Step 1: Understanding the Concept:
Molecules cross biological membranes via passive mechanisms (simple or facilitated diffusion) or active mechanisms (primary or secondary active transport) depending on their size, charge, and concentration gradients.
Step 2: Detailed Explanation:
- Simple Diffusion (A): Small, non-polar molecules cross the lipid bilayer directly without assistance. Nitrous oxide (NO), a small gas molecule, diffuses freely (A \(\rightarrow\) IV).
- Facilitated Diffusion (B): Polar molecules move down their concentration gradient through channel or carrier proteins. Glucose enters cells via GLUT transporter proteins (B \(\rightarrow\) I).
- Primary active transport (C): Solutes are pumped against their concentration gradient using energy derived directly from ATP hydrolysis. The \(\text{Na}^+/\text{K}^+\)-ATPase pump is a classic example (C \(\rightarrow\) III).
- Secondary active transport (D): Solutes are moved against their concentration gradient using energy from an electrochemical gradient established by primary active transport. Lactose is co-transported with protons via lactose permease (D \(\rightarrow\) II).
Step 3: Final Answer:
The correct matching sequence is (A)-(IV), (B)-(I), (C)-(III), (D)-(II).