Role of cell polarity dynamics and motility in pattern formation due to contact-dependent signalling

Abstract

A key challenge in biology is to understand how spatio-temporal patterns and structures arise during the development of an organism. An initial aggregate of spatially uniform cells develops and forms the differentiated structures of a fully developed organism. On the one hand, contact-dependent cell–cell signalling is responsible for generating a large number of complex, self-organized, spatial patterns in the distribution of the signalling molecules. On the other hand, the motility of cells coupled with their polarity can independently lead to collective motion patterns that depend on mechanical parameters influencing tissue deformation, such as cellular elasticity, cell–cell adhesion and active forces generated by actin and myosin dynamics. Although modelling efforts have, thus far, treated cell motility and cell–cell signalling separately, experiments in recent years suggest that these processes could be tightly coupled. Hence, in this paper, we study how the dynamics of cell polarity and migration influence the spatiotemporal patterning of signalling molecules. Such signalling interactions can occur only between cells that are in physical contact, either directly at the junctions of adjacent cells or through cellular protrusional contacts. We present a vertex model which accounts for contact-dependent signalling between adjacent cells and between non-adjacent neighbours through long protrusional contacts that occur along the orientation of cell polarization. We observe a rich variety of spatiotemporal patterns of signalling molecules that is influenced by polarity dynamics of the cells, relative strengths of adjacent and non-adjacent signalling interactions, range of polarized interaction, signalling activation threshold, relative time scales of signalling and polarity orientation, and cell motility. Though our results are developed in the context of Delta–Notch signalling, they are sufficiently general and can be extended to other contact dependent morpho-mechanical dynamics.

Minimal physicalism as a scale-free substrate for cognition and consciousness

“…Differentiated cells of multicellular eukaryotes clearly employ such QRFs (e.g. Bajpai et al 2021 ); interestingly, multi-axis morphology correlates with the presence of neurons and appears to be directly instructed by neural signaling ( Fields et al 2020 ). How the representation of 3d space in migrating cells is coupled to the representations of cell- or extra-cellular surface characteristics, bioelectric and morphogen gradients, and other morphogenetic signals remains a central question in developmental biology ( Grossberg 1978 ; Pezzulo and Levin 2015 ).…”

Role of Delta-Notch signalling molecules on cell-cell adhesion in determining heterogeneous chemical and cell morphological patterning

“…Delta-Notch signalling, which relies on contactbased lateral inhibition, is used as the model chemical system in the present paper [56–58, 61]. A model for Delta-Notch kinetics is constructed by tracking the concentration of Notch and Delta in each cell N α and D α , respectively, in cell α .…”

“…It is known that Delta-Notch signalling typically relies on contact-based lateral inhibition to regulate the expression of Delta and Notch in tissues [55]. The dynamics of various spatio-temporal patterns that are formed during this signalling is addressed by a number of theoretical and computational models [56–61]. It is known from these models that when the interactions between the cells are limited to the nearest neighbours, checkerboard pattern of Delta and Notch expressed cells are known to appear [56, 57].…”

“…The dynamics of various spatio-temporal patterns that are formed during this signalling is addressed by a number of theoretical and computational models [56–61]. It is known from these models that when the interactions between the cells are limited to the nearest neighbours, checkerboard pattern of Delta and Notch expressed cells are known to appear [56, 57]. On the other hand, some models demonstrate that when the contacts are created between non-adjacent neighbours due to cellular protrusions, then the dynamics of components associated with these contacts can give rise to a wider range of Delta-Notch patterns in the tissue [56, 58].…”

“…It is known from these models that when the interactions between the cells are limited to the nearest neighbours, checkerboard pattern of Delta and Notch expressed cells are known to appear [56, 57]. On the other hand, some models demonstrate that when the contacts are created between non-adjacent neighbours due to cellular protrusions, then the dynamics of components associated with these contacts can give rise to a wider range of Delta-Notch patterns in the tissue [56, 58]. Though these models delve into the intricacies of chemical pattern formation during Delta-Notch signalling, there are, to the best of our knowledge, very few models that also study the concomitant cell morphology patterns.…”