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The adamalysin-thrombospondin (ADAMTS) proteinases are a relatively newly described branch of the metzincin family that contain metalloproteinase, disintegrin, and thrombospondin motifs. They have been implicated in various cellular events, including cleavage of proteoglycans, extracellular matrix degradation, inhibition of angiogenesis, gonadal development, and organogenesis. However, in many cases, their normal physiological roles and their potential for dysregulation in malignancy remain to be established. The expression profile of ADAMTS1-20 in human breast carcinoma was undertaken by real-time PCR using RNA isolated from malignant tumors, nonneoplastic mammary tissue, and breast cancer cell lines to identify altered regulation that may have potential pathogenetic and prognostic significance. Our studies show that seven of the ADAMTS genes (ADAMTS1, 3, 5, 8, 9, 10, and 18) are consistently downregulated in breast carcinomas with respect to nonneoplastic mammary tissue, irrespective of the heterogeneity of the samples and the tumor type or grade (Mann-Whitney U test, P < 0.0001 for each gene). Conversely, ADAMTS4, 6, 14, and 20 are consistently up-regulated in breast carcinomas (P ‫؍‬ 0.005, P < 0.0001, P ‫؍‬ 0.003, and P ‫؍‬ 0.001, respectively). ADAMTS2, 7, 12, 13, 15, 16, 17, and 19 show no significant difference between the sample types. ADAMTS1, 2, 7, 8, 10, and 12 are expressed predominantly in stromal fibroblasts. ADAMTS3, 4, 5, 6, 9, and 13-20 inclusive are expressed predominantly in myoepithelial cells; all appear to be relatively poorly expressed in luminal epithelial cells. ADAMTS15 has emerged as being an independent predictor of survival, with RNA expression levels significantly lower (P ‫؍‬ 0.007) in grade 3 breast carcinoma compared with grade 1 and 2 breast carcinoma.

Simple reaction-diffusion fronts are examined in one and two dimensions. In one-dimensional configurations, fronts arising from either quadratic or cubic autocatalysis typically choose the minimum allowable velocity from an infinite spectrum of possible wave speeds. These speeds depend on both the diffusion coefficient of the autocatalytic species and the pseudo-first-order rate constant for the autocatalytic reaction. In the mixed-order case, where both quadratic and cubic channels contribute, the wave speed depends on the rate constants for both channels, provided the cubic channel dominates. Wave propagation is completely determined by the quadratic contribution when it is more heavily weighted. In two-dimensional configurations, with unequal diffusion coefficients, the corresponding twovariable planar fronts may become unstable to perturbations. The instability occurs when the ratio of the diffusion coefficient for the reactant to that for the autocatalyst exceeds some critical value. This critical value, in turn, depends on the relative weights of the quadratic and cubic contributions to the overall kinetics. The spatiotemporal form of the nonplanar wave in such systems depends on the width of the reaction zone, and a sequence showing Hopf, symmetry-breaking, and period-doubling bifurcations leading to chaotic behavior is observed as the width is increased.