Resonant filtering of compositional waves in multicellular networks

Theoretically predicting the stationary and traveling compositional wave patterns observed over trivial multicellular topologies is common place in biology. Systematic methods are needed to find the relationships between the forms of such waves and the underlying network topologies. Here, we introduce one such method based on the Interface Response Theory (IRT) that combines models of intracellular biochemical reactions with those of intercellular networks to analytically track time variations of concentration profiles across nontrivial cellular network topologies. Cellular chains of infinite length are shown to sustain traveling planar waves under certain conditions among the coefficients of the intracellular chemical reactions. A non-trivial cellular network composed of a finite length side chain attached to the infinite backbone leads to the formation of a standing wave pattern upstream from the site of attachment. Downstream, the wave proceeds although a limited number of frequency bands are filtered out of the original content with that number being equal to the number of cells in the side chain.