AMaLa: analysis of Directed Evolution experiments via Annealed Mutational approximated Landscape

We present Annealed Mutational approximated landscape (AMaLa), a new method to infer fitness landscapes from Directed Evolution experiment sequencing data. Directed Evolution experiments typically start from a single wild-type sequence, which undergoes Darwinian in vitro evolution acted via multiple rounds of mutation and selection with respect to a target phenotype. In the last years, Directed Evolution is emerging as a powerful instrument to probe fitness landscapes under controlled experimental condition and, thanks to the use of high-throughput sequencing of the different rounds, as a relevant testing ground to develop accurate statistical models and inference algorithms. Fitness landscape modeling strategies, either use as input data the enrichment of variants abundances and hence require observing the same variants at different rounds, or they simply assume that the variants at the last sequenced round are the results of a sampling process at equilibrium. AMaLa aims at leveraging effectively the information encoded in the time evolution of all sequenced rounds. To do so, on the one hand we assume statistical sampling independence between sequenced rounds, and on the other we gauge all possible trajectories in sequence space with a time-dependent statistical weight consisting of two contributions: (i) a statistical energy term accounting for the selection process, (ii) a simple generalized Jukes-Cantor model to describe the purely mutational step. This simple scheme allows us to accurately describe the Directed Evolution dynamics in a concrete experimental setup and to infer a fitness landscape that reproduces correctly the measures of the phenotype under selection (e.g. antibiotic drug resistance), notably outperforming widely used inference strategies. We assess the reliability of AMaLa by showing how the inferred statistical model could be used to predict relevant structural properties of the wild-type sequence, and to reproduce the mutational effects of large scale functional screening not used to train the model.