Mechanical reaction-diffusion equations in biological systems

Andrea Liu

Department of Physics and Astronomy

University of Pennsylvania




How can a wavefront propagate at a constant velocity in a medium that doesn't support waves? In chemical reaction-diffusion systems, travelling wavefronts of the concentration of a reaction product can arise as a nonlinear phenomenon. The signal propagates at constant velocity without decaying because it is amplified as it goes: more product is generated if there is a sufficiently high concentration of the product. I will discuss two very different biological systems--the developing embryo of the fruit fly Drosophila, and the developing heart of chicken embryos--which both exhibit wavefront propagation. In the fruit fly embryo, cell division does not occur everywhere at once across the embryo, but progresses as a wavefront across the embryo. Similarly, in the contracting embryonic heart, the heart cells (cardiomyocytes) do not contract all at once; rather, there is a wavefront of contraction that propagates across the heart. We have proposed that in both of these systems, it is not chemical concentration but rather mechanical stress that propagates as a nonlinear wavefront. Thus, I will argue that these two biological systems are examples of a new class of "mechanical reaction-diffusion" systems that are governed not by chemical reactions, but by stress-triggered generation of additional mechanical stress.