4,247 research outputs found
Edge effects in game theoretic dynamics of spatially structured tumours
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.Comment: 14 pages, 3 figures; restructured abstract, added histology to fig.
1, added fig. 3, discussion of EMT introduced and cancer biology expande
Evolutionary dynamics of incubation periods
The incubation period of a disease is the time between an initiating
pathologic event and the onset of symptoms. For typhoid fever, polio, measles,
leukemia and many other diseases, the incubation period is highly variable.
Some affected people take much longer than average to show symptoms, leading to
a distribution of incubation periods that is right skewed and often
approximately lognormal. Although this statistical pattern was discovered more
than sixty years ago, it remains an open question to explain its ubiquity. Here
we propose an explanation based on evolutionary dynamics on graphs. For simple
models of a mutant or pathogen invading a network-structured population of
healthy cells, we show that skewed distributions of incubation periods emerge
for a wide range of assumptions about invader fitness, competition dynamics,
and network structure. The skewness stems from stochastic mechanisms associated
with two classic problems in probability theory: the coupon collector and the
random walk. Unlike previous explanations that rely crucially on heterogeneity,
our results hold even for homogeneous populations. Thus, we predict that two
equally healthy individuals subjected to equal doses of equally pathogenic
agents may, by chance alone, show remarkably different time courses of disease.Comment: 24 pages, 8 figures, 1 tabl
A mathematical model of tumor self-seeding reveals secondary metastatic deposits as drivers of primary tumor growth
Two models of circulating tumor cell (CTC) dynamics have been proposed to
explain the phenomenon of tumor 'self-seeding', whereby CTCs repopulate the
primary tumor and accelerate growth: Primary Seeding, where cells from a
primary tumor shed into the vasculature and return back to the primary
themselves; and Secondary Seeding, where cells from the primary first
metastasize in a secondary tissue and form microscopic secondary deposits,
which then shed cells into the vasculature returning to the primary. These two
models are difficult to distinguish experimentally, yet the differences between
them is of great importance to both our understanding of the metastatic process
and also for designing methods of intervention. Therefore we developed a
mathematical model to test the relative likelihood of these two phenomena in
the subset of tumours whose shed CTCs first encounter the lung capillary bed,
and show that Secondary Seeding is several orders of magnitude more likely than
Primary seeding. We suggest how this difference could affect tumour evolution,
progression and therapy, and propose several possible methods of experimental
validation.Comment: 20 pages, 4 figure
Investigating prostate cancer tumour-stroma interactions - clinical and biological insights from an evolutionary game
BACKGROUND: Tumours are made up of a mixed population of different types of cells that include normal structures as well as ones associated with the malignancy, and there are multiple interactions between the malignant cells and the local microenvironment. These intercellular interactions, modulated by the microenvironment, effect tumour progression and represent a largely under appreciated therapeutic target. We use observations of primary tumor biology from prostate cancer to extrapolate a mathematical model: specifically; it has been observed that in prostate cancer three disparate cellular outcomes predominate: (i) the tumour remains well differentiated and clinically indolent - in this case the local stromal cells may act to restrain the growth of the cancer; (ii) early in its genesis the tumour acquires a highly malignant phenotype, growing rapidly and displacing the original stromal population (often referred to as small cell prostate cancer) - these less common aggressive tumours are relatively independent of the local microenvironment; and, (iii) the tumour co-opts the local stroma - taking on a classic stromagenic phenotype where interactions with the local microenvironment are critical to the cancer growth. METHODS: We present an evolutionary game theoretical construct that models the influence of tumour-stroma interactions in driving these outcomes. We consider three characteristic and distinct cellular populations: stromal cells, tumour cells that are self-reliant in terms of microenvironmental factors and tumour cells that depend on the environment for resources but can also co-opt stroma. 
RESULTS: Using evolutionary game theory we explore a number of different scenarios that elucidate the impact of tumour-stromal interactions on the dynamics of prostate cancer growth and progression and how different treatments in the metastatic setting can affect different types of tumors.
CONCLUSIONS: The tumour microenvironment plays a crucial role selecting the traits of the tumour cells that will determine prostate cancer progression. Equally important, treatments like hormone therapy affect the selection of these cancer phenotypes making it very important to understand how they impact prostate cancer’s somatic evolution
Supreme Court Voting Behavior - 2003 Term
The 2003 Term, for the second year, notes a liberal trend across a majority of the Tables of this Study. The voting behavior of individual Justices in 2003 was somewhat more stable this Term in that individual departures from past voting behaviors were less pronounced than in 2002. Nevertheless, the Study still demonstrates continuing instability in the voting behavior of individual Justices. This Term, statistically significant departures from past behavior by at least five Members of the Court are present on six Tables. This might suggest that the voting behavior of the Justices on these Tables is in transition, although the often-small statistical samples reported on many of these Tables also suggests caution in making (or relying upon) this inference. Bloc voting continues to control the outcome of a substantial number of the most controversial questions presented to the Court. But, as noted in the past few Studies, the voting power of conservative voting blocs seems to be losing steam. Justice O\u27Connor maintained her position as the Member of the Court most likely to cast the key swing-vote in closely divided opinions. The Study also demonstrates that Justice O\u27Connor\u27s voting behavior in state criminal cases has been a reliable indicator of the outcome of Majority Opinions in this category for a number of years. Her absence might alter decisional outcomes, not only in state criminal cases, but in the often-important cases decided by five-to-four votes of the Court
- …