Basal Signalling Through Death Receptor 5 and Caspase 3 Activates p38 Kinase To Regulate Serum Response Factor (SRF)-Mediated Myod Transcription

We have previously reported that stable expression of a dominant negative Death Receptor 5 (dnDR5) in skeletal myoblasts results in decreased basal caspase activity and decreased mRNA and protein expression of the muscle regulatory transcription factor MyoD in growth medium (GM), resulting in inhibited differentation when myoblasts are then cultured in differentiation media (DM). Further, this decreased level of MyoD mRNA was not a consequence of altered message stability, but rather correlated with decreased acetylation of histones in the distal regulatory region (DRR) of the MyoD extended promoter known to control MyoD transcription. As serum response factor (SRF) is the transcription factor known to be responsible for basal MyoD expression in GM, we compared the level of SRF binding to the non-canonical serum response element (SRE) within the DRR in parental and dnDR5 expressing myoblasts. Herein, we report that stable expression of dnDR5 resulted in decreased levels of serum response factor (SRF) binding to the CArG box in the SRE of the DRR. Total SRF expression levels were not affected, but phosphorylation indicative of SRF activation was impaired. This decreased SRF phosphorylation correlated with decreased phosphorylation-induced activation of p38 kinase. Moreover, the aforementioned signaling events affected by expression of dnDR5 could be appropriately recapitulated using either a pharmacological inhibitor of caspase 3 or p38 kinase. Thus, our results have established a signaling pathway from DR5 through caspases to p38 kinase activation, to SRF activation and the basal expression of MyoD

Microscopic Selection of Fluid Fingering Pattern

We study the issue of the selection of viscous fingering patterns in the limit of small surface tension. Through detailed simulations of anisotropic fingering, we demonstrate conclusively that no selection independent of the small-scale cutoff (macroscopic selection) occurs in this system. Rather, the small-scale cutoff completely controls the pattern, even on short time scales, in accord with the theory of microscopic solvability. We demonstrate that ordered patterns are dynamically selected only for not too small surface tensions. For extremely small surface tensions, the system exhibits chaotic behavior and no regular pattern is realized.Comment: 6 pages, 5 figure

Multidimensional Pattern Formation Has an Infinite Number of Constants of Motion

Extending our previous work on 2D growth for the Laplace equation we study here {\it multidimensional} growth for {\it arbitrary elliptic} equations, describing inhomogeneous and anisotropic pattern formations processes. We find that these nonlinear processes are governed by an infinite number of conservation laws. Moreover, in many cases {\it all dynamics of the interface can be reduced to the linear time--dependence of only one ``moment" $M_0$} which corresponds to the changing volume while {\it all higher moments, $M_l$, are constant in time. These moments have a purely geometrical nature}, and thus carry information about the moving shape. These conserved quantities (eqs.~(7) and (8) of this article) are interpreted as coefficients of the multipole expansion of the Newtonian potential created by the mass uniformly occupying the domain enclosing the moving interface. Thus the question of how to recover the moving shape using these conserved quantities is reduced to the classical inverse potential problem of reconstructing the shape of a body from its exterior gravitational potential. Our results also suggest the possibility of controlling a moving interface by appropriate varying the location and strength of sources and sinks.Comment: CYCLER Paper 93feb00

A New Class of Nonsingular Exact Solutions for Laplacian Pattern Formation

We present a new class of exact solutions for the so-called {\it Laplacian Growth Equation} describing the zero-surface-tension limit of a variety of 2D pattern formation problems. Contrary to common belief, we prove that these solutions are free of finite-time singularities (cusps) for quite general initial conditions and may well describe real fingering instabilities. At long times the interface consists of N separated moving Saffman-Taylor fingers, with ``stagnation points'' in between, in agreement with numerous observations. This evolution resembles the N-soliton solution of classical integrable PDE's.Comment: LaTeX, uuencoded postscript file

Parallel flow in Hele-Shaw cells with ferrofluids

Parallel flow in a Hele-Shaw cell occurs when two immiscible liquids flow with relative velocity parallel to the interface between them. The interface is unstable due to a Kelvin-Helmholtz type of instability in which fluid flow couples with inertial effects to cause an initial small perturbation to grow. Large amplitude disturbances form stable solitons. We consider the effects of applied magnetic fields when one of the two fluids is a ferrofluid. The dispersion relation governing mode growth is modified so that the magnetic field can destabilize the interface even in the absence of inertial effects. However, the magnetic field does not affect the speed of wave propagation for a given wavenumber. We note that the magnetic field creates an effective interaction between the solitons.Comment: 12 pages, Revtex, 2 figures, revised version (minor changes

Sources and sinks separating domains of left- and right-traveling waves: Experiment versus amplitude equations

In many pattern forming systems that exhibit traveling waves, sources and sinks occur which separate patches of oppositely traveling waves. We show that simple qualitative features of their dynamics can be compared to predictions from coupled amplitude equations. In heated wire convection experiments, we find a discrepancy between the observed multiplicity of sources and theoretical predictions. The expression for the observed motion of sinks is incompatible with any amplitude equation description.Comment: 4 pages, RevTeX, 3 figur

Ordering kinetics of stripe patterns

We study domain coarsening of two dimensional stripe patterns by numerically solving the Swift-Hohenberg model of Rayleigh-Benard convection. Near the bifurcation threshold, the evolution of disordered configurations is dominated by grain boundary motion through a background of largely immobile curved stripes. A numerical study of the distribution of local stripe curvatures, of the structure factor of the order parameter, and a finite size scaling analysis of the grain boundary perimeter, suggest that the linear scale of the structure grows as a power law of time with a craracteristic exponent z=3. We interpret theoretically the exponent z=3 from the law of grain boundary motion.Comment: 4 pages, 4 figure

Universal Power Law in the Noise from a Crumpled Elastic Sheet

Using high-resolution digital recordings, we study the crackling sound emitted from crumpled sheets of mylar as they are strained. These sheets possess many of the qualitative features of traditional disordered systems including frustration and discrete memory. The sound can be resolved into discrete clicks, emitted during rapid changes in the rough conformation of the sheet. Observed click energies range over six orders of magnitude. The measured energy autocorrelation function for the sound is consistent with a stretched exponential C(t) ~ exp(-(t/T)^{b}) with b = .35. The probability distribution of click energies has a power law regime p(E) ~ E^{-a} where a = 1. We find the same power law for a variety of sheet sizes and materials, suggesting that this p(E) is universal.Comment: 5 pages (revtex), 10 uuencoded postscript figures appended, html version at http://rainbow.uchicago.edu/~krame

Mode-coupling approach to non-Newtonian Hele-Shaw flow

The Saffman-Taylor viscous fingering problem is investigated for the displacement of a non-Newtonian fluid by a Newtonian one in a radial Hele-Shaw cell. We execute a mode-coupling approach to the problem and examine the morphology of the fluid-fluid interface in the weak shear limit. A differential equation describing the early nonlinear evolution of the interface modes is derived in detail. Owing to vorticity arising from our modified Darcy's law, we introduce a vector potential for the velocity in contrast to the conventional scalar potential. Our analytical results address how mode-coupling dynamics relates to tip-splitting and side branching in both shear thinning and shear thickening cases. The development of non-Newtonian interfacial patterns in rectangular Hele-Shaw cells is also analyzed.Comment: 14 pages, 5 ps figures, Revtex4, accepted for publication in Phys. Rev.