Condensation tendency and planar isotropic actin gradient induce radial alignment in confined monolayers

A monolayer of highly motile cells can establish long-range orientational order, which can be explained by hydrodynamic theory of active gels and fluids. However, it is less clear how cell shape changes and rearrangement are governed when the monolayer is in mechanical equilibrium states when cell motility diminishes. In this work, we report that rat embryonic fibroblasts (REF), when confined in circular mesoscale patterns on rigid substrates, can transition from the spindle shapes to more compact morphologies. Cells align radially only at the pattern boundary when they are in the mechanical equilibrium. This radial alignment disappears when cell contractility or cell-cell adhesion is reduced. Unlike monolayers of spindle-like cells such as NIH-3T3 fibroblasts with minimal intercellular interactions or epithelial cells like Madin-Darby canine kidney (MDCK) with strong cortical actin network, confined REF monolayers present an actin gradient with isotropic meshwork, suggesting the existence of a stiffness gradient. In addition, the REF cells tend to condense on soft substrates, a collective cell behavior we refer to as the ‘condensation tendency’. This condensation tendency, together with geometrical confinement, induces tensile prestretch (i.e. an isotropic stretch that causes tissue to contract when released) to the confined monolayer. By developing a Voronoi-cell model, we demonstrate that the combined global tissue prestretch and cell stiffness differential between the inner and boundary cells can sufficiently define the cell radial alignment at the pattern boundary

2-D Epithelial Tissues, Cell Mechanics, and Voronoi Tessellation

In this thesis, we develop a new computational method using Voronoi vertex model and energy to describe the cell-cell interaction among the epithelial tissue. Several studies and simulations will be showed such as equilibrium states, wound closure process, and abnormal growth. We also perform analysis on circular epithelial wound closure process

Biological Models With Time Delay

This MQP can be divided into three main chapters. For each chapter, we studied three different mathematical models, which are the Logistic Growth model, the SIR model and the Chemostat model. These biological mathematical models all have time delay in part of their processes. Based on the specific phenomenological assumptions, we have different ways of building up the model through ordinary differential equations. The goal of this project is to investigate three models with time delay. We will also perform global sensitivity analysis for each model and study how uncertainty in the output of each model can be attributed to different sources of uncertainty in the model input. Applications for each model with time delay will be provided in this project with numerical results

Foreign Dining Experience: A Feasibility Study of a Non-Chinese Food Venture at Hangzhou Dianzi University

The continued growth of the foreign student population at - Hangzhou Dianzi University (HDU) results in a higher demand for non-Chinese food in the campus dining halls. - Our goal is to help Logistics Service Corporation (LSC), the company that operates the dining halls at HDU, satisfy foreign students’ desire for non-Chinese food while aiming to achieve profit. In our analysis, we found that both foreign and domestic students desire non-Chinese cuisines and a non-Chinese food venture at HDU might be profitable. We conclude our report with recommendations for offering foreign students ways to understand the menu, preparing a trial run of the non-Chinese food venture, and expanding or repurposing dining halls at HDU