Final answer:
Cadherins require calcium ions to maintain their structure for cell adhesion, prominently in desmosomes and adherens junctions, which are critical for the cohesive integrity of tissues.
Step-by-step explanation:
The ions found in cadherins required for their rigid conformation in cell adhesion are calcium ions. These ions help maintain the structure of cadherins which are involved in forming adherens junctions, such as desmosomes. Desmosomes act as adhesive 'spots' while belt desmosomes encompass the entire cell to provide cohesive integrity to tissues. Cadherins work by spanning the intercellular space to connect cell membranes via interactions stabilized by the calcium ions. This ensures that the tissues possess the necessary strength and can adhere to each other robustly.
Moreover, the intracellular portion of cadherins connects to cytoskeletal filaments, such as keratin in the case of intermediate filaments, which further contributes to the mechanical stability of tissues. It's also worth noting that focal adhesions involving integrin-talin interactions and the associated actomyosin cytoskeleton play a significant role in cellular adhesion and rigidity sensing. These adhesions serve as signaling hubs and are crucial for maintaining cell shape, spreading, and responding to mechanical stimuli.