This work refers to the study of the batch and fed batch cultures of an industrially applicable microbial strain termed Gluconobacter suboxydans S-22, capable of converting D-sorbitol into L-sorbose and D-glucose into D-gluconic acid at extremely high substrate mass concentrations. Media based on CSL-filtrate and containing different D-sorbitol concentrations were applied to performexperim ents. Studied were the effects of D-sorbitol and L-sorbose concentrations on the kinetics of microbial growth and D-sorbitol conversion into L-sorbose, and of microbial cell metabolism on the oxygen solubility and water activity, on the oxygen transfer and uptake rates and on the bioprocess final L-sorbose yield. In order to define the process relationships and describe the kinetics of all relevant process events in a large range of reaction conditions, a mathematical model based on corresponding differential equations was developed. The applicability of the mathematical model was tested by computer simulation. Data of computer simulations fitted well to experimental data. Changes of biomass, D-sorbitol, L-sorbose and dissolved oxygen concentrations during the batch and fed batch cultures can be well explained by applied mathematical model regardless of whether they refer to the reaction system of commonly dissolved substance mass concentration (close to 200 g L–1) or to the reaction systemof extremely highly dissolved and total substance concentrations (above 700 g L–1). Excellent correlation coefficients (0.99693 – 0.99995) expressing the agreement of the theoretical with experimental data were found for compared biomass, D-sorbitol, L-sorbose and dissolved oxygen concentrations. Results confirmed the hypothesis that the water activity can be expressed as a function of oxygen solubility in the investigated reaction system.