Explanation:

- Barry J. Marshall and J. Robin Warren shared the Nobel Prize in Physiology or Medicine in 2005 for their discovery of the bacterium *Helicobacter pylori* and its role in causing gastritis and peptic ulcer disease.

- Option 2: J. Robin Warren

- Correct Answer: As the co-recipient of the 2005 Nobel Prize with Barry Marshall for their groundbreaking work on *Helicobacter pylori*.

- Option 1: Paul Lauterbur

- Won the Nobel Prize in Physiology or Medicine in 2003 for discoveries concerning magnetic resonance imaging (MRI).

- Option 3: Richard Axel

- Awarded the Nobel Prize in Physiology or Medicine in 2004 for work on the olfactory system.

- Option 4: Oliver Smithies

- Received the Nobel Prize in Physiology or Medicine in 2007 for discoveries of principles for introducing specific gene modifications in mice using embryonic stem cells.