Many cells employ cadherin complexes (c-sites) on the cell membrane to attach to neighboring cells, as well as integrin complexes (i-sites) to attach to a substrate in order to accomplish cell migration. This paper analyzes a model for the motion of a group of cells connected by c-sites. We begin with two cells connected by a single c-site and analyze the resultant motion of the system. We find that the system is irrotational. We present a result for reducing the number of c-sites in a system with c-sites between pairs of cells. This greatly simplifies the general system, and provides an exact solution for the motion of a system of two cells and several c-sites.Then a method for analyzing the general cell system is presented. This method involves 0-row-sum, symmetric matrices. A few results are presented as well as conjectures made that we feel will greatly simplify such analyses. The thesis concludes with the proposal of a framework for analyzing a dynamic cell system in which stochastic processes govern the attachment and detachment of c-sites.

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Yes / Ion channels regulate many aspects of cell physiology, including cell proliferation, motility, and migration, and aberrant expression and activity of ion channels is associated with various stages of tumor development, with K+ and Cl- channels now being considered the most active during tumorigenesis. Accordingly, emerging in vitro and preclinical studies have revealed that pharmacological manipulation of ion channel activity offers protection against several cancers. Merkel cell polyomavirus (MCPyV) is a major cause of Merkel cell carcinoma (MCC), primarily due to the expression of two early regulatory proteins termed small and large tumour antigens (ST and LT, respectively). Several molecular mechanisms have been attributed to MCPyVmediated cancer formation but thus far, no studies have investigated any potential link to cellular ion channels. Here we demonstrate that Cl- channel modulation can reduce MCPyV STinduced cell motility and invasiveness. Proteomic analysis revealed that MCPyV ST upregulates two Cl- channels; CLIC1 and CLIC4, which when silenced, inhibit MCPyV STinduced motility and invasiveness, implicating their function as critical to MCPyV-induced metastatic processes. Consistent with these data, we confirmed that CLIC1 and CLIC4 are upregulated in primary MCPyV-positive MCC patient samples. We therefore, for the first time, implicate cellular ion channels as a key host cell factor contributing to virus-mediated cellular transformation. Given the intense interest in ion channel modulating drugs for human disease, this highlights CLIC1 and CLIC4 activity as potential targets for MCPyV-induced MCC. / BBSRC DTP studentship (BB/J014443/1) and Royal Society University Research Fellowship to JM (UF100419)

Transient elevations in Ca2+ have previously been shown to promote focal adhesion disassembly and cell motility. Yet the targets of these Ca2+ transients have not been fully examined. In this study, we demonstrate that CaMK-II, a Ca2+/calmodulin dependent protein kinase, is activated in response to β1 integrin engagement with fibronectin to influence fibroblast adhesion and motility. We also show that CaMK-II is dynamically localized to the cell surface using Total Internal Reflection Fluorescence microscopy (TIRFm) and that inhibition of CaMK-II with two mechanistically distinct, membrane permeant inhibitors accelerates spreading on fibronectin, enlarges paxillin-containing focal adhesions and blocks cell motility. On the other hand, expression of constitutively active CaMK-II reduces cell attachment, eliminates paxillin from focal adhesions and decreases the phospho-tyrosine levels of both FAK and paxillin. Cell spreading, paxillin incorporation into focal adhesions and phospho-tyrosine levels of FAK and paxillin are restored when cells expressing constitutively active CaMK-II are subsequently treated with myr-AIP, a specific CaMK-II catalytic inhibitor. Like CaMK-II inhibition, constitutively active CaMK-II blocks cell motility. Thus, both CaMK-II inhibition and constitutive activation block cell motility through over-stabilization or destabilization of focal adhesions, respectively. These findings provide the first direct evidence that CaMK-II promotes focal adhesion turnover and thus enables cell motility by stimulating tyrosine dephosphorylation of focal adhesion proteins.

For years, researchers have studied the movement of cells and mathematicians have attempted to model the movement of the cell using various methods. This work is an extension of the work done by Zheltukhin and Lui (2011), Mathematical Biosciences 229:30-40, who simulated the stress and displacement of a one-dimensional cell using a model based on viscoelastic theory. The report is divided into three main parts. The first part considers viscoelastic models with a first-order constitutive equation and uses the standard linear model as an example. The second part extends the results of the first to models with second-order constitutive equations. In this part, the two examples studied are Burger model and a Kelvin-Voigt element connected with a dashpot in series. In the third part, the effects of substrate with variable stiffness are explored. Here, the effective adhesion coefficient is changed from a constant to a spatially-dependent function. Numerical results are generated using two different functions for the adhesion coefficient. Results of this thesis show that stress on the cell varies greatly across each part of the cell depending on the constitute equation we use, while the position and velocity of the cell remain essentially unchanged from a large-scale point of view.

Research in the biomedical sciences is incredibly diverse and often involves the interaction of specialists in a variety of fields. In particular, quantitative, mathematical, and computational methods are increasingly playing significant roles in studying problems arising in biomedical science. This is particularly exciting for mathematical modeling as the complexity of biological systems poses new challenges to modelers and leads to interesting mathematical problems. On the other hand mathematical modeling can provide considerable insight to laboratory and clinical researchers. In this thesis we develop mathematical representations for three biological processes that are of current interest in biomedical science. A deeper understanding of these processes is desirable not only from the standpoint of basic science, but also because of the connections these processes have with certain diseases. The processes we consider are collective cell motility, bone remodeling, and injury response in articular cartilage. Our goals are to develop mathematical representations of these processes that can provide a conceptual framework for understanding the processes at a fundamental level, that make rigorous the intuition biological researchers have developed about these processes, and that help to translate theoretical and experimental work into information that can be used in clinical settings where the primary concern is in treating diseases associated with the process.

Erbin belongs to the LAP (leucine-rich repeat and PDZ domain) family of scaffolding proteins that play important roles in orchestrating cell signaling. Here, we show that Erbin functions as a tumor suppressor in colon cancer. Analysis of Erbin expression in patient specimens reveals that Erbin is downregulated at both mRNA and protein levels in tumor tissues. Functionally, knockdown of Erbin disrupts epithelial cell polarity and increases cell proliferation in 3D culture. In addition, silencing Erbin results in an increase in the amplitude and duration of signaling through Akt and RAS/RAF pathways. Moreover, Erbin-loss induces epithelial-mesenchymal transition (EMT), which coincides with a significant increase in cell migration and invasion. Erbin interacts with KSR1 and displaces it from the RAF/MEK/ERK complex to prevent signaling propagation. Furthermore, genetic deletion of Erbin in Apc knockout mice promotes tumorigenesis and significantly reduces survival. Tumor organoids derived from Erbin/Apc double knockout mice have increased tumor initiation potential along with increased Wnt target gene expression as seen by qPCR. Collectively, the studies within this dissertation identify Erbin as a negative regulator of EMT and tumor progression by directly suppressing Akt and RAS/RAF signaling in vivo.

Durant mon travail de thèse, j'ai étudié le rôle central de l'ADF/cofiline, une protéine qui se lie au cytosquelette d'actine, décore spécifiquement les parties ‘âgées' des filaments d'actine, diminue localement par un facteur 5 la rigidité du filament et provoque la fragmentation du filament à l'interface entre les sections nues et décorées. Dans ma première étude (Suarez et al., Current Biology, 2011), j'ai utilisé la microscopie à onde évanescente et une ADF/cofiline fluorescente pour démontrer que l'ADF/cofiline est un marqueur de l'état nucléotidique (ATP, ADP-Pi ou ADP) des sous-unités d'un filament d'actine en cours de polymérisation. De plus, l'ADF/cofiline, en accélérant la dissociation du phosphate inorganique (Pi), limite la taille du cap ATP/ADP-Pi du filament d'actine, sans toutefois le réduire à une taille zéro. Des analyses statistiques sur filaments isolés établissent une corrélation parfaite entre la densité de fixation de l'ADF/cofiline et son efficacité de fragmentation. Paradoxalement, l'efficacité de fragmentation est maximale pour une densité d'ADF/cofiline de 0.5. Ceci est confirmé par des analyses supplémentaires qui montrent que les sites de fragmentation du filament coïncident avec la position des frontières entre zones décorées et zones nues. Les conséquences de ce dernier résultat paradoxal sont l'objet de ma seconde étude (McCullough et al., 2011, Biophysical Journal). En combinant différentes sources d'ADF/cofilines (vertébré et levure) et d'actines (vertébré et levure), nous montrons, sur les quatre couples actine-ADF/cofiline possibles, qu'il existe une très forte corrélation entre (1) l'efficacité de fragmentation (qui dépend de la combinaison entre actine et ADF/cofiline) et (2) la déformation du filament, mesurée à la frontière entre zone décorée et zone nue. Au cours de ma troisième étude (Reymann et al., Molecular Biology of the Cell, 2011), nous montrons que le mécanisme de fragmentation ADF/cofiline-dépendant, établi à l'échelle d'un filament isolé, peut s'appliquer aussi à l'échelle d'une comète d'actine qui comporte un réseau complexe de filaments. Mon travail de thèse a montré que le mode d'action de l'ADF/cofiline se situe à l'intersection entre mécanismes microscopiques et macroscopiques, d'une part, et entre chimie et physique, d'autre part. Les caractéristiques microscopiques des interactions de cette protéine avec un filament d'actine isolé sont fondamentales pour expliquer des évènements macroscopiques, comme la fragmentation de filaments ou de structures complexes. D'autre part, nous avons montré comment les propriétés chimiques de l'ADF/cofiline modifient les propriétés physiques locales du filament et conduisent à la fragmentation. L'ADF/cofiline a un rôle central pour l'intégration de mécanismes physico-chimiques, à l'échelle microscopique, afin d'assurer un comportement cohérent à l'échelle de la cellule. / During my thesis, I have studied the pivotal role of ADF/cofilin, a protein that binds to the actin cytoskeleton, specifically decorates ‘old' actin filament parts, decreases by a factor of 5 the local filament rigidity and triggers filament fragmentation at boundaries between decorated and non-decorated filament sections. In my first study (Suarez et al., Current Biology, 2011), I have used evanescent wave microscopy and labeled ADF/cofilin to demonstrate that ADF/cofilin is a marker of the nucleotide state (i.e. ATP, ADP-Pi or ADP) associated with the actin sub-units in actively polymerizing filaments. In addition, because ADF/cofilin accelerates inorganic phosphate (Pi) release, the size of the ATP/ADP-Pi cap is diminished, although it cannot be reduced to zero. Fragmentation events frequency, determined from a thorough analysis of a population of single filaments decorated with labeled ADF/cofilin, is perfectly correlated with the binding density of ADF/cofilin on filaments. However, the maximal severing efficiency is obtained for half ADF/cofilin density. This paradoxical result is confirmed by analysis showing that severing sites are mainly associated with boundaries between decorated and bare actin filament sections. In consequence, in a second paper (McCullough et al., Biophysical Journal, 2011), I have took part in the study of actin filament deformation in relation with severing efficiency. Using different ADF/cofilin (vertebrate and yeast) and actin (vertebrate and yeast), we have shown that filament deformation at the boundary between bare and ADF/cofilin-decorated filament sections (which depends on the ADF/cofilin/actin combination) and severing are highly correlated. During my third study, (Reymann et al., Molecular Biology of the Cell, 2011), we established that stochastic dynamics, discovered at the molecular level for single filaments (or bundles of them), is also relevant to describe the macroscopic fragmentation of a comet tail consisting of hundreds of thousands filaments. I have shown that ADF/cofilin activity is at the crossroad between macroscopic and microscopic systems, on one hand, and physics and chemistry, on the other hand. The characteristics of microscopic interactions of ADF/cofilin with a single filament are fundamental to understand the macroscopic dynamics of a fragmenting comet. In addition, we have established how the binding of ADF/cofilin (chemistry) controls the mechanical properties of the filament (physics) before fragmentation. ADF/cofilin is essential in the integration of physical and chemical mechanisms at the microscopic level, to ensure consistent behavior at the cell scale.