Quantitative evaluation of mechanosensing of cells on dynamically tunable hydrogels

Thin hydrogel films based on an ABA triblock copolymer gelator [where A is pH-sensitive poly(2-(diisopropylamino)ethyl methacrylate) (PDPA) and B is biocompatible poly(2-(methacryloyloxy)ethyl phosphorylcholine) (PMPC)] were used as a stimulus-responsive substrate that allows fine adjustment of the mechanical environment experienced by mouse myoblast cells. The hydrogel film elasticity could be reversibly modulated by a factor of 40 via careful pH adjustment without adversely affecting cell viability. Myoblast cells exhibited pronounced stress fiber formation and flattening on increasing the hydrogel elasticity. As a new tool to evaluate the strength of cell adhesion, we combined a picosecond laser with an inverted microscope and utilized the strong shock wave created by the laser pulse to determine the critical pressure required for cell detachment. Furthermore, we demonstrate that an abrupt jump in the hydrogel elasticity can be utilized to monitor how cells adapt their morphology to changes in their mechanical environment.     

Synthesis and application of imprinted polyvinylimidazole-silica hybrid copolymer for Pb determination by flow-injection thermospray flame furnace atomic absorption spectrometry

A novel ion imprinted polyvinylimidazole-silica hybrid copolymer (IIHC) was synthesized and used as a selective solid sorbent for Pb²⁺ ions preconcentration using an on-line solid phase extraction (SPE) system coupled to TS-FF-AAS. The ionic hybrid sorbent was prepared using 1-vinylimidazole and 3-(trimethoxysilyl)propylmethacrylate as monomers, Pb²⁺ ions as template, tetraethoxysilane as reticulating agent and 2,2′-azobis-isobutyronitrile as initiator. The best on-line SPE conditions concerning sorption behavior, including sample pH (6.46), buffer concentration (9.0 mmol L⁻¹), eluent (HNO₃) concentration (0.5 mol L⁻¹) and preconcentration flow rate (4.0 mL min⁻¹), were optimized by means of full factorial design and Doehlert matrix. The analytical curve ranged from 2.5 to 65.0 μg L⁻¹ (r = 0.999) with limit of detection of 0.75 μg L⁻¹; the precision (repeatability) calculated as relative standard deviation (n = 10) was 5.0 and 3.6% for Pb²⁺ concentration of 10.0 and 60.0 μg L⁻¹, respectively. From on-line breakthrough curve, column capacity was 3.5 mg g⁻¹. Preconcentration factor (PF), consumptive index (CI) and concentration efficiency (CE) were 128.0, 0.16 mL and 25.6 min⁻¹, respectively. The selective performance of the sorbent, based on relative selectivity coefficient, was compared to NIC (non imprinted copolymer) for the binary mixture Pb²⁺/Cd²⁺, Pb²⁺/Cu²⁺ and Pb²⁺/Zn²⁺. The results showed that ion imprinted polyvinylimidazole-silica hybrid polymer had higher selectivity for Pb²⁺ than NIC at 64.9, 16.0 and 8.8 folds. The developed method was successfully applied for highly sensitive and selective Pb²⁺ determination in different kinds of water samples, parenteral solutions and urine. Accuracy was also assessed by analyzing certified reference fish protein (DORM-3) and marine sediment (MESS-3 and PACS-2) with satisfactory results.     

Cubic spline functions and initial value problems

A numerical process is presented which provides a cubic spline function approximation for the solution of initial value problems in ordinary differential equations. With interpolate cubic spline functions we can achieveO(h ⁴) convergence.     

A primal-dual interior-point algorithm for nonlinear least squares constrained problems

This paper extends prior work by the authors on solving nonlinear least squares unconstrained problems using a factorized quasi-Newton technique. With this aim we use a primal-dual interior-point algorithm for nonconvex nonlinear programming. The factorized quasi-Newton technique is now applied to the Hessian of the Lagrangian function for the transformed problem which is based on a logarithmic barrier formulation. We emphasize the importance of establishing and maintaining symmetric quasi-definiteness of the reduced KKT system. The algorithm then tries to choose a step size that reduces a merit function, and to select a penalty parameter that ensures descent directions along the iterative process. Computational results are included for a variety of least squares constrained problems and preliminary numerical testing indicates that the algorithm is robust and efficient in practice.     

A large deviations principle for stochastic flows of viscous fluids

We study the well-posedness of a stochastic differential equation on the two dimensional torus ${\mathbb{T}}^2$, driven by an infinite dimensional Wiener process with drift in the Sobolev space $L^2(0,T;H^1\left({\mathbb{T}}^2\right))$. The solution corresponds to a stochastic Lagrangian flow in the sense of DiPerna Lions. By taking into account that the motion of a viscous incompressible fluid on the torus can be described through a suitable stochastic differential equation of the previous type, we study the inviscid limit. By establishing a large deviations principle, we show that, as the viscosity goes to zero, the Lagrangian stochastic Navier–Stokes flow approaches the Euler deterministic Lagrangian flow with an exponential rate function.     

Algebraic reflexivity of sets of bounded operators on vector valued Lipschitz functions

In this paper we establish algebraic reflexivity properties of subsets of bounded linear operators acting on spaces of vector valued Lipschitz functions. We also derive a representation for the generalized bi-circular projections on these spaces.     

Differential equations in Schatten classes of operators

We study a system of differential equations in Schatten classes of operators, ${\mathcal{C}_p(\mathcal{H})\,(1 \leq p < \infty}$ ), with ${\mathcal{H}}$ a separable complex Hilbert space. The systems considered are infinite dimensional generalizations of mathematical models of unsupervised learning. In this new setting, we address the usual questions of existence and uniqueness of solutions. Under some restrictions on the spectral properties of the initial conditions, we explicitly solve the system. We also discuss the long-term behavior of solutions.     

Fucoxanthin Holds Potential to Become a Drug Adjuvant in Breast Cancer Treatment: Evidence from 2D and 3D Cell Cultures

Fucoxanthin (Fx) is a carotenoid derived from marine organisms that exhibits anticancer activities. However, its role as a potential drug adjuvant in breast cancer (BC) treatment is still poorly explored. Firstly, this study investigated the cytotoxic effects of Fx alone and combined with doxorubicin (Dox) and cisplatin (Cis) on a panel of 2D-cultured BC cell lines (MCF7, SKBR3 and MDA-MB-231) and one non-tumoral cell line (MCF12A). Fucoxanthin induced cytotoxicity against all the cell lines and potentiated Dox cytotoxic effects towards the SKBR3 and MDA-MB-231 cells. The combination triggering the highest cytotoxicity (Fx 10 µM + Dox 1 µM in MDA-MB-231) additionally showed significant induction of cell death and genotoxic effects, relative to control. In sequence, the same combination was tested on 3D cultures using a multi-endpoint approach involving bioactivity assays and microscopy techniques. Similar to 2D cultures, the combination of Fx and Dox showed higher cytotoxic effects on 3D cultures compared to the isolated compounds. Furthermore, this combination increased the number of apoptotic cells, decreased cell proliferation, and caused structural and ultrastructural damages on the 3D models. Overall, our findings suggest Fx has potential to become an adjuvant for Dox chemotherapy regimens in BC treatment.     

Isometries on spaces of vector valued Lipschitz functions

This paper gives a characterization of a class of surjective isometries on spaces of Lipschitz functions with values in a finite dimensional complex Hilbert space.