  During their evolution, proteins explore sequence space via an interplay
between random mutations and phenotypic selection. Here we build upon recent
progress in reconstructing data-driven fitness landscapes for families of
homologous proteins, to propose stochastic models of experimental protein
evolution. These models predict quantitatively important features of
experimentally evolved sequence libraries, like fitness distributions and
position-specific mutational spectra. They also allow us to efficiently
simulate sequence libraries for a vast array of combinations of experimental
parameters like sequence divergence, selection strength and library size. We
showcase the potential of the approach in re-analyzing two recent experiments
to determine protein structure from signals of epistasis emerging in
experimental sequence libraries. To be detectable, these signals require
sufficiently large and sufficiently diverged libraries. Our modeling framework
offers a quantitative explanation for the variable success of recently
published experiments. Furthermore, we can forecast the outcome of time- and
resource-intensive evolution experiments, opening thereby a way to
computationally optimize experimental protocols.
