Self-Organization of Self-Clearing Beating Patterns in an Array of Locally Interacting Ciliated Cells Formulated as an Adaptive Boolean Network

Abstract

The observed spatio-temporal ciliary beat patterns on multiciliated epithelia are suspected to be the result of self-organizing processes on various levels. Here, we present an abstract epithelium model at the pluricellular level, which intends to make the self-organization of ciliary beating patterns as well as of the associated fluid transport across the airway epithelium plausible. Ciliated cells are modeled in terms of locally interacting oscillating two-state actuators. The local interactions among these boolean actuators are triggered by seeded mucus lumps. In the course of a simulation the actuators' state and the associated mucus velocity field self-organize in tandem. We suggest to consider the dynamics on multiciliated epithelia in the context of adaptive (boolean) networks. Within the framework of adaptive boolean networks ciliated cells represent the nodes and as the mucus establishes the local interactions among nodes, its distribution determines the topology of the network. Furthermore, we present the results and insights from comprehensive parameter studies. The results show evidence that so called deterministic update schemes, which are meant to represent intercellular signaling, lead to more realistic and robust dynamics and may therefore be favored by nature. Finally, we suppose that unciliated cells introduce a modular network topology on ciliated epithelia causing the self-organization taking place simultaneously in each "ciliated module". This reasoning provides the first consistent explanation for the meaning of the observed patchy expression patterns of the mucus modulation wave fields. Modularity may therefore be seen as a modular construction plan of nature for ciliated epithelia whose number of cells range over several order of magnitudes.