Mathematical modeling of quorum sensing dynamics in batch culture of luminescent bacterium <i>Photobacterium phosphoreum</i> 1889

Abstract

At the beginning of the paper, the level of necessary phenomenology of complex models is discussed. When working with complex systems, which of course include living organisms and ecological systems, it is necessary to use a phenomenological description. An illustration of the phenomenological approach is given, which captures the most significant general principles or patterns of interactions; the specific values of the parameters cannot be calculated from the first principles, but are determined empirically. An appropriate interpretation is also chosen empirically and pragmatically. However, in order to simulate a wider range of situations, it becomes necessary to lower the level of phenomenology, switch to a more detailed description of the system, introducing interaction between selected elements of the system. The requirements for a system model combining ecological, metabolic and genetic levels of cell culture description are formulated. A mathematical model of quorum sensing dynamics during the growth of batch culture of luminescent bacteria at different concentrations of the nutrient substrate has been developed. The model contains four blocks describing ecological, energy, quorum and luminescent aspects of bacterial culture growth. The model demonstrated good agreement with the experimental data obtained. When analyzing the model, three oddities in the behavior of the culture were noted, which presumably can change the idea of some processes taking place during the development of a culture of luminescent bacteria. The results obtained suggest the presence of some additional control system for the luminescent reaction via the synthesis pathways of FMN · Н2 or aliphatic aldehyde. In this case, the generalized description of the contribution of energy metabolism to luminescence only through ATP is too strong a simplification. As a result of comparing the model dynamics with the experiment, a discrepancy arose between the concentration of the substrate (peptone) measured in the experiment and its effective influence on the bacterial population growth. This discrepancy seems to indicate peptone is not the leading substrate, and growth is limited by nutrients contained in the yeast extract, the concentration of which did not change in these experiments. The discrepancies noted between the expectations and the results of experimental data processing, together with the assumptions about the causes of these discrepancies, set the direction for further experimental and theoretical studies of quorum sensing mechanisms in a culture of luminescent bacteria.

Keywords

• quorum sensing
• mathematical model
• luminescent bacteria