Edge effects in game theoretic dynamics of spatially structured tumours

 Edge effects in game theoretic dynamics of spatially structured tumours

Authors: +Artem Kaznatcheev , +Jacob Scott and +David Basanta

Abstract:
Evolutionary game theory has been used to model many situations in ecology
where different species, or different phenotypes within one species, compete
against one another. Of late, this has extended to cancer biology to understand
the dynamics of disease progression as a game between competing cellular
phenotypes. A major assumption in this modeling paradigm is that the population
is inviscid: the probability of a player with a given phenotypic strategy
interacting with another depends exclusively on the respective abundance of
those strategies in the population. While there are scenarios where this
assumption might be useful, in solid tumours, where the populations have
spatial structure, this assumption can yield misleading results. In this study
we use a recently developed mathematical tool, the Ohtsuki-Nowak transform, to
study the effect of interaction neighborhood size on a canonical evolutionary
cancer game: go vs. grow. We show that spatial structure promotes invasive (go)
strategy. By considering the change in neighbourhood size at a boundary we show
an edge effect in solid tumours. This edge effect allows a tumour with no
invasive phenotypes expressed internally to have a polyclonal boundary with
both invasive and non-invasive cells. We focus on evolutionary game dynamics
between competing cancer cells, but we anticipate that our approach can be
extended to games between other types of players where interaction
neighborhoods change at the system boundary.

Manuscript in arXiv [link].

Natural selection increases mutational robustness in complex diseases: Mendelian evidence from early versus late onset common diseases

Natural selection increases mutational robustness in complex diseases: Mendelian evidence from early versus late onset common diseases

Author: Bora E. Baysal

Background. Natural selection operates on genetically influenced phenotypic variations that confer differential survival or reproductive advantages. Common diseases are frequently associated with increased mortality and disability and complex heritable factors play an important role in their pathogenesis. Hence, common diseases should trigger the process of natural selection with subsequent population genetic response. However, empirical impact of natural selection on genetics of complex diseases is poorly understood. In this paper, I hypothesize that negative selection of diseased individuals leads to systemic genetic differences between common diseases that primarily occur before or during the reproductive years (early onset) and those that occur after the reproductive years (late onset).
Methods. To test this hypothesis, a comprehensive literature survey of highly penetrant (80% or more) nonpleiotropic, nonsyndromic susceptibility genes (hereafter defined as Mendelian phenocopies) was completed for early versus late onset common diseases, organized using the World Health Organization (WHO) ICD-10 classification scheme. An average age at sporadic disease onset of 30 years was selected for dividing early versus late onset common diseases.
Results. Mendelian phenocopies were identified for 16 primarily late onset common diseases from 9 distinct WHO diagnostic categories. Late onset common diseases with Mendelian phenocopies include papillary renal carcinoma, obesity, Alzheimer disease, Parkinson disease, frontotemporal dementia, amyotrophic lateral sclerosis, primary open angle glaucoma, age-related hearing loss, coronary artery disease, stroke, pancreatitis, thrombotic thrombocytopenic purpura, systemic lupus erythematosus, inclusion body myositis, Paget's disease of bone and focal segmental glomerulosclerosis (steroid resistant). In contrast, no Mendelian phenocopy was found for any primarily early onset common disease (p<5.8x10^-4). Thus, highly predictive rare variants are present for a subset of late onset common diseases, but not for early onset common diseases.
Discussion. These findings suggest that genetic architecture of early onset common diseases is more robust against the phenotypic expression of highly penetrant predisposing mutations than is the case for late onset common diseases. The primary candidate for increased genetic robustness in early onset common diseases is proposed to be natural selection.

PeerJ preprint [link]

Coupled Reversible and Irreversible Bistable Switches Underlying TGFβ-induced Epithelial to Mesenchymal Transition

Xiao-Jun Tianand Hang Zhang, Jianhua Xing

(Submitted on 17 Jul 2013)

Epithelial to mesenchymal transition (EMT) plays important roles in embryonic development, tissue regeneration and cancer metastasis. While several feedback loops have been shown to regulate EMT, it remains elusive how they coordinately modulate EMT response to TGF-\beta treatment. We construct a mathematical model for the core regulatory network controlling TGF-\beta-induced EMT. Through deterministic analyses and stochastic simulations, we show that EMT is a sequential two-step program that an epithelial cell first transits to partial EMT then to the mesenchymal state, depending on the strength and duration of TGF-\beta stimulation. Mechanistically the system is governed by coupled reversible and irreversible bistable switches. The SNAIL1/miR-34 double negative feedback loop is responsible for the reversible switch and regulates the initiation of EMT, while the ZEB/miR-200 feedback loop is accountable for the irreversible switch and controls the establishment of the mesenchymal state. Furthermore, an autocrine TGF-\beta/miR-200 feedback loop makes the second switch irreversible, modulating the maintenance of EMT. Such coupled bistable switches are robust to parameter variation and molecular noise. We provide a mechanistic explanation on multiple experimental observations. The model makes several explicit predictions on hysteretic dynamic behaviors, system response to pulsed stimulation and various perturbations, which can be straightforwardly tested.

link: http://arxiv.org/abs/1307.4732 

Forecasts of Cancer and Chronic Patients: Big Data Metrics of Population Health

Jacob Kuriyan, Nathaniel Cobb

(Submitted on 12 Jul 2013)

Chronic diseases and cancer account for over 75 percent of healthcare costs in the US. Increased prevention services and improved primary care are thought to decrease costs. Current models for detecting changes in the health of populations are cumbersome and expensive, and are not sensitive in the short term. In this paper we model population health as a dynamical system to predict the time evolution of the new diagnosis of chronic diseases and cancer. This provides a reliable forecasting tool and a means of measuring short-term changes in the health status of the population resulting from preventive care programs. Twelve month forecasts of cancer and chronic populations were accurate with errors lying between 3 percent and 6 percent. We confirmed what other studies have demonstrated that diabetes patients are at increased cancer risk but, interestingly, we also discovered that all of the studied chronic conditions increased cancer risk just as diabetes did, and by a similar amount. The model(i)yields a new metric for measuring performance of preventive and clinical care programs that can provide timely feedback for quality improvement programs;(ii)helps understand "savings" in the context of preventive care programs and explains how they can be calculated in the short term, even though they materialize only in the long term and(iii)provides an analytic tool and metrics to infer correlations and derive insights on the effect of changes in socio-economic factors affecting population health on improving health and lowering costs of populations.

Link to arXiv

This paper presents biomechanical considerations in tumor formation and metastasis. I wonder how results obtained from such analyses can be addressed experimentally.

Morphological instabilities of stratified epithelia: a mechanical instability in tumour formation

Thomas Risler, Markus Basan

(Submitted on 24 Jun 2013)

Interfaces between stratified epithelia and their supporting stromas commonly exhibit irregular shapes. Undulations are particularly pronounced in dysplastic tissues and typically evolve into long, finger-like protrusions in carcinomas. In a previous work (Basan et al., Phys. Rev. Lett. 106, 158101 (2011)), we demonstrated that an instability arising from viscous shear stresses caused by the constant flow due to cell turnover in the epithelium could drive this phenomenon. While interfacial tension between the two tissues as well as mechanical resistance of the stroma tend to maintain a flat interface, an instability occurs for sufficiently large viscosity, cell-division rate and thickness of the dividing region in the epithelium. Here, extensions of this work are presented, where cell division in the epithelium is coupled to the local concentration of nutrients or growth factors diffusing from the stroma. This enhances the instability by a mechanism similar to that of the Mullins-Sekerka instability in single-diffusion processes of crystal growth. We furthermore present the instability for the generalized case of a viscoelastic stroma.

The waiting time for a second mutation: an alternative to the Moran model

Here the authors present a novel formalism for understand the emergence of mutations within a population, similar to the Moran process, but based on mutation rates pulled from Poisson distributions.  This allows, per the author, for more exact (and simple) calculations for waiting times.  I pulled this one out of the 'Probability' portion of the arXiv, and it is certainly Mathematical oncology (capital M, lower case o), but as so many folks in our field use the Moran process (and probability theory in general), I thought it would be of interest.  Maybe +Dominik Wodarz would like to comment?

The waiting time for a second mutation: an alternative to the Moran model

Rinaldo B. Schinazi

(Submitted on 28 Jun 2013)

The appearance of cancer in a tissue is thought to be the result of two or more successive mutations. We propose a stochastic model that allows for an exact computation of the distribution of the waiting time for a second mutation. This models the time of appearance of the first cancerous cell in a tissue. Our model is an alternative to the Moran model with mutations.

 link to arXiv: http://arxiv.org/abs/1306.6919