Which membrane in a mitochondrion or chloroplast is most highly convoluted and folded into structures that increase surface area?

Introduction / Context:
Mitochondria and chloroplasts are double membrane bound organelles that play central roles in energy conversion in cells. Their membrane structure is highly specialized. This question focuses on which specific membrane is most highly folded, creating a large surface area for biochemical reactions such as cellular respiration.

Given Data / Assumptions:

Mitochondria have an outer and an inner membrane.
Chloroplasts also have outer and inner membranes plus internal thylakoid membranes.
Folding of membranes increases surface area for enzymes and transport proteins.

Concept / Approach:
In mitochondria, the inner membrane is thrown into numerous folds known as cristae. These folds house the components of the electron transport chain and ATP synthase complexes. The extensive folding significantly increases the available surface area for oxidative phosphorylation. In contrast, the outer mitochondrial membrane is relatively smooth and more permeable. Chloroplasts have thylakoid membranes that are also highly folded into grana, but the question specifically contrasts outer and inner membranes of mitochondria and chloroplasts, not the thylakoids. Among the listed choices, the mitochondrial inner membrane is the best known example of a highly convoluted membrane associated with energy production.

Step-by-Step Solution:
Step 1: Recall that cristae are folds of the inner mitochondrial membrane. Step 2: Understand that these folds increase surface area for the electron transport chain. Step 3: Compare this with outer membranes, which remain relatively smooth and serve more as boundaries. Step 4: Select mitochondrial inner membrane as the highly convoluted membrane among the given options.

Verification / Alternative check:
Another check is to visualize textbook diagrams. Mitochondria are almost always drawn with a smooth outer membrane and a highly folded inner membrane forming cristae. Chloroplast diagrams show stacks of thylakoids, but their outer and inner envelope membranes are not described as especially convoluted in the same way. This supports the choice of the inner mitochondrial membrane.

Why Other Options Are Wrong:
Chloroplast outer membrane: This membrane is relatively smooth and not strongly folded into projections like cristae.
Chloroplast inner membrane: Although important, it does not form the same level of folds as the mitochondrial inner membrane; most folding in chloroplasts occurs in thylakoid membranes, which are not listed here.
Both outer membranes: Outer membranes have different roles and are not the main site of extensive folding or ATP synthesis.

Common Pitfalls:
A common confusion is between the inner membranes and the internal thylakoid systems in chloroplasts. Students may also mistakenly think that any membrane in an organelle must be highly folded, but only specific ones involved directly in energy conversion show this extreme convolution.

Final Answer:
The most highly convoluted membrane among the options is the mitochondrial inner membrane, which forms cristae to support ATP production.