Mycomycin, a naturally occurring antibiotic produced by the fungus Nocardia acidophilus, has the molecular formula \(\mathrm{C}_{13} \mathrm{H}_{10} \mathrm{O}_{2}\) and the systematic name 3,5,7,8 -tridecatetraene-10,12-diynoic acid. Draw the structure of mycomycin.

First, we need to draw a chain of 13 carbon atoms to represent the tridecatetraene backbone. \[ \mathrm{C}_{1}-\mathrm{C}_{2}-\mathrm{C}_{3}-\mathrm{C}_{4}-\mathrm{C}_{5}-\mathrm{C}_{6}-\mathrm{C}_{7}-\mathrm{C}_{8}-\mathrm{C}_{9}-\mathrm{C}_{10}-\mathrm{C}_{11}-\mathrm{C}_{12}-\mathrm{C}_{13} \]

The systematic name indicates that mycomycin has four double bonds located at positions 3, 5, 7, and 8. Place double bonds between these carbon atoms. \[ \mathrm{C}_{1}-\mathrm{C}_{2}=\mathrm{C}_{3}-\mathrm{C}_{4}=\mathrm{C}_{5}-\mathrm{C}_{6}=\mathrm{C}_{7}=\mathrm{C}_{8}-\mathrm{C}_{9}-\mathrm{C}_{10}-\mathrm{C}_{11}-\mathrm{C}_{12}-\mathrm{C}_{13} \]

The systematic name also indicates that mycomycin has two triple bonds located at positions 10 and 12. Place triple bonds between these carbon atoms. \[ \mathrm{C}_{1}-\mathrm{C}_{2}=\mathrm{C}_{3}-\mathrm{C}_{4}=\mathrm{C}_{5}-\mathrm{C}_{6}=\mathrm{C}_{7}=\mathrm{C}_{8}-\mathrm{C}_{9}-\mathrm{C}_{10} \equiv \mathrm{C}_{11}-\mathrm{C}_{12} \equiv \mathrm{C}_{13} \]

Since mycomycin is a carboxylic acid, a carboxyl group (-COOH) should be added to the last carbon (C13). Replace the hydrogen atom at C13 with -COOH. \[ \mathrm{C}_{1}-\mathrm{C}_{2}=\mathrm{C}_{3}-\mathrm{C}_{4}=\mathrm{C}_{5}-\mathrm{C}_{6}=\mathrm{C}_{7}=\mathrm{C}_{8}-\mathrm{C}_{9}-\mathrm{C}_{10} \equiv \mathrm{C}_{11}-\mathrm{C}_{12} \equiv \mathrm{C}_{13} \mathrm{-COOH} \]

Finally, we need to add the remaining 9 hydrogen atoms to complete the molecule based on the molecular formula. Each carbon atom can make up to four bonds in total, so we fill in the hydrogen atoms accordingly. \[ \mathrm{H}_{3}\mathrm{C}_{1}-\mathrm{C}_{2}=\mathrm{C}_{3}-\mathrm{C}_{4}=\mathrm{C}_{5}-\mathrm{C}_{6}=\mathrm{C}_{7}=\mathrm{C}_{8}-\mathrm{C}_{9}-\mathrm{C}_{10} \equiv \mathrm{C}_{11}-\mathrm{C}_{12} \equiv \mathrm{C}_{13} \mathrm{-COOH} \] Now we have the complete structure of mycomycin: \[ \mathrm{H}_{3}\mathrm{C}_{1}-\mathrm{C}_{2}=\mathrm{C}_{3}-\mathrm{C}_{4}=\mathrm{C}_{5}-\mathrm{C}_{6}=\mathrm{C}_{7}=\mathrm{C}_{8}-\mathrm{C}_{9}-\mathrm{C}_{10} \equiv \mathrm{C}_{11}-\mathrm{C}_{12} \equiv \mathrm{C}_{13} \mathrm{-COOH} \]