I will present an evolutionary viewpoint on cancer, seen as the 2 time scales of (large-time) evolution in the genomes and of (short-time) evolution in the epigenetic landscape of a constituted genome. These views, based on pioneering works by Lineweaver, Davies and Vincent (cancer as anatomically localised backward evolution in multicellular organisms, aka atavistic theory of cancer) and by Sui Huang and collaborators (revisited Waddington epigenetic landscape), respectively, may serve as guidelines to propose a global conception of cancer as a disease that impinges on all multicellular organisms, and they may lead to innovating therapeutic strategies. Drug-induced drug resistance, the medical question we are tackling from a theoretical point of view, may be due to biological mechanisms of different natures, mere local regulation, epigenetic modifications (reversible, nevertheless heritable) or genetic mutations (irreversible), according to the extent to which the genome of the cells in the population is affected. In this respect, the modelling framework of adaptive dynamics presented here is more likely to correspond biologically to epigenetic modifications than to mutations, although eventual induction of emergent resistant cell clones due to mutations under drug pressure is not to be completely excluded. From the biologist's point of view, we study phenotypically heterogeneous, but genetically homogeneous, cancer cell populations under stress by drugs. The built-in targets for theoretical therapeutic control present in the phenotype-structured PDE models we advocate are not supposed to represent well-defined molecular effects of the drugs in use, but rather functional effects, i.e., related to cell death (cytotoxic drugs), or to proliferation in the sense of slowing down the cell division cycle without killing cells (cytostatic drugs). We propose that cell life-threatening drugs (cytotoxics) induce by far more resistance in the highly plastic cancer cell populations than drugs that only limit their growth (cytostatics), and that a rational combination of the two classes of drugs may be optimised to propose innovating therapeutic control strategies to avoid the emergence of drug resistance in tumours.

• Thematic program: Models in Cancer Therapy (2015/2016)
• Event: Workshop on "Models in Cancer Therapy" (2016)

The identification of molecular drivers in cancer has paved the way for targeted therapy. However, incomplete responses and relapse on therapy remain the biggest problem for improving patient survival. Evidence suggests that a tumor consists of a majority of cells that are sensitive to targeted therapy while few cells that are intrinsically resistant or poised to quickly adapt to drug treatment already pre-exist within this heterogeneous tumor population. Although a multitude of resistance mechanisms have been described, it was largely unknown how resistant cells behave in a heterogeneous tumor during treatment and whether a regressing tumor microenvironment could influence disease relapse. We found that targeted therapy with BRAF, ALK, or EGFR kinase inhibitors induces a complex network of secreted signals in drug-stressed melanoma and lung adenocarcinoma cells. This therapy-induced secretome (TIS) stimulates the outgrowth, dissemination, and metastasis of drug-resistant cancer cell clones in the heterogenous tumors and supports the survival of drug-sensitive cancer cells, contributing to incomplete tumour regression. The vemurafenib reactive secretome in melanoma is driven by down-regulation of the transcription factor FRA1. In situ transcriptome analysis of drug-resistant melanoma cells responding to the regressing tumour microenvironment revealed hyperactivation of multiple signalling pathways, most prominently the AKT pathway. Dual inhibition of RAF and PI3K/AKT/mTOR pathways blunted the outgrowth of the drug-resistant cell population in BRAF mutant melanoma tumours, suggesting this combination therapy as a strategy against tumour relapse. Thus, therapeutic inhibition of oncogenic drivers induces vast secretome changes in drug-sensitive cancer cells, paradoxically establishing a tumour microenvironment that supports the expansion of drug-resistant clones, but is susceptible to combination therapy.

• Thematic program: Models in Cancer Therapy (2015/2016)
• Event: Workshop on "Models in Cancer Therapy" (2016)

Oncology has benefited from major ground-breaking innovations over the last 15-years. Beyond standard chemotherapy, targeted therapies, antio-angiogenics and now immune check-point inhibitors have all fueled high expectancies in terms of increased response rate and extended survival in patients. Of note, despite huge resources engaged now to better understand tumor biology and to identify relevant genetic and/or molecular biomarkers for choosing the best drugs, increase in survival has been mostly achieved in an incremental fashion so far, with the notable exception of CML and more recently of melanoma. The ever-increasing number of druggable targets, along with the rise of new concepts such as cancer immunology, has contributed to a considerable complexification of the decision-making at bedside. Indeed, it is widely acknowledged now that combination therapy is the future of cancer treatment. As such, defining the optimal association between cytotoxics, radiotherapy, anti-angiogenic drugs, targeted therapies and now immunotherapy is a major issue that remains to be addressed. Optimal solution will not be reached anymore by standard trial-and-error empirical practice, owing to the near-infinite number of possible combinations to be tested now that would require unsustainable efforts in terms of clinical development by pharmaceutical companies. In this respect, pharmacometrics (i.e., mathematical PK/PD models) could help to identify, using in silico simulations, a reduced number of working hypothesis to be tested in priority as part of clinical trials. Reviewing recent literature in the field and giving some examples in experimental and clinical oncology with chemotherapy, anti-angiogenics and immunotherapy, we will discuss how pharmacometrics could indeed help to optimize anticancer treatments. The paradigm shift from empirical to more rationale practice is probably the next challenge in oncology.

• Thematic program: Models in Cancer Therapy (2015/2016)
• Event: Workshop on "Models in Cancer Therapy" (2016)

Cancer evolution, including resistance to treatments, can be explained by classical evolutionary principles. This contention implies that cancer cells may be confronted to several “bottlenecks” or “evolutionary traps” during the natural course or adaptation to this “new environment”. It has been shown that despite an important heterogeneity at the start, cancer cells may rely, at some stage, on few survival mechanisms or on restricted populations that exhibit cancer stem cells / de-differentiation features. We used two cell lines (U251 and U87 both derived from human glioma) treated with the most clinical relevant chemotherapy (Temozolomide, TMZ) in vitro for few days and analyzed their relative sensitivity to several drugs interfering with epigenetics. Deep sequencing of control and TMZ treated U251 cell lines allowed us to identify new genes implicated in their survival that are transiently overexpressed shortly after TMZ addition. Using single cell analysis by microfluidic Fluidigm technologies (combined C1 single cell analysis plus Biomark HD system), we have studied the expression of these genes plus some implicated in cell death program and survival mechanisms) in isolated cells (>60) from control and cells treated with TMZ. Analysis of the expression of these genes reveals that the level of genomic heterogeneity appeared to be reduced in treated cells at early stages. These preliminary results, coupled to phenotypic analyses on cell death and proliferation rates, suggest that the cell lines can undergo a first rapid selection process that reduces their heterogeneity (and proliferation capacity) but improve their resistance capacity through limited survival pathways.

• Thematic program: Models in Cancer Therapy (2015/2016)
• Event: Workshop on "Models in Cancer Therapy" (2016)

We investigate optimal therapeutical strategies combining cytotoxic and cytostatic drugs for the treatment of a solid tumour. The difficulty comes from the usual pitfalls of such treatments: emergence of drug-resistance and toxicity to healthy cells. We consider an integro-differential model for which the structuring variable is a continuous phenotype. Such models come from theoretical ecology and have been developed to understand how selection occurs in a given population of individuals. Two populations of healthy and cancer cells, both structured by a phenotype representing resistance to the drugs, are thus considered. The optimal control problem consists of minimising the number of cancer cells after some fixed time T. We first analyse the effect of constant doses on the long-time asymptotics through a Lyapunov functional. The optimal control problem is solved numerically, and for large T, we also theoretically determine the optimal strategy in a restricted class of controls.

• Thematic program: Models in Cancer Therapy (2015/2016)
• Event: Workshop on "Models in Cancer Therapy" (2016)

Glioblastoma represents the most frequent and aggressive primary brain tumor. Despite intense research and availability of extended in silico data, the mean patient survival after diagnosis is only around 15 months. Classical alkylating chemotherapy with concomitant radiation is still the standard therapeutic approach. This demonstrates that the revolution of modern precision medicine based on “big data” strategies has not resulted in approved therapeutic options and patient prognosis in this deadly disease so far. This implies that simple big data collection with bioinformatic evaluation might not be sufficient to translate into clinical benefit and close cooperations between systems biology and whet lab research is essential. Accordingly, we focus in our research cooperation on a multi-strategy approach focusing on a tight integration of 1) large-scale biobanking of viable malignant cells and cancer stem cells, 2) wet-lab cell and molecular biology and xenograft experiments; 3) extended omics analysis and 4) advanced computational biology methods. Regarding molecular factor driving tumor aggressiveness, data on a recently discovered non-coding mutation in the promoter of the telomerase reverse transcriptase (TERT) gene in human glioblastoma will be elucidated. Additionally, using publicly available gene expression profiles of glioblastoma patients we tried to bridge the existing gap of understanding the association of individual genes/mutations to complex physiological processes by the systematic investigation of the observed relationship between gene products and clinical traits. A weighted gene co-expression network approach (WGCNA) has been proposed to reconstruct gene co-expression networks in terms of large-scale gene expression profiles and as well as for the distinction genes potentially driving key cellular signaling pathways based on the centrality – lethality theorem. The WGCNA approach provides a functional interpretation in Systems Biology and leads to new insights into cancer pathophysiology. Here, we applied a systematic framework for constructing gene co-expression networks (modules) and pin-pointing key genes that may drive tumorigenesis and progression in different subclasses of GBM. Microarray data were downloaded from The Cancer Genome Atlas, corrected for batch effects using ComBat and normalized using rma and quantil normalization. Outliers were excluded using co-expression network parameters and co-expression network similarity. The resulting dataset was stratified according to the classification of Verhaak et al. and subjected to comparative Weighted Gene Co-expression analysis. The resulting modules were tested for module preservation across GBM subtypes using the connectivity and density measures. Modules of interest (both preserved and differentially interconnected) were analyzed for biological function using Term Enrichment Analysis methods and correlated to clinical traits (e.g. survival) to identify potential key driving co-expression networks. The lead modules will be then subject to cell biological and in vivo evaluation in glioblastoma models. In summary this multidisciplinary approach offers novel insights into glioblastoma aggressiveness and might uncover novel therapeutic targets.

• Thematic program: Models in Cancer Therapy (2015/2016)
• Event: Workshop on "Models in Cancer Therapy" (2016)

A growing body of evidence supports the idea that solid tumours are complex ecosystems populated by heterogeneous cells, whose dynamics can be described in terms of evolutionary and ecological principles. In this light, it has become increasingly recognised that models that are akin to those arising from mathematical ecology can complement experimental cancer research by capturing the crucial assumptions that underlie given hypotheses, and by offering an alternative means of understanding experimental results that are currently available. This talk deals with partial differential equations modelling the dynamics of structured cancer cell populations. Analyses and numerical simulations of these equations help to uncover fresh insights into the critical mechanisms underpinning tumour progression and the emergence of resistance to anti-cancer therapies.

• Thematic program: Models in Cancer Therapy (2015/2016)
• Event: Workshop on "Models in Cancer Therapy" (2016)

Failure to maintain telomeres leads to their progressive erosion at each cell division. This process is heterogeneous but eventually triggers replicative senescence, a pathway shown to protect from unlimited cell proliferation, characteristic of cancer cells. However, the mechanisms underlying its variability and its dynamics are not characterized. Here, we used a microfluidics-based live-cell imaging assay to investigate replicative senescence in individual Saccharomyces cerevisiae cell lineages. We show that most lineages experience an abrupt and irreversible transition from a replicative to an arrested state, contrasting with the common idea of a progressive transition. Interestingly, senescent lineages displayed an important heterogeneity in their timing to enter senescence despite starting from the same initial telomeres. To understand this, we built several mathematical models, successively adding layers of molecular details. We find that, in a stochastic model where the first telomere reaching a critical short length triggers senescence, the variance of the initial telomere distribution mostly accounts for senescence heterogeneity. Unexpectedly, the residual heterogeneity is structurally built in the asymmetrical telomere replication mechanism. We then theoretically studied different senescence regimes, depending on the initial telomere variance, and provided analytical solutions to derive senescence onset from telomere length. Furthermore, the microfluidics approach also revealed another class of lineages that undergo frequent reversible cell-cycle arrests. Cells with this phenotype persist only at low frequency in bulk cultures but could initiate both genomic instability and post-senescence survival through adaptation mechanisms. These data suggest that another source of heterogeneity of senescence onset consists of stochastic telomere damages that may be the basis of cancer emergence.

• Thematic program: Models in Cancer Therapy (2015/2016)
• Event: Workshop on "Models in Cancer Therapy" (2016)

We will present work on the mechanisms used for establishing or restoring epithelial integrity which are motivated by experimental work on development and wound healing in Zebrafish and drosophila and on gap closure in monolayers of MDCK cells or keratinocytes. These works concern mathematical modeling of the dynamics of epithelial tissues pulled by lamellipodal crawling or the contraction of actomyosin cables at the gap boundary. We are particularly interested in the influence of the wound/gap geometry and of the adhesion to the substrate on the closure mechanism.

• Thematic program: Models in Cancer Therapy (2015/2016)
• Event: Workshop on "Models in Cancer Therapy" (2016)

Acute leukemias are cancerous diseases of the blood forming (hematopoietic) system. A hallmark of acute leukemias is heterogeneity of their clinical course. Similar as the hematopoietic system, leukemias originate from a small population of leukemic stem cells that resist treatment and trigger relapse. Recent gene sequencing studies demonstrate that the leukemic cell mass is composed of multiple clones the contribution of which changes over time. We propose compartmental models of hierarchical cell populations to study interaction of leukemic and healthy cells. The models are given as nonlinear ordinary differential equations. They include different feedback mechanisms that mediate competition and selection of the leukemic clones and the decline of healthy cells. Examples for considered mechanism are hormonal (cytokine) feedback loops, competition within the stem cell niche and overcrowding of the bone marrow space. A combination of computer simulations and patient data analysis is applied to provide insights in the following questions: (1) Which mechanisms allow leukemic cells to out-compete their benign counterparts? (2) How do properties of leukemic clones in terms of self-renewal and proliferation change during the course of the disease? What is the impact of treatment on clonal properties? (3) How do leukemic stem cell parameters affect the clinical course and patient prognosis? (4) What is the impact of leukemic cell properties on the number of leukemic clones and their genetic interdependence? (5) How does responsiveness of leukemic cells to signals of healthy hematopoiesis influence treatment response? Do inter-individual differences in signal sensitivity of leukemic cells matter? The talk is based on joint works with Anna Marciniak-Czochra (Institute of Applied Mathematics, Heidelberg University), Anthony D. Ho, Natalia Baran and Christoph Lutz (Heidelberg University Hospital).

• Thematic program: Models in Cancer Therapy (2015/2016)
• Event: Workshop on "Models in Cancer Therapy" (2016)

Advances in genetic engineering have made it possible to reprogram individual immune cells to express receptors that recognise markers on tumour cell surfaces. The process of re-engineering T cell lymphocytes to express Chimeric Antigen Receptors(CARs), and then re-infusing the CAR-modified T cells into patients to treat various cancers is referred to as CAR T cell therapy. This therapy is being explored in clinical trials - most prominently for B Cell Acute Lymphoblastic Leukaemia (B-ALL), a common B cell malignancy, for which CAR T cell therapy has led to remission in up to 90% of patients. Despite this extraordinary response rate, however, potentially fatal inflammatory side effects occur in up to 10% of patients who have positive responses. Further, approximately 50% of patients who initially respond to the therapy eventually relapse. Significant improvement is thus necessary before the therapy can be made widely available for use in the clinic. To inform future development, we develop a mathematical model to analyze the interaction dynamics between CAR T cells, inflammatory toxicity, and individual patients' tumour burdens in silico. This talk outlines an underlying system of coupled ordinary differential equations, designed based on well-known immunological principles and widely accepted views on the mechanism of toxicity development in CAR T cell therapy for B-ALL, to form novel hypotheses on key factors in toxicity development, and reports in silico outcomes in relationship to standard and recently conjectured predictors of toxicity in a heterogeneous, randomly generated patient population. Our initial results and analyses are consistent with and connect immunological mechanisms to the clinically observed, counterintuitive hypothesis that initial tumour burden is a stronger predictor of toxicity than is the dose of CAR T cells administered to patients. We outline how the mechanism of action in CAR T cell therapy can give rise to such non-standard trends in toxicity development, and demonstrate the utility of mathematical modelling in understanding the relationship between predictors of toxicity, mechanism of action, and patient outcomes.

• Thematic program: Models in Cancer Therapy (2015/2016)
• Event: Workshop on "Models in Cancer Therapy" (2016)

Differential gene expression analysis between healthy and cancer samples is a common task. In order to identify differentially expressed genes, it is crucial to normalize the raw count data of RNA-Seq experiments. There are multiple normalization methods available but all of them are based on certain assumptions. These may or may not be suitable for the type of data they are applied on and especially if an experiment compares gene expression levels of healthy vs. rapidly growing tumor cells, the assumptions of non-differentially expressed genes or equal amounts of mRNA might not apply. Researchers therefore need to select an adequate normalization strategy for each RNA-Seq experiment. This selection includes exploration of different normalization methods as well as their comparison. We developed the NVT package, which provides a fast and simple way to analyze and evaluate multiple normalization methods via visualization and representation of correlation values, based on a user-defined set of uniformly expressed genes.

• Thematic program: Models in Cancer Therapy (2015/2016)
• Event: Workshop on "Models in Cancer Therapy" (2016)

High-grade serous ovarian cancer (HGSOC) represents the majority of ovarian cancers and disease recurrence is common, and leads to incurable disease. Emerging insights into disease progression suggest that timely detection of low volume HGSOC, not necessarily also early stage, should be the goal of any screening study. However, numerous transvaginal ultrasound (TVU) detection-based studies aimed at detecting low-volume ovarian cancer have not yielded reduced mortality rates and thus invalidate TVU as an effective HGSOC monitoring strategy in improving overall survival. Our mathematical modeling approach proposes a quantitative explanation behind the reported failure of TVU to improve HGSOC low-volume detectability and overall survival rates. We develop a novel in silico mathematical assessment of the efficacy of a unimodal TVU monitoring regimen as a strategy aimed at detecting low-volume HGSOC in cancer-positive cases, defined as cases for which the inception of the first malignant cell has already occurred. Focusing on a malignancy poorly studied in the mathematical oncology community, our model recapitulates the dynamic, temporal evolution of HGSOC progression, and is characterized by several infrequent, rate-limiting events. Our results suggest that multiple frequency TVU monitoring across various detection sensitivities does not significantly improve detection accuracy of HGSOC in an in silico cancer-positive population. This is a joint work with Doron Levy (University of Maryland, College Park) and Jung-Min Lee (Women’s Malignancies Branch, National Cancer Institute)

• Thematic program: Models in Cancer Therapy (2015/2016)
• Event: Workshop on "Models in Cancer Therapy" (2016)

We are interested in the Darwinian evolution of a population structured by a phenotypic trait. In the model, the trait can change by mutations and individuals compete for a common resource e.g. food. Mathematically, this can be described by non-local Lotka-Volterra equations. They have the property that solutions concentrate as Dirac masses in the limit of small diffusion. We review results on long-term behaviour and small mutation limits. A promising application of these models is that they can help to quantitatively understand how resistances against treatment develop. In this case, the population of cells is structured by how resistant they are to a therapy. We describe the model, give first results and discuss optimal control problems arising in this context.

• Thematic program: Models in Cancer Therapy (2015/2016)
• Event: Workshop on "Models in Cancer Therapy" (2016)