Grading schemes for breast cancer diagnosis are predominantly based on pathologists' qualitative assessment of altered nuclear structure from 2D brightfield microscopy images. However, cells are three-dimensional (3D) objects with features that are inherently 3D and thus poorly characterized in 2D. Our goal is to quantitatively characterize nuclear structure in 3D, assess its variation with malignancy, and investigate whether such variation correlates with standard nuclear grading criteria.
Methodology
We applied micro-optical computed tomographic imaging and automated 3D nuclear morphometry to quantify and compare morphological variations between human cell lines derived from normal, benign fibrocystic or malignant breast epithelium. To reproduce the appearance and contrast in clinical cytopathology images, we stained cells with hematoxylin and eosin and obtained 3D images of 150 individual stained cells of each cell type at sub-micron, isotropic resolution. Applying volumetric image analyses, we computed 42 3D morphological and textural descriptors of cellular and nuclear structure.
Principal Findings
We observed four distinct nuclear shape categories, the predominant being a mushroom cap shape. Cell and nuclear volumes increased from normal to fibrocystic to metastatic type, but there was little difference in the volume ratio of nucleus to cytoplasm (N/C ratio) between the lines. Abnormal cell nuclei had more nucleoli, markedly higher density and clumpier chromatin organization compared to normal. Nuclei of non-tumorigenic, fibrocystic cells exhibited larger textural variations than metastatic cell nuclei. At p<0.0025 by ANOVA and Kruskal-Wallis tests, 90% of our computed descriptors statistically differentiated control from abnormal cell populations, but only 69% of these features statistically differentiated the fibrocystic from the metastatic cell populations.
Conclusions
Our results provide a new perspective on nuclear structure variations associated with malignancy and point to the value of automated quantitative 3D nuclear morphometry as an objective tool to enable development of sensitive and specific nuclear grade classification in breast cancer diagnosis.
Extreme events, a type of collective behavior in complex networked dynamical systems, often can have catastrophic consequences. To develop effective strategies to control extreme events is of fundamental importance and practical interest. Utilizing transportation dynamics on complex networks as a prototypical setting, we find that making the network “mobile” can effectively suppress extreme events. A striking, resonance-like phenomenon is uncovered, where an optimal degree of mobility exists for which the probability of extreme events is minimized. We derive an analytic theory to understand the mechanism of control at a detailed and quantitative level, and validate the theory numerically. Implications of our finding to current areas such as cybersecurity are discussed.
The relation between flux and fluctuation is fundamental to complex physical systems that support and transport flows. A recently obtained law predicts monotonous enhancement of fluctuation as the average flux is increased, which in principle is valid but only for large systems. For realistic complex systems of small sizes, this law breaks down when both the average flux and fluctuation become large. Here we demonstrate the failure of this law in small systems using real data and model complex networked systems, derive analytically a modified flux-fluctuation law, and validate it through computations of a large number of complex networked systems. Our law is more general in that its predictions agree with numerics and it reduces naturally to the previous law in the limit of large system size, leading to new insights into the flow dynamics in small-size complex systems with significant implications for the statistical and scaling behaviors of small systems, a topic of great recent interest.
Mesoscopic Interactions and Species Coexistence in Evolutionary Game Dynamics of Cyclic Competitions
Evolutionary dynamical models for cyclic competitions of three species (e.g., rock, paper, and scissors, or RPS) provide a paradigm, at the microscopic level of individual interactions, to address many issues in coexistence and biodiversity. Real ecosystems often involve competitions among more than three species. By extending the RPS game model to five (rock-paper-scissors-lizard-Spock, or RPSLS) mobile species, we uncover a fundamental type of mesoscopic interactions among subgroups of species. In particular, competitions at the microscopic level lead to the emergence of various local groups in different regions of the space, each involving three species. It is the interactions among the groups that fundamentally determine how many species can coexist. In fact, as the mobility is increased from zero, two transitions can occur: one from a five- to a three-species coexistence state and another from the latter to a uniform, single-species state. We develop a mean-field theory to show that, in order to understand the first transition, group interactions at the mesoscopic scale must be taken into account. Our findings suggest, more broadly, the importance of mesoscopic interactions in coexistence of great many species.
Dynamical systems based on the minority game (MG) have been a paradigm for gaining significant insights into a variety of social and biological behaviors. Recently, a grouping phenomenon has been unveiled in MG systems of multiple resources (strategies) in which the strategies spontaneously break into an even number of groups, each exhibiting an identical oscillation pattern in the attendance of game players. Here we report our finding of spontaneous breakup of resources into three groups, each exhibiting period-three oscillations. An analysis is developed to understand the emergence of the striking phenomenon of triple grouping and period-three oscillations. In the presence of random disturbances, the triple-group/period-three state becomes transient, and we obtain explicit formula for the average transient lifetime using two methods of approximation. Our finding indicates that, period-three oscillation, regarded as one of the most fundamental behaviors in smooth nonlinear dynamical systems, can also occur in much more complex, evolutionary-game dynamical systems. Our result also provides a plausible insight for the occurrence of triple grouping observed, for example, in the U.S. housing market.
Understanding the dynamics of human movements is key to issues of significant current interest such as behavioral prediction, recommendation, and control of epidemic spreading. We collect and analyze big data sets of human movements in both cyberspace (through browsing of websites) and physical space (through mobile towers) and find a superlinear scaling relation between the mean frequency of visit〈f〉and its fluctuation σ : σ ∼〈f⟩β with β ≈ 1.2. The probability distribution of the visiting frequency is found to be a stretched exponential function. We develop a model incorporating two essential ingredients, preferential return and exploration, and show that these are necessary for generating the scaling relation extracted from real data. A striking finding is that human movements in cyberspace and physical space are strongly correlated, indicating a distinctive behavioral identifying characteristic and implying that the behaviors in one space can be used to predict those in the other.