Nonlinear studies of tumor morphological stability using a two-fluid flow model.

We consider the nonlinear dynamics of an avascular tumor at the tissue scale using a two-fluid flow Stokes model, where the viscosity of the tumor and host microenvironment may be different. The viscosities reflect the combined properties of cell and extracellular matrix mixtures. We perform a linear morphological stability analysis of the tumors, and we investigate the role of nonlinearity using boundary-integral simulations in two dimensions. The tumor is non-necrotic, although cell death may occur through apoptosis. We demonstrate that tumor evolution is regulated by a reduced set of nondimensional parameters that characterize apoptosis, cell-cell/cell-extracellular matrix adhesion, vascularization and the ratio of tumor and host viscosities. A novel reformulation of the equations enables the use of standard boundary integral techniques to solve the equations numerically. Nonlinear simulation results are consistent with linear predictions for nearly circular tumors. As perturbations develop and grow, the linear and nonlinear results deviate and linear theory tends to underpredict the growth of perturbations. Simulations reveal two basic types of tumor shapes, depending on the viscosities of the tumor and microenvironment. When the tumor is more viscous than its environment, the tumors tend to develop invasive fingers and a branched-like structure. As the relative ratio of the tumor and host viscosities decreases, the tumors tend to grow with a more compact shape and develop complex invaginations of healthy regions that may become encapsulated in the tumor interior. Although our model utilizes a simplified description of the tumor and host biomechanics, our results are consistent with experiments in a variety of tumor types that suggest that there is a positive correlation between tumor stiffness and tumor aggressiveness.

Density-dependent quiescence in glioma invasion: instability in a simple reaction-diffusion model for the migration/proliferation dichotomy.

Gliomas are very aggressive brain tumours, in which tumour cells gain the ability to penetrate the surrounding normal tissue. The invasion mechanisms of this type of tumour remain to be elucidated. Our work is motivated by the migration/proliferation dichotomy (go-or-grow) hypothesis, i.e. the antagonistic migratory and proliferating cellular behaviours in a cell population, which may play a central role in these tumours. In this paper, we formulate a simple go-or-grow model to investigate the dynamics of a population of glioma cells for which the switch from a migratory to a proliferating phenotype (and vice versa) depends on the local cell density. The model consists of two reaction-diffusion equations describing cell migration, proliferation and a phenotypic switch. We use a combination of numerical and analytical techniques to characterize the development of spatio-temporal instabilities and travelling wave solutions generated by our model. We demonstrate that the density-dependent go-or-grow mechanism can produce complex dynamics similar to those associated with tumour heterogeneity and invasion.

An undergraduate laboratory exercise examining the psychomotor stimulant effects of caffeine in laboratory rats.

This paper describes an exercise in a Systems and Behavioral Neuroscience with Laboratory class, an introductory laboratory class taken by Barnard College students majoring in a wide range of academic topics. The study took place over three weeks, allowing students to assess the effects of caffeine on motor stimulation in laboratory rats. The within-subject design involved injecting rats with three different caffeine doses and measuring five different motor outputs in a standard open field. Students completed four different assignments related to this study, demonstrating acquisition of the stated learning goals. This lab exercise allowed students to learn about basal ganglia neural circuitry and stimulant pharmacology, to work directly with an animal model, and to generate enough data to perform statistical analyses. Course evaluations suggest that students liked learning about caffeine, a stimulant many of them have personal experience consuming. They also expressed appreciation for working with rats and for learning how to analyze data. This study can easily be implemented at most undergraduate institutions under minimal cost. The wide-ranging effects of caffeine also permit for flexibility in experimental design, allowing instructors and students options for different avenues of investigation.

Predictions of tumour morphological stability and evaluation against experimental observations.

The hallmark of malignant tumours is their spread into neighbouring tissue and metastasis to distant organs, which can lead to life threatening consequences. One of the defining characteristics of aggressive tumours is an unstable morphology, including the formation of invasive fingers and protrusions observed both in vitro and in vivo. In spite of extensive biological, clinical and modelling study and research at physical scales ranging from the molecular to the tissue, the driving dynamics of tumour invasiveness are not completely understood, partly because it is challenging to observe and study cancer as a multi-scale system. Mathematical modelling has been applied to provide further insights into these complex invasive and metastatic behaviours. Modelling a solid tumour as an incompressible fluid, we consider three possible constitutive relations to describe tumour growth, namely Darcy's law, Stokes' law and the combined Darcy-Stokes law. We study the tumour morphological stability described by each model and evaluate the consistency between theoretical model predictions and experimental data from in vitro three-dimensional multicellular tumour spheroids. The analysis reveals that the Stokes model is the most consistent with the experimental observations, and that it predicts our experimental tumour growth is marginally stable. We further show that it is feasible to extract parameter values from a limited set of data and create a self-consistent modelling framework that can be extended to the multi-scale study of cancer.

Early involvement of synapsin III in neural progenitor cell development in the adult hippocampus.

Synapsin III is a synaptic vesicle-associated protein that is expressed in cells of the subgranular layer of the hippocampal dentate gyrus, a brain region known to sustain substantial levels of neurogenesis into adulthood. Here we tested the hypothesis that synapsin III plays a role in adult neurogenesis with synapsin III knockout and wild-type mice. Immunocytochemistry of the adult hippocampal dentate gyrus revealed that synapsin III colocalizes with markers of neural progenitor cell development (nestin, PSA-NCAM, NeuN, and Tuj1) but did not colocalize with markers of mitosis (Ki67 and PCNA). Because neurogenesis consists of a number of stages, the proliferation, survival, and differentiation of neural progenitor cells were systematically quantitated in the hippocampal dentate gyrus of adult synapsin III knockout and wild-type mice. We found a 30% decrease in proliferation and a 55% increase in survival of neural progenitor cells in synapsin III knockout mice. We also observed a 6% increase in the number of neural progenitor cells that differentiated into neurons. No difference in the volume of the dentate gyrus was observed between synapsin III knockout and wild-type mice. Collectively, our results demonstrate a novel role for synapsin III in regulating the proliferation of neural progenitor cells in the adult hippocampal dentate gyrus. These findings suggest a distinct function for this synaptic vesicle protein, in addition to its role in neurotransmission.

Bmi-1-green fluorescent protein-knock-in mice reveal the dynamic regulation of bmi-1 expression in normal and leukemic hematopoietic cells.

The ability to self-renew is essential for all kinds of stem cells regardless of tissue type. One of the best candidate genes involved in conferring self-renewal capacity is Bmi-1, which has been proven to be essential for the maintenance of both normal adult hematopoietic and leukemia stem cells, as well as adult neural stem cells. To investigate the possible role of Bmi-1 in other cell types that also self-renew, we generated Bmi-1-green fluorescent protein (GFP)-knock-in mice, in which GFP was expressed under the endogenous transcriptional regulatory elements of the Bmi-1 gene. Using these targeted reporter mice, we demonstrated that Bmi-1 is expressed in hematopoietic stem cells (HSCs) at its highest levels and downregulated upon commitment to differentiation. An in vivo reconstitution assay revealed that the frequency of HSCs was 1/16 in Bmi-1high c-kit+ lin -Sca-1+ bone marrow (BM) cells and 1/49 in Bmi-1 high lin- BM cells, suggesting that Bmi-1 may serve as a marker for normal HSCs. In murine leukemia models induced by P210BCR/ABL or TEL/PDGFbetaR + AML1/ETO, Bmi-1 was not overexpressed in leukemic HSCs, despite the increase in the HSC numbers. Bmi-1 was expressed at its highest levels in undifferentiated leukemia cells. Furthermore, in several other nonhematopoietic tissues, cells could be separated into distinct subpopulations with differential Bmi-1 expression. Thus, these mice allow for the isolation of viable Bmi-1-expressing cells and have the potential to become a useful tool for understanding the role of Bmi-1 in normal and cancer stem cells in multiple tissue types. Disclosure of potential conflicts of interest is found at the end of this article.

Repeated restraint stress suppresses neurogenesis and induces biphasic PSA-NCAM expression in the adult rat dentate gyrus.

Chronic restraint stress has been shown to induce structural remodelling throughout the interconnected dentate gyrus-CA3 fields. To find out how this stressor affects the rate of adult hippocampal neurogenesis, we subjected rats to acute or chronic restraint stress and assessed the proliferation, survival and differentiation of newly born cells in the dentate gyrus. We also examined polysialylated neural cell adhesion molecule expression, a molecule normally expressed in immature neurons and important for morphological plasticity. The results show that acute restraint stress did not change either the proliferation of dentate gyrus precursor cells or the expression of polysialylated neural cell adhesion molecule, whereas 3 weeks of chronic restraint stress suppressed proliferation by 24% and increased polysialylated neural cell adhesion molecule expression by 40%. The study was extended for an additional 3 weeks to trace the survival and development of the cells born after the initial 3 weeks of restraint. Rats subjected to 6 weeks of daily restraint stress exhibited suppressed cell proliferation and attenuated survival of the recently born cells after the extended time course, resulting in a 47% reduction of granule cell neurogenesis. Furthermore, 6 weeks of chronic stress significantly reduced the total number of granule cells by 13% and the granule cell layer volume by 5%. Expression of polysialylated neural cell adhesion molecule followed a biphasic time course, displaying a significant up-regulation after 3 weeks of daily restraint stress that was lost after 6 weeks of stress. These studies may help us understand the basis for hippocampal shrinkage and raise questions about the ultimate reversibility of the effects of chronic stress.