Self-organization of self-clearing beating patterns in an array of locally interacting ciliated cells formulated as an adaptive Boolean network

Abstract

We present a two-dimensional array of locally interacting virtual actuators, which exhibits selforganization towards self-cleaning spatio-temporal structures. Some of the elaborated results might be more general for dynamical systems based on local interactions. However, here, we would like to present our model under the aspect of mucociliary clearance. The observed spatio-temporal ciliary beat patterns leading to proper mucociliary transport on multiciliated epithelia are suspected to be the result of self-organizing processes on various levels. Our two-dimensional array of locally interacting system elements can be seen as an oversimplified pluricellular epithelium model, 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.

A quantitative interspecies comparison of the respiratory mucociliary clearance mechanism

“…As a general empirical cross-species model mathematically capturing the relationship between the spatio-temporal properties of the metachronal wave field and its associated mucociliary transport could not be established, we conclude that, in order to establish such a general model for mucociliary transport, further observables determining mucociliary transport need to be taken into account. The metachronal wave properties are commonly considered to self-organize out of local hydrodynamic interactions as well as to coemerge with mucociliary transport (Brumley et al 2014;Schneiter et al 2019). As the metachronal wave properties (e.g.…”

A quantitative interspecies comparison of the respiratory mucociliary clearance mechanism

“…As a general empirical cross-species model mathematically capturing the relationship between the spatio-temporal properties of the metachronal wave field and its associated mucociliary transport could not be established, we conclude that, in order to establish such a general model for mucociliary transport, further observables determining mucociliary transport need to be taken into account. The metachronal wave properties are commonly considered to self-organize out of local hydrodynamic interactions as well as to coemerge with mucociliary transport (Brumley et al 2014;Schneiter et al 2019). As the metachronal wave properties (e.g.…”

The Cilialyzer – a freely available open-source software for a standardised identification of impaired mucociliary activity facilitating the diagnostic testing for PCD

“…However, from a wider perspective, the reliability of the conventionally performed HSVM approach is inherently limited, as detached ciliated cells being immersed in culture medium can only partly re ect the quality of the primary mucociliary clearance mechanism. e MCC mechanism is an excellent example for a complex dynamical system with a localto-global character, as the local uid mechanical interactions of oscillating individual cilia are thought to generate the collective motion pa ern, which eventually generates e cient mucociliary transport [16][17][18]. How the characteristic motion pa ern of individual cilia is related to the collective ciliary motion pa ern largely remains obscure.…”

Spatial Intra- and Intercellular Alignment of Respiratory Cilia and its Relation to Function

“…The motivation for the present paper originates from the formulation and analysis of an oversimplified pluricellular epithelium model Schneiter et al (2019); Ricka (2010), which represents an array of locally interacting ciliated cells able to self-organize towards a self-cleaning virtual epithelium. When ‘constructing’ such a virtual epithelium, modelers need access to dedicated quantitative morphological information.…”

A quantitative interspecies comparison of the respiratory mucociliary clearance mechanism

“…As a general empirical cross-species model mathematically capturing the relationship between the spatio-temporal properties of the metachronal wave field and its associated mucociliary transport could not be established, we conclude that, in order to establish such a general model for mucociliary transport, further observables determining mucociliary transport need to be taken into account. The metachronal wave properties are commonly considered to self-organize out of local hydrodynamic interactions as well as to coemerge with mucociliary transport (Brumley et al 2014;Schneiter et al 2019). As the metachronal wave properties (e.g.…”

The Cilialyzer – a freely available open-source software for a standardised identification of impaired mucociliary activity facilitating the diagnostic testing for PCD

“…However, from a wider perspective, the reliability of the conventionally performed HSVM approach is inherently limited, as detached ciliated cells being immersed in culture medium can only partly re ect the quality of the primary mucociliary clearance mechanism. e MCC mechanism is an excellent example for a complex dynamical system with a localto-global character, as the local uid mechanical interactions of oscillating individual cilia are thought to generate the collective motion pa ern, which eventually generates e cient mucociliary transport [16][17][18]. How the characteristic motion pa ern of individual cilia is related to the collective ciliary motion pa ern largely remains obscure.…”

Spatial Intra- and Intercellular Alignment of Respiratory Cilia and its Relation to Function

“…The motivation for the present paper originates from the formulation and analysis of an oversimplified pluricellular epithelium model Schneiter et al (2019); Ricka (2010), which represents an array of locally interacting ciliated cells able to self-organize towards a self-cleaning virtual epithelium. When ‘constructing’ such a virtual epithelium, modelers need access to dedicated quantitative morphological information.…”

A quantitative interspecies comparison of the respiratory mucociliary clearance mechanism

“…As a general empirical cross-species model mathematically capturing the relationship between the spatio-temporal properties of the metachronal wave field and its associated mucociliary transport could not be established, we conclude that, in order to establish such a general model for mucociliary transport, further observables determining mucociliary transport need to be taken into account. The metachronal wave properties are commonly considered to self-organize out of local hydrodynamic interactions as well as to coemerge with mucociliary transport (Brumley et al 2014;Schneiter et al 2019). As the metachronal wave properties (e.g.…”

The Cilialyzer – a freely available open-source software for a standardised identification of impaired mucociliary activity facilitating the diagnostic testing for PCD

“…However, from a wider perspective, the reliability of the conventionally performed HSVM approach is inherently limited, as detached ciliated cells being immersed in culture medium can only partly re ect the quality of the primary mucociliary clearance mechanism. e MCC mechanism is an excellent example for a complex dynamical system with a localto-global character, as the local uid mechanical interactions of oscillating individual cilia are thought to generate the collective motion pa ern, which eventually generates e cient mucociliary transport [16][17][18]. How the characteristic motion pa ern of individual cilia is related to the collective ciliary motion pa ern largely remains obscure.…”

Spatial Intra- and Intercellular Alignment of Respiratory Cilia and its Relation to Function

“…The motivation for the present paper originates from the formulation and analysis of an oversimplified pluricellular epithelium model Schneiter et al (2019); Ricka (2010), which represents an array of locally interacting ciliated cells able to self-organize towards a self-cleaning virtual epithelium. When ‘constructing’ such a virtual epithelium, modelers need access to dedicated quantitative morphological information.…”