| Event Description: John Nardini, Department of Applied Mathematics, University of Colorado Boulder Investigation of a Structured Version of Fisher's Equation Recent biological research has sought to understand how biochemical signaling pathways, such as the mitogen-activated protein kinase (MAPK) signaling pathway, influence the migration of a population of cells during wound healing. Fisher's Equation has been used extensively to model this biological process due to its simple nature and ability to produce traveling wave solutions. This partial differential equation with independent variables of time and space cannot account for the effects of the MAPK signaling cascade on wound healing, however. To this end, we couple a traveling wave analysis with concepts from structured population models to derive a structured version of Fisher's Equation with independent variables of time, space, and activity with respect to a biochemical pathway. In our preliminary analysis, we prove the existence of a self-similar wave to this equation and numerically investigate how different patterns of biochemical activity can influence migration in a more complicated version of the model. |
| Location Information: Main Campus - Engineering Office Tower (View Map) 1111 Engineering DR Boulder, CO Room: 226: Applied Math Conference Room |
| Contact Information: Name: Ian Cunningham Phone: 303-492-4668 Email: amassist@colorado.edu |