Search This Blog

Loading...

Thursday, August 25, 2016

Ordinary Differential Equations in Cancer Biology

Ordinary Differential Equations in Cancer Biology

Margaret P Chapman, Claire J. Tomlin

Abstract


Ordinary differential equations (ODEs) provide a classical framework to model the dynamics of biological systems, given temporal experimental data. Qualitative analysis of the ODE model can lead to further biological insight and deeper understanding compared to traditional experiments alone. Simulation of the model under various perturbations can generate novel hypotheses and motivate the design of new experiments. This short paper will provide an overview of the ODE modeling framework, and present examples of how ODEs can be used to address problems in cancer biology.

Monday, August 8, 2016

Cancer treatment scheduling and dynamic heterogeneity in social dilemmas of tumour acidity and vasculature

Cancer treatment scheduling and dynamic heterogeneity in social dilemmas of tumour acidity and vasculature

Artem Kaznatcheev, Robert Vander Velde, Jacob G Scott, David Basanta
 

Abstract

Background: Tumours are diverse ecosystems with persistent heterogeneity in various cancer hallmarks like self-sufficiency of growth factor production for angiogenesis and reprogramming of energy-metabolism for aerobic glycolysis. This heterogeneity has consequences for diagnosis, treatment, and disease progression. Methods: We introduce the double goods game to study the dynamics of these traits using evolutionary game theory. We model glycolytic acid production as a public good for all tumour cells and oxygen from vascularization via VEGF production as a club good benefiting non-glycolytic tumour cells. This results in three viable phenotypic strategies: glycolytic, angiogenic, and aerobic non-angiogenic. Results: We classify the dynamics into three qualitatively distinct regimes: (1) fully glycolytic, (2) fully angiogenic, or (3) polyclonal in all three cell types. The third regime allows for dynamic heterogeneity even with linear goods, something that was not possible in prior public good models that considered glycolysis or growth-factor production in isolation. Conclusion: The cyclic dynamics of the polyclonal regime stress the importance of timing for anti-glycolysis treatments like lonidamine. The existence of qualitatively different dynamic regimes highlights the order effects of treatments. In particular, we consider the potential of vascular renormalization as a neoadjuvant therapy before follow up with interventions like buffer therapy.

 

 

Thursday, June 16, 2016

The Evolutionary Trade-off between Stem Cell Niche Size, Aging, and Tumorigenesis

The Evolutionary Trade-off between Stem Cell Niche Size, Aging, and Tumorigenesis

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

Abstract

Many epithelial tissues within large multicellular organisms are continually replenished by small independent populations of stem cells. These stem cells divide within their niches and differentiate into the constituent cell types of the tissue, and are largely responsible for maintaining tissue homeostasis. Mutations can accumulate in stem cell niches and change the rate of stem cell division and differentiation, contributing to both aging and tumorigenesis. Here, we create a mathematical model of the intestinal stem cell niche, crypt system, and epithelium. We calculate the expected effect of fixed mutations in stem cell niches and their expected effect on tissue homeostasis throughout the intestinal epithelium over the lifetime of an organism. We find that, due to the small population size of stem cell niches, fixed mutations are expected to accumulate via genetic drift and decrease stem cell fitness, leading to niche and tissue attrition, and contributing to organismal aging. We also explore mutation accumulation at various stem cell niche sizes, and demonstrate that an evolutionary trade-off exists between niche size, tissue aging, and the risk of tumorigenesis; where niches exist at a size that minimizes the probability of tumorigenesis, at the expense of accumulating deleterious mutations due to genetic drift. Finally, we show that the probability of tumorigenesis and the extent of aging trade-off differently depending on whether mutational effects confer a selective advantage, or not, in the stem cell niche.

Thursday, June 9, 2016

Evolutionary dynamics of CRISPR gene drives

Evolutionary dynamics of CRISPR gene drives

Charleston Noble, Jason Olejarz, Kevin Esvelt, George Church, Martin Nowak

Abstract

The alteration of wild populations has been discussed as a solution to a number of humanity's most pressing ecological and public health concerns. Enabled by the recent revolution in genome editing, CRISPR gene drives, selfish genetic elements which can spread through populations even if they confer no advantage to their host organism, are rapidly emerging as the most promising approach. But before real-world applications are considered, it is imperative to develop a clear understanding of the outcomes of drive release in nature. Toward this aim, we mathematically study the evolutionary dynamics of CRISPR gene drives. We demonstrate that the emergence of drive-resistant alleles presents a major challenge to previously reported constructs, and we show that an alternative design which selects against resistant alleles greatly improves evolutionary stability. We discuss all results in the context of CRISPR technology and provide insights which inform the engineering of practical gene drive systems.

 

 

Tuesday, June 7, 2016

tHapMix: simulating tumour samples through haplotype mixtures

tHapMix: simulating tumour samples through haplotype mixtures

Sergii Ivakhno, Camilla Colombo, Stephen Tanner, Philip Tedder, Stefano Berri, Anthony J. Cox
 

Abstract

Motivation: Large-scale rearrangements and copy number changes combined with different modes of clonal evolution create extensive somatic genome diversity, making it difficult to develop versatile and scalable variant calling tools and create well-calibrated benchmarks. Results: We developed a new simulation framework tHapMix that enables the creation of tumour sam-ples with different ploidy, purity and polyclonality features. It easily scales to simulation of hundreds of somatic genomes, while re-use of real read data preserves noise and biases present in sequencing platforms. We further demonstrate tHapMix utility by creating a simulated set of 140 somatic genomes and showing how it can be used in training and testing of somatic copy number variant calling tools. Availability and implementation: tHapMix is distributed under an open source license and can be downloaded from https://github.com/Illumina/tHapMix .

 

 

Friday, May 27, 2016

Non-linear tumor-immune interactions arising from spatial metabolic heterogeneity

Non-linear tumor-immune interactions arising from spatial metabolic heterogeneity

Mark Robertson-TessiRobert J GilliesRobert A GatenbyAlexander RA Anderson

Abstract

A hybrid multiscale mathematical model of tumor growth is used to investigate how tumoral and microenvironmental heterogeneity affect the response of the immune system. The model includes vascular dynamics and evolution of metabolic tumor phenotypes. Cytotoxic T cells are simulated, and their effect on tumor growth is shown to be dependent on the structure of the microenvironment and the distribution of tumor phenotypes. Importantly, no single immune strategy is best at all stages of tumor growth.

http://biorxiv.org/content/early/2016/05/04/038273

Sunday, April 24, 2016

Toxicity Management in CAR T cell therapy for B-ALL: Mathematical modelling as a new avenue for improvement

Toxicity Management in CAR T cell therapy for B-ALL: Mathematical modelling as a new avenue for improvement.