Calculate the number of ATPs required for FA synthesis for 6C, 10C and 16C fatty acids.

Steps to Solve

1. Understand ATP consumption in fatty acid synthesis

Fatty acid synthesis consumes ATP during the conversion of acetyl-CoA to malonyl-CoA, which is the first committed step in fatty acid synthesis. Each fatty acid molecule requires one ATP to generate one malonyl-CoA from acetyl-CoA.

2. Determine the number of acetyl-CoA units needed

For fatty acids, each unit of the fatty acid chain consists of two carbon atoms that derive from acetyl-CoA. Hence, to find out the number of acetyl-CoA needed, use the formula:

$$ \text{Number of acetyl-CoA} = \frac{\text{Number of carbon atoms}}{2} $$

3. Calculate the number of malonyl-CoA needed

Every acetyl-CoA initiates the fatty acid chain synthesis, and every additional unit requires one malonyl-CoA. Thus, the total number of malonyl-CoA needed is given by:

$$ \text{Total malonyl-CoA} = \text{Number of acetyl-CoA} + (\text{Number of acetyl-CoA} - 1) $$

This accounts for the first acetyl-CoA and each further addition from malonyl-CoA.

4. Calculate the ATP requirement

For each malonyl-CoA created, 1 ATP is consumed, therefore total ATP is calculated as:

$$ \text{Total ATP} = \text{Total malonyl-CoA} $$

Now, plug in the values for chain lengths of 6, 10, and 16 carbons.

5. Final calculations for each case

• For 6 carbons: $$ \text{Number of acetyl-CoA} = \frac{6}{2} = 3 $$ $$ \text{Total malonyl-CoA} = 3 + (3 - 1) = 5 $$ $$ \text{Total ATP} = 5 $$

• For 10 carbons: $$ \text{Number of acetyl-CoA} = \frac{10}{2} = 5 $$ $$ \text{Total malonyl-CoA} = 5 + (5 - 1) = 9 $$ $$ \text{Total ATP} = 9 $$

• For 16 carbons: $$ \text{Number of acetyl-CoA} = \frac{16}{2} = 8 $$ $$ \text{Total malonyl-CoA} = 8 + (8 - 1) = 15 $$ $$ \text{Total ATP} = 15 $$