Construction of travelling wave models of collective cell migration using variational symmetries of the Fisher KPP model #

Johannes Borgqvist, Associate professor Fredrik Ohlsson, Ruth E Baker

13:30 Tuesday in 4Q04.

Part of the Travelling waves session.

Abstract #

Lie symmetries constitute an immensely powerful mathematical tool for solving differential equations, reducing systems of differential equations to find equivalent systems of simpler form and constructing classes of differential equations. Lie symmetries are continuous transformations mapping solutions to other solutions and they are the basis for multiple Nobel Prizes in physics. However, despite the fact that numerous mechanistic models in mathematical biology consist of systems of differential equations, Lie symmetries are not commonplace in mathematical biology. In this work, we construct models of collective cell migration using Lie symmetries using the Fisher KPP model, which can give rise to travelling wave solutions, as a basis. We derive variational symmetries of the travelling wave Fisher KPP model, as well as their associated conservation laws, and a broader class of models for which these symmetries are manifest. Lastly, we construct new travelling wave models of collective cell migration using this class of models. This work demonstrates how Lie symmetries can be used to construct mechanistic models in biology.