The impact of cellular characteristics on the evolution of shape homeostasis

 The impact of cellular characteristics on the evolution of shape homeostasis

Philip Gerlee, David Basanta, Alexander R.A. Anderson

Abstract:

The importance of individual cells in a developing multicellular organism is well known but precisely how the individual cellular characteristics of those cells collectively drive the emergence of robust, homeostatic structures is less well understood. For example cell communication via a diffusible factor allows for information to travel across large distances within the population, and cell polarisation makes it possible to form structures with a particular orientation, but how do these processes interact to produce a more robust and regulated structure? In this study we investigate the ability of cells with different cellular characteristics to grow and maintain homeostatic structures. We do this in the context of an individual-based model where cell behaviour is driven by an intra-cellular network that determines the cell phenotype. More precisely, we investigated evolution with 96 different permutations of our model, where cell motility, cell death, long-range growth factor (LGF), short-range growth factor (SGF) and cell polarisation were either present or absent. The results show that LGF has the largest positive impact on achieving the target shape. SGF and polarisation also contribute, but all other capabilities essentially increase the search space, effectively making it more difficult to achieve a solution. By perturbing the evolved solutions, we found that they are highly robust to both mutations and wounding. In addition, we observed that by evolving solutions in more unstable environments they produce structures that were more robust and adaptive. In conclusion, our results suggest that robust collective behaviour is most likely to evolve when cells are endowed with long range communication, cell polarisation, and selection pressure from an unstable environment.

Link: http://arxiv.org/abs/1512.02474 

Well-posedness of a Cahn-Hilliard system modelling tumour growth with chemotaxis and active transport

Harald Garcke, Kei Fong Lam

(Submitted on 19 Nov 2015)

We consider a diffuse interface model for tumour growth consisting of a Cahn--Hilliard equation with source terms coupled to a reaction-diffusion equation. The coupled system of partial differential equations models a tumour growing in the presence of a nutrient species and surrounded by healthy tissue. The model also takes into account transport mechanisms such as chemotaxis and active transport. We establish well-posedness results for the tumour model and a variant with a quasi-static nutrient. It will turn out that the presence of the source terms in the Cahn--Hilliard equation leads to new difficulties when one aims to derive a priori estimates. However, we are able to prove continuous dependence on initial and boundary data for the chemical potential and for the order parameter in strong norms.

Link

The Implications of Small Stem Cell Niche Sizes and the Distribution of Fitness Effects of New Mutations in Aging and Tumorigenesis

Vincent L. Cannataro, Scott A. McKinley, Colette M. St. Mary

doi: http://dx.doi.org/10.1101/032813

Abstract:

Somatic tissue evolves over a vertebrate's lifetime due to the accumulation of mutations in stem cell populations. Mutations may alter cellular fitness and contribute to tumorigenesis or aging. The distribution of mutational effects within somatic cells is not known. Given the unique regulatory regime of somatic cell division we hypothesize that mutational effects in somatic tissue fall into a different framework than whole organisms; one in which there are more mutations of large effect. Through simulation analysis we investigate the fit of tumor incidence curves generated using exponential and power law Distributions of Fitness Effects (DFE) to known tumorigenesis incidence. Modeling considerations include the architecture of stem cell populations, i.e., a large number of very small populations, and mutations that do and do not fix neutrally in the stem cell niche. We find that the typically quantified DFE in whole organisms is sufficient to explain tumorigenesis incidence. Further, due to the effects of small stem cell population sizes, i.e., strong genetic drift, deleterious mutations are predicted to accumulate, resulting in reduced tissue maintenance. Thus, despite there being a large number of stem cells throughout the intestine, its compartmental architecture leads to significant aging, a prime example of Muller's Ratchet.

Link: http://biorxiv.org/content/early/2015/11/24/032813

Modeling Transitions between Responsive and Resistant States in Breast Cancer with Application to Therapy Optimization

Chun Chen, John J. Tyson, William Baumann

doi: http://dx.doi.org/10.1101/031245

• Abstract
• Info/History
• Metrics
•  Preview PDF

Abstract

We present a mathematical model that captures the transitions among three experimentally observed estrogen sensitivity phenotypes in breast cancer cells. Based on this model, a population-level model is created and used to explore the optimization of a therapeutic protocol

http://biorxiv.org/content/early/2015/11/10/031245

Physics-based multiscale mass transport model in drug delivery and tumor microenvironment

Arturas Ziemys, Milos Kojic, Mauro Ferrari

doi: http://dx.doi.org/10.1101/031252

• Abstract
• Info/History
• Metrics
•  Preview PDF

Abstract

We describe multiscale transport model, which was developed to simulate drug diffusion and convection in tissues and drug vectors. Models rely on material properties and physical laws of transport. Our methods show that drug transport analysis may provide deep insight into mechanisms of pharmacokinetics useful in nanotherapeutics and transport study within tumor microenvironment. Because the method relies on material properties and structures, the approach can help studying phenotypical differences as well.

http://biorxiv.org/content/early/2015/11/10/031252

Integrating experimental data to calibrate quantitative cancer models

Heiko Enderling

doi: http://dx.doi.org/10.1101/032102

• Abstract
• Info/History
• Metrics
•  Preview PDF

Abstract

For quantitative cancer models to be meaningful and interpretable the number of unknown parameters must be kept minimal. Experimental data can be utilized to calibrate model dynamics rates or rate constants. Proper integration of experimental data, however, depends on the chosen theoretical framework. Using live imaging of cell proliferation as an example, we show how to derive cell cycle distributions in agent-based models and averaged proliferation rates in differential equation models. We focus on a tumor hierarchy of cancer stem and progenitor non-stem cancer cells.

http://biorxiv.org/content/early/2015/11/17/032102

Agent based models to investigate cooperation between cancer cells

Joao Xavier, William Chang

doi: http://dx.doi.org/10.1101/031070 

Abstract

We present a type of agent-based model that uses off-lattice spheres to represent individual cells in a solid tumor. The model calculates chemical gradients and determines the dynamics of the tumor as emergent properties of the interactions between the cells. As an example, we present an investigation of cooperation among cancer cells where cooperators secrete a growth factor that is costly to synthesize. Simulations reveal that cooperation is favored when cancer cells from the same lineage stay in close proximity. The result supports the hypothesis that kin selection, a theory that explains the evolution of cooperation in animals, also applies to cancers.

Spatial metrics of tumour vascular organisation predict radiation efficacy in a computational model

Jacob G Scott, Alexander George Fletcher, Alexander RA Anderson, Philip K Maini

doi: http://dx.doi.org/10.1101/029595

Abstract

Intratumoural heterogeneity is known to contribute to heterogeneity in therapeutic response. Variations in oxygen tension in particular have been correlated with changes in radiation response in vitro and at the clinical scale with overall survival. Heterogeneity at the microscopic scale in tumour blood vessel architecture has been described, and is one source of the underlying variations in oxygen tension. We endeavour to determine whether histologic scale measures of the erratic distribution of blood vessels within a tumour can be used to predict differing radiation response. Using a two-dimensional hybrid cellular automaton model of tumour growth, we evaluate the effect of vessel distribution on cell survival outcomes of simulated radiation therapy. Using the standard equations for the oxygen enhancement ratio for cell survival probability under differing oxygen tensions, we calculate average radiation effect in simulated, random, vessel organizations. We go on to quantify the vessel distribution heterogeneity and measure spatial organization using Ripley's L function, a measure designed to detect deviations from spatial homogeneity. We find that under differing regimes of vessel density the correlation coefficient between the measure of spatial organization and radiation effect changes sign. This provides not only a useful way to understand the differences seen in radiation effect for tissues based on vessel architecture, but also an alternate explanation for the vessel normalization hypothesis.

http://biorxiv.org/content/early/2015/10/26/029595

Computational modelling of metastasis development in renal cell carcinoma 

Etienne Baratchart 1, 2 Sébastien Benzekry 1, 2, * Andreas Bikfalvi 3, * Thierry Colin 1, 4, 2, * Lindsay S. Cooley 3 Raphäel Pineau 3 Emeline Ribot 5 Olivier Saut 1, 2 Wilfried Souleyreau 3 

* Corresponding author

1 MONC - Modélisation Mathématique pour l'Oncologie 

IMB - Institut de Mathématiques de Bordeaux, INRIA Bordeaux - Sud-Ouest, Institut Bergonié - CRLCC Bordeaux

2 IMB - Institut de Mathématiques de Bordeaux 

3 LAMC - Laboratoire Angiogenèse et Micro-environnement des Cancers 

4 UB - Université de Bordeaux 

5 RMSB - Résonance magnétique des systèmes biologiques 

Abstract : 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.

https://hal.inria.fr/hal-01164834