Maximum principles for vectorial approximate minimisers on non-convex functionals

We establish Maximum Principles which apply to vectorial approximate minimizers of the general integral functional of Calculus of Variations. Our main result is a version of the Convex Hull Property. The primary advance compared to results already existing in the literature is that we have dropped the quasiconvexity assumption of the integrand in the gradient term. The lack of weak Lower semicontinuity is compensated by introducing a nonlinear convergence technique, based on the approximation of the projection onto a convex set by reflections and on the invariance of the integrand in the gradient term under the Orthogonal Group. Maximum Principles are implied for the relaxed solution in the case of non-existence of minimizers and for minimizing solutions of the Euler–Lagrange system of PDE.

Proteomic analysis of plasma membrane vesicles isolated from the rat renal cortex

Polarized epithelial cells are responsible for the vectorial transport of solutes and have a key role in maintaining body fluid and electrolyte homeostasis. Such cells contain structurally and functionally distinct plasma membrane domains. Brush border and basolateral membranes of renal and intestinal epithelial cells can be separated using a number of different separation techniques, which allow their different transport functions and receptor expressions to be studied. In this communication, we report a proteomic analysis of these two membrane segments, apical and basolateral, obtained from the rat renal cortex isolated by two different methods: differential centrifugation and free-flow electrophoresis. The study was aimed at assessing the nature of the major proteins isolated by these two separation techniques. Two analytical strategies were used: separation by sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) at the protein level or by cation-exchange high-performance liquid chromatography (HPLC) after proteolysis (i.e., at the peptide level). Proteolytic peptides derived from the proteins present in gel pieces or from HPLC fractions after proteolysis were sequenced by on-line liquid chromatography-tandem mass spectrometry (LC-MS/MS). Several hundred proteins were identified in each membrane section. In addition to proteins known to be located at the apical and basolateral membranes, several novel proteins were also identified. In particular, a number of proteins with putative roles in signal transduction were identified in both membranes. To our knowledge, this is the first reported study to try and characterize the membrane proteome of polarized epithelial cells and to provide a data set of the most abundant proteins present in renal proximal tubule cell membranes.

Combined affinity labelling and mass spectrometry analysis of differential cell surface protein expression in normal and prostate cancer cells

Differences in the expression of cell surface proteins between a normal prostate epithelial (1542-NP2TX) and a prostate cancer cell line (1542-CP3TX) derived from the same patient were investigated. A combination of affinity chromatographic purification of biotin-tagged surface proteins with mass spectrometry analysis identified 26 integral membrane proteins and 14 peripheral surface proteins. The findings confirm earlier reports of altered expression in prostate cancer for several cell surface proteins, including ALCAM/CD166, the Ephrin type A receptor, EGFR and the prostaglandin F2 receptor regulatory protein. In addition, several novel findings of differential expression were made, including the voltage-dependent anion selective channel proteins Porin 1 and 2, ecto-5'-nucleotidase (CD73) and Scavenger receptor B1. Cell surface protein expression changed both qualitatively and quantitatively when the cells were grown in the presence of either or both interferon INFalpha and INFgamma. Costimulation with type I and II interferons had additive or synergistic effects on the membrane density of several, mainly peripherally attached surface proteins. Concerted upregulation of surface exposed antigens may be of benefit in immuno-adjuvant-based treatment of interferon-responsive prostate cancer. In conclusion, this study demonstrates that differences in the expression of membrane proteins between normal and prostate cancer cells are reproducibly detectable following vectorial labelling with biotin, and that detailed analysis of extracellular-induced surface changes can be achieved by combining surface-specific labelling with high-resolution two-dimensional gel electrophoresis and mass spectrometry.

Proteomic analysis of plasma membrane vesicles isolated from the rat renal cortex

Polarized epithelial cells are responsible for the vectorial transport of solutes and have a key role in maintaining body fluid and electrolyte homeostasis. Such cells contain structurally and functionally distinct plasma membrane domains. Brush border and basolateral membranes of renal and intestinal epithelial cells can be separated using a number of different separation techniques, which allow their different transport functions and receptor expressions to be studied. In this communication, we report a proteomic analysis of these two membrane segments, apical and basolateral, obtained from the rat renal cortex isolated by two different methods: differential centrifugation and free-flow electrophoresis. The study was aimed at assessing the nature of the major proteins isolated by these two separation techniques. Two analytical strategies were used: separation by sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) at the protein level or by cation-exchange high-performance liquid chromatography (HPLC) after proteolysis (i.e., at the peptide level). Proteolytic peptides derived from the proteins present in gel pieces or from HPLC fractions after proteolysis were sequenced by on-line liquid chromatography-tandem mass spectrometry (LC-MS/MS). Several hundred proteins were identified in each membrane section. In addition to proteins known to be located at the apical and basolateral membranes, several novel proteins were also identified. In particular, a number of proteins with putative roles in signal transduction were identified in both membranes. To our knowledge, this is the first reported study to try and characterize the membrane proteome of polarized epithelial cells and to provide a data set of the most abundant proteins present in renal proximal tubule cell membranes.

Combined affinity labelling and mass spectrometry analysis of differential cell surface protein expression in normal and prostate cancer cells

Differences in the expression of cell surface proteins between a normal prostate epithelial (1542-NP2TX) and a prostate cancer cell line (1542-CP3TX) derived from the same patient were investigated. A combination of affinity chromatographic purification of biotin-tagged surface proteins with mass spectrometry analysis identified 26 integral membrane proteins and 14 peripheral surface proteins. The findings confirm earlier reports of altered expression in prostate cancer for several cell surface proteins, including ALCAM/CD166, the Ephrin type A receptor, EGFR and the prostaglandin F2 receptor regulatory protein. In addition, several novel findings of differential expression were made, including the voltage-dependent anion selective channel proteins Porin 1 and 2, ecto-5'-nucleotidase (CD73) and Scavenger receptor B1. Cell surface protein expression changed both qualitatively and quantitatively when the cells were grown in the presence of either or both interferon INF alpha and INF gamma. Costimulation with type I and II interferons had additive or synergistic effects on the membrane density of several, mainly peripherally attached surface proteins. Concerted upregulation of surface exposed antigens may be of benefit in immuno-adjuvant-based treatment of interferon-responsive prostate cancer. In conclusion, this study demonstrates that differences in the expression of membrane proteins between normal and prostate cancer cells are reproducibly detectable following vectorial labelling with biotin, and that detailed analysis of extracellular-induced surface changes can be achieved by combining surface-specific labelling with high-resolution two-dimensional gel electrophoresis and mass spectrometry.

Quantification of boundary definition using pulsed terahertz radiation for wedged geometries

The interaction of a terahertz beam with a sample containing a material boundary across the profile of the terahertz beam produces characteristic spectroscopic detail. A full vectorial model is presented to quantify boundary definition for a series of wedged geometries. As a result of this work, using simple geometric forms, we wish to be able to extend these ideas to characterize boundaries in more irregular samples, impacting most application areas of pulsed terahertz radiation.

On the structure of infinity-harmonic maps

Let H ∈ C 2(ℝ N×n ), H ≥ 0. The PDE system arises as the Euler-Lagrange PDE of vectorial variational problems for the functional E ∞(u, Ω) = ‖H(Du)‖ L ∞(Ω) defined on maps u: Ω ⊆ ℝ n → ℝ N . (1) first appeared in the author's recent work. The scalar case though has a long history initiated by Aronsson. Herein we study the solutions of (1) with emphasis on the case of n = 2 ≤ N with H the Euclidean norm on ℝ N×n , which we call the “∞-Laplacian”. By establishing a rigidity theorem for rank-one maps of independent interest, we analyse a phenomenon of separation of the solutions to phases with qualitatively different behaviour. As a corollary, we extend to N ≥ 2 the Aronsson-Evans-Yu theorem regarding non existence of zeros of |Du| and prove a maximum principle. We further characterise all H for which (1) is elliptic and also study the initial value problem for the ODE system arising for n = 1 but with H(·, u, u′) depending on all the arguments.