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Section: New Results

Axis 3: Quantitative cancer modeling for biological and preclinical studies

Modelling of metastasis development

Computational Modelling of Metastasis Development in Renal Cell Carcinoma [2]

Team participants: Etienne Baratchart, Sébastien Benzekry, Thierry Colin, Olivier Saut

Other participants: Andreas Bikfalvi, Lindsay S. Cooley, Raphäel Pineau, Wilfried Souleyreau (LAMC - Laboratoire Angiogenèse et Micro-environnement des Cancers), Emeline J Ribot (RMSB - Résonance magnétique des systèmes biologiques)

To improve our understanding of the biology of the metastatic colonization process, we conducted a modelling study based on multi-modal data from an orthotopic murine experimental system of metastatic renal cell carcinoma. The standard theory of metastatic colonization usually assumes that secondary tumours, once established at a distant site, grow independently from each other and from the primary tumour. Using a mathematical model describing the metastatic population dynamics under this assumption, we challenged the theory against our data that included: 1) dynamics of primary tumour cells in the kidney and metastatic cells in the lungs, retrieved by green fluorescent protein tracking, and 2) magnetic resonance images (MRI) informing on the number and size of macroscopic lesions. While the model could fit the primary tumour and total metastatic burden, the predicted size distribution was not in agreement with the MRI observations. Moreover, the model was incompatible with the growth rates of individual metastatic tumours. To explain the observed metastatic patterns, we hypothesised that metastatic foci derived from one or a few cells could aggregate, resulting in a similar total mass but a smaller number of metastases. This was indeed observed in our data and led us to investigate the effect of spatial interactions on the dynamics of the global metastatic burden. We derived a novel mathematical model for spatial tumour growth, where the intra-tumour increase in pressure is responsible for the slowdown of the growth rate. The model could fit the growth of lung metastasis visualized by magnetic resonance imaging. As a non-trivial outcome from this analysis, the model predicted that the net growth of two neighbouring tumour lesions that enter in contact is considerably impaired (of 31%±1.5%, mean ± standard deviation), as compared to the growth of two independent tumours. Together, our results have implications for theories of metastatic development and suggest that global dynamics of metastasis development is dependent on spatial interactions between metastatic lesions.

Modeling spontaneous metastasis following surgery: an in vivo-in silico approach [6]

Team participant: Sebastien Benzekry

Other participants: Amanda Tracz, Michalis Mastri, Ryan Corbelli, Dominique Barbolosis, John Ebos (Buffalo University)

Rapid improvements in the detection and tracking of early-stage tumor progression aim to guide decisions regarding cancer treatments as well as predict metastatic recurrence in patients following surgery. Mathematical models may have the potential to further assist in estimating metastatic risk, particularly when paired with in vivo tumor data that faithfully represent all stages of disease progression. Herein we describe mathematical analysis that uses data from mouse models of spontaneous metastasis developing after surgical removal of orthotopically implanted primary tumors. Both presurgical (primary tumor) and postsurgical (metastatic) growth was quantified using bioluminescence and was then used to generate a mathematical formalism based on general laws of the disease (i.e. dissemination and growth). The model was able to fit and predict pre-/post-surgical data at the level of the individual as well as the population. Our approach also enabled retrospective analysis of clinical data describing the probability of metastatic relapse as a function of primary tumor size. In these data-based models, inter-individual variability was quantified by a key parameter of intrinsic metastatic potential. Critically, our analysis identified a highly nonlinear relationship between primary tumor size and postsurgical survival, suggesting possible threshold limits for the utility of tumor size as a predictor of metastatic recurrence. These findings represent a novel use of clinically relevant models to assess the impact of surgery on metastatic potential and may guide optimal timing of treatments in neoadjuvant (presurgical) and adjuvant (postsurgical) settings to maximize patient benefit.

Migration and orientation of endothelial cells on micropatterned polymers: A simple model based on classical mechanics [11]

Team participants: Thierry Colin, Clair Poignard, Olivier Saut

Other participants: Julie Joie, Marie-Christine Durrieu (IMB - Institut de Mathématiques de Bordeaux), Yifeng Lei (French Institute of Health and Medical Research, Paris)

Understanding the endothelial cell migration on micropatterned polymers, as well as the cell orientation is a critical issue in tissue engineering, since it is the preliminary step towards cell polarization and that possibly leads to the blood vessel formation. In this work, we derive a simple agent-based model to describe the migration and the orientation of endothelial cells seeded on bioactive micropatterned polymers. The aim of the modeling is to provide a simple model that corroborates quantitatively the experiments, without considering the complex phenomena inherent to cell migration. Our model is obtained thanks to a classical mechanics approach based on experimental observations. Even though its simplicity, it provides numerical results that are quantitatively in accordance with the experimental data, and thus our approach can be seen as a preliminary way towards a simple modeling of cell migration.

Tumor-host crosstalk

Host age is a systemic regulator of gene expression impacting cancer progression [3]

Team participant: Sebastien Benzekry

Other participants: Afshin Beheshti, Lili Ma, Philip Hahnfeldt, Lynn Hlatky (CCSB - Center of Cancer and Systems Biology), J. Tyson Mcdonald (University of Houston), Michael Peluso (Cancer Risk Factor Branch, Molecular Biology Laboratory)

Aging is the major determinant of cancer incidence, which, in turn, is likely dictated in large part by processes that influence the progression of early subclinical (occult) cancers. However, there is little understanding of how aging informs changes in aggregate host signaling that favor cancer progression. In this study, we provide direct evidence that aging can serve as an organizing axis to define cancer progression-modulating processes. As a model system to explore this concept, we employed adolescent (68 days), young adult (143 days), middle-aged (551 days), and old (736 days) C57BL/6 mice as syngeneic hosts for engraftment of Lewis lung cancer to identify signaling and functional processes varying with host age. Older hosts exhibited dysregulated angiogenesis, metabolism, and apoptosis, all of which are associated with cancer progression. TGFβ1, a central player in these systemic processes, was downregulated consistently in older hosts. Our findings directly supported the conclusion of a strong host age dependence in determining the host tumor control dynamic. Furthermore, our results offer initial mechanism-based insights into how aging modulates tumor progression in ways that may be actionable for therapy or prevention.

Capturing the Driving Role of Tumor-Host Crosstalk in a Dynamical Model of Tumor Growth [4]

Team participant: Sebastien Benzekry

Other participants: Afshin Beheshti, Philip Hahnfeldt, Lynn Hlatky (CCSB - Center of Cancer and Systems Biology)

In 1999, Hahnfeldt et al. proposed a mathematical model for tumor growth as dictated by reciprocal communications between tumor and its associated vasculature, introducing the idea that a tumor is supported by a dynamic, rather than a static, carrying capacity. In this original work, the carrying capacity was equated with the variable tumor vascular support resulting from the net effect of tumor-derived angiogenesis stimulators and inhibitors. This dynamic carrying capacity model was further abstracted and developed in our recent publication to depict the more general situation where there is an interaction between the tumor and its supportive host tissue; in that case, as a function of host aging. This allowed us to predict a range of host changes that may be occurring with age that impact tumor dynamics. More generally, the basic formalism described here can be (and has been), extended to the therapeutic context using additional optimization criteria. The model depends on three parameters: one for the tumor cell proliferation kinetics, one for the stimulation of the stromal support, and one for its inhibition, as well as two initial conditions. We describe here the numerical method to estimate these parameters from longitudinal tumor volume measurements.

Metronomic oncology

Metronomic Reloaded: Theoretical Models Bringing Chemotherapy into the Era of Precision Medicine [5]

Team participant: Sebastien Benzekry

Other participants: Eddy Pasquier, Dominique Barbolosi, Joseph Ciccolini, Nicolas André (CRO2 - Centre de recherches en oncologie biologique et oncopharmacologie), Bruno Lacarelle (Clinical Pharmacokinetics), Fabrice Barlési (Service d'Oncologie Multidisciplinaire et d'Innovations Thérapeutiques)

Oncology has benefited from an increasingly growing number of groundbreaking innovations over the last decade. Targeted therapies, biotherapies, and the most recent immunotherapies all contribute to increase the number of therapeutic options for cancer patients. Consequently, substantial improvements in clinical outcomes for some disease with dismal prognosis such as lung carcinoma or melanoma have been achieved. Of note, the latest innovations in targeted therapies or biotherapies do not preclude the use of standard cytotoxic agents, mostly used in combination. Importantly, and despite the rise of bioguided (a.k.a. precision) medicine, the administration of chemotherapeutic agents still relies on the maximum tolerated drug (MTD) paradigm, a concept inherited from theories conceptualized nearly half a century ago. Alternative dosing schedules such as metronomic regimens, based upon the repeated and regular administration of low doses of chemotherapeutic drugs, have emerged as possible strategies to improve response rates while reducing toxicities. The recent changes in paradigm in the way we theorize cancer biology and evolution, metastatic spreading and tumor ecology, alongside the recent advances in the field of immunotherapy, have considerably strengthened the interest for metronomic approaches. This work aims at reviewing the recent evolutions in the field of theoretical biology of cancer and computational oncology, with a focus on the consequences these changes have on the way we administer chemotherapy. In particular, a step towards developing adaptive dosing should help to further optimize the efficacy of metronomic therapy. There is a rising trend to establish personalized medicine in oncology. Developing extensive bio-guided strategies for decision-making in the choice of drugs to be administered is now a common practice at the bedside. Similarly, developing extensive model-guided strategies for decision-making in refining dosing and scheduling should be undertaken to achieve precision medicine in oncology.

Protein-protein interaction networks

Design principles for cancer therapy guided by changes in complexity of protein-protein interaction networks [7]

Team participant: Sebastien Benzekry

Other participants: Jack A Tuszynski (Alberta University), Edward Rietman, Giannoula Lakka Klement (Newman-Lakka Institute)

The ever-increasing expanse of online bioinformatics data is enabling new ways to, not only explore the visualization of these data, but also to apply novel mathematical methods to extract meaningful information for clinically relevant analysis of pathways and treatment decisions. One of the methods used for computing topological characteristics of a space at different spatial resolutions is persistent homology. This concept can also be applied to network theory, and more specifically to protein-protein interaction networks, where the number of rings in an individual cancer network represents a measure of complexity. Results: We observed a linear correlation of R = −0.55 between persistent homology and 5-year survival of patients with a variety of cancers. This relationship was used to predict the proteins within a protein-protein interaction network with the most impact on cancer progression. By re-computing the persistent homology after computationally removing an individual node (protein) from the protein-protein interaction network, we were able to evaluate whether such an inhibition would lead to improvement in patient survival. The power of this approach lied in its ability to identify the effects of inhibition of multiple proteins and in the ability to expose whether the effect of a single inhibition may be amplified by inhibition of other proteins. More importantly, we illustrate specific examples of persistent homology calculations, which correctly predict the survival benefit observed effects in clinical trials using inhibitors of the identified molecular target. Conclusions: We propose that computational approaches such as persistent homology may be used in the future for selection of molecular therapies in clinic. The technique uses a mathematical algorithm to evaluate the node (protein) whose inhibition has the highest potential to reduce network complexity. The greater the drop in persistent homology, the greater reduction in network complexity, and thus a larger potential for survival benefit. We hope that the use of advanced mathematics in medicine will provide timely information about the best drug combination for patients, and avoid the expense associated with an unsuccessful clinical trial, where drug(s) did not show a survival benefit.