Experiments show that fitness landscapes can have a rich combinatorial structure due to epistasis and yet theory assumes that local peaks can be reached quickly. I introduce a distinction between easy landscapes where local fitness peaks can be found in a moderate number of steps and hard landscapes where finding evolutionary equilibria requires an infeasible amount of time. Hard examples exist even among landscapes with no reciprocal sign epistasis; on these, strong selection weak mutation dynamics cannot find the unique peak in polynomial time. On hard rugged fitness landscapes, no evolutionary dynamics -- even ones that do not follow adaptive paths -- can find a local fitness peak quickly; and the fitness advantage of nearby mutants cannot drop off exponentially fast but has to follow a power-law that long term evolution experiments have associated with unbounded growth in fitness. I present candidates for hard landscapes at scales from singles genes, to microbes, to complex organisms with costly learning (Baldwin effect). Even though hard landscapes are static and finite, local evolutionary equilibrium cannot be assumed.
Antibiotic resistance represents a growing health crisis that necessitates the immediate discovery of novel treatment strategies. One such strategy is the identification of sequences of drugs exhibiting collateral sensitivity, wherein the evolution of resistance to a first drug renders a population more susceptible to a second. Here, we demonstrate that sequential multi-drug therapies derived from in vitro evolution experiments can have overstated therapeutic benefit - potentially suggesting a collaterally sensitive response where cross resistance ultimately occurs. The evolution of drug resistance need not be genetically or phenotypically convergent, and where resistance arises through divergent mechanisms, the efficacy of a second drug can vary substantially. We first quantify the likelihood of this occurring by use of a mathematical model parametrised by a set of small combinatorially complete fitness landscapes for Escherichia coli. We then verify, through in vitro experimental evolution, that a second-line drug can indeed stochastically exhibit either increased susceptibility or increased resistance when following a first. Genetic divergence is confirmed as the driver of this differential response through targeted sequencing. These results indicate that the present methodology of designing drug regimens through experimental collateral sensitivity analysis may be flawed under certain ecological conditions. Further, these results suggest the need for a more rigorous probabilistic understanding of the contingencies that can arise during the evolution of drug resistance.
Purpose/Objective: We introduce a novel strategy of radiation therapy planning using canonical radiobiology principles and leveraging time to further decrease normal tissue complication probability (NTCP). Temporally feathered radiation therapy (TFRT) is presented as a strategy to reduce radiation-induced toxicity, and is compared with conventionally fractionated radiotherapy an in silico model of normal tissue radiation response. Material/Methods: As a first choice to compare conventional and temporally feathered plans, we consider the biologically equivalent dose (BED), which is the most common model used to compare different fractionation schemes in radiotherapy. We formulated a mathematical model to simulate normal tissue radiation-induced damage and recovery induced by different fractionation regimens. This model considers tissue recovery as a dynamic process rather than a static probability. Radiation response is determined by the Linear-Quadratic (LQ) model, which is widely used in radiobiology. Results: TFRT is shown to be beneficial in reducing radiation-induced toxicity to normal tissues compared to conventional treatment schedules. BED is not suitable to evaluate the success potential of TFRT because of its static nature in time, the proposed dynamical NTCP model however, demonstrates that there exists a window of opportunity for temporally feathering organs at risk whereby toxicity can be reduced without affecting tumor dosing. The high and low fractional doses delivered by temporally feathered plans to organs at risk allow increased damage recovery despite higher total doses compared to standard plans. The clinical benefit of temporally feathered plans not only depends on the combination of fractional doses considered, but also on the organ-specific recovery rate of radiation damage. In particular, we found that when comparing temporally feathered and standard plans, for each recovery rate a certain range of standard fractional doses exists in which TFRT reduces toxicity. Although the potential benefit of TFRT over conventionally fractionated radiotherapy is always higher in those ranges, there exists an optimal standard fractional dose in which toxicity induced by the temporally feathered plan is minimum. Conclusions: Our novel TFRT methodology opens a yet unexplored avenue for planning optimization in radiotherapy. Application of this technique to carefully selected cases will not only potentially allow reduction in normal tissue toxicity, but also allow dose escalation to the tumor thereby enhancing the therapeutic ratio.
Tumors are heterogeneous, evolving ecosystems, composed of sub-populations of neoplastic cells that follow distinct strategies for survival and propagation. The success of a strategy defining any single neoplastic sub-population is dependent on the distribution of other strategies, and on various components of the tumour microenvironment like cancer associated fibroblasts (CAFs). The rules mapping the population's strategy distribution to the fitness of individual strategies can be represented as an evolutionary game. In four different environments, we measure the games between treatment naive (Alectinib therapy sensitive) cells and a derivative line in which resistance was previously evolved. We find that the games are not only qualitatively different between different environments, but that targeted therapy and the presence of CAFs qualitatively switch the type of game being played. This provides the first empirical confirmation for the theoretical postulate of evolutionary game theory (EGT) in mathematical oncology that we can treat not just the player, but also the game. Although we concentrate on measuring games played by cancer cells, the measurement methodology we develop can be used to advance the study of games in other microscopic systems.