Solar cells using living micro-organisms often require the help of a redox mediator, a small molecule which carries the electrons from inside the organisms to the electrode. Ideally the mediator is able to cross biological membranes to access the source of electrons, without causing damage. The diffusion rate across membranes, reduction rate inside the micro-organism, and the absence of toxicity are key parameters. Here we use modeling, fit of fluorescence and electrochemical experimental data, and simulation to quantify the reaction rates of the main processes involved in the case of the micro-alga Chlamydomonas reinhardtii, in interaction with the redox mediator 2,6-dichloro-1,4-benzoquinone. We found that the photo-induced reduction inside algae is not the limiting process, but in contrast 10 times faster than the process of electron consumption at the electrode. The maximum current limitation is due to the slow outflow of the mediator out of algae: the molecule has a tendency to get trapped inside because of its lipophilicity. Additionally, it has an important toxicity, and we find that its mode of action is likely to cause a quasi-exponential decay of the number of active photosynthetic chains. This is consistent with known side effects of quinones (oxidative stress, electrophilic behaviour).