Abstract
Circadian clocks are found in myriad species across the tree of life. They are commonly assumed to provide a selective advantage by enabling organisms to anticipate daily environmental changes. It has proven remarkably difficult, however, to move beyond this general idea to explain precisely what advantage anticipation confers and to quantify how large this benefit is. Here, we address these challenges by developing a mathematical model of diurnally varying growth and metabolism in the cyanobacterium
Synechococcus elongatus
, which fixes carbon through photosynthesis during the day and stores a portion of it as glycogen for use during the night. Specifically, we extend the framework introduced by Hwa and coworkers (Scott
et al
., Science
330
, 1099 (2010)), which quantifies the relationship between growth and proteome composition, to a circadian context. We find that the fastest growth is achieved when glycogen production during the day is minimized to the amount required to sustain essential nighttime processes; growth then occurs exclusively during the day, in agreement with experimental observations. However, the slow relaxation of the proteome, arising from the intrinsically slow growth rate of
S. elongatus
, severely constrains the implementation of this optimal strategy: In the absence of anticipation, the cell must grow at night in order to produce proteins essential for nighttime metabolism. In contrast, with anticipation enabled by a circadian clock, the bacterium can instead adjust its proteome late in the day, allowing it to avoid less efficient nighttime growth altogether, thereby significantly enhancing its growth rate.