Crystallization of Escherichia coli Catabolite Gene Activator Protein with its DNA Binding Site: The use of Modular DNA

To obtain crystals of the Escherichia coli catabolite gene activator protein (CAP) complexed with its DNA-binding site, we have searched for crystallization conditions with 26 different DNA segments ≥28 base-pairs in length that explore a variety of nucleotide sequences, lengths, and extended 5′ or 3′ termini. In addition to utilizing uninterrupted asymmetric lac site sequences, we devised a novel approach of synthesizing half-sites that allowed us to efficiently generate symmetric DNA segments with a wide variety of extended termini and lengths in the large size range (≥28 bp) required by this protein. We report three crystal forms that are suitable for X-ray analysis, one of which (crystal form III) gives measurable diffraction amplitudes to 3 Å resolution. Additives such as calcium, n-octyl-β-d-glucopyranoside and spermine produce modest improvements in the quality of diffraction from crystal form III. Adequate stabilization of crystal form III is unexpectedly complex, requiring a greater than tenfold reduction in the salt concentration followed by addition of 2-methyl-2,4-pentanediol and then an increase in the concentration of polyethylene glycol.

Frequent Arousal from Hibernation Linked to Severity of Infection and Mortality in Bats with White-Nose Syndrome

White-nose syndrome (WNS), an emerging infectious disease that has killed over 5.5 million hibernating bats, is named for the causative agent, a white fungus (Geomyces destructans (Gd)) that invades the skin of torpid bats. During hibernation, arousals to warm (euthermic) body temperatures are normal but deplete fat stores. Temperature-sensitive dataloggers were attached to the backs of 504 free-ranging little brown bats (Myotis lucifugus) in hibernacula located throughout the northeastern USA. Dataloggers were retrieved at the end of the hibernation season and complete profiles of skin temperature data were available from 83 bats, which were categorized as: (1) unaffected, (2) WNS-affected but alive at time of datalogger removal, or (3) WNS-affected but found dead at time of datalogger removal. Histological confirmation of WNS severity (as indexed by degree of fungal infection) as well as confirmation of presence/absence of DNA from Gd by PCR was determined for 26 animals. We demonstrated that WNS-affected bats aroused to euthermic body temperatures more frequently than unaffected bats, likely contributing to subsequent mortality. Within the subset of WNS-affected bats that were found dead at the time of datalogger removal, the number of arousal bouts since datalogger attachment significantly predicted date of death. Additionally, the severity of cutaneous Gd infection correlated with the number of arousal episodes from torpor during hibernation. Thus, increased frequency of arousal from torpor likely contributes to WNS-associated mortality, but the question of how Gd infection induces increased arousals remains unanswered.

Decomposing Blaschke Products And Polynomials

The goal of this paper is to contribute to the understanding of complex polynomials and Blaschke products, two very important function classes in mathematics. For a polynomial, $f,$ of degree $n,$ we study when it is possible to write $f$ as a composition $f=g\circ h$, where $g$ and $h$ are polynomials, each of degree less than $n.$ A polynomial is defined to be \emph{decomposable }if such an $h$ and $g$ exist, and a polynomial is said to be \emph{indecomposable} if no such $h$ and $g$ exist. We apply the results of Rickards in \cite{key-2}. We show that $$C_{n}=\{(z_{1},z_{2},...,z_{n})\in\mathbb{C}^{n}\,|\,(z-z_{1})(z-z_{2})...(z-z_{n})\,\mbox{is decomposable}\},$$ has measure $0$ when considered a subset of $\mathbb{R}^{2n}.$ Using this we prove the stronger result that $$D_{n}=\{(z_{1},z_{2},...,z_{n})\in\mathbb{C}^{n}\,|\,\mbox{There exists\,}a\in\mathbb{C}\,\,\mbox{with}\,\,(z-z_{1})(z-z_{2})...(z-z_{n})(z-a)\,\mbox{decomposable}\},$$ also has measure zero when considered a subset of $\mathbb{R}^{2n}.$ We show that for any polynomial $p$, there exists an $a\in\mathbb{C}$ such that $p(z)(z-a)$ is indecomposable, and we also examine the case of $D_{5}$ in detail. The main work of this paper studies finite Blaschke products, analytic functions on $\overline{\mathbb{D}}$ that map $\partial\mathbb{D}$ to $\partial\mathbb{D}.$ In analogy with polynomials, we discuss when a degree $n$ Blaschke product, $B,$ can be written as a composition $C\circ D$, where $C$ and $D$ are finite Blaschke products, each of degree less than $n.$ Decomposable and indecomposable are defined analogously. Our main results are divided into two sections. First, we equate a condition on the zeros of the Blaschke product with the existence of a decomposition where the right-hand factor, $D,$ has degree $2.$ We also equate decomposability of a Blaschke product, $B,$ with the existence of a Poncelet curve, whose foci are a subset of the zeros of $B,$ such that the Poncelet curve satisfies certain tangency conditions. This result is hard to apply in general, but has a very nice geometric interpretation when we desire a composition where the right-hand factor is degree 2 or 3. Our second section of finite Blaschke product results builds off of the work of Cowen in \cite{key-3}. For a finite Blaschke product $B,$ Cowen defines the so-called monodromy group, $G_{B},$ of the finite Blaschke product. He then equates the decomposability of a finite Blaschke product, $B,$ with the existence of a nontrivial partition, $\mathcal{P},$ of the branches of $B^{-1}(z),$ such that $G_{B}$ respects $\mathcal{P}$. We present an in-depth analysis of how to calculate $G_{B}$, extending Cowen's description. These methods allow us to equate the existence of a decomposition where the left-hand factor has degree 2, with a simple condition on the critical points of the Blaschke product. In addition we are able to put a condition of the structure of $G_{B}$ for any decomposable Blaschke product satisfying certain normalization conditions. The final section of this paper discusses how one can put the results of the paper into practice to determine, if a particular Blaschke product is decomposable. We compare three major algorithms. The first is a brute force technique where one searches through the zero set of $B$ for subsets which could be the zero set of $D$, exhaustively searching for a successful decomposition $B(z)=C(D(z)).$ The second algorithm involves simply examining the cardinality of the image, under $B,$ of the set of critical points of $B.$ For a degree $n$ Blaschke product, $B,$ if this cardinality is greater than $\frac{n}{2}$, the Blaschke product is indecomposable. The final algorithm attempts to apply the geometric interpretation of decomposability given by our theorem concerning the existence of a particular Poncelet curve. The final two algorithms can be implemented easily with the use of an HTML