Mathematical models in biology

TL;DR

This paper presents mathematical models for various biological phenomena including aerotaxis, growth cone chemotaxis, and endothelial cell responses to shear stress, providing insights and analytical estimates consistent with experimental data.

Contribution

It introduces new mathematical models for aerotaxis, growth cone guidance, and endothelial cell mechanics, linking theoretical predictions with experimental observations.

Findings

Fast, non-methylation adaptation explains aerotaxis behavior.

Growth cone guidance can be modeled with internal switch mechanisms.

Endothelial cell deformation models align with observed morphological changes.

Abstract

Aerotaxis is the particular form of chemotaxis in which oxygen plays the role of both the attractant and the repellent. Aerotaxis occurs without methylation adaptation, and it leads to fast and complete aggregation toward the most favorable oxygen concentration. Biochemical pathways of aerotaxis remain largely elusive, however, aerotactic pattern formation is well documented. This allows mathematical modeling to test plausible hypotheses about the biochemical mechanisms. Our model demonstrates that assuming fast, non-methylation adaptation produces theoretical results that are consistent with experimental observations. We obtain analytical estimates for parameter values that are difficult to obtain experimentally. Chemotaxis in growth cones differs from gradient sensing in other animal cells, because growth cones can change their attractive or repulsive response to the same chemical gradient based on their internal calcium or cAMP levels. We create two models describing different aspects of growth cone guidance. One model describes the internal switch that determines the direction of movement. However, this model allows chemotaxis under certain conditions only, so a second model is created to propose a mechanism that allows growth cone guidance in any environment. Endothelial cells go through extensive morphological changes when exposed to shear stress due to blood flow. These morphological changes are thought to be at least partially the result of mechanical signals, such as deformations, transmitted to the cell structures. Our model describes an endothelial cell as a network of viscoelastic Kelvin bodies with experimentally obtained parameters. Qualitative predictions of the model agree with experiments.