Locating carbon in a network

In a simplified microbial pathway, three-carbon substrate P splits into a two-carbon fragment Q and one-carbon CO2. P carbon 1 becomes CO2; P carbons 2 and 3 become Q carbons 1 and 2. Two Q molecules condense to a four-carbon product R without loss or rearrangement: one supplies R positions 1 and 2, the other positions 3 and 4. Labelled and unlabelled Q molecules mix randomly. In a pulse experiment, half the P molecules have only carbon 2 labelled and half are completely unlabelled. Label does not affect reaction rates. No other carbon source enters R.