Abstract:
Cell migration along gradients in adhesion molecules (haptotaxis) is essential for develop- ment, wound healing, and immune responses, but also contributes to cancer metastasis. This thesis develops a mathematical model to understand how cells sense and respond to adhesion gradients. We extend a one-dimensional model of cell migration by coupling local adhesion strength to actin polymerization rate. This feedback allows cells to sense adhesion differences between their front and back, creating directional bias toward higher adhesion. We test the model on exponential gradients matching experimental conditions and identify four migration modes depending on cell activity: cells stuck at peaks, smooth oscillatory motion, mixed slip-stick and smooth behavior, and purely slip- stick migration. Comparison with experiments shows strong agreement. Both model and experiments demonstrate a strong bias toward higher adhesion on gradient surfaces, compared to random directionless movement on uniform surfaces. The model reproduces position-dependent behavior: nearly universal directional movement far from the peak, decreasing to random motion near the peak. We explain this through the activity differ- ence between front and back, which varies spatially along the gradient. The model also captures cell length and velocity trends, individual trajectory patterns, and behavior on inverted profiles. The main finding is that adhesion-actin coupling creates gradient sens- ing without requiring dedicated chemotaxis machinery. The activity difference between front and back determines directional strength: large activity differences produce strong haptotaxis up the adhesion gradient, while activity differences near zero eliminate direc- tional preference. This simple mechanism explains diverse experimental observations and makes testable predictions for future work.
