Title: Theory of circadian metabolism,
Abstract: Many organisms repartition their proteome in a circadian fashion in response
to the daily nutrient changes in their environment. A striking example is
provided by cyanobacteria, which perform photosynthesis during the day to fix
carbon. These organisms not only face the challenge of rewiring their proteome
every 12 hours, but also the necessity of storing the fixed carbon in the form
of glycogen to fuel processes during the night. In this manuscript, we extend
the framework developed by Hwa and coworkers (Scott et al., Science 330, 1099
(2010)) for quantifying the relatinship between growth and proteome composition
to circadian metabolism. We then apply this framework to investigate the
circadian metabolism of the cyanobacterium Cyanothece, which not only fixes
carbon during the day, but also nitrogen during the night, storing it in the
polymer cyanophycin. Our analysis reveals that the need to store carbon and
nitrogen tends to generate an extreme growth strategy, in which the cells
predominantly grow during the day, as observed experimentally. This strategy
maximizes the growth rate over 24 hours, and can be quantitatively understood
by the bacterial growth laws. Our analysis also shows that the slow relaxation
of the proteome, arising from the slow growth rate, puts a severe constraint on
implementing this optimal strategy. Yet, the capacity to estimate the time of
the day, enabled by the circadian clock, makes it possible to anticipate the
daily changes in the environment and mount a response ahead of time. This
significantly enhances the growth rate by counteracting the detrimental effects
of the slow proteome relaxation.