## 4 Discussion
The decrease in final DHA concentration for the immobilized system could also be due to limitations in mass transfer, which hinders easy transport of substrate to active sites of the enzyme present inside the immobilized matrix. This further decreases the actual substrate concentration inside alginate beads in comparison to bulk concentration in media. Whereas, the free cell system was able to access the total available substrate in the bulk medium and resulted in higher DHA production in comparison to immobilized systems. The type of carrier used could also affect the obtained results. The size of alginate beads may also be an important issue. A needle with a diameter of 1.20 mm was used to prepare the alginate beads [27]. It is supposed that the smaller diameter of the gel beads could increase the surface area of the enzyme-substrate contact and facilitate firstly glycerol oxidation and later DHA release into the reaction medium. [PERSON] et al. [28] reported that mass transfer of substrate from a bulk medium into a immobilized matrix is greatly affected by the size of the alginate bead in ethanol fermentation by _S. cerevisiae_. Reduction in bead size increased the mass transfer of substrates from the liquid to the immobilized cells, which further accelerated sugar consumption and ethanol production. In another study, [PERSON] et al. [29] examined competing effects of mass transfer hindrance and kinetics in a glucose to ethanol fermentation system by _S. cerevisiae_. An increase in diffusion resistance with the substrate decreases the availability of the substrate for microbial cells inside the immobilized matrix. Based on the obtained results, it can be concluded that an increase in initial waste glycerol concentration to 50 g:L\({}^{-1}\) did not cause a faster and greater increase in DHA productivity and reaction efficiency as compared to an initial concentration of 30 g:L\({}^{-1}\). Increasing the initial crude glycerol concentration was accompanied by an increase in associated contaminants like methanol, salts, soaps, and residual fatty acids, which could further have an inhibiting effect on the course of the bioconversion reaction [30]. It has also been reported that higher substrate (i.e., glycerol) concentration inhibits growth as well as DHA production in _G. oxydans_ cells [4]. Therefore, _G. oxydans_ cells were more prone to substrate inhibition in the reaction containing 50 g:L\({}^{-1}\) waste glycerol as compared to the reaction with 30 g:L\({}^{-1}\) concentration, which subsequently influences the DHA productivity, as well as the reaction efficiency. It was also observed that running the process for 96 h does not ensure a general increase in the final product concentration. Data analysis indicates, that in most of the conducted reactions, a maximum DHA concentration was witnessed after 72 h of biotransformation. Extending the reaction time to 96 h resulted in a reduction in DHA productivity. The reason for the decreasing DHA concentration could be it's further phosphorylation catalyzed by dihydroxyacetone kinase, which probably also occurs in cell extract [14; 31]. GlyDH, the key enzyme responsible for glycerol oxidation, exhibits the highest activity at the end of the exponential phase of bacterial growth, which could be approximately 24 h [32; 33; 34]. After more than 48 h, it may still convert the substrate, but with a significantly lower efficiency. This membrane-bound GlyDH enzyme is dependent on the pyrroloquinoline quinone (PQQ) cofactor, which transfers oxygen from glycerol to a final acceptor (oxygen) via an electron transport chain [24; 35]. In live bacterial cells, resources of PQQ are supplemented in the course of the reaction. When cells are replaced with a cell extract, the initial content of PQQ decreases successively, and if the reaction medium is not supplemented with this cofactor, it is totally consumed after a few hours, and the activity of the enzyme is lower than within the first 24-48 h [35]. It needs to be emphasized that the genome of _G.