Relationship between rate of glucose or propionate infusion and milk protein yield and concentration in dairy cows: a meta-regression

Although postruminal glucose infusion into dairy cows has increased milk protein yield in some past experiments, the same trend has not been observed in others. A meta-regression of 64 sets of observations from 29 previously published glucose and propionate infusion studies in dairy cattle, treating study and experiment(study) as random effects, was performed to establish the general effects of glucose equivalent (GlcE) infusion rate on milk true protein (MTP) yield and content, if any, and to identify independent, fixed-effect variables that accounted for the changes in MTP yield and content that were observed. Candidate explanatory variables included rate and site of infusion, diet composition and intake, BW and lactation stage of the cows, and the change in nutrient intake between GlcE and control treatments. Across all studies, according to a model containing only the random effects of study and experiment, GlcE infusion at an average of 954 g/d increased MTP yield by 26 g/d, on average, while mean MTP content was not affected. Backward step-wise elimination of potential explanatory variable from a full mixed model produced a final, reduced model for MTP yield that retained a positive, second-order quadratic effect of infusion rate of GlcE and a positive, linear effect of the change in crude protein intake (CPI) between GlcE treatment and control. This change in CPI due to GlcE infusion ranged from −0.546 to 0.173 kg/d in the data set. The model fit indicated that when CPI was allowed to drop during GlcE infusion, the effect of GlcE on MTP yield was smaller than when CPI was maintained or increased, in a manifestation of the classic protein: energy interaction. The final reduced model for MTP content contained the same explanatory variables as for MTP yield, plus a negative effect of intravenous compared with gastrointestinal infusion. Overall, the meta-analysis revealed that both MTP yield, and content were positively related to GlcE infusion rate and to the change in CPI between glucose treatment and control.


INTRODUCTION
The stimulatory effect of absorbed energy on milk true protein (MTP) yield in lactating dairy cows is well known (Hanigan et al., 1998;Hristov et al., 2004), but the underlying mechanisms remain incompletely understood.To test hypotheses about some of the mechanisms involved in the stimulation of MTP yield by NE L , glucose infusion studies have been conducted.Postruminal infusion of glucose, propionate, and amino acids into the abomasum, duodenum, or circulatory system is an essential method for measuring responses to select nutrients because it bypasses ruminal transformations.As an alternative to glucose, propionate infusions are often used to enhance gluconeogenesis and thereby elicit responses to an increased glucose supply.In some of these glucose and propionate infusion studies, MTP yield has increased (Hurtaud et al., 2000;Rulquin et al., 2004;Raggio et al., 2006), while in others it has not (Clark et al., 1977;Hurtaud et al., 1998a;Curtis et al., 2014;Nichols et al., 2016).The goal of the current work was to meta-analyze the body of published glucose and propionate infusion experiments in dairy cows to establish the general effects on MTP yield and content, if any, and to identify independent variables that accounted for the changes in MTP yield and content that were observed.Potential explanatory variables included site and rate of infusion, diet composition and intake, BW and lactation stage of the cows, and the change in nutrient intake between treatments and controls.

Data extraction and database
A literature search was conducted in February 2023 to identify studies that administered exogenous glucose or propionate to lactating dairy cows and reported their milk yield and composition.The literature search was conducted using combinations of the terms "infusion," "glucose," "propionate," "dairy cows," and "cattle" in 2 different databases: Web of Science https: / / www .webofscience.com(Thomson Reuters Science, New York, NY) and MEDLINE http: / / www .pubmed.gov(via PubMed).A flow diagram of the study selection process using the Preferred Reporting Items for Systemic Reviews and Meta-Analysis (PRISMA) according to Liberati et al., 2009 is shown in Figure 1.After identification through database searching, 247 publications were obtained and selected for initial screening.Studies were retained if they exclusively used dairy cattle and included 1) a measure of the amount of exogenous glucose or propionate infused via abomasum, rumen, duodenum or jugular vein, 2) mean values for daily milk yield and MTP content or sufficient information to calculate them, 3) the number of experimental units and an experimental design, 4) information about lactation stage, feed intake, and ration composition, and 5) a control group that did not receive glucose or propionate infusions.Studies were excluded if 1) infusions were less than 4 d in duration, 2) animals were unhealthy due to immunosuppression, exposure to heat stress, or exposure to an inflammation challenge, or 3) they did not report any measurements of dispersion between treatments (i.e., variance, or standard deviation).Overall, 29 publications met all inclusion requirements and were selected for analysis and used as a full data set for equation development (Table 1).The full data set for meta-regression contained 64 infusion treatments from 47 experiments in 29 studies, including both glucose (53 treatments) and propionate infusions (12 treatments; Table 1).Most of the treatments included in the final data set came from experiments designed as Latin squares (86% of the treatments included) and were carried out mainly in early-lactation cows (DIM ≤100, 72% of the treatments included).Out of the treatments, 94% were applied to Holstein dairy cattle, while only 6% were applied to Ayrshire cattle.

Calculations
The data extracted from individual studies included daily glucose or propionate infusion rate, mean DMI, body weight, milk yield, MTP content, stage of lactation (early, mid, or late) or DIM, infusion site (intravenous, rumen, abomasum, or duodenum), NE L , NDF, and CP contents of diets on controls and treatments.If the study explicitly reported milk protein as MTP, those values were recorded; otherwise, MTP was estimated as milk CP × 0.93 (NRC, 2001).The glucose and propionate infusion rates were converted to moles per day, assuming that 1 mol glucose weighs 180.16 g and 1 mol propionate weighs 73.07 g.Glucose and propionate infusion data were analyzed together by expressing infusion rates as moles per day of glucose equivalents (GlcE) according to the stoichiometry relationship: 1 mol propionate = 0.5 mol glucose (Bergman et al., 1966).Infusion site was a categorical variable given a value of either intravenous (IV) or gastrointestinal (GI), where GI included infusion into the rumen, abomasum, or duodenum.Dietary nutrient contents and intakes included those consumed per os plus all infusions of compounds other than glucose and propionate, such as casein (e.g., Danes et al., 2019;Vanhatalo et al., 2003a) and fatty acids (e.g., Maxin et al., 2011).In cases where energy content of the diet was presented as ME, NE L was calculated using the formula NE L (Mcal/kg) = 0.703 × ME (Mcal/kg) -0.19 (NRC, 2001).The standard deviations (SD) of each observed mean were recorded as reported or calculated from standard errors of the mean (SEM) and n as SD = SEM .× n To account for the variability in lactation stage in the data, a categorical variable with 2 levels was created: early lactation (DIM ≤100) and mid-late lactation (DIM >100).Mid and late lactations were grouped together as there was a small number of studies performed in late-lactating cows.
The purpose of our meta-analysis was to evaluate the effect of GlcE on milk protein yield and content in past experiments.Because GlcE treatments were always compared with a control with no GlcE infusion, and the variation in milk protein yield and content on controls was not of interest, we calculated the effect size of each GlcE treatment on MTP yield (ΔMTP yield) and content (ΔMTP content) as the difference between treatment and control means.These mean differences were used as the dependent variables of interest in the meta-regression.The SD of each mean difference was calculated as where T and C refer to treatment and control, respectively.Funnel plots of observed SE versus of Δ mean MTP yield, and content were constructed to assess publication bias where nonsignificant effects are not reported.In addition, mean differences between each GlcE treatment and control were calculated for potentially explanatory intakes of DM (ΔDMI), NE L (ΔNEI), NDF (ΔNDFI), and CP (ΔCPI).Summary statistics were calculated for all potential explanatory variables (Table 2), and correlation coefficients were estimated with PROC CORR of SAS (SAS Institute Inc., Cary NC) for all dependent and explanatory variables to check for collinearities (Table 3).Correlation coefficients with an absolute value ≥0.30 were considered too large for the variables to be included in the same model.

Meta-regression.
Mixed models were used to associate the infusion rate of GlcE with treatment means of ΔMTP yield and ΔMTP content.To account for the multiple, unidentified differences between studies such as experimental design, laboratory analysis methods, diet ingredients, and climate, among others, a random effect of study was included in the regression models (St-Pierre, 2001;Sauvant et al., 2008).Some of the selected publications reported more than one experiment involving a control and glucose or propionate treatment.For example, Vanhatalo et al. (2003a) had 4 continuous abomasal infusion treatments that included water, casein, glucose, and glucose + casein.In this example, water is the control for glucose infusion and casein is the control for glucose + casein infusion.Hence, for this study 2 different experiments evaluating GlcE responses were distinguished.The same principle was used for other studies (Table 1).
To account for the random variation associated with study and experiment, a 3-level, mixed effects, meta-regression model was used where experiment was nested within study (Martineau et al., 2017).The first level involved fixed effects of explanatory variables, the second level was between-experiment within-study random variation, and the third level was between-study random variation (Konstantopoulos, 2011).Additionally, to account for different variances across studies, observations of ΔMTP yield and ΔMTP content were weighted by the inverse of their squared standard errors, centered around 1.0 by dividing by the mean weight according to the methodology described by St-Pierre (2001).Random effects of study on the GlcE slope were tested and found to be non-significant so they were not included in the model.The random effects were applied to intercepts only.The full statistical model fitted using PROC GLIMMIX of SAS was: where Y i(j) is the observed effect size for the ith experiment (i = 1 to 48) nested in the jth study (j = 1 to 29), w i(j) is the observation weight, β p are fixed param- eters corresponding to the intercept and explanatory variables x i(j) , r i(j) is the random effect of experiment within study, s j is the random effect of study, and e i(j) is residual error.The random effects of study, experiment, and residual error were assumed to be independently, identically, and normally distributed around 0. Models were fit separately for ΔMTP yield and ΔMTP content.In addition, because of a high correlation between DMI and nutrient intakes, one model for each of the outcomes was fitted with DMI and dietary NE L , CP, and NDF contents as potential explanatory variables, and another model for each outcome was fitted with NE L , CP and NDF intakes as potential explanatory variables, excluding DMI.Infusion site, BW, stage of lactation, ΔDMI, and ΔCPI were also considered as potential explanatory variables in all regressions.Each fitting routine started with maximum likelihood fitting of a full model with all potential explanatory variables.The appropriate covariance structure for random effects was determined as that producing the lowest Bayesian information criterion (BIC).In all cases, an unstructured covariance structure was selected.A backward stepwise procedure was then used to remove fixed effects from the full model one at a time, removing those that decreased BIC the most.Final models were declared when BIC reached a minimum with no consideration for the P-values of individual parameter estimates.To avoid inclusion of 2 variables correlated with |R| ≥ 0.30 at any step, the 2 fixed effects were considered one at a time.To keep the same set of observations for all candidate model fits throughout the stepwise process, a truncated data set was used, excluding experiments without a complete set of observations for all potential explanatory variables for the model under consideration.Outlier detection was carried out using Cook's distance (Cook, 1997); observations were removed if Cook's distance >0.50.Final, reduced models were refitted to the full data set using restricted maximum likelihood estimation (REML) of parameters and exclusion of outliers with Cook's distance >0.50.
Funnel plots were used to visually evaluate betweenstudy heterogeneity in the data set and in the model fits.Plots were constructed for each model using the raw and studentized residuals output from PROC MIXED.Raw residuals were plotted on the x-axis, and, for the y-axis, the standard error of each residual (SE Residual ) was calculated as raw residual/studentized residual.The shaded triangle represents a pseudo 95% confidence interval, calculated as ±1.96 × SE Residual based on the method of Viechtbauer (2010).
Plots of predicted vs observed values and residual vs predicted values were generated to evaluate model goodness of fit and to detect lack of homoscedasticity or patterns of heteroscedasticity.To evaluate precision and accuracy of the fitted models, decomposition of the mean square error (MSE) and the concordance correlation coefficient (CCC) were used.MSE was calculated as: where P i and O i are the predicted and observed values, respectively.Square root of MSE (RMSE) was decomposed (Bibby and Toutenburg 1997) into mean bias, slope bias, and random error:  where R is the Pearson correlation coefficient, S O is the SD of observations, and S p represents the SD of predicted values.The CCC is the product of 2 components, R and C b , where R is a metric of precision, and C b is a bias correction factor that measures how far the regression line deviates from the line of unity and is an indicator of accuracy (Lin, 1989).The latter was calculated as follows: where in which v represents slope bias and u represents mean bias.The CCC gives values ranging from −1 to 1, where −1 represents perfect disagreement, 1 represents perfect agreement, and 0 represents no agreement between observed and predicted values.

RESULTS AND DISCUSSION
Milk protein synthesis in the mammary gland is regulated by the concerted action of hormones and nutrients (DePeters and Cant, 1992;Cant et al., 2018;Pszczolkowski and Arriola Apelo, 2020).To test hypotheses of how glucose and its homeostatic hormone insulin may be involved in regulating milk protein synthesis in dairy cows, studies of the response to infusing glucose and propionate have been performed.The infusions have stimulated MTP in some of these studies (Hurtaud et al., 2000;Raggio et al., 2006;Rius et al., 2010) but not others (Vanhatalo et al., 2003a;Curtis et al., 2014;Nichols et al., 2016).The present analysis sought to statistically summarize the effects of glucose and propionate infusion, expressed as GlcE (mol/d), on MTP yield and content in past experiments.Metaregression techniques were used to identify variables that accounted for the mean changes in MTP yield and content observed.

Equation development
Before data analysis, the presence of publication bias was assessed on the full data set through funnel plots.
Funnel plots can be employed to visually inspect the data for potential publication bias, in which smaller studies with no significant effects of treatment are not published.About 95% of the studies should appear within the triangular funnel representing the expected increase in precision of mean estimation as sample size increases.Data points that are not captured within the funnel could also suggest true differences in precision across studies or inadequacy of the fixed effects model structure (Terrin et al., 2005).Although some observations were detected outside of the 95% confidence region, they were retained in the analysis since they were not reported as outliers by the Cook's distance methodology and were used to represent true variability in the data.Funnel plot for ΔMTP yield, and content (Figure 2a,2b) exhibited bilateral symmetry indicating that publication bias was unlikely to be present.
The first step of equation development was to assess correlations between the response variables, MTP yield and content, and several independent variables that could potentially impact the response.The independent variables that were most correlated with ΔMTP yield and content were GlcE infusion rate and ΔCPI between GlcE and control treatments (R >0.27; Tables 3 and  4).Linear correlations between candidate explanatory x-variables within truncated data sets for model selection (Tables 3 and 4) were examined to avoid potential confounding effects of including variables with a correlation coefficient higher than 0.30 in the same model.Intakes of DM, CP, NDF and NE L were correlated with each other (0.23 ≤ R ≤0.85).Thus, for both MTP yield and content, one model was fitted with nutrient intake variables as candidate explanans, and a second model was fitted with nutrient concentrations plus DMI.The ΔDMI between GlcE and control treatments was highly correlated with ΔNEI and ΔNDFI (R ≥0.95; data not shown) but not with ΔCPI (R = 0.20; Table 3), so only ΔDMI and ΔCPI were considered of the 4 candidate explanatory nutritional variables, excluding ΔNEI and ΔNDFI.
For models based on nutrient intakes, CPI was correlated with BW (R = 0.31; Table 3) so CPI was inputted as a percent of BW (CPIBW).Although this transformation removed the correlation with BW, there remained correlations with NEI and ΔCPI (|R| ≥ 0.43).CPIBW was dropped early in the stepwise process of eliminating fixed effects according to BIC, which eliminated potential collinearity issues.
For models based on nutrient concentrations plus DMI, an attempt was made to remove the correlations between DMI and either BW or diet NDF (|R| ≥ 0.35; Table 4) by inputting DMI as a percent of BW (DMIBW).However, this new variable remained correlated with ΔDMI (R = 0.35).Thus, either DMI

Reyes et al.: GLUCOSE INFUSION AND MILK PROTEIN YIELD
or DMIBW were considered in candidate models, depending on which other explanatory variables were also present.Neither DMI nor DMIBW were retained in final models.Similarly, correlations of ΔDMI with diet NEL (R = 0.31), and ΔCPI with diet CP and diet NDF (|R| ≥ 0.39), were not retained in final models.
Final models for ΔMTP yield and content fitted to the full data set are presented in Table 5.Despite starting the fitting process for each outcome variable with 2 different full models -one considering nutrient intakes and the other considering nutrient concentrations plus DMI -both stepwise model reductions produced the same final model with neither intake nor concentra-tion of NEL, CP, or NDF retained.Model 1 for ΔMTP yield retained, as fixed effects, the GlcE infusion rate, the quadratic effect of GlcE infusion rate, and ΔCPI.Model 2 for ΔMTP content included the effects of GlcE infusion rate, infusion site (IV vs. GI), and ΔCPI.Consideration of these fixed effects significantly improved the funnel plot shapes (Figure 3) compared with observations alone (Figure 2).Studies mostly conformed to the funnel triangle and exhibited symmetry, indicating the data were suitable for estimating effects of GlcE on ΔMTP yield and content.Statistics used to evaluate the goodness of fit of each model are summarized in Table 5.For both models, the residual error represented by RMPSE was mostly attributed to random sources (Table 5).The CCC was higher for model 2 predicting ΔMTP content, due to a higher Pearson correlation R between prediction and observation, representing precision or random variance of the predictions, and a higher Cb, representing unbiased prediction accuracy.However, the bias was small for both models (Cb ≥0.93).Taking this information together, both models were able to capture variation in the data set with reasonably high accuracy and precision.

Effects of GlcE on MTP yield
When a random effects-only model was fitted to the full set of ΔMTP yield data, the effect size was estimated at 26 ± 5.7 g/d (mean ± SE) which was significantly different from 0 (P < 0.01) and indicates a stimulation of MTP yield with GlcE infusion across all experiments, on average.The 26 g/d MTP yield increase was associated with an average GlcE of 5.3 mol/d (954 g/d).The positive linear and negative quadratic effects of GlcE infusion rate in final, mixed model 1 (Table 5) indicates that the relationship between GlcE (mol/d) and MTP yield followed a concave curvilinear pattern.In other words, the GlcE effect was bigger at higher GlcE infusion rates up to a max at 10.5 mol/d (1890 g/d) GlcE (Figure 4).Rulquin et al. (2004) reported a quadratic increase in MTP yield with duodenal glucose infusion up to 963 g/d, followed by a decrease in yield at the highest rate of glucose infusion of 2398 g/d.A similar response was found by Hurtaud et al. (2000), where MTP yield showed a curvilinear response to duodenal glucose infusion between 0 and 2250 g/d, with a peak at 1500 g/d GlcE.The significant increase in MTP yield with GlcE infusion could be attributed to a decreased uptake of glucogenic AA from the liver for gluconeogenesis, promoting AA sequestration by the mammary gland for synthesis of protein (Al-Trad et al., 2009).However, Hurtaud et al. (2000) found that glucose infusions did not alter the concentrations of glucogenic AA.Instead, the branched-chain AA concentrations decreased (Hurtaud et al., 2000;Curtis et al., 2018).However, replacement of lost branched-chain AA through IV infusion did not stimulate MTP yield in glucose-infused cows (Curtis et al., 2018).Milk protein synthesis is controlled at the molecular level in the mammary glands by mechanistic target of rapamycin complex 1 (mTORC1), the integrated stress response (ISR), and the unfolded protein response (UPR) (Pszczolkowski and Arriola Apelo, 2020).Through these molecular controls, either glucose or hormones induced by glucose, such as insulin and IGF-1, can accelerate the rate of protein synthesis in the mammary glands.Simultaneously, these same mediators stimulate protein synthesis and AA utilization in non-mammary tissues like muscle, adipose and the splanchnic bed and can divert AA away from milk protein synthesis (Cant et al., 2022).The second-order quadratic trend detected by our meta-regression indicates an overall positive effect of GlcE infusions on dietary AA diversion toward milk.
According to model 1, the amount that MTP yield increased at a given infusion rate of GlcE was related to the ΔCPI that occurred between treatment and control.Fitting a random effects-only model to ΔDMI  revealed that, on average, DMI decreased 0.62 ± 0.22 kg/d (mean ± SE) in GlcE treatments relative to their controls (P < 0.01).A decrease in DMI has been detected in individual experiments and has been attributed to maintenance of energy balance between treatments (Maxin et al., 2011;Nichols et al., 2016;Curtis et al., 2018).However, although ΔNEI and ΔNDFI were highly correlated with ΔDMI between treatments (R ≥0.95), ΔCPI was not (R = 0.20; Table 3).The observation of negative or positive ΔCPI in the data set appeared to segregate by experiment, where several experiments were designed to offset an expected decrease in DMI during GlcE infusion by also supplying additional AA (e.g., Hurtaud et al., 2000;Rigout et al., 2003;Rulquin et al., 2004).The model fit indicates that, when CPI was allowed to drop, the effect of GlcE on MTP yield was smaller than when CPI was maintained or increased.This observation represents a classic protein: energy interaction and can explain, in large part, why some GlcE infusion experiments find an increase in MTP yield and others do not.
Several studies in the data set evaluated responses in MTP yield to GlcE at 2 different rates of MP supply (Clark et al., 1977;Kim et al., 2001;Huhtanen et al., 2002;Vanhatalo et al., 2003a;Raggio et al., 2006;Nichols et al., 2016Nichols et al., , 2019;;Danes et al., 2020;Omphalius et al., 2020).None of these studies detected an interaction between GlcE and MP supply (P ≥ 0.27).Only  through meta-regression of all studies at once, ranging broadly in CP intake from 2.21 to 5.83 kg/d, were we able to detect a significant interaction.Similarly, Daniel et al. (2016) detected an interaction between NE L and MP supplies on MTP yields (P < 0.01) in a meta-regression of 282 feeding studies with dairy cows, where the stimulation of MTP yield by NE L was greater at higher MP intakes.

Effects of GlcE on MTP content
The random effects-only model fit to ΔMTP content in the full data set resulted in an average effect size of 0.0044 ± 0.176% (mean ± SE), which was not significantly different from 0 (P = 0.80).Thus, overall, GlcE did not change MTP percentage, even though MTP yield was elevated on average.The MTP content of milk is a ratio of MTP yield to milk yield, and milk yield increased 0.85 ± 0.15 kg/d (P < 0.01) on average, according to a random effects-only model (data not shown).Glucose is the precursor for milk lactose synthesis, and lactose draws water into milk, so an effect of GlcE on lactose and milk production is not unexpected and is documented in many of the individual experiments in our data set.
Despite no mean effect of GlcE on MTP content, linear and quadratic effects of GlcE infusion rate (mol/d) were retained in a final, mixed model 2 (Table 5), as depicted in Figure 4. Some individual experiments with multiple levels of GlcE infusion reported a linear or quadratic increase in milk yield, and one also detected a quadratic increase in MTP content (Al-Trad et al., 2009).However, a quadratic decrease in MTP content was also observed in one study (Hurtaud et al., 2000).The meta-regression indicates that, overall, MTP content followed a positive, quadratic response to GlcE that was also dependent on the ΔCPI between treatment and control, as discussed above.
The majority of the treatments (78%) included in the full data set used a GI route of administration, which includes ruminal, abomasal, and duodenal infusions.The remaining treatments were IV glucose.Infusion site explained some of the variance associated with the effect of GlcE on MTP content (Table 5), in that MTP content was 0.0699 percentage units lower when GlcE was infused IV instead of GI.Glucose infused intravenously bypasses first-pass metabolism by the splanchnic bed and might be expected to supply a greater amount of glucose for mammary use.Schei et al. (2007a, b) found higher yields of milk and MTP, and MTP concentrations, when glucose was infused IV versus infused as 100% digestible starch into the abomasum.The difference was attributed to effects on splanchnic metabolism.However, we detected the opposite effect from an analysis of multiple experiments, albeit IV and GI routes of administration were never both tested in the same experiment.Glucose infused IV will have a lesser stimulatory effect on gastrointestinal hormones such as cholecystokinin, pancreatic polypeptide, and the incretins, glucose-dependent insulinotropic polypeptide and glucagon like peptide-1 (Reynolds et al., 1994).These peptides are associated with regulation of post-absorptive nutrient metabolism (Reynolds et al., 1994), glucose homeostasis, and the glucose-mediated increase in insulin and decrease in glucagon secretion from the pancreatic β-and α-cells, respectively (Baggio andDrucker, 2007, Guccio et al., 2022).To our knowledge, the effects of exogenous incretins and other gastrointestinal hormones on milk yield and composition have not been evaluated previously but the role of insulin in a glucose-induced stimulation of MTP is well supported (Mackle et al., 2000, Pszczolkowski andArriola Apelo, 2020).

CONCLUSIONS
Meta-regression of mean observations from 47 experiments in 29 published studies revealed positive, second-order quadratic effects of GlcE infusion rate on MTP yield and content in dairy cows.The effects of GlcE on MTP yield and content were dependent on the change in CPI that occurred between GlcE and control treatments.When CPI was allowed to drop, the effect of GlcE on MTP yield was smaller than when CPI was maintained or increased.This design feature may explain, in large part, why some GlcE infusion experiments find an increase in MTP yield and others do not.

Figure 1 .
Figure 1.Flow diagram of the systematic search and selection process of studies included in the meta-regression.

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Reyes et al.: GLUCOSE INFUSION AND MILK PROTEIN YIELD

Figure 2 .
Figure 2. Funnel plots of observed standard errors vs. mean changes in milk true protein mean (ΔMTP) yield (panel a) and content (panel b) in the full data set.
Reyes et al.: GLUCOSE INFUSION AND MILK PROTEIN YIELD

Figure 3 .
Figure 3. Funnel plots of standard errors of residuals vs. residual values for a) model 1: effect of infused glucose or propionate (as glucose equivalents; GlcE) on milk true protein yield (g/d), and b) model 2: effect of infused glucose or propionate (as GlcE) on milk true protein content (%) in lactating dairy cows.

Figure 4 .
Figure 4. Relationship between glucose equivalent (GlcE) infusion rate and change in milk true protein (ΔMTP) yield (panel a) and content (panels b and c) in the observations (points) and the final models from Table 5 (solid lines).ΔCPI (kg/d) for solving final models was set to the mean ΔCPI in the full data set, and infusion site was set to 0 for gastrointestinal infusions (panel b) and 1 for intravenous infusions (panel c).

Table 1 .
Reyes et al.: GLUCOSE INFUSION AND MILK PROTEIN YIELD List of studies and experiments included in the full data set (number of treatments = 64)

Table 2 .
Summary statistics of full data set (n = 64) Reyes et al.: GLUCOSE INFUSION AND MILK PROTEIN YIELD1 CPI = CP intake; Δ = within-experiment mean difference between treatment and control; GlcE = molar equivalents of glucose infused; MTP = milk true protein; NDFI = NDF intake; NEI = NE L intake.

Table 3 .
Correlation coefficients between continuous dependent and candidate explanatory variables in truncated data set for selecting mixed models to predict change in milk true protein (ΔMTP) yield (g/d) and content (%) from infused glucose equivalents (GlcE; mol/d) and nutrient intakes in lactating dairy cows (n = 50) 1 CPI = CP intake (kg/d); CPIBW = CPI as % of BW; Δ = within-experiment mean difference between treatment and control; NDFI = NDF intake (kg/d); NEI = NE L intake (Mcal/d).

Table 4 .
Correlation coefficients between continuous dependent and candidate explanatory variables in truncated data set for selecting mixed models to predict change in milk true protein (ΔMTP) yield (g/d) and content (%) from infused glucose equivalents (GlcE; mol/d), DMI and nutrient contents of diets in lactating dairy cows (n = 50)

Table 5 .
Fixed parameter estimates and fit statistics for final mixed-effects models for predicting milk true protein (MTP) yield and content from infused glucose equivalents(GlcE; mol/d) 5Study number in Table1from which outliers detected.