Mathematical Modelling of Biomass Quantity and Composition in a Methanotrophic Consortium for Real-Time Monitoring

Real-time monitoring of biomass concentration and cell population structure (cell’s geometry, cell’s concentration, ratio of cell morphotypes, ratio of producer/satellites cells) in methanotrophic consortia cultivated under non-sterile conditions remains challenging for bioprocess control. Conventional offline methods, such as optical density measurement and direct microscopy, are labor-intensive and provide only discrete time-point data. Here, we demonstrate that the physical principle of the μCheck instrument—analysis of the relaxation signal after hydrodynamic orientation of anisotropic suspended particles—can be extended to a complex methanotrophic consortium containing heterotrophic satellite bacteria. We present a mathematical model of the relaxation signal based on a Legendre-polynomial expansion, which reduces to a single-mode approximation and relates the rotational diffusion coefficient to the volume-weighted cell size and, through a polynomial correction for multiple scattering, to the cell concentration. The model was validated on eight samples from two independent cultivations at different stages (growth, stable growth, and degradation). During growth and stable cultivation, μCheck provided cell size estimates within 20% of microscopy values; during degradation, the deviation increased to 28–40%. Cell concentrations from μCheck were systematically higher than microscopy counts by a factor of 4–8, primarily because the method is insensitive to spherical monococci and small satellites. Two-mode decomposition of the relaxation curve for a sample containing rod-shaped satellites resolved the two morphological fractions to within ∼14% and ∼27%, respectively, demonstrating the feasibility of analysing multicomponent suspensions. The method provides rapid at-line trend information on cell morphology and concentration: a measurement cycle takes 1–2 min, at least 18 consecutive measurements are recorded per sample, and the result is available while the cultivation is running. With a process time scale of hours to days, this temporal resolution supports real-time monitoring of high-intensity methanotrophic cultivations. The results confirm that the technology is applicable to a non-sterile methanotrophic process and can be used for at-line monitoring of the culture, provided that method-specific limitations are taken into account.