Here's why:

* DNA replication is the process of copying DNA. While proteins play a crucial role in this process (e.g., DNA polymerase), the actual copying of the DNA sequence is done by the DNA molecule itself. It uses its own base pairing rules to create a complementary strand.

Let's look at the other options:

* Cellular respiration: This process involves numerous enzymes, which are proteins, to break down glucose and generate energy.

* Hormonal signaling: Hormones are often proteins (e.g., insulin) and they bind to protein receptors on target cells to initiate a response.

* Muscle contraction: Actin and myosin, the proteins responsible for muscle contraction, directly interact to generate movement.

Therefore, the only biological activity that doesn't directly involve proteins in its core mechanism is DNA replication.