Knot Theory: from Fox 3-colorings of links to Yang-Baxter homology and Khovanov homology

This paper is an extended account of my "Introductory Plenary talk at Knots in Hellas 2016" conference We start from the short introduction to Knot Theory from the historical perspective, starting from Heraclas text (the first century AD), mentioning R.Llull (1232-1315), A.Kircher (1602-1680), Leibniz idea of Geometria Situs (1679), and J.B.Listing (student of Gauss) work of 1847. We spend some space on Ralph H. Fox (1913-1973) elementary introduction to diagram colorings (1956). In the second section we describe how Fox work was generalized to distributive colorings (racks and quandles) and eventually in the work of Jones and Turaev to link invariants via Yang-Baxter operators, here the importance of statistical mechanics to topology will be mentioned. Finally we describe recent developments which started with Mikhail Khovanov work on categorification of the Jones polynomial. By analogy to Khovanov homology we build homology of distributive structures (including homology of Fox colorings) and generalize it to homology of Yang-Baxter operators. We speculate, with supporting evidence, on co-cycle invariants of knots coming from Yang-Baxter homology. Here the work of Fenn-Rourke-Sanderson (geometric realization of pre-cubic sets of link diagrams) and Carter-Kamada-Saito (co-cycle invariants of links) will be discussed and expanded. Dedicated to Lou Kauffman for his 70th birthday.Comment: 35 pages, 31 figures, for Knots in Hellas II Proceedings, Springer, part of the series Proceedings in Mathematics & Statistics (PROMS

Evaluation of antibiotics as a methodological procedure to inhibit free-living and biofilm bacteria in marine zooplankton culture

There is a problem with keeping culture medium completely or partially free from bacteria. The use of prokaryotic metabolic inhibitors, such as antibiotics, is suggested as an alternative solution, although such substances should not harm non-target organisms. Thus, the aim of this study was to assess the effectiveness of antibiotic treatments in inhibiting free-living and biofilm bacteria and their half-life in artificial marine environment using the copepod Acartia tonsa as bioindicador of non-harmful antibiotic combinations. Regarding to results, the application of 0.025 g L-1 penicillin G potassium + 0.08 g L-1 streptomycin sulphate + 0.04 g L-1 neomycin sulphate showed great potential for use in marine cultures and scientific experiments without lethal effects to non-target organisms. The effect of this combination starts within the first six hours of exposure and reduces up to 93 % the bacterial density, but the half-life is short, requiring replacement. No adverse changes in water quality were observed within 168 hours of exposure. As a conclusion, we can infer that this treatment was an effective procedure for zooplankton cultures and scientific experiments with the aim of measuring the role of free-living and biofilm in the marine community

Spatial and Temporal Hydrochemical Variation of a Third Order River Network in a Quasi Pristine Coastal Watershed, at Southern Bahia, Brazil

ABSTRACT Rio da Serra watershed presents well preserved fragments of rain forest at the headwaters and small farms at middle and final stretches. These features allowed the study of fluvial hydrochemistry, under quasi pristine conditions. Sampling stations were established in order to represent the basin, and visited during dry, intermediate and wet periods. Obtained results are: temperature (22.1 – 28.6 °C); electric conductivity (34 – 52 µS/cm); dissolved oxygen (35 – 110%); pH (3.8 – 7.7); total suspended solids (1.1 – 20 mg/L); chlorophyll (1.0 – 9.2 µg/L); total N (74 – 580 µmol/L); particulate N (60 – 550 µmol/L); N-NO3 (0.1 – 9.3 µmol/L); dissolved organic N (4 -70 µmol/L); total phosphorous (5.3 – 47 µmol/L); particulate P (4.4 – 59 µmol/L); P-PO4 (0.1 – 0.7 µmol/L); dissolved organic P (0.01 – 2.0 µmol/L); silicate (30 -90 µmol/L); fecal coliforms (80 – 700 CFU/100mL). In seasonal terms dissolved oxygen, electric conductivity, nitrate and silicate concentrations were higher during the dry, whereas TSS was higher during the wet period. Seasonal differences of dissolved oxygen, temperature, pH and nitrate were also detected near wetlands areas. Along the basin results showed a distinction between headwaters and other sections, revealing a control of fluvial hydrochemistry by the preserved area, mostly for the dissolved organic N and P species and phosphate

Transport of Folded Proteins by the Tat System

The twin-arginine protein translocation (Tat) system has been characterized in bacteria, archaea and the chloroplast thylakoidal membrane. This system is distinct from other protein transport systems with respect to two key features. Firstly, it accepts cargo proteins with an N-terminal signal peptide that carries the canonical twin-arginine motif, which is essential for transport. Second, the Tat system only accepts and translocates fully folded cargo proteins across the respective membrane. Here, we review the core essential features of folded protein transport via the bacterial Tat system, using the three-component TatABC system of Escherichia coli and the two-component TatAC systems of Bacillus subtilis as the main examples. In particular, we address features of twin-arginine signal peptides, the essential Tat components and how they assemble into different complexes, mechanistic features and energetics of Tat-dependent protein translocation, cytoplasmic chaperoning of Tat cargo proteins, and the remarkable proofreading capabilities of the Tat system. In doing so, we present the current state of our understanding of Tat-dependent protein translocation across biological membranes, which may serve as a lead for future investigations