SCHEMA Recombination of a Fungal Cellulase Uncovers a Single Mutation That Contributes Markedly to Stability

A quantitative linear model accurately (R^2 = 0.88) describes the thermostabilities of 54 characterized members of a family of fungal cellobiohydrolase class II (CBH II) cellulase chimeras made by SCHEMA recombination of three fungal enzymes, demonstrating that the contributions of SCHEMA sequence blocks to stability are predominantly additive. Thirty-one of 31 predicted thermostable CBH II chimeras have thermal inactivation temperatures higher than the most thermostable parent CBH II, from Humicola insolens, and the model predicts that hundreds more CBH II chimeras share this superior thermostability. Eight of eight thermostable chimeras assayed hydrolyze the solid cellulosic substrate Avicel at temperatures at least 5 °C above the most stable parent, and seven of these showed superior activity in 16-h Avicel hydrolysis assays. The sequence-stability model identified a single block of sequence that adds 8.5 °C to chimera thermostability. Mutating individual residues in this block identified the C313S substitution as responsible for the entire thermostabilizing effect. Introducing this mutation into the two recombination parent CBH IIs not featuring it (Hypocrea jecorina and H. insolens) decreased inactivation, increased maximum Avicel hydrolysis temperature, and improved long time hydrolysis performance. This mutation also stabilized and improved Avicel hydrolysis by Phanerochaete chrysosporium CBH II, which is only 55–56% identical to recombination parent CBH IIs. Furthermore, the C313S mutation increased total H. jecorina CBH II activity secreted by the Saccharomyces cerevisiae expression host more than 10-fold. Our results show that SCHEMA structure-guided recombination enables quantitative prediction of cellulase chimera thermostability and efficient identification of stabilizing mutations

Tre1 GPCR initiates germ cell transepithelial migration by regulating Drosophila melanogaster E-cadherin

Despite significant progress in identifying the guidance pathways that control cell migration, how a cell starts to move within an intact organism, acquires motility, and loses contact with its neighbors is poorly understood. We show that activation of the G protein–coupled receptor (GPCR) trapped in endoderm 1 (Tre1) directs the redistribution of the G protein Gβ as well as adherens junction proteins and Rho guanosine triphosphatase from the cell periphery to the lagging tail of germ cells at the onset of Drosophila melanogaster germ cell migration. Subsequently, Tre1 activity triggers germ cell dispersal and orients them toward the midgut for directed transepithelial migration. A transition toward invasive migration is also a prerequisite for metastasis formation, which often correlates with down-regulation of adhesion proteins. We show that uniform down-regulation of E-cadherin causes germ cell dispersal but is not sufficient for transepithelial migration in the absence of Tre1. Our findings therefore suggest a new mechanism for GPCR function that links cell polarity, modulation of cell adhesion, and invasion

On the Fekete-Szeg\"o problem for concave univalent functions

We consider the Fekete-Szeg\"o problem with real parameter $\lambda$ for the class $Co(\alpha)$ of concave univalent functions.Comment: 9 page

Partial Consistency with Sparse Incidental Parameters

Penalized estimation principle is fundamental to high-dimensional problems. In the literature, it has been extensively and successfully applied to various models with only structural parameters. As a contrast, in this paper, we apply this penalization principle to a linear regression model with a finite-dimensional vector of structural parameters and a high-dimensional vector of sparse incidental parameters. For the estimators of the structural parameters, we derive their consistency and asymptotic normality, which reveals an oracle property. However, the penalized estimators for the incidental parameters possess only partial selection consistency but not consistency. This is an interesting partial consistency phenomenon: the structural parameters are consistently estimated while the incidental ones cannot. For the structural parameters, also considered is an alternative two-step penalized estimator, which has fewer possible asymptotic distributions and thus is more suitable for statistical inferences. We further extend the methods and results to the case where the dimension of the structural parameter vector diverges with but slower than the sample size. A data-driven approach for selecting a penalty regularization parameter is provided. The finite-sample performance of the penalized estimators for the structural parameters is evaluated by simulations and a real data set is analyzed

Non-Hermitian time-dependent perturbation theory: asymmetric transitions and transitionless interactions

The ordinary time-dependent perturbation theory of quantum mechanics, that describes the interaction of a stationary system with a time-dependent perturbation, predicts that the transition probabilities induced by the perturbation are symmetric with respect to the initial an final states. Here we extend time-dependent perturbation theory into the non-Hermitian realm and consider the transitions in a stationary Hermitian system, described by a self-adjoint Hamiltonian $\hat{H}_0$, induced by a time-dependent non-Hermitian interaction $f(t) \hat{P}$. In the weak interaction (perturbative) limit, the transition probabilities generally turn out to be {\it asymmetric} for exchange of initial and final states. In particular, for a temporal shape $f(t)$ of the perturbation with one-sided Fourier spectrum, i.e. with only positive (or negative) frequency components, transitions are fully unidirectional, a result that holds even in the strong interaction regime. Interestingly, we show that non-Hermitian perturbations can be tailored to be transitionless, i.e. the perturbation leaves the system unchanged as if the interaction had not occurred at all, regardless the form of $\hat{H}_0$ and $\hat{P}$. As an application of the results, we discuss asymmetric (chiral) behavior of dynamical encircling of an exceptional point in a two- and three-level system.Comment: final version, to appear in Annals of Physic

Self-trapping transition for nonlinear impurities embedded in a Cayley tree

The self-trapping transition due to a single and a dimer nonlinear impurity embedded in a Cayley tree is studied. In particular, the effect of a perfectly nonlinear Cayley tree is considered. A sharp self-trapping transition is observed in each case. It is also observed that the transition is much sharper compared to the case of one-dimensional lattices. For each system, the critical values of $\chi$ for the self-trapping transitions are found to obey a power-law behavior as a function of the connectivity $K$ of the Cayley tree.Comment: 6 pages, 7 fig