Nonlinear modeling to describe the pattern of 15 milk protein and nonprotein compounds over lactation in dairy cows

Abstract

The protein profile of milk includes several caseins, whey proteins, and nonprotein nitrogen compounds, which influence milk's value for human nutrition and its cheesemaking properties for the dairy industry. To fill in the gap in current knowledge of the patterns of these individual nitrogenous compounds throughout lactation, we tested the ability of a parametric nonlin-ear lactation model to describe the pattern of each N compound expressed qualitatively (as % of total milk N), quantitatively (in g/L milk), and as daily yield (in g/d). The lactation model was tested on a data set of detailed milk nitrogenous compound profiles (15 frac-tions-12 protein traits and 3 nonproteins-for each expression mode: 45 traits) obtained from 1,342 cows reared in 41 multibreed herds. Our model was a modi-fied version of Wilmink's model, often used for describ-ing milk yield during lactation because of its reliability and ease of parameter interpretation from a biological point of view. We allowed the sign of the persistency coefficient (parameter c) that explained the variation in the long-term milk component (parameter a) to be positive or negative. We also allowed the short-term milk component (parameter b) to be positive or nega-tive, and we estimated a specific speed of adaptation parameter (parameter k) for each trait rather than as-sumed a value a priori, as in the original model (k = 0.05). These 4 parameters were included in a nonlinear mixed model with cow breed and parity order as fixed effects, and herd-date as random. Combinations of the positive and negative signs of the b and c parameters allowed us to identify 4 differently shaped lactation curves, all found among the patterns exhibited by the nitrogenous fractions as follows: the "zenith" curve (with a maximum peak; for milk yield and 10 other N traits), the "nadir" curve (with a minimum point; for 20 traits, including almost all those expressed in g/L of milk), the "downward" curve (continuously decreasing; for 14 traits, including almost all those in g/d), and the "upward" curve (continuously increasing; only for Kappa-casein, in % N). Direct estimation of the k parameters specific to each trait showed the large variability in the adaptation speed of fresh cows and greatly increased the model's flexibility. The results indicated that non-linear parametric mathematical models can effectively describe the different and complex patterns exhibited by individual nitrogenous fractions during lactation; therefore, they could be useful tools for interpreting milk composition variations during lactation.