When grown in the absence of methotrexate, cells carrying unstably amplified dihydrofolate reductase (dhfr) genes have a growth disadvantage that is a function of their level of gene amplification. Although this growth disadvantage is thought to drive the loss of unstably amplified dhfr genes in the absence of methotrexate, its mechanism is not understood. The present studies of murine cell lines with different levels of dhfr gene amplification demonstrate that such cells experience increased unbalanced growth (excess RNA and protein content relative to DNA content) with increased levels of dhfr gene amplification. Stathmokinetic analysis of a cell line with unstably amplified dhfr genes showed that the unbalanced growth was associated with a very low rate of G1/S transit, which suggests that amplified DNA sequences may activate a cell cycle checkpoint at the G1/S boundary. Hydroxyurea, which is known to induce rapid elimination of amplified genes at sub-cytotoxic concentrations, also inhibits the cell cycle at the G1/S transition and causes unbalanced growth. Earlier work has shown that hydroxyurea selectively targets those cells within the heterogeneous drug resistant cell populations which have the highest amplified gene dosage. The finding that unstable gene amplification and hydroxyurea have similar effects on the cell suggests that hydroxyurea may achieve this selective targeting by pushing those cells with the highest levels of gene amplification over a critical stress threshold to cause growth arrest or cell death.

Understanding relational datasets at a high level is a common data mining task and the detection and classification of community structure is one of the foremost algorithmic challenges of data science. A common approach is to model a dataset with a graph and to use the arsenal of graph mining methods to describe the properties of the data and find desired structure. This arsenal includes many numerical linear algebra techniques. A well-known approach is to calculate a few eigenpairs of a matrix associated with the graph and use the information in the eigenvalues and eigenvectors to find diverse properties of the graph. Often these eigenpairs guide graph optimization processes to more efficient nearoptimal solution. For small and quasi-regular graphs, the choice from the buffet of graph-associated matrices is often unimportant as the performance of the technique may not depend much on which graph matrix is employed. However, in large graphs with highly skewed degree distribution, there are several important considerations in this choice. The calculation cost of finding the eigenvectors and the properties that are determined from these eigenvectors both differ dramatically depending which matrix and set of eigenvectors you choose.We present maximum principles and decay rates demonstrating, for scale-free graphs, the extremal eigenvectors of adjacency matrices are fundamentally different than those related to Laplacian matrices. The results suggest that adjacency eigenpairs could be effectively used to detect community structure of a given density involving many mediumto-high-degree vertices, but that their use is likely inappropriate for locating community structure in the low-degree portions of graphs.

When grown in the absence of methotrexate, cells carrying unstably amplified dihydrofolate reductase (dhfr) genes have a growth disadvantage that is a function of their level of gene amplification. Although this growth disadvantage is thought to drive the loss of unstably amplified dhfr genes in the absence of methotrexate, its mechanism is not understood. The present studies of murine cell lines with different levels of dhfr gene amplification demonstrate that such cells experience increased unbalanced growth (excess RNA and protein content relative to DNA content) with increased levels of dhfr gene amplification. Stathmokinetic analysis of a cell line with unstably amplified dhfr genes showed that the unbalanced growth was associated with a very low rate of G1/S transit, which suggests that amplified DNA sequences may activate a cell cycle checkpoint at the G1/S boundary. Hydroxyurea, which is known to induce rapid elimination of amplified genes at sub-cytotoxic concentrations, also inhibits the cell cycle at the G1/S transition and causes unbalanced growth. Earlier work has shown that hydroxyurea selectively targets those cells within the heterogeneous drug resistant cell populations which have the highest amplified gene dosage. The finding that unstable gene amplification and hydroxyurea have similar effects on the cell suggests that hydroxyurea may achieve this selective targeting by pushing those cells with the highest levels of gene amplification over a critical stress threshold to cause growth arrest or cell death.