2.3. Mutant information

In order to evaluate the effectiveness of our methodology using the carbon homeostasis model, we specifically chose 10 mutants that are potentially associated with each model parameter based on previous studies (figure 1a). Our mutants are involved in starch turnover, sucrose transportation, the circadian clock and the sugar sensing pathway (figure 1a). We grouped the 10 mutants into four categories and explain the function of each gene within each group.

The group includes five mutants whose function is associated with the starch degradation: gwd, pwd, bam1, bam2 and amy3/bam1. gwd and pwd are the mutants of the starch phosphorylation enzymes, glucan, water dikinase (GWD)[24] and PWD [25]. These enzymes catalyse the phosphorylation of the glucan chain on the surface of starch granules, the first step of the starch degradation [2,31,32]. The importance of the phosphorylation step in regulation of starch degradation has been proposed by experimental and theoretical studies [20]. bam1 and bam2 are the β-amylases that catalyse the hydrolysis of the oligosaccharides, which produces maltose [26,27]. The expression of BAM1 and BAM2 has been known as circadian-regulated. amy3/bam1 is a double mutant of the α-amylase and β-amylase. AMY3 and BAM1 are mainly localized in guard cells and regulating stomatal opening in response to light environment [28].

The group includes the mutant associated with the sucrose flux in a leaf. sweet11/12 is the mutant of the sucrose transporters SWEET11 and SWEET12 which plays a significant role in the phloem loading of source–sink transportation in plants [12,33]. sweet11/12 shows significantly higher sucrose concentration in a leaf tissue than wild-type and it does not oscillate between day and night. Because in the carbon homeostasis model, plants are assumed to sense the deviation of sugar concentration rather than the concentration itself to synchronize the starch degradation to the external diel cycle, the phenotype of this mutant, high concentration but relatively small deviation of sugar, is suitable for our analysis, compared with other sucrose transporters such as sucrose-H⁺ cotransporters (SUCs) [33]. These genes are also known to be regulated by the circadian clock [34].

The group includes the mutants of the sugar-sensitive components of the circadian clock: prr7 and prr7/9. The transcription of PRR7 is known to be sensitive to sugar concentration and the main candidate of the sugar-dependent phase modulation of the circadian clock [19,29]. The double mutant prr7/9 has extremely longer circadian photoperiod [10]. It has been demonstrated that prr7/9 delays the onset of starch degradation [9]. These genes may correspond to the model parameters (τ_L and β_p) which reflect the time-dependent profile of starch degradation (figure 1b; electronic supplementary material, figure S1). Particularly, we can test the contribution of the clock regulation for the adjustment of starch degradation β_t.

This group includes the mutant associated with the sugar sensing pathways particularly involved in interaction between sugars and clock: kin10 and bzip63-1. KIN10 is a catalytic subunit of Snf1-related protein kinase (SnRK1) and bZIP63 is a sugar-sensitive transcription factor that regulates many pathways including the transcript level of the starch degrading enzymes. These genes are involved in the sugar-dependent phase modulation of the circadian clock, in which SnRK1 activates bZIP63 under starvation and bZIP63 transcriptionally regulates the expression of PRR7 [18,19]. If the sugar sensing is the major contributor for the adjustment of starch degradation to external photoperiods, these mutants may show the defects in the subjective photoperiod τ_L (figure 1b,c)