Connecting mathematical models of pattern formation & organization at cell and/or tissue level with experimental results

Kelsey Gasior

University of Notre Dame (Department of Applied and Computational Mathematics and Statistics)

"Understanding the influence of cell-cell contact and TGF-β signaling on the epithelial mesenchymal transition in MCF7 breast carcinoma cells"

The epithelial mesenchymal transition (EMT) is a process by which epithelial cells lose their characteristic adhesion and gain the migratory properties associated with mesenchymal cells. Triggered by exogenous factors from the surrounding microenvironment, EMT produces phenotypic and behavioral changes that are maintained even after the cell migrates away from a tumor to form a metastasis. Within the complex system of intracellular signaling pathways associated with EMT, we identify a feedback loop between E-cadherin, a transmembrane protein involved in cellular adhesion, and Slug, a transcription factor associated with the mesenchymal phenotype. Here we present a simple mathematical model using ordinary differential equations (ODEs) that examines the relationship between E-cadherin and Slug during EMT in response to exogenous pro-epithelial (cell-cell contact) and pro-mesenchymal (TGF-β signaling) factors. A cell’s ability to maintain the mesenchymal phenotype after leaving the tumor microenvironment suggests that there is a bistable switch underlying EMT. We hypothesize that a bistable switch due to a loss of cell-cell contact is reversible, while a switch due to TGF-β activation is irreversible. This model shows how changes in the tumor microenvironment and intracellular changes via signaling pathways are closely linked and the loss of cell-cell contact and activation of the TGF-β must work together to allow some cells to undergo EMT. The results of this model for E-cadherin and Slug levels are then compared to the experimental data recently generated using MCF7 breast carcinoma cells. Experiments examined changes in cell-cell contact and exogenous TGF-β and data were gathered using qPCR, flow cytometry, and immunocytochemistry (ICC). Our model works well to predict E-cadherin and Slug mRNA expression in low confluence experiments but struggles to predict the expression of either factor in high confluence environments. Ultimately, this work establishes a framework for modeling the influence of multiple factors on EMT, while also highlighting the issues that arise when comparing experimental results to theoretical predictions.
Additional authors: Sudin Bhattacharya, Michigan State University; Marlene Hauck, North Carolina State University

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Ginger Hunter

Clarkson University (Biology)

"Investigating the rules of cell contact-mediated tissue patterning using the Drosophila peripheral nervous system"

The correct spatial organization of cell types within a tissue is critical for tissue development and homeostasis. The spot pattern of sensory bristles on the dorsal thorax of the fruit fly Drosophila Melanogaster is an example of a self-organizing tissue, and failure to form and organize sensory bristles leads to impaired function of the peripheral nervous system. Experimental and theoretical results support a role for cell protrusion based, contact mediated, signaling mechanisms in the spacing of sensory bristle precursors during patterning stages. Here, we present recent results from an RNAi-mediated genetic screen designed to identify these signaling mechanisms. An expected major phenotype of the RNAi screen is the disruption of the tissue-wide sensory bristle pattern. In order to facilitate our analysis, we have developed a quantitative, computational approach towards the classification of control and mutant spot patterns. Our approach involves the detection of sensory bristle precursors in a patterning tissue, followed by extraction of features that facilitate the reproducible measurement and detection of different bristle organizations. The results of these studies so far have identified a number of genes whose knockdowns result in defects in pattern formation. Furthermore our classification system has successfully been used to identify mutant spot patterns. We anticipate that results from our screen will identify new mechanisms of cell-cell communication during peripheral nervous system patterning, as well as new tools for the quantitative analysis of spot patterns in vivo.
Additional authors: Emmanuel Asante-Asamani, Department of Mathematics, Clarkson University; Audrey Neighmond, Oberlin College; Jacob Inyang, Clarkson University; Katrina Ahn, Clarkson University; Caitlin Minardo, Clarkson University.

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Veronica Ciocanel

Duke University (Mathematics)

"Modeling and data analysis for actin-myosin dynamics and organization"

Actin filaments are polymers that interact with myosin motor proteins and play important roles in cell motility, shape, and development. Depending on its function, this dynamic network of interacting proteins reshapes and organizes in a variety of structures, including bundles, clusters, and contractile rings. Motivated by observations from the reproductive system of the roundworm C. elegans, we use an agent-based modeling framework to simulate interactions between actin filaments and myosin motor proteins inside cells. We develop techniques based on topological data analysis to understand time-series data extracted from these filament network interactions, as well as from fluorescence experiments. These measures allow us to compare the filament organization resulting from myosin motors with different properties. In particular, we have studied how different myosin motor proteins may interact to regulate various actin organizations, and provided insights into parameters that may regulate structures observed in vitro and in vivo.
Additional authors: Adriana Dawes; Scott McKinley

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Diana White

Clarkson University (Department of Mathematics)

"Understanding the regulation of growth and shedding of disks in the rod cells of zebrafish"

Retinal photoreceptor cells, rods and cones, in the eye convert light energy into electrical signals that stimulate sight. In humans, peripherally located rods are important for night vision, while centrally located cones are responsible for daytime/color vision. Rods consist of a rod outer segment (ROS), inner segment, cell body and synaptic terminal. The ROS, consisting of stacked, discrete membraneous discs, undergoes a process of continuous renewal in which newly constructed discs are added at the base (growth) and the oldest discs are shed from the tip. In normal/healthy eyes, the ROS maintains a homeostatic length by balancing growth and shedding. How this balance is controlled is unknown. New experiments have shown that ROS, when made to grow faster with the growth factor rheb, do not accelerate shedding to offset increased growth. Here, we develop and analyze a model of ROS length control, to help provide insight into (1) normal cell dynamics, and (2) the overshoot of homeostatic length when rheb is added. A 3-D ODE model is used to describe the transitions of disks from compartments corresponding to disk addition at the base, disk translocation along the ROS when mature, and those disks that are shed and undergo phagocytosis.

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