Misleading arrows? Fitness landscapes and cancer progression models 

Abstract Cancer progression models such as Oncogenetic Tress [1], Conjunctive Bayesian Networks [2], or CAPRI [3], try to infer possible restrictions in the order of accumulation of mutations using cancer cross-sectional data. These restrictions would arise from epistatic interactions between mutations. The Directed Acyclic Graphs (DAGs) returned by these methods predict the genotypes that can and cannot be observed. Since fitness landscapes are shaped by those same epistatics interactions and also specify what genotypes are accessible and inaccessible [4] we would expect a close correspondence between a fitness landscape and the DAGs inferred from evolutionary processes in that landscape. I will show here, however, that there is a many-to- many mapping between fitness landscapes and DAGs inferred from cancer progression models. I show that many fitness landscapes cannot be represented by a cancer progression DAG in the sense that no DAG can codify the genotypes that are accessible under that landscape and I propose two measures of “DAG-non-representability”. Next, using 500 different random fitness lanscapes (with 100 begin perfectly DAG-representable) I simulate cancer progression using different mutation rates and sampling regimes; I analyze 20 replicates (of 1000 genotypes) under each condition with CAPRI[3] and CBN[2]. I show that, even under constant mutation and sampling regime conditions, data obtained from the same landscape lead to inferring widely different DAGs (e.g., median Gini-Simpson index of 0.5); this one-landscape-to-many-DAGs phenomenon increases with DAG-non-representability. I also show the one-DAG-to-many-landscapes phenomenon where the same DAG is frequently inferred from very different fitness landscapes (e.g., > 50% difference in accessible genotypes). Finally, I “reverse landscape engineer” the pancreatic cancer data used in [6]: using 190 random fitness landscapes, I show that genotype frequencies similar to the empirically observed one can be obtained under fitness landscapes that are very different from each other and that produce data that lead to the inference of DAGs that are also widely different among themselves (e.g., pairwise difference in edges of DAGs > 50%). I discuss the implications of these results for the interpretation and applied use of cancer progression models. Novelty and significance This paper explicitly establishes a connection between the inference of cancer progression models and the fitness landscapes that condition that cancer progression. It shows there is a many-to- many mapping between them, even under large sample sizes, that can limit their interpretability. References [1]R. Desper, et al., J Comput Biol 6, 37 (1999). [2]M. Gerstung, M. Baudis, H. Moch, N. Beerenwinkel, Bioinformatics 25, 2809 (2009). [3]G. Caravagna, et al., PNAS 113 E4025-E4034 (2016). [4]J. Franke, A. Klözer, J. A. G. M. de Visser, J. Krug, PLoS Comput Biol 7, e1002134 (2011). [5]K. Crona, D. Greene, M. Barlow, Journal of Theoretical Biology 317, 1 (2013). [6]M. Gerstung, N. Eriksson, J. Lin, B. Vogelstein, N. Beerenwinkel, PLoS ONE 6, e27136 (2011).