Ruthenium(II)-arene complexes with biotin-containing ligands were prepared so that a novel drug delivery system based on tumor-specific vitamin-receptor mediated endocytosis could be developed. The complexes were characterized by spectroscopic methods and their in vitro anticancer activity in cancer cell lines with various levels of major biotin receptor (COLO205, HCT116 and SW620 cells) was tested in comparison with the ligands. In all cases, coordination of ruthenium resulted in significantly enhanced cytotoxicity. The affinity of Ru(II) -biotin complexes to avidin was investigated and was lower than that of unmodified biotin. Hill coefficients in the range 2.012-2.851 suggest strong positive cooperation between the complexes and avidin. To estimate the likelihood of binding to the biotin receptor/transporter, docking studies with avidin and streptavidin were conducted. These explain, to some extent, the in vitro anticancer activity results and support the conclusion that these novel half-sandwich ruthenium(II)-biotin conjugates may act as biological vectors to cancer cells, although no clear relationship between the cellular Ru content, the cytotoxicity, and the presence of the biotin moiety was observed.

The form of topological derivatives for an integral shape functional is derived for a class of semilinear elliptic equations. The convergence of finite element approximation for the topological derivatives is shown and the error estimates in the L ∞ norm are obtained. The results of numerical experiments which confirm the theoretical convergence rate are presented.

No abstract

Abstract. Framework for shape and topology sensitivity analysis in geometrical domains with cracks is established for elastic bodies in two spatial dimensions. Equilibrium problem for elastic body with cracks is considered. Inequality type boundary conditions are prescribed at the crack faces providing a non-penetration between the crack faces. Modelling of such problems in two spatial dimensions is presented with all necessary details for further applications in shape optimization in structural mechanics. In the paper, general results on the shape and topology sensitivity analysis of this problem are provided. The results are interesting on its own. In particular, the existence of the shape and topological derivatives of the energy functional is obtained. It is shown, in fact, that the level set type method [4] can be applied to shape and topology opimization of the related variational inequalities for elasticity problems in domains with cracks, with the nonpenetration condition prescribed on the crack faces. The results presented in the paper can be used for numerical solution of shape optimization and inverse problems in structural mechanics.Key words. Crack with non-penetration, shape sensitivity, derivative of energy functional, topological derivative AMS subject classifications. Primary 35J85, 74K20 Secondary 35J25, 74M151. Introduction. Shape optimization requires few mathematical results, in the framework of modelling and numerical solution, for any specific class of problems governed by partial differential equations of mathematical physics. Usually, we need to show the well posedness of the specific problem, and also we can propose a numerical method for the effective solution procedure. Hence, in order to solve a shape optimization problem we are obliged to have the results on• the existence and continuous dependence with respect to the shape of solutions to the model, which may result in the existence of optimal shapes, • the differentiability of solutions with respect to the boundary variations, which imply the existence of shape gradients and leads to some necessary conditions for optimality, of the first order and possibly of the second order which leads to the Newton method of shape optimization, • and in addition, perform the asymptotic analysis of the related boundary value problem in singularly perturbed geometrical domains and derive the form of the topological derivative for the shape functional of interest, which allows for the topology changes in the process of numerical optimization, if necessary, • and finally, we may device a numerical method and show its efficiency in numerical examples, and its convergence form the mathematical point of view.

The aim of the study was to compare the biological analyzes of the Linda River (Central Poland), which were based on three diatom indices: IO, GDI and IPS in order to select the best diatom index for the biological assessment of the lotic water quality. Additionally, the summary of the selected results of the biological and chemical analyzes was presented to show how precise the biological analyzes are as a basic tool in the assessment of the ecological status of the lotic waters. The results showed that each of the indices assessed the water in the Linda River to a specific but different quality class. The IO index showed class II of the water quality, while the IPS and GDI − class III. Statistical analysis conducted with the nonparametric Kruskal-Wallis test for independent samples (Kruskal, Wallis 1952) showed that differences in the values of individual indices * Corresponding author: szulc@biol.uni.lodz.pl at different sites were not statistically significant. It should be noticed that the IPS and GDI indices gave values that classify the water in the Linda River at least one class below.The obtained results confirmed that the biological methods are most reliable in the assessment of the water quality. These methods are less sensitive to a single impact of the environmental factors, therefore they permit accurate determination of the ecological status of the water ecosystems.

The main aim of this study was to assess the usefulness of the Biological Diatom Index (BDI) (Lenoir & Coste 1996) for the estimation of water quality in the central section of the Pilica River, located in central Poland in Łódź province. The BDI has never been used before to monitor Polish surface waters. An analysis of the correlations between the values of the BDI and selected physico-chemical parameters was performed, as was an assessment of water quality using the BDI. On the basis of value ranges proposed by Descy and Ector (1996), a good ecological status in the Pilica River was obtained, but this did not correspond with the results achieved from the physico-chemical analysis. This study proposes new value ranges for the BDI. With these new values, the ecological state of the Pilica River changed from good to moderate, which corresponded with the physicochemical analysis of the water. The new, proposed value ranges for the BDI assess more precisely the quality of water in lowland Polish rivers.

In the paper we consider a new method based on the genetic algorithm for finding the location and size of small holes in the domain, in which the coupled linear and nonlinear boundary value problems are defined. The linear and nonlinear components are connected by the transmission conditions on the interface boundary. The expansion with respect to small parameter of the shape functional for nonlinear component and the expansion of Steklov-Poincaré operator for linear component are derived in order to determine the form of topological derivative for shape functional defined for coupled model. Then the topological derivative is employed for evaluation of the probability density applied to generation of location of holes by the genetic algorithm.

Shape optimization problem for semilinear elliptic equation is considered. There is an optimal solution which is computed by the Levelset method. To this end the shape derivative of the functional is evaluated. In order to predict the topology changes the topological derivative is employed. Numerical results confirm that the proposed framework for numerical solution of shape optimization problems is efficient.