On Smarandache's form of the individual Fermat-Euler theorem

In the paper it is shown how a form of the classical FERMAT-EULER Theorem discovered by F. SMARANDACHE fits into the generalizations found by S.SCHWARZ, M.LASSAK and the author. Then we show how SMARANDACHE'S algorithm can be used to effective computations of the so called group membership

A TALE OF TWO ENZYMES: IDENTIFICATION OF AN UNKNOWN LIGAND BOUND TO CYTOCHROME P450 2A13 AND UNDERSTANDING SUBSTRATE SELECTIVITY OF CYTOCHROME P450 2E1

Cytochrome P450 (CYP) is the predominate superfamily of enzymes responsible for Phase I metabolism of drugs and other xenobiotics. Understanding the structural reasons for the substrate selectivity of these enzymes is important for both pharmacological and toxicological reasons. Two isoforms of interest from this enzyme superfamily that are CYP2A13 and CYP2E1. Cytochrome P450 2A13 (CYP2A13) is a lung specific enzyme known to activate the potent tobacco procarcinogen 4-(methylnitrosamino)-1-(3-pyridyl)-1-butanone (NNK) into two carcinogenic metabolites. CYP2A13 has been crystallized and X-ray diffraction experiments illuminated the structure of this enzyme, but with an unknown ligand present in the enzyme active site. This unknown ligand was suspected to be indole but a selective method had to be developed to differentiate among indole and its metabolites in the protein sample. We successfully modified a microbiological colorimetric assay to spectrophotometrically differentiate between indole and a number of possible indole metabolites in nanomolar concentrations by derivatization with p-dimethylaminocinnamaldehyde (DMACA). Further differentiation of indoles was made by mass spectrometry (HPLC-UV/vis-MS/MS) utilizing the chromophore generated in the DMACA conjugation as a UV signature for HPLC detection. The ligand in the crystallized protein was unambiguously identified as unsubstituted indole, which facilitated refinement of two alternate conformations of indole in the CYP2A13 crystal structure active site. Human cytochrome P450 2E1 (CYP2E1) is a xenobiotic metabolizing enzyme that is highly conserved among mammals. In addition to small molecular weight exogenous drugs like the analgesic acetaminophen and the volatile anesthetic halothane, CYP2E1 is also involved in endogenous fatty acid metabolism. To more fully understand the structural factors that contribute to the substrate selectivity of CYP2E1, it has been cocrystallized with two structurally different heme-binding compounds: indazole, a small molecular weight inhibitor and ω-imidazolyl-decanoic acid, a fatty acid analog. Comparison of the CYP2E1 structures shows that only small side chain movements are required for the accommodation of the much larger fatty acid analog. Rotation of the side chain of F298 causes a change in the active site volume from 190 Å3 in the indazole-bound structure to 440 Å3 in the ω-imidazolyl-decanoic acid-bound structure. Future work will be focused on cocrystal structures of CYP2E1 with both longer and shorter chain analogs to better understand the ability of the enzyme to metabolize a variety of fatty acids substrates

Structural comparison of cytochromes P450 2A6, 2A13, and 2E1 with pilocarpine†

This is the peer reviewed version of the following article: DeVore, N. M., Meneely, K. M., Bart, A. G., Stephens, E. S., Battaile, K. P. and Scott, E. E. (2012), Structural comparison of cytochromes P450 2A6, 2A13, and 2E1 with pilocarpine. FEBS Journal, 279: 1621–1631. doi:10.1111/j.1742-4658.2011.08412.x, which has been published in final form at http://doi.org/10.1111/j.1742-4658.2011.08412.x. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.Human xenobiotic-metabolizing cytochrome P450 (P450) enzymes can each bind and monooxygenate a diverse set of substrates, including drugs, often producing a variety of metabolites. Additionally a single ligand can interact with multiple cytochrome P450 enzymes, but often the protein structural similarities and differences that mediate such overlapping selectivity are not well understood. Even though the P450 superfamily has a highly canonical global protein fold, there are large variations in the active site size, topology, and conformational flexibility. We have determined how a related set of three human cytochrome P450 enzymes bind and interact with a common inhibitor, the muscarinic receptor agonist drug pilocarpine. Pilocarpine binds and inhibits the hepatic CYP2A6 and respiratory CYP2A13 enzymes much more efficiently than the hepatic CYP2E1 enzyme. To elucidate key amino acids involved in pilocarpine binding, crystal structures of CYP2A6 (2.4 Å), CYP2A13 (3.0 Å), CYP2E1 (2.35 Å), and a CYP2A6 mutant enzyme, CYP2A6 I208S/I300F/G301A/S369G (2.1 Å), have been determined with pilocarpine in the active site. In all four structures, pilocarpine coordinates to the heme iron, but comparisons reveal how individual amino acids lining the active sites of these three distinct human enzymes interact differently with the inhibitor pilocarpine. HYPERLINKING TO DATABASES: The atomic coordinates and structure factors have been deposited in the Protein Data Bank, Research Collaboratory for Structural Bioinformatics, Rutgers University, New Brunswick, NJ (http://www.rcsb.org/) with the following codes: CYP2A6 with pilocarpine (3T3R), CYP2A6 I208S/I300F/G301A/S369G with pilocarpine (3T3Q), CYP2A13 with pilocarpine (3T3S), and CYP2E1 with pilocarpine (3T3Z)

A Unified Dynamic Programming Framework for the Analysis of Interacting Nucleic Acid Strands: Enhanced Models, Scalability, and Speed

Dynamic programming algorithms within the NUPACK software suite enable analysis of nucleic acid sequences over complex and test tube ensembles containing arbitrary numbers of interacting strand species, serving the needs of researchers in molecular programming, nucleic acid nanotechnology, synthetic biology, and across the life sciences. Here, to enhance the underlying physical model, ensure scalability for large calculations, and achieve dramatic speedups when calculating diverse physical quantities over complex and test tube ensembles, we introduce a unified dynamic programming framework that combines three ingredients: (1) recursions that specify the dependencies between subproblems and incorporate the details of the structural ensemble and the free energy model, (2) evaluation algebras that define the mathematical form of each subproblem, (3) operation orders that specify the computational trajectory through the dependency graph of subproblems. The physical model is enhanced using new recursions that operate over the complex ensemble including coaxial and dangle stacking subensembles. The recursions are coded generically and then compiled with a quantity-specific evaluation algebra and operation order to generate an executable for each physical quantity: partition function, equilibrium base-pairing probabilities, MFE energy and proxy structure, suboptimal proxy structures, and Boltzmann sampled structures. For large complexes (e.g., 30 000 nt), scalability is achieved for partition function calculations using an overflow-safe evaluation algebra, and for equilibrium base-pairing probabilities using a backtrack-free operation order. A new blockwise operation order that treats subcomplex blocks for the complex species in a test tube ensemble enables dramatic speedups (e.g., 20–120× ) using vectorization and caching. With these performance enhancements, equilibrium analysis of substantial test tube ensembles can be performed in ≤ 1 min on a single computational core (e.g., partition function and equilibrium concentration for all complex species of up to six strands formed from two strand species of 300 nt each, or for all complex species of up to two strands formed from 80 strand species of 100 nt each). A new sampling algorithm simultaneously samples multiple structures from the complex ensemble to yield speedups of an order of magnitude or more as the number of structures increases above ≈10³. These advances are available within the NUPACK 4.0 code base (www.nupack.org) which can be flexibly scripted using the all-new NUPACK Python module

Enhanced Algorithms for Analysis and Design of Nucleic Acid Reaction Pathways

Nucleic acids provide a powerful platform for programming at the molecular level. This is possible because the free energy of nucleic acid structures is dominated by the local interactions of base pairing and base pair stacking. The nearest neighbor secondary structure model implied by these energetics has enabled development of a set of algorithms for calculating thermodynamic quantities of nucleic acid sequences. Molecular programmers and synthetic biologists continue to extend their reach to larger, more complicated nucleic acid complexes, reaction pathways, and systems. This necessitates a focus on new algorithm development and efficient implementations to enable analysis and design of such systems. Concerning analysis of nucleic acids, we collect seemingly diverse algorithms under a unified three-component dynamic programming framework consisting of: 1) recursions that specify the dependencies between subproblems and incorporate the details of the structural ensemble and the free energy model, 2) evaluation algebras that define the mathematical form of each subproblem, 3) operation orders that specify the computational trajectory through the dependency graph of subproblems. Changes to the set of recursions allows operation over the complex ensemble including coaxial and dangle stacking states, affecting all thermodynamic quantities. An updated operation order for structure sampling allows simultaneous generation of a set of structures sampled from the Boltzmann distribution in time that scales empirically sublinearly in the number of samples and leads to an order of magnitude or more speedup over repeated single-structure sampling. For the problem of sequence design for reaction pathway engineering, we introduce an optimization algorithm to minimize the multitstate test tube ensemble defect, which simultaneously designs for reactant, intermediate, and product states along the reaction pathway (positive design) and against crosstalk interactions (negative design). Each of these on-pathway or crosstalk states is represented as a target test tube ensemble containing arbitrary numbers of on-target complexes, each with a target secondary structure and target concentration, and arbitrary numbers of off-target complexes, each with vanishing target concentration. Our test tube specification formalism enables conversion of a reaction pathway specification into a set of target test tubes. Sequences are designed subject to a set of hard constraints allowing specification of properties such as sequence composition, sequence complementarity, prevention of unwanted sequence patterns, and inclusion of biological sequences. We then extend this algorithm with soft constraints, enhancing flexibility through new constraint types and reducing design cost by up to two orders of magnitude in the most highly constrained cases. These soft constraints enable multiobjective design of the multitstate test tube ensemble defect simultaneously with heuristics for avoiding kinetic traps and equalizing reaction rates to further aid reaction pathway engineering.</p

Occult solitary submucosal jejunal metastasis from esophageal carcinoma

BACKGROUND: Metastatic tumors of the intestinal tract from extra-abdominal sites are rare. In esophageal cancer, the liver, lung and the bones are the most common sites of metastases. Metastasis to intestines are very rare. CASE PRESENTATION: A 54-year old male was admitted with esophageal squamous cell carcinoma (SCC) associated with dysphagia II-III and weight loss of 20 kg. Preoperative routine staging failed to detect any metastases. A transthoracic esophagectomy and orthotopic gastric pull-up with collar esophago-gastrostomy, associated with 2-field lymphadenectomy was perfromed. During the digital placement of the naso-jejunal feeding catheter a submucosal jejunal nodule with a diameter of 1 cm, about 40 cm distal to the duodeno-jejunal fold was detected which was completely resected by jejunotomy. Histopathology of jejunal nodule showed metastasis from esophageal squamous cell carcinoma. CONCLUSION: Because of the extensic esophageal lymphatic system, an occult widespread dissemination of the tumor cells into the abdominal cavity is possible. Additional intraoperative evaluation of the small intestine and the complete abdominal cavity should be performed in every operation of esophageal carcinoma to detect possible occult intraabdominal metastases

Constrained Multistate Sequence Design for Nucleic Acid Reaction Pathway Engineering

We describe a framework for designing the sequences of multiple nucleic acid strands intended to hybridize in solution via a prescribed reaction pathway. Sequence design is formulated as a multistate optimization problem using a set of target test tubes to represent reactant, intermediate, and product states of the system, as well as to model crosstalk between components. Each target test tube contains a set of desired “on-target” complexes, each with a target secondary structure and target concentration, and a set of undesired “off-target” complexes, each with vanishing target concentration. Optimization of the equilibrium ensemble properties of the target test tubes implements both a positive design paradigm, explicitly designing for on-pathway elementary steps, and a negative design paradigm, explicitly designing against off-pathway crosstalk. Sequence design is performed subject to diverse user-specified sequence constraints including composition constraints, complementarity constraints, pattern prevention constraints, and biological constraints. Constrained multistate sequence design facilitates nucleic acid reaction pathway engineering for diverse applications in molecular programming and synthetic biology. Design jobs can be run online via the NUPACK web application

breakpointR:an R/Bioconductor package to localize strand state changes in Strand-seq data

MOTIVATION: Strand-seq is a specialized single-cell DNA sequencing technique centered around the directionality of single-stranded DNA. Computational tools for Strand-seq analyses must capture the strand-specific information embedded in these data. RESULTS: Here we introduce breakpointR, an R/Bioconductor package specifically tailored to process and interpret single-cell strand-specific sequencing data obtained from Strand-seq. We developed breakpointR to detect local changes in strand directionality of aligned Strand-seq data, to enable fine-mapping of sister chromatid exchanges, germline inversion and to support global haplotype assembly. Given the broad spectrum of Strand-seq applications we expect breakpointR to be an important addition to currently available tools and extend the accessibility of this novel sequencing technique. AVAILABILITY: R/Bioconductor package https://bioconductor.org/packages/breakpointR

The Role of Probiotics in Acne and Rosacea

Through basic science as well as animal and human clinical trials, the evidence is growing for the use of probiotics in the treatment of acne. Acne formation is dependent upon several processes, including follicular hyperkeratinization, excess sebum production, Propionibacterium acnes colonization and an inflammatory cascade. The antimicrobial properties of probiotics as well as the modification of the skin microbiome may decrease levels of P. acnes on the skin. Additionally, successful acne outcomes are influenced by compliance with topical regimens, which can commonly cause skin barrier disruption, leading to dryness and irritation. Consequently, calming inflammation as well as maintaining skin hydration and barrier repair is of primary importance when treating acne. In this chapter, we discuss how probiotics affect several factors in the pathophysiology of acne development and can improve the treatment outcomes