Neighborhoods of Starlike and Convex Functions Associated with Parabola

Let f be a normalized analytic function defined on the unit disk and fλ(z):=(1−λ)z+λf(z) for 00, a function f∈ðÂ’®ðÂ’«(α,λ) if zf′(z)/fλ(z) lies in the parabolic region Ω:={w:|w−α|0, the δ-neighbourhood of a function f∈ðÂ’žðÂ’«(α,λ) is shown to consist of functions in the class ðÂ’®ðÂ’«(α,λ)

Directed evolution of a magnetic resonance imaging contrast agent for noninvasive imaging of dopamine

The development of molecular probes that allow in vivo imaging of neural signaling processes with high temporal and spatial resolution remains challenging. Here we applied directed evolution techniques to create magnetic resonance imaging (MRI) contrast agents sensitive to the neurotransmitter dopamine. The sensors were derived from the heme domain of the bacterial cytochrome P450-BM3 (BM3h). Ligand binding to a site near BM3h's paramagnetic heme iron led to a drop in MRI signal enhancement and a shift in optical absorbance. Using an absorbance-based screen, we evolved the specificity of BM3h away from its natural ligand and toward dopamine, producing sensors with dissociation constants for dopamine of 3.3–8.9 μM. These molecules were used to image depolarization-triggered neurotransmitter release from PC12 cells and in the brains of live animals. Our results demonstrate the feasibility of molecular-level functional MRI using neural activity–dependent sensors, and our protein engineering approach can be generalized to create probes for other targets.Charles A. Dana Foundation. Brain and Immuno-ImagingRaymond and Beverley Sackler FoundationNational Institutes of Health (U.S.) (grant R01-DA28299)National Institutes of Health (U.S.) (grant DP2-OD2441)National Institutes of Health (U.S.) (grant R01-GM068664)Jacobs Institute for Molecular Engineering for Medicine. Jacobs Institute for Molecular Engineering for MedicineNational Institutes of Health (U.S.) (grant R01-DE013023

Interfering with Glycolysis Causes Sir2-Dependent Hyper-Recombination of Saccharomyces cerevisiae Plasmids

Glyceraldehyde-3-phosphate dehydrogenase (GAPDH) is a key metabolic regulator implicated in a variety of cellular processes. It functions as a glycolytic enzyme, a protein kinase, and a metabolic switch under oxidative stress. Its enzymatic inactivation causes a major shift in the primary carbohydrate flux. Furthermore, the protein is implicated in regulating transcription, ER-to-Golgi transport, and apoptosis. We found that Saccharomyces cerevisiae cells null for all GAPDH paralogues (Tdh1, Tdh2, and Tdh3) survived the counter-selection of a GAPDH–encoding plasmid when the NAD+ metabolizing deacetylase Sir2 was overexpressed. This phenotype required a fully functional copy of SIR2 and resulted from hyper-recombination between S. cerevisiae plasmids. In the wild-type background, GAPDH overexpression increased the plasmid recombination rate in a growth-condition dependent manner. We conclude that GAPDH influences yeast episome stability via Sir2 and propose a model for the interplay of Sir2, GAPDH, and the glycolytic flux

Convolution Properties of Classes of Analytic and Meromorphic Functions

General classes of analytic functions defined by convolution with a fixed analytic function are introduced. Convolution properties of these classes which include the classical classes of starlike, convex, close-to-convex, and quasiconvex analytic functions are investigated. These classes are shown to be closed under convolution with prestarlike functions and the Bernardi-Libera integral operator. Similar results are also obtained for the classes consisting of meromorphic functions in the punctured unit disk.</p

Neighborhoods of Starlike and Convex Functions Associated with Parabola

<p>Abstract</p> <p>Let <inline-formula> <graphic file="1029-242X-2008-346279-i1.gif"/></inline-formula> be a normalized analytic function defined on the unit disk and <inline-formula> <graphic file="1029-242X-2008-346279-i2.gif"/></inline-formula> for <inline-formula> <graphic file="1029-242X-2008-346279-i3.gif"/></inline-formula>. For <inline-formula> <graphic file="1029-242X-2008-346279-i4.gif"/></inline-formula>, a function <inline-formula> <graphic file="1029-242X-2008-346279-i5.gif"/></inline-formula> if <inline-formula> <graphic file="1029-242X-2008-346279-i6.gif"/></inline-formula> lies in the parabolic region <inline-formula> <graphic file="1029-242X-2008-346279-i7.gif"/></inline-formula>. Let <inline-formula> <graphic file="1029-242X-2008-346279-i8.gif"/></inline-formula> be the corresponding class consisting of functions <inline-formula> <graphic file="1029-242X-2008-346279-i9.gif"/></inline-formula> such that <inline-formula> <graphic file="1029-242X-2008-346279-i10.gif"/></inline-formula> lies in the region <inline-formula> <graphic file="1029-242X-2008-346279-i11.gif"/></inline-formula>. For an appropriate <inline-formula> <graphic file="1029-242X-2008-346279-i12.gif"/></inline-formula>, the <inline-formula> <graphic file="1029-242X-2008-346279-i13.gif"/></inline-formula>-neighbourhood of a function <inline-formula> <graphic file="1029-242X-2008-346279-i14.gif"/></inline-formula> is shown to consist of functions in the class <inline-formula> <graphic file="1029-242X-2008-346279-i15.gif"/></inline-formula>.</p

Cholesterol promotes Cytolysin A activity by stabilizing the intermediates during pore formation

Pore-forming toxins (PFTs) form nanoscale pores across target membranes causing cell death. Cytolysin A (ClyA) from Escherichia coli is a prototypical alpha-helical toxin that contributes to cytolytic phenotype of several pathogenic strains. It is produced as a monomer and, upon membrane exposure, undergoes conformational changes and finally oligomerizes to form a dodecameric pore, thereby causing ion imbalance and finally cell death. However, our current understanding of this assembly process is limited to studies in detergents, which do not capture the physicochemical properties of biological membranes. Here, using single-molecule imaging and molecular dynamics simulations, we study the ClyA assembly pathway on phospholipid bilayers. We report that cholesterol stimulates pore formation, not by enhancing initial ClyA binding to the membrane but by selectively stabilizing a protomer-like conformation. This was mediated by specific interactions by cholesterol-interacting residues in the N-terminal helix. Additionally, cholesterol stabilized the oligomeric structure using bridging interactions in the protomer-protomer interfaces, thereby resulting in enhanced ClyA oligomerization. This dual stabilization of distinct intermediates by cholesterol suggests a possible molecular mechanism by which ClyA achieves selective membrane rupture of eukaryotic cell membranes. Topological similarity to eukaryotic membrane proteins suggests evolution of a bacterial alpha-toxin to adopt eukaryotic motifs for its activation. Broad mechanistic correspondence between pore-forming toxins hints at a wider prevalence of similar protein membrane insertion mechanisms