The Influence of Higher-Order Epistasis on Biological Fitness Landscape Topography.

The effect of a mutation on the organism often depends on what other mutations are already present in its genome. Geneticists refer to such mutational interactions as epistasis. Pairwise epistatic effects have been recognized for over a century, and their evolutionary implications have received theoretical attention for nearly as long. However, pairwise epistatic interactions themselves can vary with genomic background. This is called higher-order epistasis, and its consequences for evolution are much less well understood. Here, we assess the influence that higher-order epistasis has on the topography of 16 published, biological fitness landscapes. We find that on average, their effects on fitness landscape declines with order, and suggest that notable exceptions to this trend may deserve experimental scrutiny. We conclude by highlighting opportunities for further theoretical and experimental work dissecting the influence that epistasis of all orders has on fitness landscape topography and on the efficiency of evolution by natural selection.

Should evolutionary geneticists worry about higher-order epistasis?

Natural selection drives evolving populations up the fitness landscape, the projection from nucleotide sequence space to organismal reproductive success. While it has long been appreciated that topographic complexities on fitness landscapes can arise only as a consequence of epistatic interactions between mutations, evolutionary genetics has mainly focused on epistasis between pairs of mutations. Here we propose a generalization to the classical population genetic treatment of pairwise epistasis that yields expressions for epistasis among arbitrary subsets of mutations of all orders (pairwise, three-way, etc.). Our approach reveals substantial higher-order epistasis in almost every published fitness landscape. Furthermore we demonstrate that higher-order epistasis is critically important in two systems we know best. We conclude that higher-order epistasis deserves empirical and theoretical attention from evolutionary geneticists.

Cellular automaton simulation examining progenitor hierarchy structure effects on mammary ductal carcinoma in situ.

A computer simulation is used to model ductal carcinoma in situ, a form of non-invasive breast cancer. The simulation uses known histological morphology, cell types, and stochastic cell proliferation to evolve tumorous growth within a duct. The ductal simulation is based on a hybrid cellular automaton design using genetic rules to determine each cell's behavior. The genetic rules are a mutable abstraction that demonstrate genetic heterogeneity in a population. Our goal was to examine the role (if any) that recently discovered mammary stem cell hierarchies play in genetic heterogeneity, DCIS initiation and aggressiveness. Results show that simpler progenitor hierarchies result in greater genetic heterogeneity and evolve DCIS significantly faster. However, the more complex progenitor hierarchy structure was able to sustain the rapid reproduction of a cancer cell population for longer periods of time.

Gene knockout experiments to quantify a G2/M genetic network simulation for mammary cancer susceptibility.

A G2/M genetic network simulation is trained with tumor incidence data from knockout experiments. The genetic network is implemented using a neural network; knockout genotypes are simulated by removing nodes in the neural network. Two analyses are used to interpret the resulting network weights. We use a novel approach of fixing the network topology that allows knockout TSG (tumor suppressor gene) data from multiple studies to overlap and indirectly inform one another. The trained simulation is validated by reproducing qualitative mammary cancer susceptibilities of ATM, BRCA1, and p53 TSGs. The work described is valuable because it allows TSG mammary cancer susceptibility to be quantified using genetic network topology and in vivo knockout data.

Embedded landscapes.

In this paper we introduce embedded landscapes as an extension of NK landscapes and MAXSAT problems. This extension is valid for problems where the representation can be expressed as a simple sum of subfunctions over subsets of the representation domain. This encompasses many additive constraint problems and problems expressed as the interaction of subcomponents, where the critical features of the subcomponents are represented by subsets of bits in the domain. We show that embedded landscapes of fixed maximum epistasis K are exponentially sparse in epistatic space with respect to all possible functions. We show we can compute many important statistical features of these functions in polynomial time including all the epistatic interactions and the statistical moments of hyperplanes about the function mean and hyperplane mean. We also show that embedded landscapes of even small fixed K can be NP-complete. We can conclude that knowing the epistasis and many of the hyperplane statistics is not enough to solve the exponentially difficult part of these general problems and that the difficulty of the problem lies not in the epistasis itself but in the interaction of the epistatic parts.