Installing hydrolytic activity into a completely <i>de novo </i>protein framework

The design of enzyme-like catalysts tests our understanding of sequence-to-structure/function relationships in proteins. Here we install hydrolytic activity predictably into a completely de novo and thermostable α-helical barrel, which comprises seven helices arranged around an accessible channel. We show that the lumen of the barrel accepts 21 mutations to functional polar residues. The resulting variant, which has cysteine–histidine–glutamic acid triads on each helix, hydrolyses p-nitrophenyl acetate with catalytic efficiencies that match the most-efficient redesigned hydrolases based on natural protein scaffolds. This is the first report of a functional catalytic triad engineered into a de novo protein framework. The flexibility of our system also allows the facile incorporation of unnatural side chains to improve activity and probe the catalytic mechanism. Such a predictable and robust construction of truly de novo biocatalysts holds promise for applications in chemical and biochemical synthesis

Quantitative Convergence Assessment for MCMC via CUSUMS

Yu (1995) provides a novel convergence diagnostic for MCMC which provides a qualitative measure of mixing for Markov chains via a cusum path plot for univariate parameters of interest. The method is based upon the output of a single replication of an MCMC sampler and is therefore widely applicable and simple to use. One criticism of the method is that it is subjective in its interpretation, since it is based upon a graphical comparison of two cusum path plots. In this paper, we develop a quantitative measure of smoothness which we can associate with any given cusum path, and show how we can use this measure to obtain a quantitative measure of mixing. In particular, we derive the large sample distribution of this smoothness measure, so that objective inference is possible. In addition, we show how this quantitative measure may also be used to provide an estimate of the burn-in length for any given sampler. We discuss the utility of this quantitative approach, and highlight a problem whi..