APPLYING NONLINEAR MIXED REGRESSION MODELS IN THE DESIGN OF NEW PROBIOTIC PRODUCTS

WEISE B.; BRU E.; JUÁREZ TOMÁS M. S.; ESPECHE M. C.; VERA PINGITORE E.; NADER-MACIAS M. E.

Congreso; XXV INTERNATIONAL BIOMETRIC CONFERENCE; 2010

Probiotic products which can be used in the pharmaceutical or veterinary industry contain living microorganism with beneficial characteristics; these products can be used for the prevention or therapy of humans or animals infections. In the sequential phases of the development of new probiotics, different mathematical models are applied to study the functional and technological characteristics of the selected bacteria. To evaluate the optimization of biomass production, the bacterial growth curves are described by a 4-parameter modified Gompertz model to estimate the initial optical density, the lag phase, the highest final optical density and the maximal growth rate. The biofilm formation, predicted by the auto-aggregation ability, or formation of multicellular clumps between micro-organism of the same strain, can be adjusted to a model of exponential association (a model from the Box Lucas family). The estimated parameters of this model are the maximal auto-aggregation percentage and the auto-aggregation rate i.e. the velocity of auto-aggregation. The functional properties referred to the resistance of microorganisms to gastrointestinal conditions (enzymes, pH, and bile salts) are evaluated through the application of a 4-parameter Weibull model estimating the failure rate and mean lifetime. To study the resistance of the bacteria to the freeze-drying process and the effect of excipients and prebiotic substances on the viability and stability of the product, a 3-parameter model of exponential decay is applied to estimate the maximum of viable cells, the amplitude (the difference between maximal and minimal number of viable cells) and the decay rate. Constrained nonlinear regression was performed to estimate the corresponding parameters; to calculate the standard errors of the estimated parameters, the bootstrapping technique is applied. To evaluate the multivariate effects of different conditions (e.g. temperature, initial pH, and culture media) on the growth, auto-aggregation or decay parameters, the nonlinear mixed-effects model was applied using restricted maximum likelihood (Lindstrom and Bates 1990). The different statistical and mathematical models described allow an easier and faster way to evaluate the behaviour of probiotic microorganisms in the different steps and assays required for their inclusion in novel pharmaceutical or veterinary products.