Spatially embedded growing small-world networks.

Networks in nature are often formed within a spatial domain in a dynamical manner, gaining links and nodes as they develop over time. Motivated by the growth and development of neuronal networks, we propose a class of spatially-based growing network models and investigate the resulting statistical network properties as a function of the dimension and topology of the space in which the networks are embedded. In particular, we consider two models in which nodes are placed one by one in random locations in space, with each such placement followed by configuration relaxation toward uniform node density, and connection of the new node with spatially nearby nodes. We find that such growth processes naturally result in networks with small-world features, including a short characteristic path length and nonzero clustering. We find no qualitative differences in these properties for two different topologies, and we suggest that results for these properties may not depend strongly on the topology of the embedding space. The results do depend strongly on dimension, and higher-dimensional spaces result in shorter path lengths but less clustering.

Real-time motion analysis reveals cell directionality as an indicator of breast cancer progression.

Cancer cells alter their migratory properties during tumor progression to invade surrounding tissues and metastasize to distant sites. However, it remains unclear how migratory behaviors differ between tumor cells of different malignancy and whether these migratory behaviors can be utilized to assess the malignant potential of tumor cells. Here, we analyzed the migratory behaviors of cell lines representing different stages of breast cancer progression using conventional migration assays or time-lapse imaging and particle image velocimetry (PIV) to capture migration dynamics. We find that the number of migrating cells in transwell assays, and the distance and speed of migration in unconstrained 2D assays, show no correlation with malignant potential. However, the directionality of cell motion during 2D migration nicely distinguishes benign and tumorigenic cell lines, with tumorigenic cell lines harboring less directed, more random motion. Furthermore, the migratory behaviors of epithelial sheets observed under basal conditions and in response to stimulation with epidermal growth factor (EGF) or lysophosphatitic acid (LPA) are distinct for each cell line with regard to cell speed, directionality, and spatiotemporal motion patterns. Surprisingly, treatment with LPA promotes a more cohesive, directional sheet movement in lung colony forming MCF10CA1a cells compared to basal conditions or EGF stimulation, implying that the LPA signaling pathway may alter the invasive potential of MCF10CA1a cells. Together, our findings identify cell directionality as a promising indicator for assessing the tumorigenic potential of breast cancer cell lines and show that LPA induces more cohesive motility in a subset of metastatic breast cancer cells.

Mapping the evolution of scientific fields.

Despite the apparent cross-disciplinary interactions among scientific fields, a formal description of their evolution is lacking. Here we describe a novel approach to study the dynamics and evolution of scientific fields using a network-based analysis. We build an idea network consisting of American Physical Society Physics and Astronomy Classification Scheme (PACS) numbers as nodes representing scientific concepts. Two PACS numbers are linked if there exist publications that reference them simultaneously. We locate scientific fields using a community finding algorithm, and describe the time evolution of these fields over the course of 1985-2006. The communities we identify map to known scientific fields, and their age depends on their size and activity. We expect our approach to quantifying the evolution of ideas to be relevant for making predictions about the future of science and thus help to guide its development.