix-Marseille University, Marseille, France (5) CINaM, Aix-Marseille University UMR7325 / UPR3118, Centre National de la Recherche Scientifique UMR7325 / UPR3118

Acknowledgments

J. Ou's PhD is financed by a grant from Ecole Doctorale 62 -Sciences de la vie, Aix-Marseille University. The authors thank PACA Canceropôle, Conseil Régional PACA and Institut National du Cancer for financial support.

• PBPK modeling: quantitative PK estimations and predictions • Development of a computational model describing the distribution of dendrimers in the organism depending on their characteristics

• Partition coefficients (Kp)

• Permeability (P)

Current model

Future model

Internal evaluation of the model

Comparison of blood PK parameters (Cmax and AUC) calculated from observed data (obs) and predicted (pred) from the PBPK model for each dendrimer


Is Habermas' Philosophy of Religion Still Critical ?

Frédéric Menager (Communication Belfast Queen's University Critical research on religion Center) Jürgen Habermas' latest book will most likely divide readers into two categories: those who, remaining attached to the philosopher of communication, will be surprised by such a thematic and methodological evolution, and those who had carefully read the Theory of Communicative Action and had been able to perceive in the analysis of the Durkheimian anthropology of religion the clue to a future topicality. Habermas laid the groundwork for a genuine political philosophy of religion inspired by North American theories of justice in his later writings. His aim was to define the legitimacy of citizens and social groups, of which faith communities are prominent examples, to argue on the basis of their beliefs.

However, even for more sophisticated readers, Habermas's genealogical approach may come as a surprise.

However, this new work must be considered as a major work, and it must allow us, as we propose here, to take stock of Habermas's philosophy of religion, which, without being completed, is nevertheless now capable of being understood in its overall structure. We have chosen for this conference to focus on the question of the Critique and the critical potential of his philosophy of religion.

For some, Habermas' entire philosophy has lost its potential to critique society and has become the framework for thinking about a reasonable social democracy that seeks to build consensus through communication based on the use of public reason.

It would have turned its back on the revolutionary potential of Critical Theory and would have been the very example of the cold tendency of Critical Theory

which would have abandoned all conflictuality. This is, for example, the theory developed by the Greek Marxist philosopher Stathis Kouvelakis when he tries to reinterpret the history of the Frankfurt School as a political betrayal of the impetus of the founding fathers that Habermas and then Honneth would have watered down. However, in the precise field of the philosophy of religion, one could think that these remarks are not lacking in relevance insofar as a deep inflection has indeed taken place between the way in which the first theorists of the Frankfurt School used concepts coming from the theological domain by making them secular but by keeping their emotional charge and their power of political and ethical mobilization and the way in which Habermas approaches the question of religion. Habermas, unlike his predecessors, first addressed religion in a perfectly explicit way, even if this was late in his work, he abandoned all traces and remainings of theological conceptions and images of religious inspiration. He would have chosen to develop a communicational rationalism which appears as an extension of Kant's doctrine of judgment on the scale of political and social theory. Such a finding might therefore lend credence to the idea that Habermas' philosophy of religion doesn't include anymore critical aspects in the meaning we understand this word in contemporanean political theory. But, once again, such an assessment should be nuanced by the fact that Habermas' thought on religion is not monolithic and even that his latest evolutions made it much more complex to seize. Moreover, it shouldn't be forgotten that the notion of Critique has a double dimension : it is not only the exploitation of the power of religion to inspire a critique of the society on which we will focus on, but also on the critique of religion itself. A secular use of theological concepts can't emerge without a previous overcoming of the religion itself as doctrine truth-oriented towards a conception of religion conceived rather as a meaning-oriented worldview.

It seems necessary here to distinguish three different steps in our presentation.

The first theoretical body of work that Habermas devoted to religion is therefore that of fundamental anthropology. From this point of view, his contribution does not appear to be very original at first sight, since it could be summarized as the organization of a dialogue between Durkheim and George Herbert Mead on the question of the fundamental modalities of the social bond. However, this dialogue will not be without consequences for the sociology of European religion, and we can read today a particularly vivid trace of it in the work of Hans Jonas, who will undoubtedly have retained from Habermas the need to integrate Mead's pragmatism into a holistic social theory and to make the latter more interaction. From this point of view, Mead was a central reference point for describing the modes of formation and structuring of communication and action within human communities. However, Habermas will note that Mead does not succeed in explaining a faculty of pre-language symbolization that is always present, an always-already present symbolic that is embodied, for example, in rites or sacred objects or even images and representations, and emanates from an immanent collective authority that does not itself depend on rules or norms. For Habermas, a second stage in the exploration of the symbolic is therefore necessary: that which consists in thinking about the place of the symbolic in the religious, the only one capable of bringing completeness to the theory of the communicational community and of going beyond the logic of language interaction alone. It is in the inadequacies of Mead's model that Habermas' interest in an anthropology of religion is born.

Habermas's criticism of Mead's incomplete theory of society stems from his reading and epistemological approach to Durkheim's theory of religion. Unlike Mead, Durkheim's characteristic is to abandon psychology and the ontogenetic conditions of the emergence of normativity in order to focus on the social fact and the phylogenetic structuring. On the two aspects criticized by Mead, Habermas notes that Durkheim's theory of religion allows for an account of these blind spots and of the place of the symbolic in the religious and, by extension, of the role of religion in the emergence of the communicational community.

A certain evolution in Durkheim's theory of religion is highlighted by Habermas: the study of Australian totemism provides Durkheim with the means to distinguish more strictly between beliefs and practices, in contrast, it should be noted, to Mead's continuism between gestures and symbols. This distinction leads Durkheim to focus on sacred material objects and their symbolic function. These objects thus represent a form of mediation between the domain of practice and that of mental representations: they synthesize collective ideals, materializing them in signs, totems, flags, relics, and various objects. Habermas tries to reconstitute the foundations of the communicational community by articulating the actionist and linguistic pragmatics coming from Mead and the normative pre-language theory of the sacred coming from Durkheim. It is thus the putting into language of the sacred, which is according to Habermas, the key to the emergence of the communicational community and the spring of the triple articulation between the symbolic, the religious and the communicational. Thus, at the roots of the definition of the communicational community is a reflection on the social mechanisms stemming from religion and their articulation with other symbolic forms such as language.

A second aspect of Habermas's interest in religion is his involvement in discussions related to theories of justice: Habermas thus rethinks the relationship of philosophy to religion on a dialogical model, emphasizing that his own post-metaphysical conception of philosophy is accompanied by a new negativity in the history of philosophy: the end of the possibility for philosophers to enact the conditions of the good and exemplary life. The ethical dimension of philosophy stops at the elaboration of formal frameworks and procedures for the adoption of norms and not at their contents, and is more a matter of a general meta-ethics. The pluralism of the democratic society empirically marks the demonstration of the impossibility of any axiological and ethical monism, even when it seems guaranteed by the seal of rationality. It is conceivable that only this particular form of rationality, which is communicative rationality, allows such a conclusion. Such a postulate would be impossible within the framework of the classical demonstrative rationality to which philosophy was attached since the opposition Logos and Doxa inherited from the Greeks. Empirically, the maintenance of religious beliefs in our democratic societies proves, according to Habermas, that their cognitive and ethical contribution is not null. If this were the case, they would have effectively disappeared, no longer being able to claim any legitimate ethical contribution. The empirical fact of their existence is enough to prove the reality of their ethical and semantic relevance. Reason. This epistemic bias is accompanied by recommendations as to the civic virtues required: the traditional civic expression of democratic voting, for example, is one that abstracts from personal religious motivations in its preferences. This amounts to adopting epistemic and civic positions constitutive of the secular spirit that can never be compensated in return by a self-limiting use of reason by secular citizens.

The balance of reciprocal obligations within society is not respected. In one case, that of secular citizens, a limitation within an already mastered cognitive field is demanded, in the other case the adoption of new cognitive models is demanded.

The recognition of religions as interpretative communities thus contains a restrictive aspect insofar as the interpretation of the contents of faith is not public, and an extensive aspect insofar as their legitimacy to propose their ethical conceptions to the argumentative exchange is reaffirmed beyond any submission to the process of public reason. Furthermore, the contents of experience of the members of the faith community are not comprehensible as religious experiences by philosophy or by secular discourse. Philosophy cannot claim a methodical atheism, even when it decides to break with the post-Hegelian tradition of taking up and transforming theological concepts and metaphors in the discourse of Reason. The ethical abstention possesses therefore a value, not only in itself ethical, but also methodological and epistemic, in that philosophy remains bearer of universalizable concepts that cannot know contents of internal language games. In order to base his argument in a principled way, Habermas adopts a deflationary version of Rawls's critique, which comes from the dialogue between Robert Audi and Nicholas Wolterstorff.

For the latter, in particular, the principle of public reason invoked by Rawls does not respect the requirement of impartiality demanded of the liberal State, insofar as it is a principle of non-neutral "secular justification". The requirement to use public reason constitutes a form of epistemic bias for Reason. This epistemic bias is accompanied by recommendations as to the civic virtues required: the traditional civic expression of democratic voting, for example, is one that abstracts from personal religious motivations in its preferences. This amounts to adopting epistemic and civic positions constitutive of the secular spirit that can never be compensated in return by a self-limiting use of reason by secular citizens. The balance of reciprocal obligations within society is not respected. In one case, that of secular citizens, a limitation within an already mastered cognitive field is demanded, in the other case the adoption of new cognitive models is demanded. The limitation as to the preference for Revelation asked of the believing citizen requires a costly theoretical position because it is empirically true that these citizens base most of their practical moral obligations or deontological conceptions on their religious convictions.

Finally, the third moment of Habermas's reflection on religion is the one we have entered: the genealogical moment. According to Habermas, there is a line that starts from Spinoza, crosses Kant's work and aims rather at founding a philosophy that privileges a functionalist analysis of religion and announces the approach of the social sciences. Where Hobbes does not push the audacity to the point of metaphysical creativity but remains in the immanentization of the theological field within the Politics, Spinoza does not hesitate for his part to confront his theory of Deus Sive Natura to the Mosaic doctrine in order to extract the potential of rationality from the Scriptures in the service of his doctrine. Another new account of modernity seems to begin: in order to position himself clearly, Habermas will confront the previous great German theories of modernity, which he explicitly writes are pursuing goals opposite to his own. In his eyes, these theories embody a form of cultural criticism that systematically aims to find in the present the identical reconduction of past patterns in a concealed form. However, this pattern should not be confused with the transformations that the Frankfurt philosopher mentioned earlier when he emphasized Kant's dialogue with theological concepts from Lutheranism. For Habermas, such a dialogue creates new forms of thought and justifies the recognition of the "new" theological concepts.

In order to position himself clearly, Habermas confronts the previous great German theories of modernity, which he explicitly writes down as pursuing goals opposite to his own. In his eyes, these theories embody a form of cultural criticism that systematically aims to find in the present the identical reconduction of past patterns in a concealed form. However, this pattern should not be confused with the transformations that the Frankfurt philosopher mentioned earlier when he emphasized Kant's dialogue with theological concepts from Lutheranism. For Habermas, such a dialogue creates new forms of thought and justifies the recognition of an authentic modernity. Presenting a quick overview of the conceptions of modernity in German thought, he points out that Critical Theory was the only philosophical movement that did not adopt this pattern of repetition because of the revolutionary hope that was summoned in the writings of its predecessors. Habermas will in fact defend that there is a third way, the beginnings of which are to be found in the first Frankfurt School and of which he gives an example from the correspondence between Horkheimer and Benjamin. Contrary to what the main theorists of secularization claim, these historical evolutions must be conceived as progress in terms of knowledge. However, the process of secularization cannot be equated with a continuous progress of Reason as in a neo-Kantian scheme. Benjamin is there to remind us of the tragic tension between this phenomenon of progress in knowledge and the moral imbalance that results from the inherent evil of history, the victims of injustice and the weight of the faults that humanity inherits. A theory of secularization can only be accompanied by a critical theory of society, and this explains the safeguarding of theological content combined with the use of social sciences and a research program of multidisciplinary analysis of society. We are thus witnessing a justification of the genealogical method as proceeding from a synthesis between these two aspects.

This three-step description should now allow us to attempt to answer the question we posed at the beginning of this paper. One of the two aspects of the question we are dealing with seems to be simpler to elucidate, namely whether Habermas's thought incorporates a critique of religion itself, and thus to know what it has inherited from the German critique of religion. First of all, it should be noted that, in Fundamental Anthropology. It is the theory of religion that comes to remedy the insufficiencies of Mead's theory of action. Thus, religion plays an essential anthropological role here insofar as it allows Habermas to stress that the purely cultural and immaterial aspects of social exchange are irreplaceable. One notices here the important step away from the Marxist tradition, which takes place from two angles. On the one hand, the concrete and material aspect of the society is not so much apprehensible by the institutions or by the economic exchanges and the social positions as by the sum of the concrete interactions that produce the action and the language. Communication and action thus maintain a link of reciprocal fusion. Moreover, this concrete and material aspect is thus insufficient to account for social processes and the form of collective symbolization proper to the passage from a logic of interactions to a logic of universal communication is allowed by religion. If we now turn to the theory of justice aspect, we realize, not without surprise, the importance of the concessions that Habermas makes to the fundamentally theological critique of Wolterstorff's Public Reason. Finally, the genealogical logic of his last work relies heavily on the notion of axial epoch inspired by Karl Jaspers and which thus underlies the idea that religion is in a certain way a necessary stage in the development of historical consciousness.

To conclude univocally that there is no criticism of religion in Habermas's thought would be hasty, however. First of all, because when Habermas adopts Durkheim's sociological theory, he does so in order to combine it with Mead's theory of action and language. We must then recognize that Mead corrects Durkheim as much as Durkheim corrects Mead and that action and language become privileged processes preceding the appearance of symbolic thought. Moreover, we must remember here how much Durkheim's approach creates the conditions for a purely secular social approach to the religious phenomenon As far as the question of the theory of justice is concerned, Habermas will certainly have criticized the notion of Public Reason, but he will also have created a kind of stress-test in order to define the conditions under which communities of faith can validly employ arguments inspired by religious beliefs. Two preconditions are necessary: the recognition of the legitimacy of other discourses on truth and thus of religious and ethical pluralism, and the recognition of the primacy of the discourse of science over the discourse of Faith. Thus, faith communities are also subject to a minimal rule of public Reason necessary for democratic dialogue.

Finally, the notion of axial period is in line with the idea of the impossibility of confusing the emergence of a religion with a discourse on Revelation. If the great religions emerge in a certain period of the history of humanity, it is also because the technical development, therefore the language and the action have reached a certain level of maturity which allows the development of a complex symbolization.

Habermas's theory of the history of religions is directly linked to his anthropology of action. Indeed, Habermas' vision refutes any possibility that religion is a discourse aimed at truth but rather at meaning, and is thus in line with Cassirer's discourse on symbolization. As far as the aspect linked to the theories of justice is concerned, we have seen that the requirement of a kind of stress-test limits the recognition of the critical symbolization faculty of religion. This tokenizing faculty is really only a stage that has to be overcome by the establishment of norms. When Habermas recognizes the benefits of this symbolization, it is when it leads to normative application. Habermas uses the example of Martin Luther King to emphasize the hopeful potential of religion as an example of the culmination of religion's critical potential against injustice. However, this critical and contentious impulse must be resolved in the Law and thus in the Norm. The real critique here is a Critique of Law, here, of the law that creates segregation, a critique of which religion can mobilize the emotional and moral aspects, but which only ends in the elaboration of the new Law, thus in the insertion of religious values into the discourse of public Reason. This is the great difference between Habermas and Horkheimer for example: the latter thought that it was symbolization that had a critical function. Habermas thinks that it is when symbolization is exceeded and externalized in the ethical norm that the critical potential of religion is expressed. From this point of view, it would be quite interesting to compare Habermas with the great Protestant theologian Bonhoeffer, and it would not be surprising to find links: I am convinced that the ethical model of a critique by religion of society is for Habermas the German Confessing Church of the Second World War, the one that resisted Hitler at the cost of his life (Bonhoeffer was murdered by the Nazis).

Finally, the genealogical aspect of Habermas's thought also remains critical insofar as it is critical of the theories of secularization and that it refuses a world subjected only to forms inherited from religious symbolization and that, at the same time, it does not recognize the absolute novelty of modernity, the idea that it makes of itself as a pure historical overcoming is rejected by Habermas to the extent that

  The fallibilist role newly devolved to philosophy thus leads to attribute to other instances of the differentiated society, such as communities of faith, a role of co-construction of ethical contents for which philosophy simply determines the modalities of adoption and the guiding principles. Religion fulfills, in part, a function of proposing what the good life ought to be, although it does not have a monopoly in this task in our modern secular democracies. However, it has a reciprocal relation to philosophy that should be redefined as reciprocal learning, which implies a redefinition of religion within the communicative community and of its communicative externalization modalities. The recognition of religions as interpretative communities thus contains a restrictive aspect insofar as the interpretation of the contents of faith is not public, and an extensive aspect insofar as their legitimacy to propose their ethical conceptions to the argumentative exchange is reaffirmed beyond any submission to the process of public reason. Habermas thus draws a line in the sand with regards to dialogue and inter-comprehension within the framework of the communicative community.Furthermore, the contents of experience of the members of the faith community are not comprehensible as religious experiences by philosophy or by secular discourse. Philosophy cannot claim a methodical atheism, even when it decides to break with the post-Hegelian tradition of taking up and transforming theological concepts and metaphors in the discourse of Reason. The ethical abstention possesses therefore a value, not only in itself ethical, but also methodological and epistemic, in that the philosophy remains bearer of universalizable concepts that cannot know contents of internal language games In order to base his argument in a principled way, Habermas adopts a deflationary version of Rawls's critique, which comes from the dialogue between Robert Audi and Nicholas Wolterstorff. For the latter, in particular, the principle of public reason invoked by Rawls does not respect the requirement of impartiality demanded of the liberal State, insofar as it is a principle of non-neutral "secular justification". Thus the requirement to use public reason constitutes a form of epistemic bias for

  Kant will continue this movement within the welcoming framework of the Au lärung movement in order to link his own criticism of religion to the use of the rational content of the religious tradition. The originality of this first approach and of the genealogy drawn up here between Spinoza and Kant should be noted: what constitutes the summa divisio of subsequent philosophical developments is the attitude towards the existing content of religion, which thus oscillates between avoidance and separation on the Hobbesian side and transformation on the Spinozist and Kantian side. Here Habermas departs quite considerably from the Straussian account of modernity, which identified from Machiavelli to Spinoza via Hobbes a gradual rise of philosophical disbelief and a single continuous line.

A

  second question remains open: did Habermas admit the critical role of religion towards society? Here again, a quick examination of the three modalities is necessary: Concerning fundamental anthropology, the question actually seems irrelevant because it is difficult to define in what way such an anthropology, which claims to explain the role of religion as the founder of the original norms of society, could be critical. It is actually at the antipodes of the anarchist anthropology of authors like Scott or Clastres if we remain in a critical anthropology of politics.However, we can say that by considering that the rite is first and the symbolization second, that the act is first and its narrative justification second, Habermas seems to us to see religion here as a Critique of violence, of the potential violence of the gesture. If another mode of symbolization than gesture and speech is required, it is because in reality pure gesture and speech contain seeds of violence that only Obligation prevents. Religion then becomes a relative of law: It is in fact the thesis that a historian of Greece like Louis Gernet defended. Religion is opposed to the unleashing of violence of the pre-symbolic relations. It is a criticism of the facticity of the world, of the literalness of its interpretation.