Friday, December 11, 2015

The impact of cellular characteristics on the evolution of shape homeostasis

 The impact of cellular characteristics on the evolution of shape homeostasis


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.

Monday, December 7, 2015

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

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

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.

Tuesday, November 24, 2015

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

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

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Sunday, November 22, 2015

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

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

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

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

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

Integrating experimental data to calibrate quantitative cancer models

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

Tuesday, November 10, 2015

Agent based models to investigate cooperation between cancer cells

Wednesday, October 28, 2015

Spatial metrics of tumour vascular organisation predict radiationefficacy in a computational model

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

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.

Thursday, October 22, 2015

Computational modelling of metastasis development in renal cell carcinoma

Computational modelling of metastasis development in renal cell carcinoma 

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.