Calculating complexity of large randomized libraries

Sampling Strategies for Experimentally Mapping Molecular Fitness Landscapes Using High-Throughput Methods

Empirical studies of genotype-phenotype-fitness maps of proteins are fundamental to understanding the evolutionary process, in elucidating the space of possible genotypes accessible through mutations in a landscape of phenotypes and fitness effects. Yet, comprehensively mapping molecular fitness landscapes remains challenging since all possible combinations of amino acid substitutions for even a few protein sites are encoded by an enormous genotype space. High-throughput mapping of genotype space can be achieved using large-scale screening experiments known as multiplexed assays of variant effect (MAVEs). However, to accommodate such multi-mutational studies, the size of MAVEs has grown to the point where a priori determination of sampling requirements is needed. To address this problem, we propose calculations and simulation methods to approximate minimum sampling requirements for multi-mutational MAVEs, which we combine with a new library construction protocol to experimentally validate our approximation approaches. Analysis of our simulated data reveals how sampling trajectories differ between simulations of nucleotide versus amino acid variants and among mutagenesis schemes. For this, we show quantitatively that marginal gains in sampling efficiency demand increasingly greater sampling effort when sampling for nucleotide sequences over their encoded amino acid equivalents. We present a new library construction protocol that efficiently maximizes sequence variation, and demonstrate using ultradeep sequencing that the library encodes virtually all possible combinations of mutations within the experimental design. Insights learned from our analyses together with the methodological advances reported herein are immediately applicable toward pooled experimental screens of arbitrary design, enabling further assay upscaling and expanded testing of genotype space.

Biomathematical description of synthetic peptide libraries

Libraries of randomised peptides displayed on phages or viral particles are essential tools in a wide spectrum of applications. However, there is only limited understanding of a library's fundamental dynamics and the influences of encoding schemes and sizes on their quality. Numeric properties of libraries, such as the expected number of different peptides and the library's coverage, have long been in use as measures of a library's quality. Here, we present a graphical framework of these measures together with a library's relative efficiency to help to describe libraries in enough detail for researchers to plan new experiments in a more informed manner. In particular, these values allow us to answer-in a probabilistic fashion-the question of whether a specific library does indeed contain one of the "best" possible peptides. The framework is implemented in a web-interface based on two packages, discreteRV and peptider, to the statistical software environment R. We further provide a user-friendly web-interface called PeLiCa (Peptide Library Calculator, http://www.pelica.org), allowing scientists to plan and analyse their peptide libraries.

Probabilistic methods in directed evolution: library size, mutation rate, and diversity

Directed evolution has emerged as an important tool for engineering proteins with improved or novel properties. Because of their inherent reliance on randomness, directed evolution protocols are amenable to probabilistic modeling and analysis. This chapter summarizes and reviews in a nonmathematical way some of the probabilistic works related to directed evolution, with particular focus on three of the most widely used methods: saturation mutagenesis, error-prone PCR, and in vitro recombination. The ultimate aim is to provide the reader with practical information to guide the planning and design of directed evolution studies. Importantly, the applications and locations of freely available computational resources to assist with this process are described in detail.

A highly scalable peptide-based assay system for proteomics

We report a scalable and cost-effective technology for generating and screening high-complexity customizable peptide sets. The peptides are made as peptide-cDNA fusions by in vitro transcription/translation from pools of DNA templates generated by microarray-based synthesis. This approach enables large custom sets of peptides to be designed in silico, manufactured cost-effectively in parallel, and assayed efficiently in a multiplexed fashion. The utility of our peptide-cDNA fusion pools was demonstrated in two activity-based assays designed to discover protease and kinase substrates. In the protease assay, cleaved peptide substrates were separated from uncleaved and identified by digital sequencing of their cognate cDNAs. We screened the 3,011 amino acid HCV proteome for susceptibility to cleavage by the HCV NS3/4A protease and identified all 3 known trans cleavage sites with high specificity. In the kinase assay, peptide substrates phosphorylated by tyrosine kinases were captured and identified by sequencing of their cDNAs. We screened a pool of 3,243 peptides against Abl kinase and showed that phosphorylation events detected were specific and consistent with the known substrate preferences of Abl kinase. Our approach is scalable and adaptable to other protein-based assays.

When second best is good enough: another probabilistic look at saturation mutagenesis

We developed new criteria for determining the library size in a saturation mutagenesis experiment. When the number of all possible distinct variants is large, any of the top-performing variants (e.g., any of the top three) is likely to meet the design requirements, so the probability that the library contains at least one of them is a sensible criterion for determining the library size. By using a criterion of this type, one may significantly reduce the library size and thus save costs and labor while minimally compromising the quality of the best variant discovered. We present the probabilistic tools underlying these criteria and use them to compare the efficiencies of four randomization schemes: NNN, which uses all 64 codons; NNB, which uses 48 codons; NNK, which uses 32 codons; and MAX, which assigns equal probabilities to each of the 20 amino acids. MAX was found to be the most efficient randomization scheme and NNN the least efficient. TopLib, a computer program for carrying out the related calculations, is available through a user-friendly Web server.