During the development of an organism, cells must coordinate and organize to generate the correct shape, structure, and spatial patterns of tissues and organs, a process known as morphogenesis. The morphogenesis of embryonic tissues is supported by multiple processes that induce the precise physical deformations required for tissues to ultimately form organs with complex geometries. Among the most active players shaping the morphogenetic path are fine-tuned changes in cell adhesion. We review here recent advances showing that changes of a local, pair-wise property defined at the cell-cell contact level has important global consequences for embryonic tissue topology, being determinant in defining both the geometric and material properties of early embryo tissues.
One of the most fundamental constraints underlying the process of morphogenesis is that the acquisition of non-trivial shapes by the forming tissues has to take place without an external agent inducing such changes [1][2][3][4][5]. In consequence, the different, fine tuned deformations of the embryonic tissue must be the outcome of the collective and coordinated behaviour of different groups of cells which, while changing their mechanical properties in a consistent way, will eventually differentiate and give functionality to the emerging tissue [6][7][8][9][10][11][12][13][14]. In such processes, underlying core physical properties define the phenotypical frame [15][16][17][18] over which selective pressures will act. At the structural level, one must take into account geometrical considerations related to tissue morphology and, even deeper in the identification of the rawest structure, the topological properties of the embryonic tissue [18][19][20][21]. Roughly speaking, the identification of topological properties is a fundamental way to characterize the kind of structure we are dealing with: Whether the structure contains holes, whether the object is tubular-like or spherical-like or, more fundamentally, what the pattern of connection of the different core elements of the system is [18,20,22,23]. Importantly, the topological characterization is performed regardless of the geometric details, although the topological structure acts as a constraint for the potential geometries. Being topology at such fundamental level of characterization, natural key questions arise: How are the different topological patterns regulated? Is there a feedback between topological structure and material properties? How are different topological phenotypes achieved in front of other potential ones?
Any process producing stress is susceptible to trigger a topological change and other collective phenomena like e.g., active migration [24][25][26] or topological sorting [6,[27][28][29][30], may as well underlie global tissue structural rearrangements. In this report, we will focus on the role * bernat.corominas-murtra@uni-graz.at of cell adhesion triggering collective changes on the topology of the tissue organization leading to functional phenotypic traits [14,16,18,21,[31][32][33][34][35][36]. We conclude that the dialog established between cell adhesion changes and topology is one of the main drivers of morphogenesis.
One of the most fundamental characterizations of the structure of the embryonic tissue arises from the network of cell-cell contacts [18,20,21,37]. We will refer to the topology of cell-cell contacts to a particular network structure defined from just considering cells and contacts among them, regardless of any geometric property at any scale. The structure of contacts, when one deals with n ≥ 3 cells, may have several realizations, since there are several ways to arrange the cells -see fig. 1. Every of such realizations, to which we will refer to as g 1 , …, g N , will define a topology of interactions -i.e., a networkwhose particular structure is grasped by the adjacency matrix, A(g k ) [38]. Elements of the adjacency matrix a ij will be proportional to the surface of the contact, in case the cells c i , c j are in contact, or zero, in case cells c i , c j are not in contact. If we are only interested on the raw topological structure, the elements of the adjacency matrix will be just either one or zero, depending on whether the contact exists or not, respectively. Topological changes, also known as topological transitions -see Box 1-, between structural cell configurations will be represented by changes in the adjacency matrix.
Cell adhesion is a fundamental mechanism for maintaining and shaping tissue architecture. Far from acting as a simple mechanical glue, cell adhesion works as a highly regulated mechanochemical process that coordinates tissue structure and maintenance [7,8,12,14,28,31,[39][40][41]. Across metazoans, a substantial fraction of the genome encodes proteins associated with cell-cell and cell-matrix adhesion [40,42,43]. These cell adhesion molecules (CAMs) are typically grouped into several major families, including cadherins, integrins, immunoglobulin superfamily CAMs, and selectins. Generally, CAMs are transmembrane proteins that mediate adhesion outside the cell and connect to the cytoskeleton inside the cell [7,[44][45][46]. Through these connections, adhesion complexes couple external chemical signals, mechanical forces, and tissue-scale tensions to intracellular responses [11,42,[47][48][49][50][51].
In spite of the enormous complexity of the adhesion machinery described above, several mechanical phenomena can be studied from a simplified version of the membrane structure -see Fig. 2A. Indeed, since more than a decade, several features of the adhesion dynamics have been studied from the perspective of the theory of foams, establishing an analogy between soap bubbles with potentially var
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