A good presentation of (-2,3,2s+1)-type Pretzel knot group and R-covered foliation

Let K_s be a (-2,3,2s+1)-type Pretzel knot (s >= 3) and E(K_s)(p/q) be a closed manifold obtained by Dehn surgery along K_s with a slope p/q. We prove that if q>0, p/q >= 4s+7 and p is odd, then E(K_s)(p/q) cannot contain an R-covered foliation. This result is an extended theorem of a part of works of Jinha Jun for (-2,3,7)-Pretzel knot.Comment: 18 page

Connecting protein and mRNA burst distributions for stochastic models of gene expression

The intrinsic stochasticity of gene expression can lead to large variability in protein levels for genetically identical cells. Such variability in protein levels can arise from infrequent synthesis of mRNAs which in turn give rise to bursts of protein expression. Protein expression occurring in bursts has indeed been observed experimentally and recent studies have also found evidence for transcriptional bursting, i.e. production of mRNAs in bursts. Given that there are distinct experimental techniques for quantifying the noise at different stages of gene expression, it is of interest to derive analytical results connecting experimental observations at different levels. In this work, we consider stochastic models of gene expression for which mRNA and protein production occurs in independent bursts. For such models, we derive analytical expressions connecting protein and mRNA burst distributions which show how the functional form of the mRNA burst distribution can be inferred from the protein burst distribution. Additionally, if gene expression is repressed such that observed protein bursts arise only from single mRNAs, we show how observations of protein burst distributions (repressed and unrepressed) can be used to completely determine the mRNA burst distribution. Assuming independent contributions from individual bursts, we derive analytical expressions connecting means and variances for burst and steady-state protein distributions. Finally, we validate our general analytical results by considering a specific reaction scheme involving regulation of protein bursts by small RNAs. For a range of parameters, we derive analytical expressions for regulated protein distributions that are validated using stochastic simulations. The analytical results obtained in this work can thus serve as useful inputs for a broad range of studies focusing on stochasticity in gene expression

Promoting Essential Laminations

We show that every co--orientable taut foliation F of an orientable, atoroidal 3-manifold admits a transverse essential lamination. If this transverse lamination is a foliation G, the pair F,G are the unstable and stable foliation respectively of an Anosov flow. Otherwise, F admits a pair of transverse very full genuine laminations. In the second case, M satisfies the weak geometrization conjecture - either its fundamental group contains Z+Z or it is word-hyperbolic. Moreover, if M is atoroidal, the mapping class group of M is finite, and any automorphism homotopic to the identity is isotopic to the identity.Comment: 56 pages, 11 figures; version 3: final version, incorporates referee's suggestion

Protonation States of Remote Residues Affect Binding-Release Dynamics of the Ligand but not the Conformation of apo Ferric Binding Protein

We have studied the apo (Fe3+ free) form of periplasmic ferric binding protein (FbpA) under different conditions and we have monitored the changes in the binding and release dynamics of H2PO4- that acts as a synergistic anion in the presence of Fe3+. Our simulations predict a dissociation constant of 2.2$\pm$0.2 mM which is in remarkable agreement with the experimentally measured value of 2.3$\pm$0.3 mM under the same ionization strength and pH conditions. We apply perturbations relevant for changes in environmental conditions as (i) different values of ionic strength (IS), and (ii) protonation of a group of residues to mimic a different pH environment. Local perturbations are also studied by protonation or mutation of a site distal to the binding region that is known to mechanically manipulate the hinge-like motions of FbpA. We find that while the average conformation of the protein is intact in all simulations, the H2PO4- dynamics may be substantially altered by the changing conditions. In particular, the bound fraction which is 20$\%$ for the wild type system is increased to 50$\%$ with a D52A mutation/protonation and further to over 90$\%$ at the protonation conditions mimicking those at pH 5.5. The change in the dynamics is traced to the altered electrostatic distribution on the surface of the protein which in turn affects hydrogen bonding patterns at the active site. The observations are quantified by rigorous free energy calculations. Our results lend clues as to how the environment versus single residue perturbations may be utilized for regulation of binding modes in hFbpA systems in the absence of conformational changes.Comment: 26 pages, 4 figure

Lac repressor mediated DNA looping: Monte Carlo simulation of constrained DNA molecules complemented with current experimental results

Tethered particle motion (TPM) experiments can be used to detect time-resolved loop formation in a single DNA molecule by measuring changes in the length of a DNA tether. Interpretation of such experiments is greatly aided by computer simulations of DNA looping which allow one to analyze the structure of the looped DNA and estimate DNA-protein binding constants specific for the loop formation process. We here present a new Monte Carlo scheme for accurate simulation of DNA configurations subject to geometric constraints and apply this method to Lac repressor mediated DNA looping, comparing the simulation results with new experimental data obtained by the TPM technique. Our simulations, taking into account the details of attachment of DNA ends and fluctuations of the looped subsegment of the DNA, reveal the origin of the double-peaked distribution of RMS values observed by TPM experiments by showing that the average RMS value for anti-parallel loop types is smaller than that of parallel loop types. The simulations also reveal that the looping probabilities for the anti-parallel loop types are significantly higher than those of the parallel loop types, even for loops of length 600 and 900 base pairs, and that the correct proportion between the heights of the peaks in the distribution can only be attained when loops with flexible Lac repressor conformation are taken into account. Comparison of the in silico and in vitro results yields estimates for the dissociation constants characterizing the binding affinity between O1 and Oid DNA operators and the dimeric arms of the Lac repressor. © 2014 Biton et al

The Carmaphycins: New Proteasome Inhibitors Exhibiting an alpha,beta-Epoxyketone Warhead from a Marine Cyanobacterium

Two new peptidic proteasome inhibitors were isolated as trace components from a Curacao collection of the marine cyanobacterium Symploca sp. Carmaphycin A (1) and carmaphycin B (2) feature a leucine-derived a,beta-epoxyketone warhead directly connected to either methionine sulfoxide or methionine sulfone. Their structures were elucidated on the basis of extensive NMR and MS analyses and confirmed by total synthesis, which in turn provided more material for further biological evaluations. Pure carmaphycins A and B were found to inhibit the beta 5 subunit (chymotrypsin-like activity) of the S. cerevisiae 20S proteasome in the low nanomolar range. Additionally, they exhibited strong cytotoxicity to lung and colon cancer cell lines, as well as exquisite antiproliferative effects in the NCI60 cell-line panel. These assay results as well as initial structural biology studies suggest a distinctive binding mode for these new inhibitors.FAPESP (Brazil)NIH/NCI [CA100851, CA127622, GM61300