True protein secretion

In most of the formulation models, the equation from Swanson (Reference Swanson1977) predicting net crude protein (CP) requirement for scurf is used:

(1)$${\rm{CP\, scur}}{{\rm{f}}_{{\rm{secretion}}}}\left( {\rm g/day} \right) = 0.2{\rm{ }} \times {\rm{ B}}{{\rm{W}}^{0.60}}$$

Swanson’s prediction was retained but adjusted to take into account that not all CP is TP:

(2)$${\rm{TP\, scur}}{{\rm{f}}_{{\rm{secretion}}}}\left( {{\rm{g/day}}} \right) = 0.2{\rm{ }} \times {\rm{ B}}{{\rm{W}}^{0.60}} \times {\rm{ }}0.86{\rm{ }} = {\rm{ }}0.17{\rm{ }} \times {\rm{ B}}{{\rm{W}}^{0.60}}$$

where 0.86 represents the TP/CP ratio of scurf, based on its AA composition, detailed below, and total N content; here and throughout the text, BW is in kg.

Amino acids

The secretion of AA into scurf is obtained by multiplying TP scurf_secretion by its AA composition, estimated using the head, hide, feet and tail composition reported by Williams (Reference Williams1978) and van Amburgh et al. (Reference Van Amburgh, Collao-Saenz, Higgs, Ross, Recktenwald, Raffrenato, Chase, Overton, Mills and Foskolos2015). The mean from these studies, corrected for incomplete recovery of AA with 24-h hydrolyses (Lapierre et al., Reference Lapierre, Binggeli, Sok, Pellerin and Ouellet2019), is reported on a TP basis in Table 1.

(3)$${\rm{AA\, scur}}{{\rm{f}}_{{\rm{secretion}}}}\left( {{\rm{g/day}}} \right){\rm{ }} = {\rm{ }}0.17{\rm{ }} \times {\rm{ B}}{{\rm{W}}^{0.60}} \times {\rm{ }}\left[ {{\rm{A}}{{\rm{A}}_{{\rm{corr}} - {\rm{Scurf}}}}} \right]/100$$

where (AA_corr–Scurf) is in g AA/100 g TP.

Table 1 Amino acid (AA) composition of protein secretions used in the calculation of efficiency of utilization of AA in lactating dairy cows

¹ g AA_corr: AA composition corrected to account for incomplete recovery of AA with 24-h hydrolysis; TP = true protein.

² g AA_calc: AA composition calculated from the primary structure of the reference protein of each family; see text for details.

True protein secretion

Most formulation models predict endogenous urinary daily protein losses according to Swanson (Reference Swanson1977), at 2.75 g/BW^0.50. To better quantify the AA required to cover this loss, a literature review was conducted to quantify the composition of urinary N. Force is to admit that literature is scarce on that domain in dairy cattle (Dijkstra et al., Reference Dijkstra, Oenema, van Groenigen, Spek, van Vuuren and Bannink2013b). The major N metabolites in endogenous urinary N losses are: urea synthesized from endogenous sources, endogenous purine derivative (PD), creatinine and creatine, hippuric acid and 3-methyl-His. Therefore, endogenous N urinary loss is not a protein secretion per se. From studies with low CP dietary intake, daily excretion of endogenous urea has been quantified as 10 mg N/BW per day (Hutchinson and Morris, Reference Hutchinson and Morris1936; Biddle et al., Reference Biddle, Evans and Trout1975; Marini and Van Amburgh, Reference Marini and Van Amburgh2005; Wickersham et al., Reference Wickersham, Titgemeyer, Cochran, Wickersham and Gnad2008a and Reference Wickersham, Titgemeyer, Cochran, Wickersham and Mooref2008b). To predict creatinine excretion, a database using exclusive dairy breeds, with growing and mature animals (111 treatment means from 24 publications from 1979 to 2015: Supplementary Material S1) was built. Urinary excretion of creatinine was regressed to 25.5 mg creatinine/BW per day, representing 9.46 ± 0.157 mg N/BW per day. Creatine excretion was evaluated as 0.37 that of creatinine (Blaxter and Wood, Reference Blaxter and Wood1951; Nehring et al., Reference Nehring, Zelck and Schiemann1965; Bristow et al., Reference Bristow, Whitehead and Cockburn1992). Urinary excretion of endogenous PD was assumed to average 27.1 mg N/BW^0.75 per day (483 µmol/BW^0.75: reviews from Tas and Susenbeth, Reference Tas and Susenbeth2007; Fujihara and Shem, Reference Fujihara and Shem2011). Daily urinary excretion of 3-methyl-His (µmol) was evaluated at 50.4 + 3.54 × BW (Harris and Milne, Reference Harris and Milne1981).

Using the database from Spek et al. (Reference Spek, Dijkstra, van Duinkerken, Hendriks and Bannink2013), the ‘measured’ endogenous urinary N excretion was calculated as non-urea urinary excretion plus endogenous urea (predicted as described above) minus estimation of PD derived from absorbed microbial protein (Chen and Gomes, Reference Chen and Gomes1992). The sum of predictions described above represented 54% of the ‘measured’ endogenous urinary N excretion. As previously mentioned, hippuric acid is another N metabolite excreted in urine. Hippuric acid is formed in the liver to detoxify benzoic acid originating from rumen fermentation of dietary phenolic compounds. Although this excretion cannot be purely defined as ‘endogenous’, it has probably been included in previous predictions of endogenous urinary N excretion. When determined, it averaged 25.7% of non-urea N urinary excretion (Nehring et al., Reference Nehring, Zelck and Schiemann1965; Bristow et al., Reference Bristow, Whitehead and Cockburn1992; Kool et al., Reference Kool, Hoffland, Hummelink and van Groenigen2006). Including hippuric acid to the ‘endogenous’ urinary excretion, the calculated v. ‘measured’ values from Spek’s database were not different (29.3 ± 4.5 v. 33.4 ± 15.4 g N/day), but there was a strong slope bias. The potential hippuric acid excretion was best related, in the database, to the proportion of urea N in urinary N excretion. Using this relationship to evaluate hippuric acid excretion, the calculated endogenous urinary N excretion averaged 33.2 ± 11.2 g N/day compared with 33.4 g N/day for the 84 treatment means ‘measured’ as described above. Although smaller, there remained a slope bias that could not be corrected, indicating an important gap in our knowledge on the composition of urinary N excretion. Besides hippuric acid, most of the estimations of urinary excretion were based on BW, and the sum of endogenous urinary N excretions was expressed relative to BW, averaging 53 mg N/BW (or 0.053 g N/BW) per day. Using a totally different approach, the prediction of daily endogenous urinary N loss averages 50 mg N/BW in the formulation model of the Institut National de Recherche Agronomique (INRA, 2018), very similar to our prediction and roughly twice as large as the Swanson (Reference Swanson1977) prediction. As these compounds are expressed in g N/day, there is no need to convert from CP to TP. Therefore,

(4)$${\rm{TP\, endogenous\, urinar}}{{\rm{y}}_{{\rm{secretion}}}}\left( {{\rm{g/day}}} \right){\rm{ }} = {\rm{ }}0.33{\rm{ }} \times {\rm{ BW}}$$

where 0.33 is derived from 0.053 × 6.25.

Amino acid composition

The reason for revisiting endogenous urinary excretion was to identify which AA were upstream of these urinary excretions. After the examination of metabolic pathways yielding each of these urinary excreted compounds, only endogenous urea and 3-methyl-His excretions require a direct input of essential AA (EAA), if we exclude Arg from true EAA. Indeed, endogenous PD are synthesized from Asp, Gln and Gly; creatine and creatinine from Arg and Gly (it requires S-adenosyl Met, but as for other metabolic pathways, this does not represent a net Met requirement); and hippuric acid is synthesized from Gly. Endogenous urea excretion is assumed to have a revisited whole empty body AA composition (Williams, Reference Williams1978; Rohr and Lebzien, Reference Rohr and Lebzien1991; Ainslie et al., Reference Ainslie, Fox, Perry, Ketchen and Barry1993; Van Amburgh et al., Reference Van Amburgh, Collao-Saenz, Higgs, Ross, Recktenwald, Raffrenato, Chase, Overton, Mills and Foskolos2015); the mean of these studies, corrected for incomplete recovery of AA with 24-h hydrolyses, is reported on a TP basis in Table 1. Therefore, to determine AA secretion in endogenous urinary N output, we need first to calculate endogenous urea excretion,

(5)$${\rm{TP\, endogenous\, urinary \hyphen ure}}{{\rm{a}}_{{\rm{secretion}}}}\left( {{\rm{g/day}}} \right){\rm{ }} = {\rm{ }}0.0625{\rm{ }} \times {\rm{ BW}},$$

where 0.0625 was derived from 0.010 g N/day × 6.25; and multiply this secretion by the corresponding AA_corr composition, assumed to be that of whole empty body (Table 1).

(6)$${\rm{AA\, endogenous\, urinar}}{{\rm{y}}_{{\rm{secretion}}}}\left( {{\rm{g/day}}} \right){\rm{ }} = 0.0625{\rm{ }} \times {\rm{ BW }} \times {\rm{ }}\left[ {{\rm{A}}{{\rm{A}}_{{\rm{corr}} - {\rm{WholeEmptyBody}}}}} \right]/100$$

where (AA_{corr–WholeEmptyBody}) is in g AA/100 g TP.

To complete the estimation of His excretion in endogenous urinary loss, 3-methyl His urinary excretion, as described above (mg His/day = 7.82 + 0.55 × BW), needs to be added. And finally, to complete the estimation of contribution of Arg to urinary N excretion, we need to include its contribution to creatinine and creatine, that is, 0.052 × BW g Arg/day.

True protein secretion

This is certainly protein secretion with the largest discrepancy in its prediction varying, for example, between 337 and 621 g/day for a cow eating 23 kg/day of a 16.5% CP diet when predicted with five formulation models (Lapierre et al., Reference Lapierre, Larsen, Sauvant, Van Amburgh and Van Duinkerken2018). Reasons for this high discrepancy are inherent to the difficulty in performing its measurements and to the ambiguous definition of MFP. First, the determination of MFP in ruminants cannot be done as simply as in monogastrics where MFP is measured in animals fed an N-free diet. Predictions of MFP in ruminants have been based on regressing intake of digestible CP on CP intake with the negative intercept estimated as MFP, averaging, for example, 34, 33 and 29 g CP/kg DM intake (DMI) in earlier studies (Holter and Reid, Reference Holter and Reid1959; Waldo and Glenn, Reference Waldo and Glenn1984) comparable to 32 and 27 g CP/kg DMI reported in more recent studies (Jonker et al., Reference Jonker, Kohn and Erdman1998; Kauffman and St-Pierre, Reference Kauffman and St-Pierre2001). In a meta-analysis using 65 growing-finishing cattle studies (291 treatment means) and 43 dairy cow studies (164 treatment means), Marini et al. (Reference Marini, Fox and Murphy2008) obtained an intercept of 30 g CP/kg DMI when ignoring the multidimensionality of the relationship with other parameters. Predictions of MFP have also been calculated subtracting predicted undigested feed N from fecal N when animals were fed low CP diets (29.4 g CP/kg DMI; Swanson, Reference Swanson1977). However, it has been demonstrated that MFP losses are related more closely to feces output than to feed intake (Swanson, Reference Swanson1977): for this reason, some formulation models have based their estimation of MFP on indigestible DM (CNCPS; Fox et al., Reference Fox, Tedeschi, Tylutki, Russell, Van Amburgh, Chase, Pell and Overton2004) or the outflow of organic matter from the digestive tract (NorFor, 2011; INRA, 2018). However, because of the uncertainty related to the estimation of DM digestibility, the National Research Council (2001) predicted MFP based on DMI.

However, the values obtained from the methods described above are not strictly a measure of loss of true protein from endogenous origin. Indeed, it was already raised at the beginning of the 1980s that these estimations of MFP included bacteria and bacterial debris (Swanson, Reference Swanson and Owens1982) and then the question ‘Is the source of bacteria primarily waste N rather than a metabolic cost to the animal?’ was raised (question from Trenkle: Swanson, Reference Swanson and Owens1982). Indeed, the metabolic demand for MFP should be only derived from endogenous secretions originating directly from AA (either from arterial supply and small intestinal digestion) and not from urea recycled into microbial protein. Therefore, NRC (2001), recognizing that a part of this fecal material contains undigested ruminal microbial CP, assumed that 50% of indigestible microbial protein appears in the feces and should be excluded from initial MFP prediction.

To improve the estimation of endogenous secretions through the gut in dairy cows, Ouellet et al. (Reference Ouellet, Demers, Zuur, Lobley, Seoane, Nolan and Lapierre2002 and Reference Ouellet, Berthiaume, Holtrop, Lobley, Martineau and Lapierre2010) adapted an isotopic dilution approach used in pigs (e.g. Lien et al., Reference Lien, Sauer, Mosenthin, Souffrant and Dugan1997) and sheep (Sandek et al., Reference Sandek, Krawielitzki, Kowalczyk, Kreienbring, Schoenhusen, Gabel, Zebrowska, Hagemeister and Voigt2001). This approach allowed the development of a model delineating the contribution of undigested rumen bacteria synthesized from endogenous secretions or from urea to fecal N, thus allowing the exclusion of the latter from MFP. Because endogenous proteins have multiple origins (saliva, gastric juices, bile, pancreatic secretions, sloughed epithelial cells and mucin: Tamminga et al., Reference Tamminga, Schulze, Van Bruchem and Huisman1995), it is a challenge to determine the isotopic enrichment of the precursor pool when using a dilution approach. Values obtained using the enrichment of the mucosa as representative of endogenous secretions have been retained for this revision. Furthermore, the metabolic cost of the loss of undigested endogenous secretion across the upper gut should be measured at the ileum, because the endogenous secretions flowing out of the small intestine and disappearing across the hindgut do not result in absorbed AA. Endogenous fecal loss was, therefore, adjusted using a factor of 1.13, representing the ratio of ileal endogenous flow divided by fecal endogenous flow, measured in dairy cows (Ouellet et al., Reference Ouellet, Valkeners, Holtrop, Lobley and Lapierre2007). Therefore, the prediction of endogenous ileal flow calculated using the enrichment of gut mucosa was retained as a basis for the estimation of MFP, averaging 14.9 g CP/kg DMI (Lapierre et al., Reference Lapierre, Lobley, Ouellet, Doepel and Pacheco2007).

Although MFP is calculated relative to DMI, as discussed above, it has been recognized that the driving force of MFP should be indigestible DM (Swanson, Reference Swanson1977). However, because of the uncertainties associated with estimating DM digestibility, we propose to still use DMI as a basis to predict MFP, but to include the neutral detergent fiber of the ration (NDF, %DM) based on Marini et al. (Reference Marini, Fox and Murphy2008) regression of total tract digestibility of N v. N content of the diet. This inclusion will partially account for diet DM digestibility. The Marini equation also included a carbohydrate fermentation rate (fast, medium or none), but for practical purposes and to remove subjectivity, the average of three values was used to derive the final equation. Therefore, the equation of Marini et al. (Reference Marini, Fox and Murphy2008) was adjusted to yield the value mentioned above at 14.9 g CP/kg DMI for cows fed diets at 36% NDF (in the rations in Ouellet et al., Reference Ouellet, Demers, Zuur, Lobley, Seoane, Nolan and Lapierre2002, Reference Ouellet, Valkeners, Holtrop, Lobley and Lapierre2007 and Reference Ouellet, Berthiaume, Holtrop, Lobley, Martineau and Lapierre2010). In addition, endogenous secretions occurring across the hindgut also create a demand on AA as demonstrated in pigs (Zhu et al., Reference Zhu, Lapierre, Rademacher, de Lange and Ball2003). Based on observations in sheep (Sandek et al., Reference Sandek, Krawielitzki, Kowalczyk, Kreienbring, Schoenhusen, Gabel, Zebrowska, Hagemeister and Voigt2001), this demand was estimated as 60% of N ileal flow of small intestinal endogenous secretion, the latter averaging 5.1 g CP/kg DMI in dairy cows (Ouellet et al., Reference Ouellet, Valkeners, Holtrop, Lobley and Lapierre2007). Due to the scarcity of data on the exact origin of this hindgut N, it is assumed that half of this input originated from endogenous proteins and the other half from urea. Therefore, the estimation of MFP excretion (g CP/day) = (11.62 + 0.134 ×NDF_%DM) × DMI. Note that we keep the term metabolic fecal protein, although the small intestinal loss was truly predicted at the ileum. Based on its AA composition, detailed below, and N content, a ratio of 0.73 for TP/CP of MFP is calculated and

(7)$${\rm{TP\, MF}}{{\rm{P}}_{{\rm{secretion}}}}\left( {{\rm{g/day}}} \right) = \left( {8.5{\rm{ }} + {\rm{ }}0.1{\rm{ }} \times {\rm{ ND}}{{\rm{F}}_{{\rm{\% DM}}}}} \right) \times {\rm{DMI}}$$

where NDF_%DM is the percentage of NDF in the ration; here and throughouot the text, DMI is in kg/day.

Amino acid composition

The AA composition of MFP is based on the AA composition of ruminal and abomasal isolates from Ørskov et al. (Reference Ørskov, McLeod and Kyle1986) and the endogenous flow at the ileum in pigs (Jansman et al., Reference Jansman, Smink, Van Leeuwen and Rademacher2002), assuming that 70% of MFP is from undigested endogenous duodenal flow and the remaining 30% from the intestine (Ouellet et al., Reference Ouellet, Demers, Zuur, Lobley, Seoane, Nolan and Lapierre2002 and Reference Ouellet, Berthiaume, Holtrop, Lobley, Martineau and Lapierre2010). The averaged composition corrected for incomplete recovery of AA with 24-h hydrolyses is reported on a TP basis in Table 1. Therefore, individual AA secretion in MFP is calculated as:

(8)$${\rm{AA}}\,{\rm{MF}}{{\rm{P}}_{{\rm{secretion}}}}({\rm{g}}/{\rm{day}}) = [(8.5 + 0.1 \times {\rm{ND}}{{\rm{F}}_{{\rm{\% DM}}}}) \times {\rm{DMI}}] \times [{\rm{A}}{{\rm{A}}_{{\rm{corr}} - {\rm{MFP}}}}]/100$$

where (AA_corr–MFP) is in g AA/100 g TP.

True protein secretion

Milk true protein secretion is certainly the most accurate measurement of export protein to make. The factor used to convert the measured milk N concentration into CP varies between 6.34 and 6.39. Based on the AA composition of milk protein, 6.34 would be the best factor (Karman and van Boekel, Reference Karman and van Boekel1986; authors’ calculations), but using different factors only has a limited impact on the estimation of MPY, smaller than 1%. Similar to other protein secretions, it has to be expressed as TP. If the TP/CP ratio is not known, NPN content of milk is assumed to be 4.9% (DePeters and Cant, Reference DePeters and Cant1992).

Amino acid composition

Although critical in the definition of AA requirements, milk AA composition has not been recently investigated. Indeed, early studies reported (1) that the EAA composition of milk produced from cows fed urea and ammonium N as the sole source of N differed by <3% from the EAA composition of milk from control cows (Syvaöja and Virtanen, Reference Syvaöja and Virtanen1965), and (2) that a change in the forage–grain ratio of the ration did not alter the AA composition of milk (Featherston et al., Reference Featherston, Frazeur, Hill, Noller and Parmelee1964). From these observations, it has been assumed that the AA composition of milk protein is fairly constant, and this dogma has not been really challenged. Therefore, milk AA composition is still assumed to be constant, although this issue might need to be re-addressed with improved techniques to measure AA concentration. The same approach as that used in Swaisgood (Reference Swaisgood and Jensen1995) has been adopted to determine the AA composition of milk TP. Milk AA composition has been calculated based on the primary structure of reference protein of each family as detailed by Farrell et al. (Reference Farrell, Jimenez-Flores, Bleck, Brown, Butler, Creamer, Hicks, Hollar, Ng-Kwai-Hang and Swaisgood2004). Based on the distribution of milk proteins reported in 15 manuscripts published between 1980 and 2012 (Supplementary Material S2), protein fractions in milk TP were assumed to be 82.4% casein (as a percentage of total protein: 35.2% αs1-casein; 7.6% αs2-casein; 30.9% β-casein; 8.7% κ-casein) and 17.6% whey (as a percentage of total protein: 3.7% α-lactalbumin; 10.5% β-lactoglobulin; 1.04% albumin; 1.64% IgG1; 0.21% IgG2; 0.04% IgA; 0.33% IgM; 0.21% lactoferrin). The AA composition of milk protein calculated using this procedure is presented in Table 1. Therefore, individual AA secretion in milk protein is calculated as:

(9)$${\rm{AA}}\,{\rm{Mil}}{{\rm{k}}_{{\rm{secretion}}}}({\rm{g}}/{\rm{day}}) = {\rm{MPY}}({\rm{g}}/{\rm{day}}) \times [{\rm{A}}{{\rm{A}}_{{\rm{calc}} - {\rm{Milk}}}}]/100$$

where AA_calc-Milk is in g/100 g TP.

Using this approach for milk, there is no need to do any correction for potential loss due to an incomplete recovery with hydrolyses. Due to the high diversity of proteins included in other types of secretions, an approach similar to milk protein cannot be used for these former proteins; therefore, the only way to obtain their AA composition is by hydrolysis. To correctly sum the AA in protein secretions, we used corrected AA concentrations for all protein secretions and calculated AA concentrations for milk.

Databases

The calculations described above were applied to two databases, one used for the development of models, and the second for their validation. The developmental database included 208 publications (807 treatment means) and was an extension of the database used by Roman-Garcia et al. (Reference Roman-Garcia, White and Firkins2016) with studies added to offer a wider range of AA supply. An independent validation database was also built, including 32 publications (129 treatment means). The summary statistics of developmental and validation databases are presented in Tables 2 and 3, respectively. Publications included in the developmental database and in the validation database are listed in Supplementary Material S3. In both databases, studies have been coded to look specifically at the increment of MP supply. The relationship between MPY and MP supply depicts the overall meta-design (Figure 1).

Table 2 Summary statistics of the developmental database (n = 807) from studies conducted in lactating dairy cows

MP = metabolizable protein; MP_adj = metabolizable protein supply minus endogenous urinary loss; DE = digestible energy.

Table 3 Summary statistics of the validation database (n = 129) from studies conducted in lactating dairy cows

MP = metabolizable protein; MP_adj = metabolizable protein supply minus endogenous urinary loss; DE = digestible energy.

Figure 1 Relationship between milk true protein yield and metabolizable protein (MP) supply in lactating dairy cows in the developmental and validation databases.

Statistics

Models predicting Eff_MP were developed using variables that were strong predictors of the sum of protein secretions when tested individually: MP_adj, digestible energy intake (DEI), days in milk (DIM) and parity (primiparous v. multiparous). Digestible energy was used because metabolizable energy requires the estimation of urinary N, unknown until the efficiency is predicted, and net energy requires, in addition, the quantification of MPY: both are unknown that we are trying to predict. Digestible energy was predicted based on nutrient digestibility (Daley et al., Reference Daley, Armentano, Kononoff, Prestegaard and Hanigan2018; de Souza et al., Reference de Souza, Tempelman, Allen, Weiss, Bernard and VandeHaar2018). Models tested the linear and quadratic effects of (1) MP_adj, (2) MP_adj and DEI and (3) MP_adj/DEI; DIM and parity were tested in all models.

Models were developed using the rma.mv function from the metafor package in R. Potential outlying and influential observations and studies were detected using the rstandard, the rstudent and the cook.distance functions in the metafor package. All relationships were graphed and evaluated using the ggplot function of the ggplot2 package for R (Wickham, Reference Wickham2016). Using the rma.mv function of metafor, the hierarchy of studies, as a random effect, was taken into account. For example, two or more different studies could be reported in the same experiment; therefore, data were fitted to a three-level mixed-effect meta-regression model. To weigh data by √N, the V argument was set to zero and the R argument was used to specify a known matrix, that is, diag(1/developmental_database$Nexp0.5), with an unknown multiplicative variance component which was then estimated by metafor (Viechtbauer, Reference Viechtbauer2018). Unbiased estimates of fixed effects and valid estimates of SE were obtained using the robust function in the metafor package with publication as the clustering variable. The use of robust function does not change the weight matrix but only affects the way the variance–covariance matrix of the fixed effects and downstream SE and P values are computed (Viechtbauer, Reference Viechtbauer2017a and Reference Viechtbauer2017b). Model performance was evaluated using RMSE and root mean squared prediction error (RMSPE) for the development and validation databases as a percentage of the observed mean. Mean bias and slope bias, which are two MSE decomposition terms, were also computed and expressed as a percentage of MSE (Theil, Reference Theil1966; Bibby and Toutenburg, Reference Bibby and Toutenburg1978). Concordance correlation coefficients (CCC; Lin, 1989 and Reference Lin1992) and the corrected Akaike’s information criterion (AICc; Hurvich and Tsai, Reference Hurvich and Tsai1993) are also reported. Ideal models are those with RMSE closest to 0, CCC closest to 1, mean and slope biases closest to 0, and smallest AICc.

Factors affecting efficiency

We initially tested the models using MP_adj as a surrogate of individual AA_adj to delineate which model(s) would yield the best goodness of fit. Three models are reported in Table 4: Eff_MP as a function of MP_adj and its squared term (equation 12); the latter plus DEI and its squared term (equation 13); and the ratio of MP_adj/DEI and its squared term (equation 14); DIM and parity were significant in the three models. The inclusion of DEI, either as an independent term (equation 13) or as a ratio with MP_adj (equation 14), improved the goodness of fit compared with MP terms alone (Figure 2), as shown by a substantial reduction of AICc, a large decrease in slope bias in both the developmental and validation databases and an increased CCC (Table 4). The improvement of the relationship of Eff_MP with MP_adj/DEI compared with MP_adj can also be visually appreciated in Figure 3. This agrees with a better prediction of MPY when energy supply is included in the model than based only on MP supply (Doepel et al., Reference Doepel, Pacheco, Kennelly, Hanigan, López and Lapierre2004) or with a final model which includes both protein and energy supplies (Daniel et al., Reference Daniel, Friggens, Chapoutot, Van Laar and Sauvant2016). Although equation (13) yielded a slightly lower AICc than equation (14), in the validation database, the slope bias was larger with the former equation and CCC was lower. Currently, two European systems, the DVE/OEB (Van Duinkerken et al., Reference Van Duinkerken, Blok, Bannink, Cone, Dijkstra, Van Vuuren and Tamminga2011) and NorFor (2011), are using the ratio of MP/NE_L available for milk to predict the efficiency of lactation and MPY; Sauvant et al. (Reference Sauvant, Catalapiedra-Hijar, Delaby, Daniel, Faverdin and Nozière2015) estimated that Eff_MP was better related to MP/DMI than MP/NE_L. Another main advantage of using the ratio is the practicality of transferring results to ‘cows of the future’ eating more and producing more than cows from the studies included in the current review. In theory, predictive equations should be used within the range of values of predictors used for their development. Even if cows in commercial farms are eating more than observations in the developmental database, the ratio MP_adj/DEI remains within the limits of current observations, whereas MP_adj and DEI of high-producing dairy cows are already higher than the maxima observed in the developmental database. Therefore, we decided to use MP_adj/DEI as the driving force of Eff_MP and apply the same concept to individual AA_adj. Results for Eff_AA, equations (15) to (24), are presented in Table 5. All estimates were highly significant (P < 0.01) for all variables except parity (P < 0.05). Globally, the trends were very similar for the estimation of Eff_AA compared with Eff_MP, that is, very low mean and slope bias in the developmental database and a mean bias of ±5% MSE in the validation database. In both databases, His and Trp were used with the highest efficiency, and Phe and Thr with the lowest. Values are in the same range as previously reported for combined efficiency (Lapierre et al., Reference Lapierre, Lobley, Ouellet, Doepel and Pacheco2007; Van Amburgh et al., Reference Van Amburgh, Collao-Saenz, Higgs, Ross, Recktenwald, Raffrenato, Chase, Overton, Mills and Foskolos2015) except for Arg being much higher and Lys and Met being lower. The large difference for Arg is due to the change in the prediction of AA in endogenous urinary loss: the current proposition involves an important loss of Arg related to creatine and creatinine urinary excretion decreasing substantially Arg_adj. Also, Arg displayed high CCC but had a large slope bias in the validation database, probably related to the uncertainty of its true supply due to unknown and unaccounted supply from de novo synthesis. In fact, for this reason, although given for a comparison, the current estimates for Arg should not be used. It is also important to note that the current estimates could only be used to predict efficiency until the minimal predicted efficiency is reached according to the quadratic function: after that threshold ratio of AAadj/DEI, the function will not apply. These threshold ratios are in AA_adj/DEI (g/MJ): 0.31, 0.67, 1.23, 0.92, 0.32, 0.82, 0.58, 0.15 and 0.73 for His, Ile, Leu, Lys, Met, Phe, Thr, Trp and Val, respectively. In the validation database, only one treatment mean was higher than the threshold ratio for His at 0.32, whereas the ratios were all lower than the threshold values in the validation database.

Table 4 Models of efficiency of utilization of metabolizable protein (MP)¹ in lactating dairy cows

AICc = corrected Akaike’s information criterion; CCC = concordance correlation coefficient; RMSPE = root mean squared prediction error.

¹ Efficiency of utilization of MP = (true protein secretion in milk + scurf + metabolic fecal protein)/MP_adj × 100.

² MP_adj (kg/d): metabolizable protein supply minus endogenous urinary loss; DEI (MJ/d): digestible energy intake; DIM: days in milk; parity (1 = primiparous; 0 = multiparous).

Figure 2 Observed (•) and residual (▴) values of efficiency of utilization of metabolizable protein in the function of efficiency predicted according to equations (12), (13) and (14) (see text for details of the equations) in lactating dairy cows in the validation database.

Figure 3 Relationship between efficiency of utilization of metabolizable protein (MP) and MP adjusted (MP supply minus endogenous urinary loss) or the ratio of MP adjusted/digestible energy (DE) intake in lactating dairy cows in the developmental database. Efficiency is calculated as (true protein in milk + scurf + metabolic fecal)/MP adjusted.

Table 5 Models of efficiency of utilization of individual amino acids (AA)¹ in lactating dairy cows

CCC = concordance correlation coefficient; RMSPE = root mean squared prediction error.

¹ Efficiency of utilization of AA = (AA secretion in milk + scurf + metabolic fecal protein)/AA_adj × 100.

² AA_adj (g/d): net flow of digestible AA supply minus endogenous urinary loss; DEI (MJ/d): digestible energy intake; DIM: days in milk; parity (1 = primiparous; 0 = multiparous); all estimates were significant: P < 0.01 for all parameters except parity where P < 0.05.

Degree of significance = ^$P ≤ 0.10; *P ≤ 0.05; ***P ≤ 0.001.

Efficiency of utilization and prediction of milk true protein yield

The ultimate goal in the estimation of Eff_MP and Eff_AA is the prediction of MPY which was calculated either as:

(25)$${\rm{MPY}} = {\rm{M}}{{\rm{P}}_{{\rm{adj}}}} \times {\rm{ Ef}}{{\rm{f}}_{{\rm{MP}}}} - {\rm{ }}\left( {{\rm{TP\, scur}}{{\rm{f}}_{{\rm{secretion}}}} + {\rm{TP MF}}{{\rm{P}}_{{\rm{secretion}}}}} \right)$$

or

(26)$${\eqalign{\rm{MPY}} = ({\rm{A}}{{\rm{A}}_{{\rm{adj}}}} \times {\rm{Ef}}{{\rm{f}}_{{\rm{AA}}}} - ({\rm{AA}}\,{\rm{scur}}{{\rm{f}}_{{\rm{secretion}}}} + {\rm{AA}}\,{\rm{MF}}{{\rm{P}}_{{\rm{secretion}}}}))/[{\rm{A}}{{\rm{A}}_{{\rm{calc}} - {\rm{Milk}}}}] \times 100$$

First it appeared clearly that the prediction of Eff_MP based solely on MP_adj (equation 12) predicts MPY with a low CCC in both databases (Table 6). As observed for the prediction of the efficiencies themselves, adding DEI to MP into the prediction equations greatly improved the predictions of MPY. Adding DEI as an independent variable (equation 13) improved CCC; slope bias contributed to a greater proportion of the total prediction error, but the total error decreased in the validation database (Table 6). Finally, the equation, including the ratio MP_adj/DEI, provided the best goodness of fit in the two databases, with the highest CCC. For a comparison, a model was developed to predict the sum of protein secretions (MPY + MFP + scurf) directly from MP_adj, MP_adj × MP_adj, DEI, DIM and parity; MPY was then calculated as predicted protein secretions minus (MFP + scurf). The equation is:

(27)$${\rm{Protein\, secretions}} = 160{\rm{ }}\left( { \pm 79} \right) + 381\left( { \pm 74} \right) \times {\rm{M}}{{\rm{P}}_{{\rm{adj}}}} -74\left( { \pm 19} \right) \times {\rm{M}}{{\rm{P}}_{{\rm{adj}}}} \times {\rm{M}}{{\rm{P}}_{{\rm{adj}}}} + 2.49\left( { \pm 0.22} \right) \times {\rm{DEI}} - 0.6\left( { \pm 0.1} \right) \times {\rm{DIM}}-100\left( { \pm 21} \right) \times {\rm{parity}}\left( {1 = {\rm{primiparous}},0 = {\rm{multiparous}}} \right)$$

Table 6 Predicted milk true protein yield (MPY, g/d) based on estimates of the efficiency of utilization of metabolizable protein (Eff_MP) or predicted directly in lactating dairy cows

CCC = concordance correlation coefficient; RMSPE = root mean squared prediction error.

¹ Equations detailed in the text; MPY = Eff_MP × MP_adj – (scurf true protein + metabolic fecal true protein); MP_adj (kg/d): metabolizable protein supply minus endogenous urinary loss.

² Equation detailed in the text.

The squared term of DEI was not significant (P = 0.93). Predictions from this model are detailed in Table 6 and are not as good as those obtained when Eff_MP was predicted with equation (14). Moreover, a strong slope bias was observed in the validation database. Inclusion of the ratio MP_adj/NE_L supply in predictive models of Eff_MP to predict MPY also yielded the best predictions when different formulation models were compared (Lapierre et al., Reference Lapierre, Larsen, Sauvant, Van Amburgh and Van Duinkerken2018). Therefore, predicted Eff_AA from equations (15) to (24), for each EAA, were used to predict MPY (Table 7). All AA are yielding fairly similar predictions of MPY except Arg. A comparison between observed and predicted MPY was also made using several combinations to explore the impact of individual Eff_AA. Five combinations, all excluding predictions from Arg, are presented in Table 7, which are: the lowest of MPY predicted from Eff_AA (MinAA), the mean of nine MPY predicted from Eff_AA (MeanAA), the mean of MinAA and MeanAA (MinMeanAA) and the mean of estimations from His, Lys and Met (HLM). All predictions provided good fitness with observed MPY, and this is probably one of the limitations of the database and current work actually available. Although we extended the database from Roman-Garcia et al. (Reference Roman-Garcia, White and Firkins2016), trying to increase the number of studies where the supply of only one AA was changed at the time, in most of the studies variations of AA supply were achieved through a change in protein supply which affected simultaneously the supply of all AA. MinAA might be too severe, as the efficiency of a single AA might be maximized if only this one is in short supply (e.g. Lapierre and Ouellet, Reference Lapierre and Ouellet2015). Until we have further development, MinMeanAA might be a prudent option as it ponders an average predicted MPY with the prediction from AA most probably in shortest supply. By doing so, it would certainly be fortuitous to verify which AA is yielding the lowest prediction as this might provide a tool to identify the AA with the shortest supply relative to estimated requirements.

Table 7 Prediction of milk true protein yield (MPY, g/day) based on estimates of the efficiency of utilization of amino acids (Eff_AA) in lactating dairy cows

CCC = concordance correlation coefficient; RMSPE = root mean squared prediction error.

¹ MPY = (Eff_aa × AA_adj – (AA in scurf + AA in metabolic fecal))/concentration of AA in milk × 100; AA_adj (g/d): net flow of digestible AA supply minus endogenous urinary loss.

² Min: minimum predicted MPY; mean: average predicted MPY; max: maximum predicted MPY; HLM: average predicted MPY from His, Lys and Met; Arg predicted MPY excluded from all the combinations.