Deriving fractional rate of degradation of logistic-exponential (LE) model to evaluate early in vitro fermentation.

Water-soluble components of feedstuffs are mainly utilized during the early phase of microbial fermentation, which could be deemed an important determinant of gas production behavior in vitro. Many studies proposed that the fractional rate of degradation (FRD) estimated by fitting gas production curves to mathematical models might be used to characterize the early incubation for in vitro systems. In this study, the mathematical concept of FRD was developed on the basis of the Logistic-Exponential (LE) model, with initial gas volume being zero (LE0). The FRD of the LE0 model exhibits a continuous increase from initial (FRD 0) toward final asymptotic value (FRD F) with longer incubation time. The relationships between the FRD and gas production at incubation times 2, 4, 6, 8, 12 and 24 h were compared for four models, in addition to LE0, Generalization of the Mitscherlich (GM), c th order Michaelis-Menten (MM) and Exponential with a discrete LAG (EXPLAG). A total of 94 in vitro gas curves from four subsets with a wide range of feedstuffs from different laboratories and incubation periods were used for model testing. Results indicated that compared with the GM, MM and EXPLAG models, the FRD of LE0 model consistently had stronger correlations with gas production across the four subsets, especially at incubation times 2, 4, 6, 8 and 12 h. Thus, the LE0 model was deemed to provide a better representation of the early fermentation rates. Furthermore, the FRD 0 also exhibited strong correlations (P < 0.05) with gas production at early incubation times 2, 4, 6 and 8 h across all four subsets. In summary, the FRD of LE0 model provides an alternative to quantify the rate of early stage incubation, and its initial value could be an important starting parameter of rate.