Final answer:
The nuclear lamina is a supportive meshwork of intermediate filaments within the nucleus, just under the inner nuclear membrane, crucial for maintaining nuclear shape and structure.
Step-by-step explanation:
The thin filamentous meshwork within the nucleus that is bound by integral membrane proteins of the inner surface of the nuclear envelope in animal cells is called the nuclear lamina. The nuclear lamina is a network of intermediate filaments, predominantly composed of proteins known as lamins, which are located just underneath the inner nuclear membrane. It provides essential structural support and maintains the shape of the nucleus. The nuclear envelope, which houses the nuclear lamina, is a dual-layered structure consisting of an outer and an inner phospholipid bilayer. This envelope also includes nuclear pores, which are protein-lined openings that regulate the exchange of materials between the nucleus and the cytoplasm, crucial for proper cellular function.