Final answer:
When the α and β subunits of an integrin are experimentally linked in their extracellular domains, they could bind to their ligands, but without transmembrane and cytoplasmic domains, they cannot propagate signals into the cell or participate in focal adhesions.
Step-by-step explanation:
You are investigating the interactions of integrin α and β subunits and isolate the extracellular portion of an integrin as a soluble α/β heterodimer. The created molecules would bind to the extracellular domain but lack the associated transmembrane and cytoplasmic domains. The extracellular domain, where ligand binding takes place, is critical for activating the integrin's function. If you experimentally link the α and β subunits at the bases of their legs, promoting their ligand-binding regions to approach one another, you would theoretically enable the extracellular domains to bind their specific ligands. However, without the transmembrane and cytoplasmic domains, there will be no propagation of the signal into the cell's interior, thus no activation of intracellular pathways.
In the context of focal adhesions, the integrin's transmembrane region connects the extracellular ligand-binding to intracellular actin cytoskeletal structures through a variety of intracellular proteins. Inside-out signaling can activate integrins to bind extracellular matrix, but in your model, this signaling cascade is incomplete due to the absence of the transmembrane and cytoplasmic domains. This would hinder the integrin's ability to participate in forming or strengthening focal adhesions, which are crucial for cell adhesion and signaling.