Live-cell imaging and mathematical analysis of the "community effect" in apoptosis.

As a cellular intrinsic mechanism leading to cellular demise, apoptosis was thoroughly characterized from a mechanistic perspective. Nowadays there is an increasing interest in describing the non-cell autonomous or community effects of apoptosis, especially in the context of resistance to cancer treatments. Transitioning from cell-centered to cell population-relevant mechanisms adds a layer of complexity for imaging and analyzing an enormous number of apoptotic events. In addition, the community effect between apoptotic and living cells is difficult to be taken into account for complex analysis. We describe here a robust and easy to implement method to analyze the interactions between cancer cells, while under apoptotic pressure. Using this approach we showed as proof-of-concept that apoptosis is insensitive to cellular density, while the proximity to apoptotic cells increases the probability of a given cell to undergo apoptosis.

Robustness of spatio-temporal regularization in perfusion MRI deconvolution: An application to acute ischemic stroke.

PURPOSE: The robustness of a recently introduced globally convergent deconvolution algorithm with temporal and edge-preserving spatial regularization for the deconvolution of dynamic susceptibility contrast perfusion magnetic resonance imaging is assessed in the context of ischemic stroke. THEORY AND METHODS: Ischemic tissues are not randomly distributed in the brain but form a spatially organized entity. The addition of a spatial regularization term allows to take into account this spatial organization contrarily to the sole temporal regularization approach which processes each voxel independently. The robustness of the spatial regularization in relation to shape variability, hemodynamic variability in tissues, noise in the magnetic resonance imaging apparatus, and uncertainty on the arterial input function selected for the deconvolution is addressed via an original in silico validation approach. RESULTS: The deconvolution algorithm proved robust to the different sources of variability, outperforming temporal Tikhonov regularization in most realistic conditions considered. The limiting factor is the proper estimation of the arterial input function. CONCLUSION: This study quantified the robustness of a spatio-temporal approach for dynamic susceptibility contrast-magnetic resonance imaging deconvolution via a new simulator. This simulator, now accessible online, is of wide applicability for the validation of any deconvolution algorithm. Magn Reson Med 78:1981-1990, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Reliable stability prediction to manage research or marketed vaccines and pharmaceutical products. "Avoid any doubt for the end-user of vaccine compliance at time of administration".

A major challenge for the pharmaceutical/vaccine industry is to anticipate and test/control product stability, regardless of the time/temperature profile of the product, from release to administration. Current empirical stability protocols performed to ensure product stability remain limited to the prediction of product stability in a thermal excursion (cold chain break) during their long-term storage. As recently recommended by the World Health Organization, mathematical models can be used for shelf-life and stability predictions. Therefore, various approaches have been published with good performance for simple chemical reactions. However, for biomolecules/vaccines, more complex reaction profiles require more complex models to predict their stability with a good level of confidence. This complexity constitutes a real scientific challenge because the number of model parameters increases with model complexity and need to be balanced with the limited number and quality of the available experimental data. We have developed a dedicated method/software based on different vaccines/pharmaceutical case studies. This predictive method considers phenomenological models, five levels of model confidence assessment, predictive quality value and simulated designs of experiment to improve and define the limits within which the prediction models can be used, and to increase model/prediction confidence to the required regulatory and scientific levels. This artificial intelligence system should help to avoid any doubt of stability at time of vaccine injection.

In silico study of the influence of intensity and duration of blood flow reduction on cell death through necrosis or apoptosis during acute ischemic stroke.

Ischemic stroke involves numerous and complex pathophysiological mechanisms including blood flow reduction, ionic exchanges, spreading depressions and cell death through necrosis or apoptosis. We used a mathematical model based on these phenomena to study the influences of intensity and duration of ischemia on the final size of the infarcted area. This model relies on a set of ordinary and partial differential equations. After a sensibility study, the model was used to carry out in silico experiments in various ischemic conditions. The simulation results show that the proportion of apoptotic cells increases when the intensity of ischemia decreases, which contributes to the model validation. The simulation results also show that the influence of ischemia duration on the infarct size is more complicated. They suggest that reperfusion is beneficial when performed in the early stroke but may be either inefficacious or even deleterious when performed later after the stroke onset. This aggravation could be explained by the depolarisation waves which might continue to spread ischemic damage and by the speeding up of the apoptotic process leading to cell death. The effect of reperfusion on cell death through these two phenomena needs to be further studied in order to develop new therapeutic strategies for stroke patients.

A modelling approach to explore some hypotheses of the failure of neuroprotective trials in ischemic stroke patients.

Ischemic stroke is the third cause of death in industrialised countries, but no satisfactory treatment is currently available. The hundreds of neuroprotective drugs developed to block the ischemic cascade gave very promising results in animal models but the clinical trials performed with these drugs showed no beneficial effects in stroke patients. Many hypotheses were advanced to explain this discrepancy, among which the morphological and functional differences between human and rodent brains. This discrepancy could be partly due to the differences in white matter and glial cell proportions between human and rodent brains. In order to test this hypothesis, we built a mathematical model of the main early pathophysiological mechanisms of stroke in rodent and in human brains. This model is a two-scale model and relies on a set of ordinary differential equations. We built two versions of this model (for human and rodent brains) differing in their white matter and glial cell proportions. Then, we carried out in silico experiments with various neuroprotective drugs. The simulation results obtained with a sodium channel blocker show that the proportion of penumbra recovery is much higher in rodent than in human brain and the results are similar with some other neuroprotective drugs tested during phase III trials. This in silico investigation suggests that the proportions of glial cells and white matter have an influence on neuroprotective drug efficacy. It reinforces the hypothesis that histological and morphological differences between rodent and human brains can partly explain the failure of these agents in clinical trials.

Modelling methodology in physiopathology.

Diseases are complex systems. Modelling them, i.e. systems physiopathology, is a quite demanding, complicated, multidimensional, multiscale process. As such, in order to achieve the goal of the model and further to optimise a rather-time and resource-consuming process, a relevant and easy to practice methodology is required. It includes guidance for validation. Also, the model development should be managed as a complicated process, along a strategy which has been elaborated in the beginning. It should be flexible enough to meet every case. A model is a representation of the available knowledge. All available knowledge does not have the same level of evidence and, further, there is a large variability of the values of all parameters (e.g. affinity constant or ionic current) across the literature. In addition, in a complex biological system there are always values lacking for a few or sometimes many parameters. All these three aspects are sources of uncertainty on the range of validity of the models and raise unsolved problems for designing a relevant model. Tools and techniques for integrating the parameter range of experimental values, level of evidence and missing data are needed.

A pharmacologically based multiscale mathematical model of angiogenesis and its use in investigating the efficacy of a new cancer treatment strategy.

Tumor angiogenesis is the process by which new blood vessels are formed and enhance the oxygenation and growth of tumors. As angiogenesis is recognized as being a critical event in cancer development, considerable efforts have been made to identify inhibitors of this process. Cytostatic treatments that target the molecular events of the angiogenesis process have been developed, and have met with some success. However, it is usually difficult to preclinically assess the effectiveness of targeted therapies, and apparently promising compounds sometimes fail in clinical trials. We have developed a multiscale mathematical model of angiogenesis and tumor growth. At the molecular level, the model focuses on molecular competition between pro- and anti-angiogenic substances modeled on the basis of pharmacological laws. At the tissue scale, the model uses partial differential equations to describe the spatio-temporal changes in cancer cells during three stages of the cell cycle, as well as those of the endothelial cells that constitute the blood vessel walls. This model is used to qualitatively assess how efficient endostatin gene therapy is. Endostatin is an anti-angiogenic endogenous substance. The gene therapy entails overexpressing endostatin in the tumor and in the surrounding tissue. Simulations show that there is a critical treatment dose below which increasing the duration of treatment leads to a loss of efficacy. This theoretical model may be useful to evaluate the efficacy of therapies targeting angiogenesis, and could therefore contribute to designing prospective clinical trials.

Quantitative risk assessment from farm to fork and beyond: a global Bayesian approach concerning food-borne diseases.

A novel approach to the quantitative assessment of food-borne risks is proposed. The basic idea is to use Bayesian techniques in two distinct steps: first by constructing a stochastic core model via a Bayesian network based on expert knowledge, and second, using the data available to improve this knowledge. Unlike the Monte Carlo simulation approach as commonly used in quantitative assessment of food-borne risks where data sets are used independently in each module, our consistent procedure incorporates information conveyed by data throughout the chain. It allows "back-calculation" in the food chain model, together with the use of data obtained "downstream" in the food chain. Moreover, the expert knowledge is introduced more simply and consistently than with classical statistical methods. Other advantages of this approach include the clear framework of an iterative learning process, considerable flexibility enabling the use of heterogeneous data, and a justified method to explore the effects of variability and uncertainty. As an illustration, we present an estimation of the probability of contracting a campylobacteriosis as a result of broiler contamination, from the standpoint of quantitative risk assessment. Although the model thus constructed is oversimplified, it clarifies the principles and properties of the method proposed, which demonstrates its ability to deal with quite complex situations and provides a useful basis for further discussions with different experts in the food chain.

Local spatio-temporal encoding of raw perfusion MRI for the prediction of final lesion in stroke.

We address the medical image analysis issue of predicting the final lesion in stroke from early perfusion magnetic resonance imaging. The classical processing approach for the dynamical perfusion images consists in a temporal deconvolution to improve the temporal signals associated with each voxel before performing prediction. We demonstrate here the value of exploiting directly the raw perfusion data by encoding the local environment of each voxel as a spatio-temporal texture, with an observation scale larger than the voxel. As a first illustration for this approach, the textures are characterized with local binary patterns and the classification is performed using a standard support vector machine (SVM). This simple machine learning classification scheme demonstrates results with 95% accuracy on average while working only raw perfusion data. We discuss the influence of the observation scale and evaluate the interest of using post-processed perfusion data with this approach.

Role of astrocytes in grey matter during stroke: a modelling approach.

The astrocytic response to stroke is extremely complex and incompletely understood. On the one hand, astrocytes are known to be neuroprotective when extracellular glutamate or potassium is slightly increased. But, on the other hand, they are considered to contribute to the extracellular glutamate increase during severe ischaemia. A mathematical model is used to reproduce the dynamics of the membrane potentials, intracellular and extracellular concentrations and volumes of neurons and astrocytes during ischaemia in order to study the role of astrocytes in grey matter during the first hour of a stroke. Under conditions of mild ischaemia, astrocytes are observed to take up glutamate via the glutamate transporter, and potassium via the Na/K/Cl cotransporter, which limits glutamate and potassium increase in the extracellular space. On the contrary, under conditions of severe ischaemia, astrocytes appear to be unable to maintain potassium homeostasis. Moreover, they are shown to contribute to the excitotoxicity process by expelling glutamate out of the cells via the reversed glutamate transporter. A detailed understanding of astrocytic function and influence on neuron survival during stroke is necessary to improve the neuroprotective strategies for stroke patients.

Analysis of temozolomide resistance in low-grade gliomas using a mechanistic mathematical model.

Understanding how tumors develop resistance to chemotherapy is a major issue in oncology. When treated with temozolomide (TMZ), an oral alkylating chemotherapy drug, most low-grade gliomas (LGG) show an initial volume decrease but this effect is rarely long lasting. In addition, it has been suggested that TMZ may drive tumor progression in a subset of patients as a result of acquired resistance. Using longitudinal tumor size measurements from 121 patients, the aim of this study was to develop a semi-mechanistic mathematical model to determine whether resistance of LGG to TMZ was more likely to result from primary and/or from chemotherapy-induced acquired resistance that may contribute to tumor progression. We applied the model to a series of patients treated upfront with TMZ (n = 109) or PCV (procarbazine, CCNU, vincristine) chemotherapy (n = 12) and used a population mixture approach to classify patients according to the mechanism of resistance most likely to explain individual tumor growth dynamics. Our modeling results predicted acquired resistance in 51% of LGG treated with TMZ. In agreement with the different biological effects of nitrosoureas, none of the patients treated with PCV were classified in the acquired resistance group. Consistent with the mutational analysis of recurrent LGG, analysis of growth dynamics using mathematical modeling suggested that in a subset of patients, TMZ might paradoxically contribute to tumor progression as a result of chemotherapy-induced resistance. Identification of patients at risk of developing acquired resistance is warranted to better define the role of TMZ in LGG.

Cloning of a pine germin-like protein (GLP) gene promoter and analysis of its activity in transgenic tobacco Bright Yellow 2 cells.

Germins and germin-like proteins (GLPs) constitute a large and highly diverse family of ubiquitous plant cell wall proteins. These proteins seem to be involved in many developmental stages and stress-related processes, but their exact participation in these processes generally remains obscure. In Pinus caribaea Morelet, the PcGER1 gene is expressed uniquely in embryo tissues, and encodes a GLP ionically bound to the walls of pine embryo cells maintained in 2,4-D-containing medium. We have cloned a genomic fragment including the 1520 bp 5'-upstream promoter region of PcGER1. This sequence contains, in its 1200 bp distal part, several cis elements (e.g. SEF4, 60 kDa protein, ABA RE and Dof recognition sites) present in genes responding to hormones and/or expressed in embryo or seed tissues, or during germination. The PcGER1 promoter sequence was cloned upstream of the GUS (beta-glucuronidase) reporter gene and transferred to tobacco Bright Yellow 2 (BY-2) cells via Agrobacterium tumefaciens-mediated transformation. Promoter activity and growth performances of transgenic asynchronous cell suspensions were analysed in the presence or absence of 2,4-D and/or BA. Optimal growth, maximum cell-wall yield and PcGER1 promoter activity were observed in the presence of 2,4-D and BA at day 4, the end of the exponential growth phase where 70-75% cells have a 2C DNA content. Analysis of promoter activity during the cell cycle in an aphidicoline-synchronized culture suggested that the expression is maximum in G1 cells. We also showed that under optimal growth conditions, 5' promoter deletions decreased the activity of the reporter gene. We discuss the function of this gene with regards to cell growth. Accession number: The PcGER1 promoter sequence was submitted to the genbank database under the accession number AY077704.

Overexpression of a heterologous sam gene encoding S-adenosylmethionine synthetase in flax (Linum usitatissimum) cells: Consequences on methylation of lignin precursors and pectins.

The Arabidopsis thaliana sam1 gene encoding S-adenosylmethionine synthetase (EC 2.5.1.6) was transferred to flax (Linum usitatissimum) cells via Agrobacterium tumefaciens. This enzyme catalyses the conversion of methionine to S-adenosylmethionine (SAM), the major methyl group donor in living cells. The aim of this work was to study the consequences of an increased SAM-synthetase (SAM-S) activity in transgenic cell lines on both the production of mono- and dimethoxylated lignin monomers and the degree of methylesterification of pectins. Hypocotyls were cocultivated with Agrobacterium tumefaciens strain GV3101 (pGV2260) harbouring the pO35SSAM binary vector carrying the sam1 gene under the control of the 35S promoter and the nptII gene for selection of putative transformed cells. Most of the transgenic cell lines exhibited a significant (up to 3.2-fold) increase in SAM-S activity compared to the controls. The results showed that for the cell lines analysed this transformation had no effect on caffeic acid O-methyltransferase (COMT, EC 2.1.1.68) in vitro activity, degree of methoxylation of lignin precursors or lignin deposition, pectin methyltransferase (PMT, EC 2.1.1) in vitro activity, but led to an increase of pectin methylesterification in friable and fast-growing transgenic cell lines.

A structural model of the VEGF signalling pathway: emergence of robustness and redundancy properties.

The vascular endothelial growth factor (VEGF) is known as one of the main promoter of angiogenesis - the process of blood vessel formation. Angiogenesis has been recognized as a key stage for cancer development and metastasis. In this paper, we propose a structural model of the main molecular pathways involved in the endothelial cells response to VEGF stimuli. The model, built on qualitative information from knowledge databases, is composed of 38 ordinary differential equations with 78 parameters and focuses on the signalling driving endothelial cell proliferation, migration and resistance to apoptosis. Following a VEGF stimulus, the model predicts an increase of proliferation and migration capability, and a decrease in the apoptosis activity. Model simulations and sensitivity analysis highlight the emergence of robustness and redundancy properties of the pathway. If further calibrated and validated, this model could serve as tool to analyse and formulate new hypothesis on th e VEGF signalling cascade and its role in cancer development and treatment.

Mathematical model approach to describe tumour response in mice after vaccine administration and its applicability to immune-stimulatory cytokine-based strategies.

Immunotherapy is a growing therapeutic strategy in oncology based on the stimulation of innate and adaptive immune systems to induce the death of tumour cells. In this paper, we have developed a population semi-mechanistic model able to characterize the mechanisms implied in tumour growth dynamic after the administration of CyaA-E7, a vaccine able to target antigen to dendritic cells, thus triggering a potent immune response. The mathematical model developed presented the following main components: (1) tumour progression in the animals without treatment was described with a linear model, (2) vaccine effects were modelled assuming that vaccine triggers a non-instantaneous immune response inducing cell death. Delayed response was described with a series of two transit compartments, (3) a resistance effect decreasing vaccine efficiency was also incorporated through a regulator compartment dependent upon tumour size, and (4) a mixture model at the level of the elimination of the induced signal vaccine (k 2) to model tumour relapse after treatment, observed in a small percentage of animals (15.6%). The proposed model structure was successfully applied to describe antitumor effect of IL-12, suggesting its applicability to different immune-stimulatory therapies. In addition, a simulation exercise to evaluate in silico the impact on tumour size of possible combination therapies has been shown. This type of mathematical approaches may be helpful to maximize the information obtained from experiments in mice, reducing the number of animals and the cost of developing new antitumor immunotherapies.

A tumor growth inhibition model for low-grade glioma treated with chemotherapy or radiotherapy.

PURPOSE: To develop a tumor growth inhibition model for adult diffuse low-grade gliomas (LGG) able to describe tumor size evolution in patients treated with chemotherapy or radiotherapy. EXPERIMENTAL DESIGN: Using longitudinal mean tumor diameter (MTD) data from 21 patients treated with first-line procarbazine, 1-(2-chloroethyl)-3-cyclohexyl-l-nitrosourea, and vincristine (PCV) chemotherapy, we formulated a model consisting of a system of differential equations, incorporating tumor-specific and treatment-related parameters that reflect the response of proliferative and quiescent tumor tissue to treatment. The model was then applied to the analysis of longitudinal tumor size data in 24 patients treated with first-line temozolomide (TMZ) chemotherapy and in 25 patients treated with first-line radiotherapy. RESULTS: The model successfully described the MTD dynamics of LGG before, during, and after PCV chemotherapy. Using the same model structure, we were also able to successfully describe the MTD dynamics in LGG patients treated with TMZ chemotherapy or radiotherapy. Tumor-specific parameters were found to be consistent across the three treatment modalities. The model is robust to sensitivity analysis, and preliminary results suggest that it can predict treatment response on the basis of pretreatment tumor size data. CONCLUSIONS: Using MTD data, we propose a tumor growth inhibition model able to describe LGG tumor size evolution in patients treated with chemotherapy or radiotherapy. In the future, this model might be used to predict treatment efficacy in LGG patients and could constitute a rational tool to conceive more effective chemotherapy schedules.

A model of vascular tumour growth in mice combining longitudinal tumour size data with histological biomarkers.

Optimising the delivery of antiangiogenic drugs requires the development of drug-disease models of vascular tumour growth that incorporate histological data indicative of cytostatic action. In this study, we formulated a model to analyse the dynamics of tumour progression in nude mice xenografted with HT29 or HCT116 colorectal cancer cells. In 30 mice, tumour size was periodically measured, and percentages of hypoxic and necrotic tissue were assessed using immunohistochemistry techniques on tumour samples after euthanasia. The simultaneous analysis of histological data together with longitudinal tumour size data prompted the development of a semi-mechanistic model integrating random effects of parameters. In this model, the peripheral non-hypoxic tissue proliferates according to a generalised-logistic equation where the maximal tumour size is represented by a variable called 'carrying capacity'. The ratio of the whole tumour size to the carrying capacity was used to define the hypoxic stress. As this stress increases, non-hypoxic tissue turns hypoxic. Hypoxic tissue does not stop proliferating, but hypoxia constitutes a transient stage before the tissue becomes necrotic. As the tumour grows, the carrying capacity increases owing to the process of angiogenesis. The model is shown to correctly predict tumour growth dynamics as well as percentages of necrotic and hypoxic tissues within the tumour. We show how the model can be used as a theoretical tool to investigate the effects of antiangiogenic treatments on tumour growth. This model provides a tool to analyse tumour size data in combination with histological biomarkers such as the percentages of hypoxic and necrotic tissue and is shown to be useful for gaining insight into the effects of antiangiogenic drugs on tumour growth and composition.

Exploration of beneficial and deleterious effects of inflammation in stroke: dynamics of inflammation cells.

The inflammatory process during stroke consists of activation of resident brain microglia and recruitment of leucocytes, namely neutrophils and monocytes/macrophages. During inflammation, microglial cells, neutrophils and macrophages secrete inflammatory cytokines and chemokines, and phagocytize dead cells. The recruitment of blood cells (neutrophils and macrophages) is mediated by the leucocyte-endothelium interactions and more specifically by cell adhesion molecules. A mathematical model is proposed to represent the dynamics of various brain cells and of immune cells (neutrophils and macrophages). This model is based on a set of six ordinary differential equations and explores the beneficial and deleterious effects of inflammation, respectively phagocytosis by immune cells and the release of pro-inflammatory mediators and nitric oxide (NO). The results of our simulations are qualitatively consistent with those observed in experiments in vivo and would suggest that the increase of phagocytosis could contribute to the increase of the percentage of living cells. The inhibition of the production of cytokines and NO and the blocking of neutrophil and macrophage infiltration into the brain parenchyma led also to the improvement of brain cell survival. This approach may help to explore the respective contributions of the beneficial and deleterious roles of the inflammatory process in stroke, and to study various therapeutic strategies in order to reduce stroke damage.

A mathematical model of ion movements in grey matter during a stroke.

The development of cytotoxic oedema during a stroke consists in cell swelling and shrinking of the extracellular space. This phenomenon is triggered by ion movements through voltage-gated channels, exchangers and pumps. During ischaemia, sodium, calcium and chloride enter the neurons whereas potassium and glutamate are expelled out of the cells. A mathematical model is proposed to represent the long-term dynamics of membrane potentials, cell volumes and ionic concentrations in intracellular and extracellular spaces during a stroke and to study the influence of each ionic current on cell swelling. The model relies on electrophysiological mechanisms and takes into account the behaviour of two types of cells: neurons and also astrocytes known to play a key role in the excitotoxic process in grey matter. The results obtained when a severe or a moderate ischaemia is simulated are consistent with those observed in the in vitro and in vivo experiments. As this model appears to be robust, it is used to perform illustrative simulations aimed at studying the effect of some channel blockers on cell swelling. This approach may help to explore new therapeutic strategies in order to reduce stroke damage.

Mathematical modelling of an ischemic stroke: an integrative approach.

Understanding the mechanisms and the time and spatial evolution of penumbra following an ischemic stroke is crucially important for developing therapeutics aimed at preventing this area from evolving towards infarction. To help in integrating the available data, we decided to build a formal model. We first collected and categorised the major available evidence from animal models and human observations and summarized this knowledge in a flow-chart with the potential key components of an evolving stroke. Components were grouped in ten sub-models that could be modelled and tested independently: the sub-models of tissue reactions, ionic movements, oedema development, glutamate excitotoxicity, spreading depression, NO synthesis, inflammation, necrosis, apoptosis, and reperfusion. Then, we figured out markers, identified mediators and chose the level of complexity to model these sub-models. We first applied this integrative approach to build a model based on cytotoxic oedema development following a stroke. Although this model includes only three sub-models and would need to integrate more mechanisms in each of these sub-models, the characteristics and the time and spatial evolution of penumbra obtained by simulation are qualitatively and, to some extent, quantitatively consistent with those observed using medical imaging after a permanent occlusion or after an occlusion followed by a reperfusion.