Mutation rate is a crucial evolutionary parameter that has typically been treated as a constant in population genetic analyses. However, mutation rate is likely to vary among co-existing individuals within a population, due to genetic polymorphisms, heterogeneous environmental influences, and random physiological fluctuations. We explore the consequences of such mutation rate heterogeneity in a model allowing an arbitrary distribution of mutation rate among individuals, either with or without inheritance. We find that variation of mutation rate about the mean results in a higher probability of producing zero or many simultaneous mutations on a genome. Moreover, it increases the frequency of higher order mutants even under ongoing mutation and selection. We gain a quantitative understanding of how this frequency depends on moments of the mutation rate distribution and selection coefficients. In particular, in a two-locus model, heterogeneity leads to a relative increase in double mutant frequency proportional to the squared coefficient of variation of the mutation rate. Relative effect sizes increase with the number of loci. Finally, this clustering of deleterious mutations into fewer individuals results in a higher population mean fitness. Our results imply that mutation rate heterogeneity allows a population to maintain a higher level of adaptedness to its current environment, while simultaneously harboring greater genetic diversity in the standing variation, which could be crucial for future adaptation to a new environment. Our results also have implications for interpreting mutation rate estimates and mutant frequencies in data.
We present a compartment model that explains melanoma cell response and resistance to mono and combination therapies. Model parameters were estimated by utilizing an optimization algorithm to identify parameters that minimized the difference between predicted cell populations and experimentally measured cell numbers. The model was then validated with in vitro experimental data. Our simulations show that although a specific timing of the combination therapy is effective in controlling tumor cell populations over an extended period of time, the treatment eventually fails. We subsequently predict a more optimal combination therapy that incorporates an additional drug at the right moment.
Stochasticity in the Genotype-Phenotype Map: Implications for the Robustness and Persistence of Bet-Hedging
DanielNichol, MarkRobertson-Tessi, PeterJeavons, Alexander RAAnderson
For the last few decades modern biology has focused on quantifying, understanding and mapping the genetic characteristics of cells. This genotype-driven perspective has led to significant advances in our understanding and treatment of diseases such as cancer e.g. the discovery of driver mutations and the development of molecularly-targeted therapeutics. However, this perspective has largely ignored the functional outcome of genetic changes: the cellular phenotype. In part, this is simply because phenotypes are neither easy to define or measure as they critically depend on both genotype and context. Heterogeneity at the gene scale has been known for sometime, and there has been significant effort invested in trying to find patterns within it, but much less is understood about how this heterogeneity manifests itself in phenotypic change, i.e. the genotype-phenotype map (GP-map). This mapping is not one-to-one but many-to-many and is fundamentally the junction at which both genes and environment meet to produce phenotypes. Many genotypes produce similar phenotypes, and multiple phenotypes can emerge from a single genotype. To further complicate matters, genetically identical cells in uniform environments still exhibit phenotypic heterogeneity. Therefore a central open question in biology today is how can we connect the abundance of genomic data with cell phenotypic behaviour, this is especially pertinent to the issue of treatment resistance as many therapies act on cellular phenotypes. Our focus here is to tackle the GP-map question through the use of the simplest functional mapping we can define that also captures phenotypic heterogeneity: a molecular switch. Molecular switches are ubiquitous in biology, observed in many organisms and naturally map molecular components to decisions (i.e. phenotypes). Often stochastic in nature, such switches can be the difference between life or death in environments that fluctuate unpredictably, since they will ensure that at least some offspring are adapted to future environments. For convenience we use Chemical Reaction Networks (CRNs) to define the map of gene products to phenotypes, allowing us to investigate the impact of distinct mappings (CRNs) and perturbations to them. We observe that key biological properties naturally emerge, including both robustness and persistence. Robustness may explain why such bet hedging strategies are common in biology, and not readily destroyed through mutation. Whereas persistence may explain the apparent paradox of bet-hedging - why does phenotypic hedging exist in environments beneficial to only one of the phenotypes, when selection necessarily acts against it? The structure of the molecular switch, itself subject to selection, can slow the loss of hedging to ensure a survival mechanism even against environmental catastrophes which are very rare. Critically, these properties when taken together have profound and significant implications for the emergence of treatment resistance, since the timescale of extinction depends heavily on the underlying GP-map.