Directed enzyme evolution: climbing fitness peaks one amino acid at a time

Directed evolution can generate a remarkable range of new enzyme properties. Alternate substrate specificities and reaction selectivities are readily accessible in enzymes from families that are naturally functionally diverse. Activities on new substrates can be obtained by improving variants with broadened specificities or by step-wise evolution through a sequence of more and more challenging substrates. Evolution of highly specific enzymes has been demonstrated, even with positive selection alone. It is apparent that many solutions exist for any given problem, and there are often many paths that lead uphill, one step at a time

Engineering Enzyme Specificity Using Computational Design of a Defined-Sequence Library

Engineered biosynthetic pathways have the potential to produce high-value molecules from inexpensive feedstocks, but a key limitation is engineering enzymes with high activity and specificity for new reactions. Here, we developed a method for combining structure-based computational protein design with library-based enzyme screening, in which inter-residue correlations favored by the design are encoded into a defined-sequence library. We validated this approach by engineering a glucose 6-oxidase enzyme for use in a proposed pathway to convert D-glucose into D-glucaric acid. The most active variant, identified after only one round of diversification and screening of only 10,000 wells, is approximately 400-fold more active on glucose than is the wild-type enzyme. We anticipate that this strategy will be broadly applicable to the discovery of new enzymes for engineered biological pathways.United States. Office of Naval Research. Young Investigator Program (Grant N000140510656)National Science Foundation (U.S.) (Synthetic Biology Engineering Research Center. Grant EEC-0540879)MIT Faculty Start-up FundCodon Devices, Inc

Analytic urns

This article describes a purely analytic approach to urn models of the generalized or extended P\'olya-Eggenberger type, in the case of two types of balls and constant ``balance,'' that is, constant row sum. The treatment starts from a quasilinear first-order partial differential equation associated with a combinatorial renormalization of the model and bases itself on elementary conformal mapping arguments coupled with singularity analysis techniques. Probabilistic consequences in the case of ``subtractive'' urns are new representations for the probability distribution of the urn's composition at any time n, structural information on the shape of moments of all orders, estimates of the speed of convergence to the Gaussian limit and an explicit determination of the associated large deviation function. In the general case, analytic solutions involve Abelian integrals over the Fermat curve x^h+y^h=1. Several urn models, including a classical one associated with balanced trees (2-3 trees and fringe-balanced search trees) and related to a previous study of Panholzer and Prodinger, as well as all urns of balance 1 or 2 and a sporadic urn of balance 3, are shown to admit of explicit representations in terms of Weierstra\ss elliptic functions: these elliptic models appear precisely to correspond to regular tessellations of the Euclidean plane.Comment: Published at http://dx.doi.org/10.1214/009117905000000026 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org