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The oil drop model for proteins basically refers to the fact that in water, oil sticks together to form an oil droplet rather than being dispersed throughout the water in many droplets.

Why? - Because of the hydrophobic effect. hydrophobic hydrocarbon chains cause water to form "cages" around them (this is because water cannot hydrogen bond to the protein so makes extra hydrogen bonds to itself), becoming more ordered and therefore losing entropy (S) which is unfavourable.

This is the same for hydrophobic residues in the protein chain. If exposed, water will become ordered around them, losing entropy. The hydrophobic effect aims to minimise this entropic loss by burying the hydrophobic residues within the core of the protein. Hydrophobic residues can form relatively strong Van der waals forces with each other while the polar residues can form H-bonds with the water molecules.

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