A recent numerical cell model, which explains observed light and carbonate system effects on particulate organic and inorganic carbon (POC and PIC) production rates under the assumption of internal pH homeostasis, is extended for stable carbon isotopes (12C, 13C). Aim of the present study is to mechanistically understand the stable carbon isotopic fractionation signal (ε) in POC and PIC and furthermore the vital effect(s) included in measured εPIC values. The virtual cell is divided into four compartments, for each of which the 12C as well as the 13C carbonate system kinetics are implemented. The compartments are connected to each other via trans-membrane fluxes. In contrast to existing carbon fractionation models, the presented model calculates the disequilibrium state for both carbonate systems and for each compartment. It furthermore calculates POC and PIC production rates as well as εPOC and εPIC as a function of given light conditions and the compositions of the external carbonate system. Measured POC and PIC production rates as well as εPIC values are reproduced well by the model (comparison with literature data). The observed light effect on εPOC (increase of εPOC with increasing light intensities), however, is not reproduced by the basic model set-up, which is solely based on RubisCO fractionation. When extending the latter set-up by assuming that biological fractionation includes further carbon fractionation steps besides the one of RubisCO, the observed light effect on εPOC is also reproduced. By means of the extended model version, four different vital effects that superimpose each other in a real cell can be detected. Finally, we discuss potential limitations of the εPIC proxy.