Final answer:
A substance that increases the permeability of the inner mitochondrial membrane to protons, like DNP, would promote weight loss by impairing ATP production and increasing metabolic rate, but also poses severe health risks such as overheating.
Step-by-step explanation:
If there is a substance that makes the lipid bilayer of the inner mitochondrial membrane highly permeable to (H+) protons, it would likely promote weight loss, as it impairs energy production. Dinitrophenol (DNP) acts as such an uncoupler, disrupting the proton gradient that is essential for the synthesis of ATP through oxidative phosphorylation. By making the inner mitochondrial membrane "leaky" to protons, DNP decreases the proton concentration in the intermembrane space, which is needed to drive ATP synthase. Without this gradient, the potential energy cannot be harnessed to phosphorylate ADP to ATP efficiently.
Due to the impaired energy production, the body has to metabolize more fats and carbohydrates to meet its energy demand, resulting in weight loss. However, because the energy from the electron transport chain is released as heat rather than being stored as ATP, using DNP also caused people to overheat, leading to dangerous and sometimes lethal high fevers. This is why DNP was removed from the FDA's approved list in 1938.