title: Hierarchy and extremes in selections from pools of randomized proteins.
abstract: Variation and selection are the core principles of Darwinian evolution, but 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 the same sequence diversity but built around different "frameworks" typically have vastly different responses; second, the distribution of responses of the best binders in a library follows a simple scaling law. We show how an elementary probabilistic model based on extreme value theory rationalizes the latter finding. Our results have implications for designing synthetic protein libraries, estimating the density of functional biomolecules in sequence space, characterizing diversity in natural populations, and experimentally investigating evolvability (i.e., the potential for future evolution).
authors.affiliation: Laboratoire Interdisciplinaire de Physique, CNRS and Université Grenoble Alpes, 38000 Grenoble, France;
authors.forename: Sébastien
authors.initials: S
authors.lastname: Boyer
authors.affiliation: Laboratoire Interdisciplinaire de Physique, CNRS and Université Grenoble Alpes, 38000 Grenoble, France;
authors.forename: Dipanwita
authors.initials: D
authors.lastname: Biswas
authors.affiliation: Laboratoire Interdisciplinaire de Physique, CNRS and Université Grenoble Alpes, 38000 Grenoble, France;
authors.forename: Ananda
authors.initials: A
authors.lastname: Kumar Soshee
authors.affiliation: Laboratoire Interdisciplinaire de Physique, CNRS and Université Grenoble Alpes, 38000 Grenoble, France;
authors.forename: Natale
authors.initials: N
authors.lastname: Scaramozzino
authors.affiliation: Laboratoire de Biochimie, Chimie-Biologie-Innovation UMR8231, CNRS and Ecole Supérieure de Physique et Chimie Industrielles ParisTech, Paris Sciences & Lettres Research University, 75005 Paris, France.
authors.forename: Clément
authors.initials: C
authors.lastname: Nizak
authors.affiliation: Laboratoire Interdisciplinaire de Physique, CNRS and Université Grenoble Alpes, 38000 Grenoble, France; olivier.rivoire@ujf-grenoble.fr.
authors.forename: Olivier
authors.initials: O
authors.lastname: Rivoire
mesh_terms: D000595:Amino Acid Sequence; D000818:Animals; D061505:Cell Surface Display Techniques; D019020:Directed Molecular Evolution / Q000379:methods* / Q000706:statistics & numerical data; D004926:Escherichia coli / Q000235:genetics; D059014:High-Throughput Nucleotide Sequencing; D006801:Humans; D015233:Models, Statistical; D008969:Molecular Sequence Data; D019151:Peptide Library; D011506:Proteins / Q000737:chemistry* / Q000235:genetics*; D015203:Reproducibility of Results; D016415:Sequence Alignment
chemical_list: D019151:Peptide Library; D011506:Proteins
keywords: antibodies; biological diversity; directed evolution; extreme values; phage display