Evolution rapidly optimizes stability and aggregation in lattice proteins despite pervasive landscape valleys and mazes

Fitness landscapes are widely used to visualize the dynamics and long-term outcomes of evolution. The fitness landscapes of genetic sequences are characterized by high dimensionality and \"ruggedness\" due to sign epistasis. Ascending from low to high fitness on such landscapes can be difficult because adaptive trajectories get stuck at low-fitness local peaks. Compounding matters, recent computational complexity arguments have proposed that extremely long, winding adaptive paths may be required to even reach local peaks, a \"maze-like\" landscape topography. The extent to which peaks and mazes shape the mode and tempo of evolution is poorly understood due to empirical limitations and the abstractness of many landscape models. We develop a biophysically-grounded computational model of protein evolution based on two novel extensions of the classic hydrophobic-polar lattice model of protein folding. First, rather than just considering fold stability we account for the tradeoff between stability and aggregation propensity. Second, we use a \"hydrophobic zipping\" algorithm to kinetically generate ensembles of post-translationally folded structures. Our stability-aggregation fitness landscape exhibits extensive sign epistasis and local peaks galore. We confirm the postulated existence of maze-like topography in our biologically-grounded landscape. Although these landscape features frequently obstruct adaptive ascent to high fitness and virtually eliminate reproducibility of evolutionary outcomes, many adaptive paths do successfully complete the long ascent from low to high fitness. This delicate balance of \"hard but possible\" adaptation could occur more broadly provided that the optimal outcomes possible under a tradeoff are improved by rare constraint-breaking substitutions.