Genetic Background of Micellar and Soluble Calcium and Phosphorus Predicted From Bovine Milk Mid-infrared Spectra 


 BackgroundMid-infrared spectroscopy (MIRS) is a valuable tool to determine milk composition and quality, and to collect data at population level. In milk, Ca and P are partitioned between micellar (MP) and soluble phase (SP), both with important effects on milk coagulation properties; in particular, greater mineral content in MP translates into better milk coagulation ability. Nevertheless, the high analytic costs of gold standard quantification methods hamper the possibility to deepen partition of minerals in MP and SP on a large scale. In this study, MP and SP of Ca and P were predicted from mid-infrared spectra of 111,653 individual milk samples from 9,519 Italian Holstein cows. Sources of non-genetic variation for MP and SP of Ca and P were investigated, and their genetic associations with milk yield, quality and coagulation properties were estimated.ResultsThe MP of Ca and P decreased with parity but increased along the lactation, resembling the trend of protein content. Both MP and SP of Ca and P showed exploitable genetic variation and were heritable, and they were associated with traits of interest for the dairy industry, in particular milk yield and protein content. Furthermore, negative correlations between the two phases of the same mineral were estimated. The MP was negatively related to milk yield.ConclusionsThe MP and SP of the same mineral are negatively correlated, meaning that it is possible to improve mineral partition toward MP, in order to get milk with better technological properties. The current selection index of Italian Holstein breed gives positive emphasis on milk protein (content and yield) and thus it is indirectly improving the MP of Ca and P while reducing their SP content. Future research will focus on the genomic architecture of such traits to evaluate the role of potential specific genes in the determination of these mineral fractions in cow milk.

investigated. Moreover, heritability of and genetic correlations between these predicted new traits, Values of MY, FP, PP, casein percentage (CP), and SCS deviating more than 3 standard 122 deviations from the corresponding mean were set to missing. Parity ranged from 1 to 15 and DIM 123 from 5 to 305 d; cows of parity ≥ 5 were grouped in the same class. Cows that changed herd 124 during the investigated period and with unknown parents were removed from the data. Finally, 125 lactations with less than 5 test-day records were discarded from the dataset, as well as 126 contemporary groups (herd-test-date, HTD) with less than 5 cows sampled. The final dataset 127 consisted of 111,653 test-day records from 9,519 HO cows in 338 herds. A summary (mean and 128 variation) of the traits included in the study is reported in Table 1. 129 130

Statistical analysis 131
Sources of variation for SP, MP, and MP/SP of Ca and P were investigated using the HPMIXED 132 procedure of SAS software v. 9.4 (SAS Institute Inc., Cary, NC), according to the following linear 133 model: 134 Yijklmno = µ + Mi + Yj +Sk + Pl + (S  P)kl + Hm + Cn + eijklmno, 135 where yijklmno is the phenotypic record (SP, MP, or MP/SP of Ca or P); µ is the overall intercept of 136 the model; Mi is the fixed effect of the ith month of sampling (i = 1 to 12); Yj is the fixed effect of the 137 jth year of sampling (j = 2011 to 2019); Sk is the fixed effect of the kth DIM class of the cow (k = 1 138 to 30; 10 d classes); Pl is the fixed effect of the lth parity of the cow (l = 1 to 5); (S  P)kl is the fixed 139 interaction effect between DIM class and parity; Hm is the random effect of the mth herd ~N(0, σ 2 H),

140
where σ 2 H is the herd variance; Cn is the random effect of the nth cow ~N(0, σ 2 C), where σ 2 C is the 141 cow variance; and eijklmno is the random residual ~N(0, σ 2 e), where σ 2 e is the error variance. 142 Six generations of ancestors were traced back, leading to 31,645 individuals in the pedigree. 143 Variance and covariance components were estimated in ASReml software v. 4.1 [17] using single-144 trait and bivariate repeatability animal models, respectively. The general form of the model looked 145 as: 146 where y is the vector of phenotypic records of the trait(s); b is the vector of fixed effects of 148 contemporary group (10,504 HTD), parity (5 classes), and stage of lactation (30 DIM classes of 10 vector of solutions for random additive genetic effect of the animal; and e is the vector of random 151 residuals. The incidence matrices X, Zw, and Za linked the corresponding effects to the dependent 152 variable y. Random effects were assumed to be normally distributed with means zero and 153 variance-covariance structures of additive genetic, permanent environmental, and residual effects 154 in the bivariate analyses that were G⊗A, W⊗I, and R⊗I, respectively, where G is the 2 x 2 155 additive genetic (co)variance matrix, W is the 2 x 2 (co)variance matrix of permanent 156 environmental effects, R is the residual (co)variance matrix, A is the additive genetic relationship 157 matrix among individuals, I is an identity matrix of appropriate order, and ⊗ is the Kronecker 158 product. The phenotypic variance (σ 2 p), heritability (h 2 ), repeatability (t), genetic correlation ( where σ w 2 is the permanent environmental variance; σ a 2 is the additive genetic variance; σ p12 and 162 σ a12 are the phenotypic and additive genetic covariances between trait 1 and trait 2, σ p1 2 and σ p2 2 163 are the phenotypic variances of traits 1 and 2; and σ a1 2 and σ a2 2 are the additive genetic variances 164 of traits 1 and 2. 165 166

Sources of variation of micellar and soluble calcium and phosphorous 168
Based on visual inspection of data, Ca and P in MP and SP followed a normal distribution. All the 169 fixed effects included in the model were significant (p < 0.001) in explaining the variation of Ca and 170 explain the variation of the SP of P (Table 2). Phosphorus and Ca showed a similar pattern across 173 months of sampling ( Figure 1). In particular, both the MP/SP of Ca and P exhibited the lowest 174 values in late spring (May) and summer. The greatest MP/SP was observed in first-parity cows for whereas the SP of Ca had an opposite trend to that of SP of P. In fact, Ca in SP tended to 178 increase with parity, while P in SP decreased with parity and was the greatest in first lactation 179 ( Figure 2). 180 The pattern of Ca and P in MP across DIM resembled the typical lactation curve of FP and PP, i.e., 181 it showed a minimum in early lactation and progressively increased while approaching the end of 182 lactation. At the same time, Ca and P in SP decreased from early to late lactation. As a result, the 183 MP/SP of both minerals decreased during the first 30 DIM and increased thereafter. 184 185

Genetic parameters 186
Overall, the phases and the MP/SP of both Ca and P were moderately heritable (Table 3), with h 2 187 and t that averaged 0.52 and 0.63, respectively. Moreover, h 2 of mineral phases mirrored that of 188 PP (0.469 ± 0.014) and was greater than that of FP (0.356 ± 0.011). The trait with the lowest h 2 189 was the MP/SP of P (0.472 ± 0.013) 190 The strongest and weakest rp were estimated between the two MP (0.896 ± 0.002) and between 191 the two SP (-0.132 ± 0.008), respectively. As regards ra, the MP and MP/SP of Ca were positively 192 strongly correlated with MP and MP/SP of P, and the SP of both Ca and P were negatively 193 genetically correlated with the other two fractions (Table 3). 194 The rp and ra of minerals fractions with MY, PP, FP, SCS, and MCP are reported in Table 4. The 195 MP was negatively genetically associated with MY, with moderate magnitude for both Ca and P; 196 on the other hand, the genetic correlation between MY and SP was 0.277 ± 0.036 in the case of 197 Ca and close to zero in the case of P. As a result, the MP/SP ratios were negatively associated 198 with MY (Table 4). The opposite was observed for correlations with PP; in fact, the MP of both 199 minerals were positively strongly associated with PP. In general, correlations of Ca and P phases 200 with FP were weaker than those with PP. On the other hand, correlations of Ca and P fractions 201 with SCS were weak or close to zero. Except for SP of P, all fractions of Ca and P showed 202 favourable rp and ra with RCT. The rp and ra with k20 were favourable with MP and MP/SP of both 203 minerals; in fact, despite weak, rp and ra between SP and k20 were unfavourable in both minerals 204 (Table 4). The same was observed for a30, with rp and ra that were favourable with MP and MP/SP, 205 and unfavourable with SP.

Data overview 209
The average MY and composition mirrored the official mean performance of Italian HO and was in 210 accordance with the literature [9][10][11]13]. Considering MP/SP of Ca an P, previous research is not 211 concordant about the average value in bovine milk, because both MP and SP are strongly affected 212 by the method used for their quantification [19]. In the present study, the Ca MP/SP (3.44 w/w) was 213 higher than the ratios (2.20 to 2.68 w/w) reported in the literature using filtration techniques to 214 separate the micellar from the soluble phase [6,19,20] reported in other studies [6,19,20]; this was not surprising considering that only inorganic P was 223 quantified in such studies and thus the contribution of phosphorylated protein was not taken into 224

account. 225
The drop of MP/SP observed between May and June was due to a change in the partition of salts reported h 2 of 0.423 ± 0.027, 0.430 ± 0.027, 0.446 ± 0.024, and 0.531 ± 0.028 for PP, CP, total Ca, 236 and total P, respectively. Similarly, using random regression models, h 2 of MIRS-predicted Ca 237 (average: 0.54 ± 0.04) and P (average: 0.42 ± 0.04) were estimated in the HO population [22]. 238 Furthermore, the trend of h 2 across DIM was similar for Ca and P, with a minimum in early lactation 239 and a subsequent increase until mid-lactation [21]. The moderate to high h 2 explained why the 240 MP/SP of Ca and P were heritable as well. It was not possible to compare h 2 of MP/SP with other 241 studies, since to the authors' knowledge, no information on genetic parameters of mineral fractions 242 in bovine milk is currently available. Apart from the MP/SP of P, the repeatability of other Ca and P 243 fractions was greater than 0.60, suggesting that few records predicted from milk spectra are 244 adequate to catch the variability of the phenotype and get a reliable estimate of cows' mean for the 245 phenotype itself. 246 According to the correlations, it can be stated that MP of Ca and P were closely related, which is 247 likely attributable to their complementary and structural role in casein micelle. On the other hand, 248 this was not valid for the soluble fractions. In fact, SP of Ca and P were negatively correlated each 249 other ( worldwide, ra and rp of mineral fractions with PP and MY were also estimated in the current study 259 (Table 4). In general, the negative correlation between MP and MY confirmed that lower 260 concentration of micellar Ca and P is observed in high-producing cows. This was in accordance 261 with studies reporting both ra and rp of MY with PP and casein content [23]. The micellar Ca and P 262 was correlated favourably with PP and FP, both phenotypically and genetically (Table 4). From the 263 genetic point of view, it is possible to confirm that an indirect favourable selection for the MP of Ca and P currently exists in Italian HO, since the selection index emphasises PP (3%), protein yield 265 (36%), FP (2%) and fat yield (8%), and does not attribute any weight to MY [24]. Nevertheless, the 266 ra and rp of Ca SP with MY were positive, while those of P SP with MY were close to zero (Table  267 4). In general, this further supports that MP and SP are characterized by a different genetic 268 background in dairy cattle and perhaps this idea could be extended to other minerals involved in 269 micellar structure, like Mg. Based on the correlations estimated between SP of the two minerals 270 and milk PP (Table 4), the amount of Ca present in the SP is more associated than SP P with milk 271 PP, both phenotypically and genetically. This also may suggest that there are different genetic and