Hierarchy and extremes in selections from pools of randomized proteins

TL;DR

This study investigates how the diversity of randomized protein libraries influences their response to selection, revealing key factors that affect evolvability and guiding the design of synthetic proteins.

Contribution

It introduces a probabilistic model based on extreme value theory to explain the variability in responses of protein libraries with different frameworks.

Findings

Libraries with same diversity but different frameworks respond differently.

Response distribution follows a simple scaling law.

Model rationalizes the observed response patterns.

Abstract

Variation and selection are the core principles of Darwinian evolution, yet quantitatively relating the diversity of a population to its capacity to respond to selection is challenging. Here, we examine this problem at a molecular level in the context of populations of partially randomized proteins selected for binding to well-defined targets. We built several minimal protein libraries, screened them in vitro by phage display and analyzed their response to selection by high-throughput sequencing. A statistical analysis of the results reveals two main findings: first, libraries with same sequence diversity but built around different "frameworks" typically have vastly different responses, second, the distribution of responses within a library follows a simple scaling law. We show how an elementary probabilistic model based on extreme value theory rationalizes these findings. Our results have implications for designing synthetic protein libraries, for estimating the density of functional biomolecules in sequence space, for characterizing diversity in natural populations and for experimentally investigating the concept of evolvability, or potential for future evolution.