Local approximations for maximum partial subgraph problem

We deal with MAXH₀-FREE PARTIAL SUBGRAPH. We mainly prove that 3-locally optimum solutions achieve approximation ratio (δ₀+1)/(B+2+ν₀), where B=max_v∈Vd_G(v), δ₀=min_v∈V(H0)d_H0(v) and ν₀=(|V(H₀)|+1)/δ₀. Next, we show that this ratio rises up to 3/(B+1) when H₀=K₃. Finally, we provide hardness results for MAXK₃-FREE PARTIAL SUBGRAPH.     

Novel fiber-optic biosensor based on immobilized glutathione S-transferase and sol–gel entrapped bromcresol green for the determination of atrazine

The aim of this work was to investigate, for the first time, the potential of the enzyme glutathione S-transferase I (isoenzyme GST-I) for uses in analytical chemistry. A novel fiber-optic biosensor for the detection and determination of the triazine herbicide atrazine was developed based on maize GST-I expressed in E. coli. The sensing bioactive material was a three-layer mini-sandwich. The enzyme was immobilized on the outer layer that consisted of a hydrophilic polyvinylidenefluoride membrane. This membrane was supported on an inner glass disk by means of an intermediate binder sol–gel layer that incorporated bromcresol green (BCG). The biosensor operated in a static mode at 25 °C and the rate of the enzymatic reaction, using atrazine as a substrate, served as an analytical signal. A calibration curve was obtained for atrazine, with analytically useful concentration range 2.52–125 μM. The sensor detection limit was 0.84 μM. The reproducibility of atrazine sensing was in the order of ±3–5%. The method was successfully applied to the determination of this herbicide in real water samples, without sample preparation steps. Atrazine recovery ranged between 85 and 110%. No interference from other pesticides, such as alachlor and carbaryl was observed in the absence of atrazine. The immobilized enzyme retained about 75% of its original activity after 1 month use. Simply unscrewing the terminal holding ring of the probe and placing a new bioactive sandwich could easily replace a deteriorated mini-sandwich.     

Universal series induced by approximate identities and some relevant applications

We prove the existence of series ∑a_nψ_n, whose coefficients (a_n) are in ∩_p>1?^p and whose terms (ψ_n) are translates by rational vectors in R^d of a family of approximations to the identity, having the property that the partial sums are dense in various spaces of functions such as Wiener’s algebra W(C₀,?¹), C_b(R^d), C₀(R^d), L^p(R^d), for every p∈[1,∞), and the space of measurable functions. Applying this theory to particular situations, we establish approximations by such series to solutions of the heat and Laplace equations as well as to probability density functions.     

Stockpiling under price uncertainty and storage capacity constraints

A model is presented for the operation of an agent whose responsibility is to purchase and perhaps stockpile sufficient quantities of a certain commodity in order to satisfy an exogenous constant demand per time period. This is the situation faced by a state agency which is responsible for the purchasing of oil products to satisfy the demand of a country in which demand for energy has stabilized at a certain level.An important feature of the model is that the price of the commodity is described by a stochastic process. This reflects the volatility of prices of oil products. Furthermore, the model takes storage capacity constraints explicitly into account, and thus can help to assess the optimal level of storage capacity expansion.The relevant stochastic dynamic programming equations are derived and solved for the least cost function, which turns out to be piecewise linear in the inventory level. The storage capacity enters only in the computation of the constant term of the value function. The solution of the dynamic programming equation leads also to the optimal purchasing strategy of agencies with different levels of flexibility in their policy: in the model, an agency can be allowed or not to resell from the stock and it can have finite or infinite storage capacity.     

Assigning vibrational spectra of ferryl-oxo intermediates of cytochrome C oxidase by periodic orbits and molecular dynamics

Complexity is inherent in biological molecules not only because of the large number of atoms but also because of their nonlinear interactions responsible for chaotic behaviours, localized motions, and bifurcation phenomena. Thus, versatile spectroscopic techniques have been invented to achieve temporal and spatial resolution to minimize the uncertainties in assigning the spectra of complex molecules. Can we associate spectral lines to specific chemical bonds or species in a large molecule? Can energy stay localized in a bond for a substantial period of time to leave its spectroscopic signature? These longstanding problems are investigated by studying the resonance Raman spectra of ferryl-oxo intermediates of cytochrome c oxidase. The difference spectra of isotopically substituted ferryl oxygen ((16)O minus (18)O) in the cytochrome c oxidase recorded in several laboratories show one or two prominent positive peaks which have not been completely elucidated yet. By applying the hierarchical methods of nonlinear mechanics, and particularly the study of periodic orbits in the active site of the enzyme, in conjunction with molecular dynamics calculations of larger systems which include the embraced active site by the protein and selected protonated/deprotonated conformations of amino acids, we translate the spectral lines to molecular motions. It is demonstrated that for the active site stable periodic orbits exist for a substantial energy range. Families of periodic orbits which are associated with the vibrations of Fe(IV)=O bond mark the regions of phase space where nearby trajectories remain localized, as well as assign the spectral bands of the active site in the protein matrix. We demonstrate that proton movement adjacent to active site, which occurs during the P --> F transition, can lead to significant perturbations of the Fe(IV)=O isotopic difference vibrational spectra in cytochrome c oxidase, without a change in oxidation state of the metal sites. This finding links spectroscopic characteristics to protonation events occurring during enzymatic turnover.     

Probing the environment of cu(b) in heme-copper oxidases

Time-resolved step-scan FTIR (TRS2-FTIR) and density functional theory have been applied to probe the structural dynamics of CuB in heme-copper oxidases at room temperature. The TRS2-FTIR data of cbb3 from Pseudomonas stutzeri indicate a small variation in the frequency of the transient CO bound to CuB in the pH/pD 7-9 range. This observation in conjunction with density functional theory calculations, in which significant frequency shifts of the nu(CO) are observed upon deprotonation and/or detachment of the CuB ligands, demonstrates that the properties of the CuB ligands including the cross-linked tyrosine, in contrast to previous reports, remain unchanged in the pH 7-9 range. We attribute the small variations in the nu(CO) of CuB to protein conformational changes in the vicinity of CuB. Consequently, the split of the heme Fe-CO vibrations (alpha-, beta-, and gamma-forms) is not due to changes in the ligation and/or protonation states of the CuB ligands or to the presence of one or more ionizable groups, as previously suggested, but the result of global protein conformational changes in the vicinity of CuB which, in turn, affect the position of CuB with respect to the heme Fe.