On improved regularity of weak solutions of some degenerate,Anisotropic elliptic systems

Summary We consider a (possibly) vector-valued function u: R^N, Rⁿ, minimizing the integral , 2-2/(n*1)<p<2, whereD _i u=u/x _i or some more general functional retaining the same behaviour, we prove higher integrability for Du: D₁ u,..., D_n–1 u L^p/(p-1) and D_nu L²; this result allows us to get existence of second weak derivatives: D(D₁ u),...,D(D_n–1u)L² and D(D_n u) L _p.This work has been supported by MURST and GNAFA-CNR.     

Cotransport-induced instability of membrane voltage in tip-growing cells

A salient feature of stationary patterns in tip-growing cells is the key role played by the symports and antiports, membrane proteins that translocate two ionic species at the same time. It is shown that these cotransporters destabilize generically the membrane voltage if the two translocated ions diffuse differently and carry a charge of opposite (same) sign for symports (antiports). The orders of magnitude obtained for the time and length scale are in agreement with experiments. A weakly nonlinear analysis characterizes the bifurcation.     

Parity-breaking bifurcation and global oscillation in patterns of ion channels

Stationary spatiotemporal pattern formation emerging from the electric activity of biological membranes is widespread in cells and tissues. A known key instability comes from the self-aggregation of membrane channels. In a two-dimensional geometry, we show that the primary pattern undergoes four secondary instabilities: Eckhaus-like, period-halving, drift instabilities, and a global oscillation. The stability diagram is determined. The parity-breaking (drift) bifurcation of channel density is characterized analytically and numerically.     

Screening of matrix metalloproteinases available from the protein data bank: insights into biological functions, domain organization, and zinc binding groups

A total of 142 matrix metalloproteinase (MMP) X-ray crystallographic structures were retrieved from the Protein Data Bank (PDB) and analyzed by an automated and efficient routine, developed in-house, with a series of bioinformatic tools. Highly informative heat maps and hierarchical clusterograms provided a reliable and comprehensive representation of the relationships existing among MMPs, enlarging and complementing the current knowledge in the field. Multiple sequence and structural alignments permitted better location and display of key MMP motifs and quantification of the residue consensus at each amino acid position in the most critical binding subsites of MMPs. The MMP active site consensus sequences, the C-alpha root-mean-square deviation (RMSd) analysis of diverse enzymatic subsites, and the examination of the chemical nature, binding topologies, and zinc binding groups (ZBGs) of ligands extracted from crystallographic complexes provided useful insights on the structural arrangements of the most potent MMP inhibitors.     

Regularity for minimizers of functionals with p – q growth

We prove higher integrability for the gradient of vector-valued minimizers of some integral functionals with p – q growth. Received February 9, 1998     

Hybrid continuum–coarse-grained modeling of erythrocytes

The red blood cell (RBC) membrane is a composite structure, consisting of a phospholipid bilayer and an underlying membrane-associated cytoskeleton. Both continuum and particle-based coarse-grained RBC models make use of a set of vertices connected by edges to represent the RBC membrane, which can be seen as a triangular surface mesh for the former and a spring network for the latter. Here, we present a modeling approach combining an existing continuum vesicle model with a coarse-grained model for the cytoskeleton. Compared to other two-component approaches, our method relies on only one mesh, representing the cytoskeleton, whose velocity in the tangential direction of the membrane may be different from that of the lipid bilayer. The finitely extensible nonlinear elastic (FENE) spring force law in combination with a repulsive force defined as a power function (POW), called FENE–POW, is used to describe the elastic properties of the RBC membrane. The mechanical interaction between the lipid bilayer and the cytoskeleton is explicitly computed and incorporated into the vesicle model. Our model includes the fundamental mechanical properties of the RBC membrane, namely fluidity and bending rigidity of the lipid bilayer, and shear elasticity of the cytoskeleton while maintaining surface-area and volume conservation constraint. We present three simulation examples to demonstrate the effectiveness of this hybrid continuum–coarse-grained model for the study of RBCs in fluid flows.     

Toward a fragment-based approach to MMPs inhibitors: an expedite and efficient synthesis of N-hydroxylactams

Matrix metalloproteinases (MMPs), a class of zinc-enzymes over-activated in many pathologies, such as arthritis and cancer, can be efficiently inhibited by a variety of molecules bearing zinc-binding groups (ZBGs). The hydroxamic acid moiety represents one of the most potent and widely exploited ZBG but the poor target selectivity and in vivo toxicity have tempered the initial enthusiasm for this class of potential therapeutics. These drawbacks might be circumvented, at least in part, by increasing the structural constraints around the hydroxamic moiety. Following this strategy we designed and prepared N-hydroxylactam molecules of different size through a synthetic protocol based on a ring closing metathesis amenable to a fragment-based approach potentially leading to a large molecular diversity.