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.

Molecular Landscape of the Coagulome of Oral Squamous Cell Carcinoma.

BACKGROUND: Hemostatic complications, ranging from thromboembolism to bleeding, are a significant source of morbidity and mortality in cancer patients. The tumor coagulome represents the multiple genes and proteins that locally contribute to the equilibrium between coagulation and fibrinolysis. We aimed to study the coagulome of Oral Squamous Cell Carcinoma (OSCC) and examine its link to the tumor microenvironment (TME). METHODS: We used data from bulk tumor DNA/RNA-seq (The Cancer Genome Atlas), single-cell RNA-seq data and OSCC cells in culture. RESULTS: Among all tumor types, OSCC was identified as the tumor with the highest mRNA expression levels of F3 (Tissue Factor, TF) and PLAU (urokinase type-plasminogen activator, uPA). Great inter- and intra-tumor heterogeneity were observed. Single-cell analyses showed the coexistence of subpopulations of pro-coagulant and pro-fibrinolytic cancer cells within individual tumors. Interestingly, OSCC with high F3 expressed higher levels of the key immune checkpoint molecules CD274/PD-L1, PDCD1LG2/PD-L2 and CD80, especially in tumor dendritic cells. In vitro studies confirmed the particularity of the OSCC coagulome and suggested that thrombin exerts indirect effects on OSCC cells. CONCLUSIONS: OSCC presents a specific coagulome. Further studies examining a possible negative modulation of the tumor's adaptive immune response by the coagulation process are warranted.

Which features of an outpatient treatment for COVID-19 would be most important for pandemic control? A modelling study.

The global pandemic of coronavirus disease 2019 (COVID-19) has challenged healthcare systems worldwide. Lockdown, social distancing, and screening are thought to be the best means of stopping the virus from spreading and thus of preventing hospital capacity from being overloaded. However, it has also been suggested that effective outpatient treatment can control pandemics. We adapted a mathematical model of the beneficial effect of lockdown on viral transmission and used it to determine which characteristics of outpatient treatment would stop an epidemic. The data on confirmed cases, recovered cases, and deaths were collected from Santé Publique France. After defining components of the epidemic flow, we used a Morris global sensitivity analysis with a 10-level grid and 1000 trajectories to determine which of the treatment parameters had the largest effect. Treatment effectiveness was defined as a reduction in the patients' contagiousness. Early treatment initiation was associated with better disease control-as long as the treatment was highly effective. However, initiation of a treatment with a moderate effectiveness rate (5%) after the peak of the epidemic was still better than poor distancing (i.e. when compliance with social distancing rules was below 60%). Even though most of today's COVID-19 research is focused on inpatient treatment and vaccines, our results emphasize the potentially beneficial impact of even a moderately effective outpatient treatment on the current pandemic.

Diurnal dynamics of phloem loading: theoretical consequences for transport efficiency and flow characteristics.

Phloem transport is the process by which plants internally distribute assimilates. The loading of assimilates near the photosynthetic source is responsible for generating enough osmotic pressure to drive sap flow towards the sink tissues where assimilates are consumed. Phloem loading is variable and subject to a diurnal cycle. It is dominated by photosynthesis during the day and by degradation of leaf starch to sugars at night. Most studies ignore the effect of the loading cycle on transport and assume that sugar flow operates at equilibrium. In this study, phloem transport was simulated for three successive days using a finite element model of time-dependent Münch-Horwitz equations. The spatial and temporal distributions of phloem pressure, sucrose concentration, sap velocity and sucrose flux were predicted for five different time variations in sucrose loading. Results showed that periodic loading induces an alternance of two distinct transport phases: one with high pressure, concentration and sucrose flux magnitudes and another with low magnitudes. In contrast, phloem water velocity remained remarkably stable. The alternating phases persisted over time and, under source-driven variation, transport did not reach steady-state conditions for the tested configuration. However, the impact of loading dynamics on transport was mitigated by pathway effects. Oscillations were not only delayed as one travelled away from the source, their amplitude was also reduced over distance. That behaviour stabilized the supply of sucrose to the sink, which continued at moderate levels during the dark cycles. This finding suggests that transport would assist night conversion of starch to sugars in the leaf to prevent carbon starvation at distant sinks in the early morning. The propagation velocity of pressure/concentration waves in phloem was predicted to vary by a factor up to 2.5 depending on the time series chosen to describe the dynamics of loading. Finally, the model predicted that up to 87% of the amount of sucrose loaded over 48 h would be unloaded under time-dependent loading, whereas only 76% would under constant-rate loading. This additional efficiency was periodic. It did not increase significantly the overall efficiency of the system but could be responsible for inducing rhythms in sink activity.

[Mathematical modeling: an essential tool for the study of therapeutic targeting in solid tumors]. / La modélisation mathématique, un outil essentiel pour l'étude du ciblage thérapeutique des tumeurs solides.

Recent progress in biology has made the study of the medical treatment of cancer more effective, but it has also revealed the large complexity of carcinogenesis and cell signaling. For many types of cancer, several therapeutic targets are known and in some cases drugs against these targets exist. Unfortunately, the target proteins often work in networks, resulting in functional adaptation and the development of resilience/resistance to medical treatment. The use of mathematical modeling makes it possible to carry out system-level analyses for improved study of therapeutic targeting in solid tumours. We present the main types of mathematical models used in cancer research and we provide examples illustrating the relevance of these approaches in molecular oncobiology.

A surface model of nonlinear, non-steady-state phloem transport.

Phloem transport is the process by which carbohydrates produced by photosynthesis in the leaves get distributed in a plant. According to Münch, the osmotically generated hydrostatic phloem pressure is the force driving the long-distance transport of photoassimilates. Following Thompson and Holbrook[35]'s approach, we develop a mathematical model of coupled water-carbohydrate transport. It is first proven that the model presented here preserves the positivity. The model is then applied to simulate the flow of phloem sap for an organic tree shape, on a 3D surface and in a channel with orthotropic hydraulic properties. Those features represent an significant advance in modelling the pathway for carbohydrate transport in trees.

Mathematical modelling unveils the essential role of cellular phosphatases in the inhibition of RAF-MEK-ERK signalling by sorafenib in hepatocellular carcinoma cells.

The RAS-RAF-MEK-ERK cascade is a key oncogenic signal transduction pathway activated in many types of tumours in humans. Sorafenib, the medical treatment of reference against advanced stages of hepatocellular carcinoma (HCC), inhibits the RAF-MEK-ERK cascade in HCC cells. Based on previous studies suggesting that this cascade is an important target of sorafenib in HCC cells, we explored its regulation using mathematical modelling and ordinary differential equations. We analysed the dynamic regulation of the core components of the RAF-MEK-ERK cascade in three human HCC cell lines (Huh7, Hep3B and PLC/PRF5) with heterogeneous responses to sorafenib. In silico predictions derived from our mathematical model suggested that the disappearance of phosphorylated MEK and ERK proteins catalysed by cellular phosphatases is an essential mechanism underlying the anti-ERK efficacy of sorafenib in HCC cells. This prediction was experimentally validated using specific inhibitors of the phosphatases PP2A (Protein Phosphatase 2A) and DUSP1/6 (Dual-specificity phosphatases 1/6). These findings highlight an unexpected mode of action of sorafenib on the kinome of HCC cells, and open new perspectives regarding the therapeutic targeting of the RAF-MEK-ERK cascade in this context.

Modeling of the migration of endothelial cells on bioactive micropatterned polymers.

In this paper, a macroscopic model describing endothelial cell migration on bioactive micropatterned polymers is presented. It is based on a system of partial differential equations of Patlak-Keller-Segel type that describes the evolution of the cell densities. The model is studied mathematically and numerically. We prove existence and uniqueness results of the solution to the differential system. We also show that fundamental physical properties such as mass conservation, positivity and boundedness of the solution are satisfied. The numerical study allows us to show that the modeling results are in good agreement with the experiments.