TABLE 1.

List of symbols used in this study.

Symbol	Unit	Description
C, Ci	mol C cell–1	Carbon content of a cell; ‘i’ refers to the initiation of the SIP incubation, i.e., time-point t = 0.
C max	mol C cell–1	Carbon content of a cell just before binary cell division; Cmax/2 corresponds to the carbon content just after binary cell division.
s	-	Cell cycle stage, calculated from the C content as s = C/(Cmax/2) – 1.
⟨C⟩	mol C cell–1	Carbon content of a cell averaged over the cell cycle. It is equal to the average in a population of cells with perfectly unsynchronized cell cycles. It is related to Cmax according to ⟨C⟩ = Cmax/(2⋅ln(2)) and ⟨C⟩ = Cmax⋅ln(2) for cells assimilating C with zero-order and first-order kinetics, respectively (Koch, 1966).
x, xi	-	13C atom fraction of a cell, defined as x = 13C/(12C+13C); ‘i’ refers to t = 0.
$x_S^E$	-	Source-normalized excess 13C atom fraction of a cell (Eq. 10).
r	mol C cell–1 h–1	Cell-specific rate of carbon assimilation by a cell.
⟨r⟩	mol C cell–1 h–1	Average cell-specific C assimilation rate in a population.
k	h–1	Carbon-specific rate of carbon assimilation by a cell.
t	h	Doubling time; time needed for a cell to double its carbon content. Calculated as τ = Cmax/(2⋅r) and τ=(ln2)/k for a cell assimilating C with zero-order and first-order kinetics, respectively.
ρ	mol C μm–3	Carbon density of a cell.
x S,tar	-	13C atom fraction of the target source provided externally during the SIP incubation.
x S,alt	-	13C atom fraction of an alternative carbon source; can be external (e.g., present in the environment of the cell) or internal (present in the form of intra-cellular C storage inclusions).
x S,eff	-	Effective 13C atom fraction of the carbon source (Eq. 6).
f tar	-	Fraction of C assimilated by the cell from the target source; the remaining fraction of C is assimilated from the alternative C source (falt = 1 – ftar).
θ	-	Probability density function (PDF) describing the distribution of C among cells in a population. Given by Eq. 16 and 18 for a population with perfectly unsynchronized and partially synchronized cell cycles, respectively. Examples shown in Figure 4B, Supplementary Figures 3 and 4).
ζ	-	Probability density function (PDF) describing the distribution of $x_S^E$ in a population of cells assimilating C with zero-order kinetics. Examples shown in Figure 4C.
γ	-	Degree of cell cycle synchronicity characterizing the distribution of C content among cells in a population with partially synchronized cell cycles. Examples shown in Supplementary Figures 4A,B.
X net	-	Net amount of element assimilated by the cell (Ea) relative to the final element content in the cell (Ef). Calculated according to Xnet = Ea/Ef. Used, for instance, by Dekas et al. (2019). For a cell that did not divide during the SIP incubation, Xnet = $x_S^E$ (Supplementary Material, Section “Relationships Between $x_S^E$, Xnet, Fxnet and KA.”).
Fxnet, KA	-	Net amount of element assimilated by the cell (Ea) relative to the initial element content in the cell (Ei). Calculated according to Fxnet = KA = Ea/Ei. Parameter Fxnet was introduced by Popa et al. (2007), while parameter KA was introduced by Stryhanyuk et al. (2018). For a cell that did not divide during the SIP incubation, Fxnet = KA = $x_S^E/(1-x_S^E)$ (Supplementary Material, Section “Relationships Between $x_S^E$, Xnet, Fxnet and KA.”).