Pairwise and higher-order epistatic effects among somatic cancer mutations across oncogenesis

Cancer occurs as a consequence of multiple somatic mutations that lead to uncontrolled cell growth. Mutual exclusivity and co-occurrence of mutations imply--but do not prove--that they can exert synergistic or antagonistic epistatic effects on oncogenesis. Knowledge of these interactions, and the consequent trajectories of mutation and selection that lead to cancer has been a longstanding goal within the cancer research community. Recent research has revealed mutation rates and scaled selection coefficients for specific recurrent variants across many cancer types. However, estimation of pairwise and higher-order effects--essential to estimation of the trajectory of likely cancer genotoypes--has been a challenge. Therefore, we have developed a continuous-time Markov chain model that enables the estimation of mutation origination and fixation (flux), dependent on somatic cancer genotype. Coupling the continuous-time Markov chain model with a deconvolution approach provides estimates of underlying mutation rates and selection across the trajectory of oncogenesis. We demonstrate computation of fluxes and selection coefficients in a somatic evolutionary model for the four most frequently variant driver genes (TP53, LRP1B, KRAS and STK11) from 565 cases of lung adenocarcinoma. Our analysis reveals multiple antagonistic epistatic effects that reduce the possible routes of oncogenesis, and inform cancer research regarding viable trajectories of somatic evolution whose progression could be forestalled by precision medicine. Synergistic epistatic effects are also identified, most notably in the somatic genotype TP53+LRP1B for mutations in the KRAS gene, and in somatic genotypes containing KRAS or TP53 mutations for mutations in the STK11 gene. Large positive fluxes of KRAS variants were driven by large selection coefficients, whereas the flux toward LRP1B mutations was substantially aided by a large mutation rate for this gene. The approach enables inference of the most likely routes of site-specific variant evolution and estimation of the strength of selection operating on each step along the route, a key component of what we need to know to develop and implement personalized cancer therapies.