Effect of Population Size and Mutation Rate on the Evolution of RNA Sequences on an Adaptive Landscape Determined by RNA Folding.

The dynamics of populations evolving on an adaptive landscape depends on multiple factors, including the structure of the landscape, the rate of mutations, and effective population size. Existing theoretical work often makes ad hoc and simplifying assumptions about landscape structure, whereas experimental work can vary important parameters only to a limited extent. We here overcome some of these limitations by simulating the adaptive evolution of RNA molecules, whose fitness is determined by the thermodynamics of RNA secondary structure folding. We study the influence of mutation rates and population sizes on final mean population fitness, on the substitution rates of mutations, and on population diversity. We show that evolutionary dynamics cannot be understood as a function of mutation rate µ, population size N, or population mutation rate Nµ alone. For example, at a given mutation rate, clonal interference prevents the fixation of beneficial mutations as population size increases, but larger populations still arrive at a higher mean fitness. In addition, at the highest population mutation rates we study, mean final fitness increases with population size, because small populations are driven to low fitness by the relatively higher incidence of mutations they experience. Our observations show that mutation rate and population size can interact in complex ways to influence the adaptive dynamics of a population on a biophysically motivated fitness landscape

Recasting the cancer stem cell hypothesis: Unification using a continuum model of microenvironmental forces

Purpose of review Here, we identify shortcomings of standard compartment-based mathematical models of cancer stem-cells, and propose a continuous formalism which includes the tumor microenvironment. Recent findings Stem-cell models of tumor growth have provided explanations for various phenomena in oncology including, metastasis, drug- and radio-resistance, and functional heterogeneity in the face of genetic homogeneity. While some of the newer models allow for plasticity, or de-differentiation, there is no consensus on the mechanisms driving this. Recent experimental evidence suggests that tumor microenvironment factors like hypoxia, acidosis, and nutrient deprivation have causative roles. Summary To settle the dissonance between the mounting experimental evidence surrounding the effects of the microenvironment on tumor stemness, we propose a continuous mathematical model where we model microenvironmental perturbations like forces, which then shape the distribution of stemness within the tumor. We propose methods by which to systematically measure and characterize these forces, and show results of a simple experiment which support our claims

Solving the Puzzle of Metastasis: The Evolution of Cell Migration in Neoplasms

BACKGROUND: Metastasis represents one of the most clinically important transitions in neoplastic progression. The evolution of metastasis is a puzzle because a metastatic clone is at a disadvantage in competition for space and resources with non-metastatic clones in the primary tumor. Metastatic clones waste some of their reproductive potential on emigrating cells with little chance of establishing metastases. We suggest that resource heterogeneity within primary tumors selects for cell migration, and that cell emigration is a by-product of that selection. METHODS AND FINDINGS: We developed an agent-based model to simulate the evolution of neoplastic cell migration. We simulated the essential dynamics of neoangiogenesis and blood vessel occlusion that lead to resource heterogeneity in neoplasms. We observed the probability and speed of cell migration that evolves with changes in parameters that control the degree of spatial and temporal resource heterogeneity. Across a broad range of realistic parameter values, increasing degrees of spatial and temporal heterogeneity select for the evolution of increased cell migration and emigration. CONCLUSIONS: We showed that variability in resources within a neoplasm (e.g. oxygen and nutrients provided by angiogenesis) is sufficient to select for cells with high motility. These cells are also more likely to emigrate from the tumor, which is the first step in metastasis and the key to the puzzle of metastasis. Thus, we have identified a novel potential solution to the puzzle of metastasis

Using State Space Exploration to Determine How Gene Regulatory Networks Constrain Mutation Order in Cancer Evolution

Cancer develops via the progressive accumulation of somatic mutations, which subvert the normal operation of the gene regulatory network of the cell. However, little is known about the order in which mutations are acquired in successful clones. A particular sequence of mutations may confer an early selective advantage to a clone by increasing survival or proliferation, or lead to negative selection by triggering cell death. The space of allowed sequences of mutations is therefore constrained by the gene regulatory network. Here, we introduce a methodology for the systematic exploration of the effect of every possible sequence of oncogenic mutations in a cancer cell modelled as a qualitative network. Our method uses attractor identification using binary decision diagrams and can be applied to both synchronous and asynchronous systems. We demonstrate our method using a recently developed model of ER-negative breast cancer. We show that there are differing levels of constraint in the order of mutations for different combinations of oncogenes, and that the effects of ErbB2/HER2 over-expression depend on the preceding mutations

Peto's paradox revisited : theoretical evolutionary dynamics of cancer in wild populations

If the occurrence of cancer is the result of a random lottery among cells, then body mass, a surrogate for cells number, should predict cancer incidence. Despite some support in humans, this assertion does not hold over the range of different natural animal species where cancer incidence is known. Explaining the so-called Peto's paradox' is likely to increase our understanding of how cancer defense mechanisms are shaped by natural selection. Here, we study how body mass may affect the evolutionary dynamics of tumor suppressor gene (TSG) inactivation and oncogene activation in natural animal species. We show that the rate of TSG inactivation should evolve to lower values along a gradient of body mass in a nonlinear manner, having a threshold beyond which benefits to adaptive traits cannot overcome their costs. We also show that oncogenes may be frequently activated within populations of large organisms. We then propose experimental settings that can be employed to identify protection mechanisms against cancer. We finally highlight fundamental species traits that natural selection should favor against carcinogenesis. We conclude on the necessity of comparing genomes between populations of a single species or genomes between species to better understand how evolution has molded protective mechanisms against cancer development and associated mortality

Natural resistance to cancers: a Darwinian hypothesis to explain Peto’s paradox

<p>Abstract</p> <p>Background</p> <p>Peto's paradox stipulates that there is no association between body mass (a surrogate of number of cells and longevity) and cancer prevalence in wildlife species. Resolving this paradox is a very promising research direction to understand mechanisms of cancer resistance. As of present, research has been focused on the consequences of these evolutionary pressures rather than of their causes.</p> <p>Discussion</p> <p>Here, we argue that evolution through natural selection may have shaped mechanisms of cancer resistance in wildlife species and that this can result in a threshold in body mass above which oncogenic and tumor suppressive mechanisms should be increasingly purified and positively selected, respectively.</p> <p>Summary</p> <p>We conclude that assessing wildlife species in their natural ecosystems, especially through theoretical modeling, is the most promising way to understand how evolutionary processes can favor one or the other pathway. This will provide important insights into mechanisms of cancer resistance.</p

Evolutionary foundations for cancer biology

New applications of evolutionary biology are transforming our understanding of cancer. The articles in this special issue provide many specific examples, such as microorganisms inducing cancers, the significance of within-tumor heterogeneity, and the possibility that lower dose chemotherapy may sometimes promote longer survival. Underlying these specific advances is a large-scale transformation, as cancer research incorporates evolutionary methods into its toolkit, and asks new evolutionary questions about why we are vulnerable to cancer. Evolution explains why cancer exists at all, how neoplasms grow, why cancer is remarkably rare, and why it occurs despite powerful cancer suppression mechanisms. Cancer exists because of somatic selection; mutations in somatic cells result in some dividing faster than others, in some cases generating neoplasms. Neoplasms grow, or do not, in complex cellular ecosystems. Cancer is relatively rare because of natural selection; our genomes were derived disproportionally from individuals with effective mechanisms for suppressing cancer. Cancer occurs nonetheless for the same six evolutionary reasons that explain why we remain vulnerable to other diseases. These four principles—cancers evolve by somatic selection, neoplasms grow in complex ecosystems, natural selection has shaped powerful cancer defenses, and the limitations of those defenses have evolutionary explanations—provide a foundation for understanding, preventing, and treating cancer