Take out a sample at every time point and extract total RNA. Submit RNA for sequencing (RNA-Seq). Quantify degradative products using any method you use. In principle you don't have to perform 2 experiments simultaneously. Do one where you grow your culture and quantify degradative products at certain points. Then repeat the exact thing but instead extract RNA at those points and submit for sequencing. Do each one in triplicates and if error is small then you can say that certain genes were expressed when certain biproducts formed.

As like Max described, sampling should be done at different time interval, centrifuge the medium to pellatize the cells. Use the supernatant for degradative product estimation by colorimetric method/elisa (depends upon the compound to be analyzed) and cell can be used for total rna extraction. Calorimetric estimation can be done in different way either by measure the substrate utilized or by measuring product formed