Censored Least Squares for Imputing Missing Values in PARAFAC Tensor Factorization.

Tensor factorization is a dimensionality reduction method applied to multidimensional arrays. These methods are useful for identifying patterns within a variety of biomedical datasets due to their ability to preserve the organizational structure of experiments and therefore aid in generating meaningful insights. However, missing data in the datasets being analyzed can impose challenges. Tensor factorization can be performed with some level of missing data and reconstruct a complete tensor. However, while tensor methods may impute these missing values, the choice of fitting algorithm may influence the fidelity of these imputations. Previous approaches, based on alternating least squares with prefilled values or direct optimization, suffer from introduced bias or slow computational performance. In this study, we propose that censored least squares can better handle missing values with data structured in tensor form. We ran censored least squares on four different biological datasets and compared its performance against alternating least squares with prefilled values and direct optimization. We used the error of imputation and the ability to infer masked values to benchmark their missing data performance. Censored least squares appeared best suited for the analysis of high-dimensional biological data by accuracy and convergence metrics across several studies.

Cell Adhesiveness Serves as a Biophysical Marker for Metastatic Potential.

Tumors are heterogeneous and composed of cells with different dissemination abilities. Despite significant effort, there is no universal biological marker that serves as a metric for metastatic potential of solid tumors. Common to disseminating cells from such tumors, however, is the need to modulate their adhesion as they detach from the tumor and migrate through stroma to intravasate. Adhesion strength is heterogeneous even among cancer cells within a given population, and using a parallel plate flow chamber, we separated and sorted these populations into weakly and strongly adherent groups; when cultured under stromal conditions, this adhesion phenotype was stable over multiple days, sorting cycles, and common across all epithelial tumor lines investigated. Weakly adherent cells displayed increased migration in both two-dimensional and three-dimensional migration assays; this was maintained for several days in culture. Subpopulations did not show differences in expression of proteins involved in the focal adhesion complex but did exhibit intrinsic focal adhesion assembly as well as contractile differences that resulted from differential expression of genes involved in microtubules, cytoskeleton linkages, and motor activity. In human breast tumors, expression of genes associated with the weakly adherent population resulted in worse progression-free and disease-free intervals. These data suggest that adhesion strength could potentially serve as a stable marker for migration and metastatic potential within a given tumor population and that the fraction of weakly adherent cells present within a tumor could act as a physical marker for metastatic potential. SIGNIFICANCE: Cancer cells exhibit heterogeneity in adhesivity, which can be used to predict metastatic potential.