Chemokine stromal cell-derived factor-1 (SDF-1) is expressed by bone marrow (BM) stromal cells and plays key roles in BM cell migration. Modulation of its expression could affect the migratory capacity of cells trafficking the BM, such as hematopoietic progenitor and leukemic cells. Transforming growth factor-beta1 (TGF-beta1) is present in the BM environment and constitutes a pivotal molecule controlling BM cell proliferation and differentiation. We used the BM stromal cell line MS-5 as a model to investigate whether SDF-1 expression constitutes a target for TGF-beta1 regulation and its functional consequences. We show here that TGF-beta1 down-regulates SDF-1 expression, both at the mRNA level, involving a decrease in transcriptional efficiency, and at the protein level, as detected in lysates and supernatants from MS-5 cells. Reduction of SDF-1 in supernatants from TGF-beta1-treated MS-5 cells correlated with decreased, SDF-1-dependent, chemotactic, and transendothelial migratory responses of the BM model cell lines NCI-H929 and Mo7e compared with their responses to supernatants from untreated MS-5 cells. In addition, supernatants from TGF-beta1-exposed MS-5 cells had substantially lower efficiency in promoting integrin alpha4beta1-mediated adhesion of NCI-H929 and Mo7e cells to soluble vascular cell adhesion molecule-1 (sVCAM-1) and CS-1/fibronectin than their untreated counterparts. Moreover, human cord blood CD34+ hematopoietic progenitor cells displayed SDF-1-dependent reduced responses in chemotaxis, transendothelial migration, and up-regulation of adhesion to sVCAM-1 when supernatants from TGF-beta1-treated MS-5 cells were used compared with supernatants from untreated cells. These data indicate that TGF-beta1-controlled reduction in SDF-1 expression influences BM cell migration and adhesion, which could affect the motility of cells trafficking the bone marrow.

This paper presents a general notion of Mahalanobis distance for functional data that extends the classical multivariate concept to situations where the observed data are points belonging to curves generated by a stochastic process. More precisely, a new semi-distance for functional observations that generalize the usual Mahalanobis distance for multivariate datasets is introduced. For that, the development uses a regu-

We enlarge the number of available functional depths by introducing the kernelized functional spatial depth (KFSD). KFSD is a local-oriented and kernel-based version of the recently proposed functional spatial depth (FSD) that may be useful for studying functional samples that require an analysis at a local level. In addition, we consider supervised functional classification problems, focusing on cases in which the differences between groups are not extremely clear-cut or the data may contain outlying curves. We perform classification by means of some available robust methods that involve the use of a given functional depth, including FSD and KFSD, among others. We use the functional k -nearest neighbor classifier as a benchmark procedure. The results of a simulation study indicate that the KFSD-based classification approach leads to good results. Finally, we consider two real classification problems, obtaining results that are consistent with the findings observed with simulated curves.