The evolution of carrying capacity in constrained and expanding tumour cell populations

Cancer cells are known to modify their micro-environment such that it can sustain a larger population, or, in ecological terms, they construct a niche which increases the carrying capacity of the population. It has however been argued that niche construction, which benefits all cells in the tumour, would be selected against since cheaters could reap the benefits without paying the cost. We have investigated the impact of niche specificity on tumour evolution using an individual based model of breast tumour growth, in which the carrying capacity of each cell consists of two components: an intrinsic, subclone-specific part and a contribution from all neighbouring cells. Analysis of the model shows that the ability of a mutant to invade a resident population depends strongly on the specificity. When specificity is low selection is mostly on growth rate, while high specificity shifts selection towards increased carrying capacity. Further, we show that the long-term evolution of the system can be predicted using adaptive dynamics. By comparing the results from a spatially structured vs.\ well-mixed population we show that spatial structure restores selection for carrying capacity even at zero specificity, which a poses solution to the niche construction dilemma. Lastly, we show that an expanding population exhibits spatially variable selection pressure, where cells at the leading edge exhibit higher growth rate and lower carrying capacity than those at the centre of the tumour.Comment: Major revisions compared to previous version. The paper is now aimed at tumour modelling. We now start out with an agent-based model for which we derive a mean-field ODE-model. The ODE-model is further analysed using the theory of adaptive dynamic

Exploiting evolution to treat drug resistance: Combination therapy and the double bind

Although many anti cancer therapies are successful in killing a large percentage of tumour cells when initially administered, the evolutionary dynamics underpinning tumour progression mean that often resistance is an inevitable outcome, allowing for new tumour phenotypes to emerge that are unhindered by the therapy. Research in the field of ecology suggests that an evolutionary double bind could be an effective way to treat tumours. In an evolutionary double bind two therapies are used in combination such that evolving resistance to one leaves individuals more susceptible to the other. In this paper we present a general evolutionary game theory model of a double bind to study the effect that such approach would have in cancer. Furthermore we use this mathematical framework to understand recent experimental results that suggest a synergistic effect between a p53 cancer vaccine and chemotherapy. Our model recapitulates the experimental data and provides an explanation for its effectiveness based on the commensalistic relationship between the tumour phenotypes

The impact of cellular characteristics on the evolution of shape homeostasis

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 the fitness of the evolved solutions. 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

Bridging scales in cancer progression: Mapping genotype to phenotype using neural networks

In this review we summarize our recent efforts in trying to understand the role of heterogeneity in cancer progression by using neural networks to characterise different aspects of the mapping from a cancer cells genotype and environment to its phenotype. Our central premise is that cancer is an evolving system subject to mutation and selection, and the primary conduit for these processes to occur is the cancer cell whose behaviour is regulated on multiple biological scales. The selection pressure is mainly driven by the microenvironment that the tumour is growing in and this acts directly upon the cell phenotype. In turn, the phenotype is driven by the intracellular pathways that are regulated by the genotype. Integrating all of these processes is a massive undertaking and requires bridging many biological scales (i.e. genotype, pathway, phenotype and environment) that we will only scratch the surface of in this review. We will focus on models that use neural networks as a means of connecting these different biological scales, since they allow us to easily create heterogeneity for selection to act upon and importantly this heterogeneity can be implemented at different biological scales. More specifically, we consider three different neural networks that bridge different aspects of these scales and the dialogue with the micro-environment, (i) the impact of the micro-environment on evolutionary dynamics, (ii) the mapping from genotype to phenotype under drug-induced perturbations and (iii) pathway activity in both normal and cancer cells under different micro-environmental conditions

Computational Methods and Results for Structured Multiscale Models of Tumor Invasion

We present multiscale models of cancer tumor invasion with components at the molecular, cellular, and tissue levels. We provide biological justifications for the model components, present computational results from the model, and discuss the scientific-computing methodology used to solve the model equations. The models and methodology presented in this paper form the basis for developing and treating increasingly complex, mechanistic models of tumor invasion that will be more predictive and less phenomenological. Because many of the features of the cancer models, such as taxis, aging and growth, are seen in other biological systems, the models and methods discussed here also provide a template for handling a broader range of biological problems

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