Mesangial cell-derived transforming growth factor-β1 reduces macrophage adhesiveness with consequent deactivation

Mesangial cell-derived transforming growth factor-β1 reduces macrophage adhesiveness with consequent deactivation. Adhesion of macrophages is a crucial event that determines the number and function of macrophages at inflammatory sites. The aim of this study was to elucidate the role of mesangial cells in the regulation of macrophage adhesiveness. J774.2 macrophages were suspended in serial dilutions of mesangial cell conditioned medium (MC medium) and seeded on plastic tissue culture plates. MC medium did not affect the initial adhesion of macrophages but induced subsequent detachment in a concentration-dependent manner. A similar effect was observed when macrophages were plated on plastic coated with laminin, collagen type IV or Matrigel. The reduced adhesiveness was reversible, and cell viability was unaffected by MC medium, indicating that the effect is not due to cytotoxicity. Conditioned media from fibroblastic, epithelial and endothelial cell lines did not induce macrophage detachment. To identify the active component in MC medium, we examined the involvement of transforming growth factor-β1 (TGF-β1) in the process. Mesangial cells constitutively expressed TGF-β1 mRNA, and MC medium contained the active form of TGF-β1. Exogenously added TGF-β1 induced macrophage detachment in a dose-dependent manner, and an anti-TGF-β1 neutralizing antibody partially abolished the activity of MC medium, indicating the involvement of TGF-β1 as an active component. Compared to adherent cells, detached macrophages showed reduced mitogenic activity and blunted induction of IL-1β and IL-6 in response to lipopolysaccharide. These data demonstrate that TGF-β1 is a mesangial cell-derived factor that impairs adhesiveness of macrophages and confers blunted responses to a specific stimulus. These findings suggest one potential mechanism for macrophage clearance from inflamed glomeruli

From the Hofstadter to the Fibonacci butterfly

We show that the electronic spectrum of a tight-binding Hamiltonian defined in a quasiperiodic chain with an on-site potential given by a Fibonacci sequence, can be obtained as a superposition of Harper potentials. The electronic spectrum of the Harper equation is a fractal set, known as Hofstadter butterfly. Here we show that is possible to construct a similar butterfly for the Fibonacci potential just by adding harmonics to the Harper potential. As a result, the equations in reciprocal space for the Fibonacci case have the form of a chain with a long range interaction between Fourier components. Then we explore the transformation between both spectra, and specifically the origin of energy gaps due to the analytical calculation of the components in reciprocal space of the potentials. We also calculate some localization properties by finding the correlator of each potential.Comment: 7 pages, 4 figure

Striped periodic minimizers of a two-dimensional model for martensitic phase transitions

In this paper we consider a simplified two-dimensional scalar model for the formation of mesoscopic domain patterns in martensitic shape-memory alloys at the interface between a region occupied by the parent (austenite) phase and a region occupied by the product (martensite) phase, which can occur in two variants (twins). The model, first proposed by Kohn and Mueller, is defined by the following functional: $${\cal E}(u)=\beta||u(0,\cdot)||^2_{H^{1/2}([0,h])}+ \int_{0}^{L} dx \int_0^h dy \big(|u_x|^2 + \epsilon |u_{yy}| \big)$$ where $u:[0,L]\times[0,h]\to R$ is periodic in $y$ and $u_y=\pm 1$ almost everywhere. Conti proved that if $\beta\gtrsim\epsilon L/h^2$ then the minimal specific energy scales like $\sim \min\{(\epsilon\beta/L)^{1/2}, (\epsilon/L)^{2/3}\}$, as $(\epsilon/L)\to 0$. In the regime $(\epsilon\beta/L)^{1/2}\ll (\epsilon/L)^{2/3}$, we improve Conti's results, by computing exactly the minimal energy and by proving that minimizers are periodic one-dimensional sawtooth functions.Comment: 29 pages, 3 figure

Froth-like minimizers of a non local free energy functional with competing interactions

We investigate the ground and low energy states of a one dimensional non local free energy functional describing at a mean field level a spin system with both ferromagnetic and antiferromagnetic interactions. In particular, the antiferromagnetic interaction is assumed to have a range much larger than the ferromagnetic one. The competition between these two effects is expected to lead to the spontaneous emergence of a regular alternation of long intervals on which the spin profile is magnetized either up or down, with an oscillation scale intermediate between the range of the ferromagnetic and that of the antiferromagnetic interaction. In this sense, the optimal or quasi-optimal profiles are "froth-like": if seen on the scale of the antiferromagnetic potential they look neutral, but if seen at the microscope they actually consist of big bubbles of two different phases alternating among each other. In this paper we prove the validity of this picture, we compute the oscillation scale of the quasi-optimal profiles and we quantify their distance in norm from a reference periodic profile. The proof consists of two main steps: we first coarse grain the system on a scale intermediate between the range of the ferromagnetic potential and the expected optimal oscillation scale; in this way we reduce the original functional to an effective "sharp interface" one. Next, we study the latter by reflection positivity methods, which require as a key ingredient the exact locality of the short range term. Our proof has the conceptual interest of combining coarse graining with reflection positivity methods, an idea that is presumably useful in much more general contexts than the one studied here.Comment: 38 pages, 2 figure

Flatness is a Criterion for Selection of Maximizing Measures

For a full shift with Np+1 symbols and for a non-positive potential, locally proportional to the distance to one of N disjoint full shifts with p symbols, we prove that the equilibrium state converges as the temperature goes to 0. The main result is that the limit is a convex combination of the two ergodic measures with maximal entropy among maximizing measures and whose supports are the two shifts where the potential is the flattest. In particular, this is a hint to solve the open problem of selection, and this indicates that flatness is probably a/the criterion for selection as it was conjectured by A.O. Lopes. As a by product we get convergence of the eigenfunction at the log-scale to a unique calibrated subaction

Some New Results on Complex-Temperature Singularities in Potts Models on the Square Lattice

We report some new results on the complex-temperature (CT) singularities of $q$-state Potts models on the square lattice. We concentrate on the problematic region $Re(a) < 0$ (where $a=e^K$) in which CT zeros of the partition function are sensitive to finite lattice artifacts. From analyses of low-temperature series expansions for $3 \le q \le 8$, we establish the existence, in this region, of complex-conjugate CT singularities at which the magnetization and susceptibility diverge. From calculations of zeros of the partition function, we obtain evidence consistent with the inference that these singularities occur at endpoints $a_e, \ a_e^*$ of arcs protruding into the (complex-temperature extension of the) FM phase. Exponents for these singularities are determined; e.g., for $q=3$, we find $\beta_e=-0.125(1)$, consistent with $\beta_e=-1/8$. By duality, these results also imply associated arcs extending to the (CT extension of the) symmetric PM phase. Analytic expressions are suggested for the positions of some of these singularities; e.g., for $q=5$, our finding is consistent with the exact value $a_e,a_e^*=2(-1 \mp i)$. Further discussions of complex-temperature phase diagrams are given.Comment: 26 pages, latex, with eight epsf figure