Table 2. Parameters from the model, their definitions, derivation and units.

Symbol	Definition	Derivation	Quantity	Units
Measured parameters
Ce, Be	External CO2 and concentration	Measured [DIC] and pH	Independent variable	mol m−3
δCe, δBe	δ13C of external CO2 &	Calculated from δ13C of DIC and pH	Independent variable	‰PDB
FFIX	Average carbon fixation rate	Division rate, mol C org per cell	Measured variable	mol s−1
FCAL	Average calcification rate	Division rate, mol calcite per cell	Measured variable	mol s−1
PIC:POC	Particulate inorganic to particulate organic carbon ratio of biomass	FCAL/FFIX	Measured variable	Molar ratio
TCR	Total carbon assimilation rate	FCAL+FFIX	Measured variable	mol s−1
δCorg	δ13C of organic material	Measured directly	Measured variable	‰PDB
δCcal	δ13C of calcite	Measured directly	Measured variable	‰PDB
rcell	Cell radius	Measured directly	Measured variable	m
SAcell, Vcell	Cell surface area and volume	Functions of rcell	Measured variable	m2&m3
Rho	Cellular organic carbon density	This study, consistent with Reinfelder77	20 × 10−15	mol m−3
Parameters from literature
	Carbon isotopic fractionation during calcification	Zeebe and Wolf-Gladrow44	+1 (from )	‰PDB
, , , , ,	Kinetic carbon isotopic fractionation factors	Zeebe and Wolf-Gladrow44	−13, −22, −11, −20, −1, −10	‰PDB
kp1, km1, kp4, km4	Kinetic rate constants	Calculated from Zeebe and Wolf-Gladrow44	T and S dependent.	various—dependent on reaction
,	Ion product of water	Calculated from (ref. 78)	T and S dependent.	mol2 m−6
,	1st acidity constant of carbonic acid	Calculated from Lueker et al.79	T and S dependent.	mol m−3
	Specific activity of CA for hydration reaction	Inferred from bovine erythrocyte CA45	2.7 × 107	M−1 s−1
pHi, pHx, pHv	pH in compartments i, x & v.	ref. 33	7.0, 7.9 & 7.1.	free scale
fx, fv	Scale factor for compartments x & v	TEM images80,81	1.1 & 0.6	dimensionless
Sx, Sv	Shape factor for compartments x & y	TEM images80,81	6 & 4	dimensionless
Fitted parameters
fe	Effective carbon isotopic fractionation during C-fixation by Rubisco	Fitted parameter	−14.3	‰PDB
PCei	Cell membrane permeability to CO2	Fitted parameter	9.3 × 10−4	ms−1
PBei (T0, TU)	Cell membrane permeability to HCO3−	Fitted parameter	7.8 × 10−8, 5.1 × 10−6	ms−1
G	Effective concentration ratio of the coported ion at the cell membrane	Fitted parameter	2.7	ratio
[CA]i, [CA]x, [CA]v	[CA] in compartments i, x & v.	Inferred	0.1–1	mol m−3

See supplementary information for values for measured parameters generated in this study.