Mathematical Modelings for Angiogenesis - A Cellular Automaton Model and its Continuous Model

Keisuke Matsuya, Hiroki Kurihara, Tetsuji Tokihiro

(Submitted on 22 Jan 2015)

Based on recent experiments with time-lapse fluorescent imaging, we propose a cellular automaton model for the dynamics of vascular endothelial cells (ECs) in angiogenic morphogenesis. The model successfully reproduces cell mixing behavior, elongation and bifurcation of blood vessels. The results suggest that the two-body interaction between ECs, which is repulsive in short distance and become attractive in moderately long distance, is essential to the dynamics of ECs, in particular, to the cell mixing behavior. The corresponding analytically solvable differential equation model is also proposed.

link: http://arxiv.org/abs/1501.05406

Dynamics of preventive and reactive cancer control using low-impact treatments

Andrei R. R. Akhmetzhanov, Michael E. Hochberg

doi: http://dx.doi.org/10.1101/014589

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Abstract

Cancer poses danger because of its unregulated growth, development of resistant subclones, and metastatic spread to vital organs. Although the major transitions in cancer development are increasingly well understood, we lack quantitative theory for how preventive measures and post-excision ('reactive') treatments are predicted to affect risks of obtaining a life threatening cancer or relapse, respectively. We employ analytical and numerical models to evaluate how continuous measures such as life style changes, and certain non-targeted and targeted treatments affect both neoplastic growth and the frequency of resistant clones. We find that preventive measures can have a negligible impact on pre-cancerous lesions and yet achieve considerable reductions in risk of invasive cancer. Importantly, our model, based on realistic parameter estimates, predicts that daily cancer cell arrest levels of 0.2-0.3% produce optimal outcomes for prevention, whereas for reaction the level is 0.3-0.4%. For similar cancer cell populations, prevention outcomes are, on average, always better than reactive ones. This is because reactive measures are more likely to select for faster growing subclones with higher probabilities of resistance, highlighting the difficulty in countering relapse regardless of therapeutic impact on cancer cell populations. We discuss these results and other important mitigating factors that need to be taken into consideration in a comparative understanding of preventive versus reactive treatments.

link: http://biorxiv.org/content/early/2015/01/29/014589

Edge effects in game theoretic dynamics of spatially structured tumors

Edge effects in game theoretic dynamics of spatially structured tumours

Artem Kaznatcheev, Jacob G Scott, DavidBasanta

doi: http://dx.doi.org/10.1101/014233

Abstract

Background: Analysing tumour architecture for metastatic potential usually focuses on phenotypic differences due to cellular morphology or specific genetic mutations, but often ignore the cell's position within the heterogeneous substructure. Similar disregard for local neighborhood structure is common in mathematical models. Methods: We view the dynamics of disease progression as an evolutionary game between cellular phenotypes. A typical assumption in this modeling paradigm is that the probability of a given phenotypic strategy interacting with another depends exclusively on the abundance of those strategies without regard local heterogeneities. We address this limitation by using the Ohtsuki-Nowak transform to introduce spatial structure to the go vs. grow game. Results: We show that spatial structure can promote the invasive (go) strategy. By considering the change in neighbourhood size at a static boundary -- such as a blood-vessel, organ capsule, or basement membrane -- we show an edge effect that allows a tumour without invasive phenotypes in the bulk to have a polyclonal boundary with invasive cells. We present an example of this promotion of invasive (EMT positive) cells in a metastatic colony of prostate adenocarcinoma in bone marrow. Interpretation: Pathologic analyses that do not distinguish between cells in the bulk and cells at a static edge of a tumour can underestimate the number of invasive cells. We expect our approach to extend to other evolutionary game models where interaction neighborhoods change at fixed system boundaries.

Link: http://biorxiv.org/content/early/2015/01/23/014233

Cancer Metastasis: Collective Invasion in Heterogeneous Multicellular Systems

Adrien Hallou, Joel Jennings, Alexandre Kabla

(Submitted on 31 Dec 2014)

Heterogeneity within tumour cell populations is associated with an increase in malignancy and appears to play an important role during cancer metastasis. Using in silico experiments, we study the interplay between collective behaviours and cell motility heterogeneities in a model system. Working with tumour spheroids that contain two non-proliferating cell populations of different motile properties, we explore the conditions required for maximal invasion into surrounding tissues. We show emerging spatial patterns of cellular organisation and invasion which are consistent with in vitro and in vivo observations. This demonstrates that mechanical interactions at the cellular level are sufficient to account for many of the observed morphologies of invasion and that heterogeneity in cell motility can be more important than average mechanical properties in controlling the fate of large cell populations.

link: http://arxiv.org/abs/1501.00065

Estimating stem cell fractions in hierarchically organized tumors

Benjamin Werner, Jacob G Scott, Andrea Sottoriva, Alexander RA Anderson, Arne Traulsen, Philipp M Altrock

doi: http://dx.doi.org/10.1101/013672

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Abstract

Cancers arise as a result of genetic and epigenetic alterations. These accumulate in cells during the processes of tissue development, homeostasis and repair. Many tumor types are hierarchically organized and driven by a sub-population of cells often called cancer stem cells. Cancer stem cells are uniquely capable of recapitulating the tumor and can be highly resistant to radio- and chemotherapy treatment. We investigate tumor growth patterns from a theoretical standpoint and show how significant changes in pre- and post-therapy tumor dynamics are tied to the dynamics of cancer stem cells. We identify two characteristic growth regimes of a tumor population that can be leveraged to estimate cancer stem cell fractions in vivo using simple linear regression. Our method is a mathematically exact result, parameter free and does not require any microscopic knowledge of the tumor properties. A more accurate quantification of the direct link between the sub-population driving tumor growth and treatment response promises new ways to individualize treatment strategies.

link: http://biorxiv.org/content/early/2015/01/11/013672

Joint fitting reveals hidden interactions in tumor growth

Lucas Barberis, Miaguel Ángel Pasquale, Carlos Alberto Condat

(Submitted on 27 Mar 2014)

Tumor growth is often the result of the simultaneous development of two or more cancer cell populations. Their interaction between them characterizes the system evolution. To obtain information about these interactions we apply the recently developed vector universality (VUN) formalism to various instances of competition between tumor populations. The formalism allows us: (a) to quantify the growth mechanisms of a HeLa cell colony, describing the phenotype switching responsible for its fast expansion, (b) to reliably reconstruct the evolution of the necrotic and viable fractions in both in vitro and in vivo tumors using data for the time dependences of the total masses, and (c) to show how the shedding of cells leading to subspheroid formation is beneficial to both the spheroid and subspheroid populations, suggesting that shedding is a strong positive influence on cancer dissemination.

link: http://arxiv.org/abs/1403.7161