**Core Concept**
Haemoproteins are a class of proteins that contain a haem group, which is a prosthetic group consisting of an iron atom coordinated to a porphyrin ring. These proteins play crucial roles in various biological processes, including oxygen transport, electron transfer, and catalysis. Haemoproteins are essential for maintaining cellular homeostasis.

**Why the Correct Answer is Right**
Adenylate kinase is an enzyme that catalyzes the reversible transfer of a phosphate group from ATP to AMP, resulting in the formation of two molecules of ADP. Unlike other haemoproteins, adenylate kinase does not contain a haem group in its structure. This is because its primary function is to regulate energy metabolism in cells, rather than participating in redox reactions or oxygen transport.

**Why Each Wrong Option is Incorrect**
**Option A:** Catalase is a haemoprotein that contains a haem group and plays a crucial role in decomposing hydrogen peroxide into water and oxygen. It is a key enzyme in protecting cells from oxidative damage.
**Option B:** Tryptophan pyrrolase is a haemoprotein that contains a haem group and is involved in the metabolism of tryptophan. It catalyzes the conversion of tryptophan to kynurenine, a key step in the kynurenine pathway.
**Option C:** Cytochrome c is a haemoprotein that contains a haem group and plays a critical role in the electron transport chain. It is involved in the transfer of electrons from cytochrome c1 to cytochrome c oxidase, ultimately leading to the production of ATP.

**Clinical Pearl / High-Yield Fact**
Haemoproteins are often involved in redox reactions, which can lead to the formation of reactive oxygen species (ROS). ROS can cause oxidative damage to cellular components, including proteins, lipids, and DNA. Understanding the role of haemoproteins in maintaining cellular homeostasis is essential for appreciating the pathophysiology of various diseases, including cancer, neurodegenerative disorders, and cardiovascular disease.

**✓ Correct Answer: D. Adenylate kinase**