**Core Concept**
Cephalosporins are a class of beta-lactam antibiotics that work by inhibiting cell wall synthesis in bacteria. They bind to penicillin-binding proteins (PBPs) located inside the bacterial cell wall, resulting in a disruption of the cell wall synthesis process.

**Why the Correct Answer is Right**
The correct mechanism of action of cephalosporins involves the inhibition of PBPs by binding to the beta-lactam ring. This binding causes a conformational change in the PBP, leading to a decrease in the transpeptidase activity. As a result, the cross-linking of peptidoglycan layers is impaired, ultimately leading to cell lysis and bacterial death. Cephalosporins are able to penetrate the bacterial cell wall and reach the PBPs due to their ability to diffuse through the porin channels in the bacterial outer membrane.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because it does not accurately describe the mechanism of action of cephalosporins. While some antibiotics may work by inhibiting protein synthesis, cephalosporins specifically target cell wall synthesis.
* **Option B:** This option is incorrect because it describes the mechanism of action of aminoglycoside antibiotics, not cephalosporins. Aminoglycosides work by binding to the 30S subunit of the bacterial ribosome, causing misreading of mRNA and subsequent inhibition of protein synthesis.

**Clinical Pearl / High-Yield Fact**
Cephalosporins are generally considered safe for patients with penicillin allergy, as they have a different side chain that is not recognized by the immune system. However, it's essential to note that some patients with a history of penicillin allergy may still experience an allergic reaction to cephalosporins.

**Correct Answer: C. Inhibition of cell wall synthesis by binding to penicillin-binding proteins.**