# Data paper: Contribution of lipids to the net carbon balance across the liver and associated measurement uncertainty in dairy cows

José Miguel Rodríguez-López, Gonzalo Cantalapiedra-Hijar, Sophie Lemosquet, Isabelle Ortigues Marty

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José Miguel Rodríguez-López, Gonzalo Cantalapiedra-Hijar, Sophie Lemosquet, Isabelle Ortigues Marty. Data paper: Contribution of lipids to the net carbon balance across the liver and associated measurement uncertainty in dairy cows. Animal - Open Space, In press. hal-05407120

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1 Data paper: Contribution of lipids to the net carbon balance across the liver

2 and associated measurement uncertainty in dairy cows

3 J.M. Rodriguez-Lopez<sup>a,1</sup>, G. Cantalapiedra-Hijar<sup>a</sup>, S. Lemosquet<sup>b</sup>, I. Ortigues-Marty<sup>a</sup>

4

5 <sup>a</sup> UMR1213 Herbivores, INRAE, Université Clermont Auvergne, VetAgro Sup, 63122

6 Saint-Genès-Champanelle, France

7 <sup>b</sup> PEGASE, INRAE, Institut Agro, 35590 Saint Gilles, France

8

9 <sup>1</sup>Present address: Institut Polytechnique UniLaSalle, Université d'Artois, ULR 7519,
10 Equipe PETALES, 60000 Beauvais, France

11

12 Corresponding author:

13 José RODRIGUEZ-LOPEZ <jose.rodriguez@unilasalle.fr>

14

15 Abstract

16 Livestock systems are becoming more efficient and require physiological data to
17 better estimate the nutritional requirements of animals. The liver plays a central role
18 in nutrient processing and metabolism. To better understand liver function, five
19 lactating Jersey cows (78 ± 12 days in milk) were surgically fitted with blood catheters
20 in the mesenteric vein (for para-aminohippuric acid (pAH) infusion), portal (PV) and
21 hepatic veins (HV), and in the mesenteric artery (MA). They were fed four iso-
22 energetic treatment diets [(starch vs fiber rich diets) x (low vs normal protein diets)]
23 according to a 4x4 Latin Square design; each treatment lasted 28 days. The data
24 reported in this study presents all the metabolite concentrations (albumin, amino
25 acids, beta-hydroxybutyrate, carbon dioxide, glucose, insulin, lactate, non-esterified
26 fatty acids (NEFA), oxygen, phospholipids, total cholesterol, total lipids, total proteins,
27 triglycerides, triiodothyronine, thyroxine, urea and volatile fatty acids) measured in
28 the PV, HV and MA per cow, treatment diet and period. Blood or plasma flow per
29 blood vessel was determined using the Fick principle and the pAH measurements.
30 The afferent (MA and PV) and efferent (HV) fluxes were calculated for most of the
31 carbon-containing metabolites (excluding NEFA, hormones and proteins for which
32 only the concentrations are reported). The net carbon balance across the liver was
33 then calculated as the difference between afferent and efferent fluxes, per cow and
34 treatment diet. Laboratory methods were evaluated by Quality Assurance
35 procedures, which may be used to select the appropriate analytical method for a
36 study. The expanded measurement uncertainty (MU) associated with the net carbon
37 balance across the liver was then determined considering the individual MU of each
38 parameter involved in the calculation. The latter were calculated from statistical
39 distribution of quantity values derived from Quality Assurance procedures (Type A
40 approach; for most of the metabolites) or from other kinds of information when this
41 was not possible (Type B approach; for total lipids, total amino acids and carbon
42 dioxide). The present data may be used to better understand the hepatic metabolism
43 of dairy cows, the MU of nutrient fluxes and the net carbon balance across the liver,
44 and to evaluate the accuracy of existing prediction models. The large expanded
45 measurement uncertainty of the carbon balance values is useful to understand the
46 limits of interpretation of the present net flux data.
47

47

48 **Keywords:** fatty acids, nutrient flux, hepatic metabolism, validation, Quality
49 Assurance

50
<table><tr><td>Subject</td><td>Nutrition</td></tr><tr><td>Specific subject area</td><td>Hepatic metabolism in lactating Jersey dairy cows</td></tr><tr><td>Type of data</td><td>Tables, calculation spreadsheets, code and text.</td></tr><tr><td>How data were acquired</td><td>Data were acquired from a 4x4 Latin Square experiment with dairy cows surgically fitted with blood catheters in the portal and hepatic veins as well as in the artery for blood sampling. They include all data contributing to the calculation of in vivo net hepatic fluxes, i.e. blood and plasma flows, and metabolite concentrations in the blood or plasma. Table 1 lists all metabolites.</td></tr><tr><td>Data format</td><td>Raw, pre-treated and calculated data.</td></tr><tr><td>Parameters for data collection</td><td>Blood samples were analysed for metabolites as listed in Table 1.</td></tr><tr><td>Description of data collection</td><td>All data were cleaned (removal of outliers) and organised in spreadsheets. Missing data are justified in the text.</td></tr><tr><td>Data source location</td><td>Institution: INRAE<br>City/Town/Region: Theix, 63122 Saint-Genès Champanelle<br>Country: France<br>Latitude and longitude (and GPS coordinates, if possible) for collected samples/data: 45°43'8.94" N 3°01'7.93" E</td></tr><tr><td>Data accessibility</td><td>Repository name: https://entrepot.recherche.data.gouv.fr</td></tr></table>
<table><tr><td></td><td>Data identification number: <a href="https://doi.org/10.57745/7DJ3HA">https://doi.org/10.57745/7DJ3HA</a><br/>Link<br/><a href="https://entrepot.recherche.data.gouv.fr/privateurl.xhtml?token=9c8d7b04-30de-4186-8dd7-409fcb2548aa">https://entrepot.recherche.data.gouv.fr/privateurl.xhtml?token=9c8d7b04-30de-4186-8dd7-409fcb2548aa</a></td></tr><tr><td>Related research article</td><td>Cantalapiedra-Hijar, G., Lemosquet, S., Rodriguez-Lopez, J.M., Messad, F., Ortigues-Marty, I., 2014. Diets rich in starch increase the posthepatic availability of amino acids in dairy cows fed diets at low and normal protein levels. Journal of Dairy Science, 97, 5151-5166. DOI: 10.3168/jds.2014-8019</td></tr></table>

52

## 53 Value of the Data

54 • The data offers net hepatic fluxes of a very large spectrum of metabolites including of the lipid fraction, which is usually not measured due to the complexity and diversity of lipid molecules in blood and their difficulties of measurement.

58 • The data is useful to explore the major contributors to the net carbon balance across the liver, which are relevant to nutrient exchange and regulation between organs and tissues.

61 • The data includes Quality Assurance results used to calculate uncertainty of measurements and the contribution of individual measurements to the net carbon balance across the liver.

64 • The data indicates that the quantification of plasma lipids may not substantially improve the accuracy of the net carbon balance across the liver.
66 • The large uncertainty associated to the net carbon balance across the liver
67 and to some of its components limits the scope of inference of results.

68 • The Quality Assurance methodology presented can be used to select the
69 appropriate laboratory method for a study.

70

71 **Data Description**

72 The different files and their contents are listed below:

73 - Data1_C_balance: Concentrations of metabolites, blood & plasma flows and the
74 resulting net C balance across the liver per cow, treatment diet and period (raw
75 and calculated data; Excel file).

76 - Data2_Other_metabolites: Results of additional metabolites, not included in the C
77 balance calculation (raw data; Excel file).

78 - Data3_Intakes_MilkYield: Mean DM intakes, body weight and milk yield per cow,
79 treatment diet and period (raw data; Excel file).

80 - Data4_CarbonBalance_Uncertainty: calculation of the overall measurement
81 uncertainty associated with the hepatic C balance per cow, treatment diet and
82 period (raw data; Excel file).

83 - Example_uncertainty domination: an example of the
84 detailed calculations of the measurement uncertainty associated to a given
85 concentration of lactate (explanations; Word file).

86 - Uncertainty domination: detailed calculations of Type A and Type
87 B measurement uncertainty of metabolites used in the C balance (calculations in
88 Excel file).

89 - Macro_description: code information about the excel macro presented in the
90 Data4_CarbonBalance_Uncertainty file (explanations; Word file).
91

92 **Experimental Design, Materials and Methods**

93 **Animals and experimental design**

94 The experimental design, the animals and the methods were described in detail in
95 Cantalapiedra-Hijar et al. (2014) and Rodriguez-Lopez et al. (2016). Briefly five (4 + 1
96 extra observation) multiparous Jersey cows in their mid-lactation (78 ± 12 days in
97 milk; see "Data3_Intakes_MilkYield" file) were used in a 4x4 Latin Square design with
98 a 2x2 factorial arrangement of treatments [(starch vs fiber rich diets) x (low vs normal
99 protein diets)]. Animals were surgically fitted with catheters in the portal, hepatic,
100 mesenteric, ruminal veins, and mesenteric artery. Feed allowances were limited
101 throughout the experiment to ensure isoenergetic and isonitrogenous intakes across
102 dietary treatments. Daily rations were fractionated in equal meals distributed every 3
103 hours (days 1 to 24) or every 1 hour (days 25 to 28) for the animal metabolism to
104 reach a steady state. Each treatment lasted 28 days, and nutrient flux measurements
105 were conducted on day 27 of each treatment.

106

107 **Net hepatic flux measurement**

108 Para-aminohippuric acid (pAH) was infused into the mesenteric and ruminal venous
109 catheters to measure blood and plasma flow. Blood was collected hourly (from 11:30
110 to 16:30 h; 30 min before and after each meal) for determination of blood hematocrit,
111 pAH, glucose, L-lactate, beta-hydroxybutyrate, volatile fatty acids, urea N, oxygen
112 and carbon dioxide. Blood samples were centrifuged and plasma collected for
113 analysis of plasma pAH, total lipids and individual long-chain fatty acids, triglycerides,
114 non-esterified fatty acids, choline in phospholipids, total cholesterol, individual amino
115 acids, ammonia, albumin, total protein, insulin, triiodothyronine and thyroxine in
116 individual samples (see "Data1_C_Balance" and "Data2_Other_Metabolites" files).

117 Analytical methods are indicated in Table 1.

118 Total plasma lipids were extracted from 5 mL of pooled plasma samples (n=6) with a

119 mixture of chloroform and methanol (2:1, v/v) according to the method of Folch et al.

120 (1957), modified by Bligh et Dyer (1959) for plasma matrix, and total lipid

121 concentrations were determined gravimetrically. Long-chain fatty acids were then

122 extracted from total lipids and transmethylated by BF3-methanol 14%. Their detailed

123 composition was determined by gas-liquid chromatography and flame ionization

124 detection (Perichrom, France) on a high-resolution polar glass capillary column (100

125 m long, i.d.: 0.25 mm), type CP-Sil 88 (Varian, France) with H₂ as carrier gas as

126 previously described by Scislowski et al. (2004). Total long-chain fatty acids were

127 quantified using C19:0 as the internal standard. Identification and calculation of the

128 response coefficient of each individual long-chain fatty acids were achieved using the

129 quantitative mix C4–C24 fatty acid methyl esters (FAME mix C2-C24, 18919-1AMP,

130 Ico, Bellefonte, USA).

131

132 **Calculations of net hepatic carbon fluxes**

133 Daily mean blood (or plasma) concentrations, blood (or plasma) flow, and net

134 metabolite fluxes were calculated for each cow × treatment (see "Data1_C_Balance"

135 file). Afferent and efferent metabolite fluxes were calculated from the mean (n = 6)

136 values (Cantalapiedra-Hijar, 2014) as:

137 - Blood/plasma metabolite flux in the portal vein = [Blood/plasma flow in the

138 portal vein] x [Blood/plasma concentration of the metabolite in the portal vein]
139 - Blood/plasma metabolite flux in hepatic artery = [Blood/plasma flow in the hepatic artery] x [Blood/plasma concentration of the metabolite in the hepatic artery]
140
141

142 - Blood/plasma metabolite flux in the hepatic vein = [Blood/plasma flow in the hepatic vein] x [Blood/plasma concentration of the metabolite in the hepatic vein]
143
144

145 - Net balance across the liver = Flux in the hepatic vein – [flux in the portal vein + flux in the hepatic artery]
146
147

147 Moles of metabolites were converted into moles of carbon applying the conversion coefficients listed in Tables 2 and 3.
148

149 Concerning the plasma lipid composition, the different classes of lipids and their content in carbons are presented in Fig. 1. For the calculations, we considered 1) the main categories of plasma lipids in bovines, which are the cholesterol esters, free cholesterol, phospholipids, triglycerides and non-esterified fatty acids (Delavaud et al., 2019, 2022; Halmemies-Beauchet-Filleau et al., 2013), 2) their chemical composition and 3) the methods used for their analysis.
150
151
152
153
154

155 - Cholesterol esters and free cholesterol are both included in the analysis of total cholesterol, as cited in Table 1. The carbon concentration is 27 moles C per mole of total cholesterol, long chain fatty acids excluded.
156
157

158 - Phospholipids are determined through the analysis of choline. Choline is present in lecithin, lysolecithin and sphingomyelin, which together contribute for 96% of total phospholipids (Noble et al., 1969) in lactating cows. The majority of phospholipids in bovine plasma is present as lecithin and lysolecithin in lactating cows (70-88% lecithin and 1-5% lysolecithin, Noble et al., 1969; Imhasly et al., 2015) as in tallow fed veal calves (81% lecithin and 162
164 5% lysolecithin; Jenkins et al., 1986). In lecithin and lysolecithin, one mole of
165 choline (5 C per mole) is associated to one mole of glycerol (3 C per mole, not
166 quantified in the analysis of triglycerides), resulting in the carbon concentration
167 of 8 moles per mole of 'analysed' choline, long chain fatty acids excluded.

168 As for sphingomyelin (22 moles of carbon per mole of 'analysed' choline), it
169 contributes 7 to 20% to total phospholipids in lactating cows depending on the
170 diet as reported in a single publication (Noble et al., 1969). We considered that
171 assuming a fixed proportion of sphingomyelin in phospholipids at a
172 concentration of 22 C per mole of 'analysed' choline might not necessarily
173 improve the accuracy as compared with applying a uniform concentration of
174 8 C per mole of 'analysed' choline (as that of lecithin and lysolecithin) without
175 any assumption on proportion of sphingomyelin. For the sake of simplicity, we
176 therefore applied the concentration of 8 C per 'analysed' choline, long chain
177 fatty acids excluded.

178 The other forms of phospholipids (phosphatidyl ethanolamine, phosphatidyl
179 serine), which altogether represent between 3 to 4% of phospholipids in dairy
180 cows (Noble et al., 1969), were not analysed and not included in the
181 calculation of carbon flux. The calculation of carbon associated with
182 phospholipids therefore includes some inaccuracy.

183 - Triglycerides are quantified by the analysis of glycerol, analysed as in Table 1.
184 The carbon concentration is 3 moles C per mole of analysed glycerol from
185 triglycerides, long chain fatty acids excluded.

186 - Finally, the long chain fatty acids present in all four fractions, non-esterified
187 fatty acids, triglycerides, phospholipids and cholesterol esters were all
188 quantified in the long chain fatty acid analysis (Fig. 1) and the exact number of
189 carbons was applied.

190 As a result, the carbon from the lipid fraction was calculated, in moles, as (27 x moles
191 of total cholesterol) + (8 x moles of 'analysed' choline in phospholipids) + (3 x moles
192 of glycerol) + (moles of C in the long chain fatty acid fraction, see Table 3). The
193 approximations required in the calculation of lipid carbons, in particular in
194 phospholipids, result therefore in acknowledged limitations.

195

196 Missing data

197 Unfortunately, a few catheters became non-functional with time. As a result, no
198 sampling could be obtained from one cow (cow 1, period 4: normal crude protein with
199 fiber rich diets) and from 3 hepatic vein catheters (cow 2, period 4: normal crude
200 protein with starch rich diets; cow 3, period 4: low crude protein with starch rich diets;
201 and cow 3, period 3: normal crude protein with starch rich diets), see Table 4. When
202 hepatic vein data are missing, net hepatic and net splanchnic fluxes cannot be
calculated, and treatment comparisons should be done on least square means
203 instead of raw means. Missing hepatic vein data has no impact on net portal drained
204 visceral fluxes.

205
206 Concerning the total lipid analysis, the sample size of available portal or arterial blood
207 samples was insufficient to analyze lipid content for cows with non-functional hepatic
208 vein catheters. Finally for all cows, even when sample size was not limiting, some
209 individual long-chain fatty acids (dimethyl acetal (DMA) 16-1, DMA-18:1 n-11 cis,
210 C22:1 n-9, C18:1 n-12 trans, C18:1 n-13 trans, conjugated linoleic acid (CLA)
211 10trans, 12cis, C22:5 n-6, C20:3 n-3, and C22:6 n-3) were undetectable with the
212 analytical procedure used. All these missing values appear as NA (Not Available) in
213 the Data files. They limit the statistical analyses that can be derived to analyse

214 results on lipids and carbon balance.

215

216 **Quality assurance**

217 For laboratory methods, the performance of assays was determined according to

218 Quality Assurance methods by application the NFV03-110 norm (AFNOR, 1998). In

219 brief, standard curves were analysed for each metabolite, with at least six

220 concentration levels repeated over at least five days. Linearity, detection and

221 quantification limits were calculated as described in the NFV03-110 norm (AFNOR,
222 1998).

223 Table 5 reports the results of Quality Assurance for metabolites, as determined in our

224 laboratory and as available, and the averaged, minimum and maximum values of

225 measured concentrations. For lactate, two Quality Assurance results are shown, they

226 differ in the range of lactate concentrations in the calibration curve. Because the

227 relationship between concentrations and optical densities is curvilinear, results for the

228 0.000-1.250 mmol/L concentration range were considered for the detection and

229 quantification limits while results for the 0.000-4.000 mmol/L concentration range
230 were considered for the measurement uncertainty in a conservative approach.

231 No validation method had been conducted for amino acids and long chain fatty acids,
232 and only partial validation results were used.

233

234 **Measurement uncertainty**

235 The measurement uncertainty is defined as the *parameter associated with the result*

236 of a measurement, which characterizes the dispersion of the values that could

237 reasonably be attributed to the measurand" (Ellison and Williams, 2012). Uncertainty
budgets are helpful to dissociate measurement and biological sources of variation
and to prioritise improvement of measurement methods. They rely on the
identification of all sources of variation (analytical methods, biological materials,
personnel in charge of the measurements, equipment and facilities) which can be
represented in a cause-and-effect diagram (Fig. 2). Uncertainty associated to a
single component may be a simple SD, but when a measurand is associated to
several components, as the net fluxes are, the uncertainty of each component need
be considered. The expanded uncertainty is used to calculate the confidence interval
that includes 95% of the quantity values. Rodriguez-Lopez et al. (2016) developed
the calculation of the expanded measurement uncertainty (U(Y)) of net fluxes of
nutrients and of the net carbon balance across the liver; net hepatic metabolite fluxes
being determined from two measurements, blood/plasma flows and blood/plasma
metabolite concentrations, each associated with multiple sources of uncertainty.
While the theoretical basis of the calculation is presented in Rodriguez-Lopez et al.
(2016), its operational implementation is reported in this article. We applied the same
calculation method to each cow × treatment with more metabolites being measured
on all available samples, as compared with Rodriguez-Lopez et al. (2016).
In a first step, the expanded measurement uncertainty was calculated for each
individually measured metabolite concentration based either on Quality Assurance
results (Type A) or, when not available, on other knowledge (Type B). Type A is
defined as the use of the statistical distribution of quantity values obtained from
series of measurements and characterised by SD. In this purpose, a linear
regression equation is established (Equation 1, Fig. 3) to express the overall
measurement uncertainty for a given, theoretical, concentration of a metabolite
where calibration standard curves are available. To calculate theoretical
concentrations, we used the relationship between each measured optical density for each metabolite concentration level of the calibration curves. The overall measurement uncertainty was then calculated from the SE of the optical density values, measured at each concentration level of the curves, as described by Kragten (1994; Fig. 3). For more information, see

« Example_uncertainty_calculation_Lactate_Explanations » and
« uncertainty_CALCULATION_AllMetabolites » files.

Type B approach was used when Quality Assurance results were not available.

Strictly, type B is also characterized by SD and evaluated from probability density functions based on experimental observations or other information (Rodriguez-Lopez et al., 2016). In this article, we used the CV of repeated measurements. In the case of amino acids, we used the precision of the stable isotope ratio analysis of leucine (Calder and Smith, 1988). For long chain fatty acids, we used the repeatability of the analysis of the C19:0 internal standard added to each sample before the extraction of total lipids (for more information, see "Uncertainty_CALCULATION_AllMetabolites" file).

The outcome of this first step is the elaboration of empirical uncertainty functions, one for each metabolite (Equation 1, Fig. 3).

In a second step, the expanded measurement uncertainty was calculated for the net carbon balance across the liver as described in Rodriguez-Lopez et al. (2016; see "Data4_CarbonBalance_Uncertainty" file). We want to alert the reader that, to determine the overall measurement uncertainty of the net carbon balance across the liver, all intermediate calculations must be incorporated into a single equation, as previously described by Rodriguez-Lopez et al. (2016). In contrast to the calculation of individual metabolite net flux, the expanded measurement uncertainty of the net carbon balance across the liver requires the use of the mean (rather than the
288 individual measurements) of the pAH concentration values per cow, treatment and
289 blood vessel. As a result, the values of the net carbon balance across the liver
290 calculated for each cow and treatment differ from those values obtained by summing
291 the individual net fluxes of each metabolite. Accordingly, values in the net carbon
292 balance across the liver differ between the "Data1_C_Balance" file and
293 "Data4_CarbonBalance_Uncertainty" files. In summary, values of the carbon balance
294 were obtained from the "Data1_C_Balance" file, more precise, while values of the
295 expanded measurement uncertainty were obtained from the
296 "Data4_CarbonBalance_Uncertainty" file (see Table 6). Finally, the contribution of
297 each measurement to the overall measurement uncertainty is determined with the
298 macro named 'input data & compute' and reported in the file
299 "Data4_CarbonBalance_Uncertainty".

300

301 Conclusions

302 As reported by Cantalapiedra-Hijar et al. (2014), the transfer of N from feed to milk at
303 the both levels of dietary protein was improved with starch rich diets due to lower
304 energy requirements of the portal drained viscera and higher microbial N flow to the
305 duodenum. The present article presents the supporting data for these findings, along
306 with additional data on net lipid fluxes and net carbon balance across the liver. A
307 major novelty of the present article is to explicitly quantify the uncertainty of all
308 measurements and calculated values, emphasising the importance of considering
309 uncertainties in the biological interpretation of data and when defining their scope of
310 inference. More generally, we strongly recommend that rigorous quality controls of
311 laboratory measurements used in any research study, even for the most routine
312 analyses, are systematically conducted before the start of the study and according to
313 strict Quality Assurance procedures in order to decide whether the accuracy and
314 precision of the analytical methods are adapted to the expected concentrations. Type
315 A approach is recommended. The additional data presented here indicates that the
316 quantification of plasma lipids may not substantially improve the accuracy of the net
317 carbon balance across the liver. The large uncertainty associated to this balance and
318 some of its components limits the scope of inference of the results.

319

320 **Ethics approval**

321 The experiment was conducted in accordance with national legislation on animal
322 care (Certificate of Authorisation to Experiment on Living Animals, no. 004495;
323 Ministry of Agriculture, Paris, France).

324

325 **ORCIDs**

326 Cantalapiedra-Hijar G. https://orcid.org/0000-0001-9486-8238

327 Lemosquet S. https://orcid.org/0000-0002-1077-1285

328 Ortigues-Marty I. https://orcid.org/0000-0002-0399-013X

329 Rodriguez-Lopez J.M. https://orcid.org/0009-0004-8391-1535

330

331 **Author contributions**

332 **Cantalapiedra-Hijar G.:** Conceptualisation, Investigation, Formal analysis, Data
333 curation, Validation, Writing – review & editing

334 **Lemosquet S.:** Conceptualisation, Writing – review & editing

335 **Ortigues-Marty I.:** Conceptualisation, Investigation, Methodology, Project
336 administration, Funding acquisition, Supervision, Validation, Writing – original draft,
337 Writing – review & editing
338 **Rodriguez-Lopez J.M.:** Conceptualisation, Investigation, Formal analysis, Data

339 curation, Validation, Writing – original draft, Writing – review & editing

340

341 **Declaration of interest**

342 NA

343

344 **Acknowledgements**

345 We thank D. Durand, D. Rémond and P. Gaydier (INRAE) for animal surgery, C.

346 Chantelazue, A.-S. Bage, V. Largeau, S. Rudel, D. Roux, C. Mathevon, J.B. Teuma

347 and L. Mouly (INRAE) for technical assistance. We thank J.M. Feinberg for providing

348 the code used to compute the expanded measurement uncertainty of the net carbon

349 balance across the liver. Authors are also thankful to D. Bauchart and D. Gruffat for

350 their help with lipid analysis and data.

351

352 **Financial support statement**

353 The research received financial support from the Commission of the European

354 Communities (Brussels, Belgium; project FP7-KBBE-2007-1 ‘Rednex’) and Adisseo

355 (Commentry, France). G. Cantalapiedra-Hijar was supported by a scholarship from

356 the PHASE department (INRAE).

357

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396 Halmemies-Beauchet-Filleau, A., Kairenius, P., Ahvenjärvi, S., Toivonen, V., Huhtanen, P., Vanhatalo, A., Givens, D.I., Shingfield, K.J., 2013. Effect of forage conservation method on plasma lipids, mammary lipogenesis, and milk fatty acid composition in lactating cows fed diets containing a 60:40 forage-to-concentrate ratio. Journal of Dairy Science 96, 5267-5289 http://dx.doi.org/10.3168/jds.2013-6571

402 Imhasly, S., Bieli, C., Naegeli, H., Nyström, L., Ruetten, M., Gerspach, C., 2015.

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408 Kraft, G., Ortigues-Marty, I., Durand, D., Rémond, D., Jarde, T., Bequette, B.J., Savary-Auzeloux, I., 2011. Adaptations of hepatic amino acid uptake and net utilisation contribute to nitrogen economy or waste in lambs fed nitrogen- or energy-imbalanced diets. Animal 5, 678-690.

412 Kragten, J., 1994. Tutorial review. Calculating standard deviations and confidence intervals with a universally applicable spreadsheet technique. Analyst 119, 2161-2165.

415 Lowry O.H., Rosebrough, N.J., Farr, A.L., Randall R.J., 1951. Protein measurement with the Folin phenol reagent. Journal of Biological Chemistry 193, 265-275

417 Majdoub, L., Vermorel, M., Ortigues-Marty, I., 2003. Intraruminal propionate supplementation modifies hindlimb energy metabolism without changing the net splanchnic release of glucose in growing lambs. British Journal of Nutrition 89, 39-50.

420 Ngo, T. T., Phan, A. P. H., Yam, C. F., Lenhoff, H. F., 1982. Interference in determination of ammonia with the hypochlorite-alkaline phenol method of Berthelot. Analytical Chemistry 54, 46-49.

423 Noble, R.C., Steele, W., Moore, J.H., 1969. Dietary fatty acids and the plasma phospholipids of the lactating cow. Journal of Dairy Research 36, 393-398

425 Ormsby, A.A., 1942. A direct colorimetric method for the determination of urea in blood and urine. Journal of Biological Chemistry 146, 595-604.
427 Reynolds, C.K., Huntington, G.B., Tyrrell, H.F., Reynolds, P.J., 1988. Net metabolism
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431 Rodriguez Lopez, J. M., Cantalapiedra Hijar, G., Durand, D., Thomas, A., Ortigues-Marty, I., 2014. Influence of the para-aminohippuric acid analysis method on the net hepatic flux of nutrients in lactating cows. Journal of Animal Science 92, 1074-1082.
432
433
434 DOI: 10.2527/jas.2013-7359

435 Rodriguez Lopez, J. M., Feinberg, M., Durand, D., Cantalapiedra Hijar, G., Thomas, A., Ortigues-Marty, I. (2016). Evaluation of the expanded measurement uncertainty in the determination of the net flux of nutrients and carbon atoms through the liver in ruminants. Accreditation and Quality Assurance 21, 131-142. DOI: 10.1007/s00769-015-1187-3

440 Richmond, W., 1973. Preparation and Properties of a Cholesterol Oxidase from
441 Nocardia sp. and Its Application to the Enzymatic Assay of Total cholesterol in
442 Serum. Clinical Chemistry 19, 1350-1356.

443 Savary-Auzeloux, I., Kraft, G., Bequette, B.J., Papet, I., Rémond, D., Ortigues-Marty, I., 2010. Dietary nitrogen-to-energy ratio alters amino acid partition in the whole body and among the splanchnic tissues of growing rams. Journal of Animal Science 88, 2122-2131 doi:10.2527/jas.2009-2062

447 Scislowski, V., Durand, D., Gruffat, D., Motta, C., Bauchart, D., 2004. Linoleate
448 supplementation in steers modifies lipid composition of plasma lipoproteins but does
449 not alter their fluidity. British Journal of Nutrition 91, 575-584
450 Somogyi, M., 1945. Determination of blood sugar. Journal of Biological Chemistry
451 160, 69-73.

452 Takayama, M., Itoh, S., Nagasaki, T., Tanimizu, I., 1977. A new enzymatic method
453 for determination of serum choline - containing phospholipids. Clinical Chemistry
454 Acta 79, 93-98. doi: 10.1016/0009-8981(77)90465-x.

455 Williamson, D.H., Mellanby, J., Krebs, A., 1962. Enzymatic determination of D (-)-β-
456 Hydroxybutyric acid and acetoacetic acid in blood. Biochemistry Journal 82, 90-96.
457
<table><caption>**Table 1.** Analytical methods for plasma and blood metabolites measured for each lactating Jersey cow (n=5) fed each treatment diet [(starch vs fiber rich diet) x (low vs normal protein diet)].</caption><thead><tr><th>Metabolite</th><th>Matrix</th><th>Method</th><th>Equipment</th><th>Reference</th></tr></thead><tbody><tr><td>Albumin</td><td>Plasma</td><td>Kit 1306.123, Sobioda, Montbonnot Saint-Martin, France</td><td>Spectrophotometer Libra S22</td><td>Savary-Auzeloux et al. (2010)</td></tr><tr><td>Amino acids</td><td>Plasma</td><td>Isotopic dilution</td><td>Gas chromatography-mass spectrometry (Trace GC/Automass Multi, Thermofinnigan, Courtaboeuf, France)</td><td>Kraft et al. (2011)</td></tr><tr><td>Ammonia</td><td>Plasma</td><td>Enzymic method using glutamate dehydrogenase</td><td>Spectrophotometer Libra S22</td><td>Ngo et al. (1982)</td></tr><tr><td>Beta-hydroxybutyrate</td><td>Blood</td><td>Williamson et al. (1962) after deproteinisation with perchloric acid (0.6M)</td><td>Spectrophotometer Libra S22</td><td>Majdoub et al. (2003)</td></tr><tr><td>Carbon dioxide</td><td>Blood</td><td>Hemoximeter ABL 5</td><td>ABL700Blood Gas Analyser Radiometer A/S, Copenhagen, Denmark</td><td>Cantalapiedra-Hijar et al. (2014)</td></tr><tr><td>Choline in phospholipids</td><td>Plasma</td><td>Enzymic method based on the Trinder reaction Kit W1306.170, Sobioda Montbonnot Saint-Martin, France</td><td>Spectrophotometer Libra S22</td><td>Takayama et al. (1977)</td></tr><tr><td>Glucose</td><td>Blood</td><td>Bergmeyer et al. (1974) after deproteinisation with perchloric acid (0.6M)</td><td>Spectrophotometer Libra S22</td><td>Majdoub et al. (2003)</td></tr><tr><td>Hematocrit</td><td>Blood</td><td>15 000 g for 2 min</td><td>Micro-centrifuge</td><td>Cantalapiedra-Hijar et al. (2014)</td></tr><tr><td>Insulin</td><td>Plasma</td><td>Radio immuno assay, 07-260105 MP Biomedicals, Illkirch, France</td><td>Gamma counter</td><td></td></tr><tr><td>L-Lactate</td><td>Blood</td><td>Gutmann and Wahlefeld (1974) after deproteinisation with perchloric acid (0.6M)</td><td>Spectrophotometer Libra S22</td><td>Majdoub et al. (2003)</td></tr><tr><td>Long chain fatty acid composition of total lipids</td><td>Plasma</td><td>Partition equilibrium of analytes between a stationary phase</td><td>Gas-liquid chromatograph</td><td>Scislowski et al., (2004)</td></tr></tbody></table>
<table>
  <tr>
    <td>Non-esterified<br/>fatty acids<br/>Oxygen</td>
    <td>Plasma<br/>Blood</td>
    <td>and a gaseous<br/>mobile phase.<br/>C Wako kit, Unipath<br/>SA, Dardilly, France<br/>Hemoximeter ABL 5</td>
    <td>Spectrophotometer<br/>Libra S22<br/>ABL700Blood Gas<br/>Analyser<br/>Radiometer A/S,<br/>Copenhagen,<br/>Denmark<br/>Spectrophotometer<br/>Libra S22</td>
    <td>Majdoub et al. (2003)<br/>Cantalapiedra-Hijar et<br/>al. (2014)<br/>Rodriguez-Lopez et al.<br/>(2014)</td>
  </tr>
  <tr>
    <td>Para-<br/>aminohippuric<br/>acid<br/>Total cholesterol</td>
    <td>Blood<br/>and<br/>plasma<br/>Plasma</td>
    <td>After deacetylation<br/>Kit 1306.147,<br/>Sobodia,<br/>Montbonnot Saint-<br/>Martin, France<br/>Extraction by a<br/>mixture of<br/>chloroform and<br/>methanol (2:1, v/v)</td>
    <td>Spectrophotometer<br/>Libra S22<br/>Separatory funnels<br/>(100 to 250 mL,<br/>Elvetec); rotary<br/>vacuum evaporator<br/>(IKA®-Werke<br/>GmbH, Staufen,<br/>Germany); flat-<br/>bottomed boiling<br/>balloons (100 to<br/>250 mL, Elvetec);<br/>Sartorius phase<br/>separator paper<br/>(150 mm, grade<br/>480, Elvetec);<br/>precision balance<br/>Spectrophotometer<br/>Libra S22</td>
    <td>Allain et al. (1974),<br/>Flegg (1973),<br/>Richmond (1973)<br/>Folch et al. (1957)<br/>modified by Bligh and<br/>Dyer (1959)</td>
  </tr>
  <tr>
    <td>Total proteins</td>
    <td>Plasma</td>
    <td>Enzymic method<br/>based on the Folin<br/>reaction</td>
    <td>Spectrophotometer<br/>Libra S22</td>
    <td>Lowry et al. (1951)</td>
  </tr>
  <tr>
    <td>Triglycerides</td>
    <td>Plasma</td>
    <td>Enzymic method<br/>with production of<br/>hydrogen<br/>peroxide, Kit TRG<br/>100, Sobioda<br/>laboratories,<br/>Genoble, France</td>
    <td>Spectrophotometer<br/>Libra S22</td>
    <td>Fossati and Prencipe<br/>(1982)</td>
  </tr>
  <tr>
    <td>Triiodothyronine</td>
    <td>Plasma</td>
    <td>Radio immuno<br/>assay, 06B-256447<br/>MP Biomedicals,<br/>Illkirch, France</td>
    <td>Gamma counter</td>
    <td></td>
  </tr>
  <tr>
    <td>Thyroxine</td>
    <td>Plasma</td>
    <td>Radio immuno<br/>assay, 06B-257215<br/>MP Biomedicals,<br/>Illkirch, France</td>
    <td>Gamma counter</td>
    <td></td>
  </tr>
  <tr>
    <td>Urea-N</td>
    <td>Blood</td>
    <td>KitS-1000,<br/>BioMérieux, Marcy<br/>l'Etoile, France</td>
    <td>Spectrophotometer<br/>Libra S22</td>
    <td>Ormsby (1942)</td>
  </tr>
  <tr>
    <td>Volatile fatty<br/>acids</td>
    <td>Blood</td>
    <td>Separation by ion<br/>exchange, after<br/>deproteinisation<br/>(Somogyi, 1945),<br/>and elution by NaOH<br/>(25 mmol/L)</td>
    <td>Gas<br/>chromatograph<br/>Peri 2000</td>
    <td>Reynolds et al. (1988)</td>
  </tr>
</table>
462 **Table 2.** Number of moles of carbon per mole of metabolite: major energy-yielding
463 metabolites, urea and amino acids measured in plasma or blood samples from each
464 lactating Jersey cow (n=5) fed each treatment diet [(starch vs fiber rich diet) x (low vs
465 normal protein diet)].

<table><thead><tr><th>Metabolite</th><th>Mole C /<br>mole<br>metabolite</th><th>Amino acids</th><th>Mole C /<br>mole<br>amino<br>acid</th></tr></thead><tbody><tr><td>Acetate</td><td>2</td><td>Alanine</td><td>3</td></tr><tr><td>Beta-hydroxybutyrate</td><td>4</td><td>Asparagine</td><td>4</td></tr><tr><td>Butyrate</td><td>4</td><td>Aspartate</td><td>4</td></tr><tr><td>Cholesterol</td><td>27</td><td>Cysteine +<br>cystine</td><td>3</td></tr><tr><td>Choline + glycerol in<br>phospholipids</td><td>8</td><td>Glutamate</td><td>5</td></tr><tr><td>CO<sub>2</sub></td><td>1</td><td>Glutamine</td><td>5</td></tr><tr><td>Glucose</td><td>6</td><td>Glycine</td><td>2</td></tr><tr><td>Glycerol in triglycerides</td><td>3</td><td>Histidine</td><td>6</td></tr><tr><td>Lactate</td><td>3</td><td>Iso Leucine</td><td>6</td></tr><tr><td>Propionate</td><td>3</td><td>Leucine</td><td>6</td></tr><tr><td>Urea</td><td>1</td><td>Lysine</td><td>6</td></tr><tr><td></td><td></td><td>Methionine</td><td>5</td></tr><tr><td></td><td></td><td>Phenylalanine</td><td>9</td></tr><tr><td></td><td></td><td>Proline</td><td>5</td></tr><tr><td></td><td></td><td>Serine</td><td>3</td></tr><tr><td></td><td></td><td>Threonine</td><td>4</td></tr><tr><td></td><td></td><td>Tyrosine</td><td>9</td></tr><tr><td></td><td></td><td>Valine</td><td>5</td></tr></tbody></table>

466

467
468 **Table 3.** Number of moles of carbon per mole of metabolite: Long chain fatty acids
469 measured in plasma samples from each lactating Jersey cow (n=5) fed each
470 treatment diet [(starch vs fiber rich diet) x (low vs normal protein diet)].

471

<table><thead><tr><th>Metabolite</th><th>Mole C / mole nutrient</th><th>Nutrient</th><th>Mole C / mole nutrient</th><th>Nutrient</th><th>Mole C / mole nutrient</th></tr></thead><tbody><tr><td>Linear FA</td><td></td><td>Cis MUFA</td><td></td><td>N-6 PUFA</td><td></td></tr><tr><td>C12:0</td><td>12</td><td>C12:1 n-9 cis</td><td>12</td><td>C18:2 n-6 cis,cis</td><td>18</td></tr><tr><td>C14:0</td><td>14</td><td>C16:1 n-9 cis</td><td>16</td><td>C18:2 n-6 cis, trans</td><td>18</td></tr><tr><td>C15:0</td><td>15</td><td>C18:1 n-9 cis</td><td>18</td><td>CLA 9cis,11trans</td><td>18</td></tr><tr><td>C16:0</td><td>16</td><td>C18:1 n-11 cis</td><td>18</td><td>CLA 10trans,12cis</td><td>18</td></tr><tr><td>C17:0</td><td>17</td><td>C18:1 n-12 cis</td><td>18</td><td>CLA cis,cis</td><td>18</td></tr><tr><td>C18:0</td><td>18</td><td>C18:1 n-13 cis</td><td>18</td><td>CLA trans,trans</td><td>18</td></tr><tr><td>C20:0</td><td>20</td><td>C18:1 n-14cis</td><td>18</td><td>C18:3 n-6</td><td>18</td></tr><tr><td>C21:0</td><td>21</td><td>C20:1 n-11</td><td>20</td><td>C20:2 n-6</td><td>20</td></tr><tr><td>C22:0</td><td>22</td><td>C22:1 n-9</td><td>22</td><td>C20:3 n-6</td><td>20</td></tr><tr><td>C23:0</td><td>23</td><td>C24:1 n-9</td><td>24</td><td>C20:3 conjugated</td><td>20</td></tr><tr><td>Branched chain FA</td><td></td><td>Trans MUFA</td><td></td><td>C20:4 n-6</td><td>20</td></tr><tr><td>iso14</td><td>14</td><td>C16:1 n-9 trans</td><td>16</td><td>C20:4 conjugated</td><td>20</td></tr><tr><td>DMA-14</td><td>15</td><td>C18:1 n-6 to 8 trans</td><td>18</td><td>C22:2 n-6</td><td>22</td></tr><tr><td>iso15</td><td>15</td><td>C18:1 n-9 trans</td><td>18</td><td>C22:4 n-6</td><td>22</td></tr><tr><td>DMA-15</td><td>16</td><td>C18:1 n-10-11 trans</td><td>18</td><td>N-3 PUFA</td><td></td></tr><tr><td>iso16</td><td>16</td><td>C18:1 n-12 trans</td><td>18</td><td>C18:3 n-3</td><td>18</td></tr><tr><td>DMA-16</td><td>17</td><td>C18:1 n-13 trans</td><td>18</td><td>C20:3 n-3</td><td>20</td></tr><tr><td>DMA iso16</td><td>17</td><td>C18:1 n-12-13 trans</td><td>18</td><td>C20:4 n-3</td><td>20</td></tr><tr><td>DMA-16:1</td><td>17</td><td></td><td></td><td>C20:5 n-3</td><td>20</td></tr><tr><td>iso17</td><td>17</td><td></td><td></td><td>C22:5 n-3</td><td>22</td></tr><tr><td>ante17</td><td>17</td><td></td><td></td><td>C22:6 n-3</td><td>22</td></tr><tr><td>DMA-17</td><td>18</td><td></td><td></td><td>n-9 PUFA</td><td></td></tr><tr><td>DMA iso17</td><td>18</td><td></td><td></td><td>C20:3 n-9</td><td>20</td></tr><tr><td>DMA ante17</td><td>18</td><td></td><td></td><td></td><td></td></tr><tr><td>Iso18</td><td>18</td><td></td><td></td><td></td><td></td></tr><tr><td>DMA-18</td><td>19</td><td></td><td></td><td></td><td></td></tr><tr><td>DMA-18:1 n-9 cis</td><td>19</td><td></td><td></td><td></td><td></td></tr><tr><td>DMA-18:1 n-11 cis</td><td>19</td><td></td><td></td><td></td><td></td></tr></tbody></table>

472 Abbreviations: FA = fatty acids; DMA = dimethyl acetal; MUFA = mono-unsaturated fatty acids; PUFA = poly-unsaturated fatty acids

474

475

476

477

478

479

480

481

482

483

484

485
486 **Table 4.** Available and missing data per lactating Jersey cow (n=5), treatment diet
487 [(starch vs fiber rich diet) x (low vs normal protein diet)] and period. The available
488 data come from functional blood catheters. Missing data is due to non-functional
489 blood catheters<sup>a</sup>. If not specified, all blood catheters in a cow were functional (or
490 not).

491

<table><thead><tr><th></th><th>Period 1</th><th>Period 2</th><th>Period 3</th><th>Period 4</th></tr></thead><tbody><tr><td>LS</td><td></td><td></td><td></td><td></td></tr><tr><td>Functional</td><td>Cow 5</td><td>Cow 4</td><td>Cow 1 + Cow 2</td><td>Cow 3 (MA &amp; PV)</td></tr><tr><td>Non-Functional</td><td></td><td></td><td></td><td>Cow 3 (HV)</td></tr><tr><td>HS</td><td></td><td></td><td></td><td></td></tr><tr><td>Functional</td><td>Cow 4</td><td>Cow 1 + Cow 5</td><td>Cow 3 (MA &amp; PV)</td><td>Cow 2 (MA &amp; PV)</td></tr><tr><td>Non-Functional</td><td></td><td></td><td>Cow 3 (HV)</td><td>Cow 2 (HV)</td></tr><tr><td>LF</td><td></td><td></td><td></td><td></td></tr><tr><td>Functional</td><td>Cow 1 + Cow 3</td><td>Cow 2</td><td>Cow 4</td><td>Cow 5</td></tr><tr><td>Non-Functional</td><td></td><td></td><td></td><td></td></tr><tr><td>HF</td><td></td><td></td><td></td><td></td></tr><tr><td>Functional</td><td>Cow 2</td><td>Cow 3</td><td>Cow 5</td><td>Cow 4</td></tr><tr><td>Non-Functional</td><td></td><td></td><td></td><td>Cow 1</td></tr></tbody></table>

492

493 Abbreviations: LS = low protein content and starch rich diet; LF = low protein content and fiber rich diet; HS = normal protein content and starch rich diet; HF = normal protein content and fiber rich diet.
494 HV = Hepatic Vein; MA = Mesenteric Artery; PV = Portal Vein
495

496

497 <sup>a</sup>Concerning total lipid analysis, cows with non-functional hepatic vein catheters also did not have enough blood to analyze lipid content in portal or arterial blood.
498
499
500
501
502
<table><caption>**Table 5.** Results of Quality Assurance for the analytical methods of measured metabolites in each lactating Jersey cow (n=5) fed each treatment diet [(starch vs fiber rich diet) x (low vs normal protein diet)], according to procedures recommended by AFNOR (1988)</caption><thead><tr><th rowspan="2">Metabolite</th><th colspan="5">Metabolite concentration in plasma or blood</th><th rowspan="2">Limit of detection<br>mmol/L</th><th rowspan="2">Limit of<br>quantification<br>mmol/L</th><th colspan="3">Linearity</th></tr><tr><th>Minimum<br>value<br>(mmol/L)</th><th>Maximum<br>value<br>(mmol/L)</th><th>Mean MA<br>value ± SD<br>(mmol/L)</th><th>Mean PV<br>value ± SD<br>(mmol/L)</th><th>Mean HV<br>value ±<br>SD<br>(mmol/L)</th><th>r<sup>2</sup></th><th>Minimum<br>value<br>(mmol/L)</th><th>Maximum value<br>(mmol/L)</th></tr></thead><tbody><tr><td>Acetate</td><td>1.224</td><td>3.644</td><td>1.876 ±<br>0.3772</td><td>2.707 ±<br>0.5064</td><td>2.709 ±<br>0.4230</td><td>0.107</td><td>0.405</td><td>0.9984</td><td>0.000</td><td>5.000</td></tr><tr><td>Albumin</td><td>0.295</td><td>0.789</td><td>0.532 ±<br>0.1574</td><td>0.525 ±<br>0.1548</td><td>0.518 ±<br>0.1532</td><td>0.215</td><td>0.236</td><td>0.9998</td><td>0.075</td><td>0.752</td></tr><tr><td>Ammonia</td><td>0.142</td><td>1.715</td><td>0.781 ±<br>0.3715</td><td>0.804 ±<br>0.3909</td><td>0.811 ±<br>0.3948</td><td>0.121</td><td>0.184</td><td>0.9996</td><td>0.000</td><td>0.500</td></tr><tr><td>Beta-hydroxybutyrate</td><td>0.502</td><td>1.232</td><td>0.767 ±<br>0.1236</td><td>0.909 ±<br>0.1266</td><td>1.000 ±<br>0.1227</td><td>0.259</td><td>0.406</td><td>0.9998</td><td>0.500</td><td>1.000</td></tr><tr><td>Butyrate</td><td>0.016</td><td>0.185</td><td>0.031 ±<br>0.0106</td><td>0.128 ±<br>0.0353</td><td>0.042 ±<br>0.0150</td><td>0.004</td><td>0.013</td><td>0.9984</td><td>0.000</td><td>0.150</td></tr><tr><td>Cholesterol</td><td>1.856</td><td>4.733</td><td>3.373 ±<br>0.7335</td><td>3.376 ±<br>0.7527</td><td>3.487 ±<br>0.7089</td><td>0.557</td><td>1.223</td><td>0.9996</td><td>0.000</td><td>10.363</td></tr><tr><td>Choline +<br>glycerol in<br>phospholipids</td><td>1.609</td><td>3.252</td><td>2.516 ±<br>0.4645</td><td>2.507 ±<br>0.4709</td><td>2.544 ±<br>0.4292</td><td>0.115</td><td>0.173</td><td>0.9999</td><td>0.000</td><td>3.870</td></tr><tr><td>Glucose</td><td>2.504</td><td>3.838</td><td>2.967 ±<br>0.1995</td><td>2.951 ±<br>0.2022</td><td>3.282 ±<br>0.2581</td><td>0.190</td><td>0.306</td><td>0.9983</td><td>0.600</td><td>2.000</td></tr><tr><td>Glycerol in<br>triglycerides</td><td>0.069</td><td>0.217</td><td>0.127 ±<br>0.0413</td><td>0.132 ±<br>0.0383</td><td>0.128 ±<br>0.0315</td><td>0.071</td><td>0.103</td><td>0.9990</td><td>0.000</td><td>0.570</td></tr><tr><td>Lactate<sup>1</sup></td><td>0.231</td><td>0.709</td><td>0.368 ±<br>0.0897</td><td>0.451 ±<br>0.1109</td><td>0.350 ±<br>0.1067</td><td>0.650</td><td>0.867</td><td>0.9959</td><td>0.000</td><td>1.250</td></tr><tr><td>Lactate<sup>2</sup></td><td>0.231</td><td>0.709</td><td>0.368 ±<br>0.0897</td><td>0.451 ±<br>0.1109</td><td>0.350 ±<br>0.1067</td><td>1.366</td><td>1.774</td><td>0.9976</td><td>0.000</td><td>4.000</td></tr><tr><td>Non-esterified<br>fatty acids</td><td>0.043</td><td>0.187</td><td>0.090 ±<br>0.0303</td><td>0.115 ±<br>0.0275</td><td>0.075 ±<br>0.0193</td><td>0.034</td><td>0.048</td><td>0.9998</td><td>0.000</td><td>1.000</td></tr></tbody></table>
<table><tr><td>Propionate</td><td>0.038</td><td>0.733</td><td>0.074 ±<br>0.0164</td><td>0.422 ±<br>0.1046</td><td>0.084 ±<br>0.0151</td><td>0.051</td><td>0.165</td><td>0.9987</td><td>0.000</td><td>2.000</td></tr><tr><td>Urea</td><td>1.058</td><td>6.844</td><td>3.298 ±<br>1.7248</td><td>3.113 ±<br>1.6762</td><td>3.286 ±<br>1.7938</td><td>0.330</td><td>0.703</td><td>0.9994</td><td>0.000</td><td>12.500</td></tr></table>

508 Abbreviations: MA = Mesenteric Artery; PV = Portal Vein; HV = Hepatic Vein
509
510 ¹ Quality Assurance results for lactate measured on a calibration curve ranging from 0.000 to 1.250 mmol/L.
511 ² Quality Assurance results for lactate measured on a calibration curve ranging from 0.000 to 4.000 mmol/L.

512
Table 6. Net carbon balance across the liver and the associated expanded measurement uncertainty (U(Y)) per lactating Jersey cow (n=5), treatment diet [(starch vs fiber rich diet) x (low vs normal protein diet)] and period.

517

<table><thead><tr><th>Cow</th><th>Treatment Diet</th><th>Period</th><th>Net C balance<sup>a</sup><br>(mmol C/min)</th><th>U(Y)<sup>b</sup></th><th>Uncertainty Range</th><th>Main contribution to uncertainty budget</th></tr></thead><tbody><tr><td>1</td><td>LS</td><td>3</td><td>-21.42</td><td>799.75</td><td>[-821.17; 778.33]</td><td>Total cholesterol in PV (65%)</td></tr><tr><td>1</td><td>LF</td><td>1</td><td>2.62</td><td>1 918.01</td><td>[-1 915.39; 1 920.63]</td><td>Total cholesterol in PV (72%)</td></tr><tr><td>1</td><td>HS</td><td>2</td><td>32.46</td><td>1 381.58</td><td>[-1 349.12; 1 414.04]</td><td>Total cholesterol in PV (71%)</td></tr><tr><td>2</td><td>LS</td><td>3</td><td>22.14</td><td>749.63</td><td>[-727.49; 771.77]</td><td>Total cholesterol in HV (48%)</td></tr><tr><td>2</td><td>LF</td><td>2</td><td>102.50</td><td>1 807.00</td><td>[-1 704.50; 1 909.50]</td><td>Total cholesterol in PV (41%)</td></tr><tr><td>2</td><td>HF</td><td>1</td><td>33.25</td><td>1 646.98</td><td>[-1 613.73; 1 680.23]</td><td>Total cholesterol in HV (38%)</td></tr><tr><td>3</td><td>LF</td><td>1</td><td>3.90</td><td>1 191.81</td><td>[-1 187.91; 1 195.71]</td><td>Total cholesterol in PV (38%)</td></tr><tr><td>3</td><td>HF</td><td>2</td><td>1.52</td><td>1 096.53</td><td>[-1 095.01; 1 098.05]</td><td>Total cholesterol in PV (36%)</td></tr><tr><td>4</td><td>LS</td><td>2</td><td>287.96</td><td>697.05</td><td>[-409.09; 985.01]</td><td>Total cholesterol in PV (40%)</td></tr><tr><td>4</td><td>LF</td><td>3</td><td>17.37</td><td>1 537.79</td><td>[-1 520.42; 1 555.16]</td><td>Total cholesterol in HV (48%)</td></tr><tr><td>4</td><td>HS</td><td>1</td><td>27.35</td><td>782.45</td><td>[-755.10; 809.80]</td><td>Butyrate in PV (29%)</td></tr><tr><td>4</td><td>HF</td><td>4</td><td>46.25</td><td>1 058.61</td><td>[-1 012.36; 1 104.86]</td><td>Total cholesterol in PV (39%)</td></tr><tr><td>5</td><td>LS</td><td>1</td><td>106.67</td><td>653.20</td><td>[-546.53; 759.87]</td><td>Total cholesterol in HV (45%)</td></tr><tr><td>5</td><td>LF</td><td>4</td><td>64.61</td><td>1 957.46</td><td>[-1 892.85; 2 022.07]</td><td>Acetate in HV (49%)</td></tr><tr><td>5</td><td>HS</td><td>2</td><td>2.91</td><td>960.27</td><td>[-957.36; 963.18]</td><td>Total cholesterol in HV (42%)</td></tr><tr><td>5</td><td>HF</td><td>3</td><td>-11.92</td><td>1 370.64</td><td>[-1 382.56; 1 358.72]</td><td>Total cholesterol in HV (47%)</td></tr></tbody></table>

518

Abbreviations: LS = low protein content and starch rich diet; LF = low protein content and fiber rich diet; HS = normal protein content and starch rich diet; HF = normal protein content and fiber rich diet;

HV = Hepatic Vein; PV = Portal Vein

521

522

a Net carbon balance across the liver calculated as the sum of each individual net hepatic flux of plasma or blood per metabolite taken from "Data1_C_balance" file.

b Expanded measurement uncertainty per cow, treatment and period taken from "Data4_CarbonBalance_Uncertainty" file.

527

528
529 **Figure captions**

530

**Fig. 1.** The origin of the carbon from the lipid fraction of plasma samples from each
531
lactating Jersey cow fed each treatment diet [(starch vs fiber rich diet) x (low vs
532
normal protein diet)]. The grey compartments represent the chemical lipid fractions in
533
plasma. The boxes represent the analysed fractions, with the plain arrows pointing to
534
the analysed molecule of the transport form and the dotted arrows to the long chain
535
fatty acid fraction. Phospholipid-choline was assumed to originate totally from lecithin
536
and lysolecithin on the basis that in tallow fed veal calves (Jenkins et al., 1986)
537
phospholipid-choline is present at 86% as lecithin and lysolecithin.
538

539

539

<figure><img src="image_2.png" /></figure>

540

541
Fig. 2. Cause-and-effect diagram of the measurement model (reproduced from Rodriguez Lopez, et al., 2016) applied to each lactating Jersey cow and treatment diet [(starch vs fiber rich diet) x (low vs normal protein diet)].

Abbreviations: $C_i$ ($i$ = infusion (inf), portal vein (PV), hepatic vein (HV) or mesenteric artery (MA)) = para-aminohippuric acid (pAH) concentration in infused solution (g/L) or in PV, HV or MA (mg/L); $F^{(i)}$ = net hepatic plasma flux of a metabolite $j$ determined in plasma (mmol/min); $G^{(j)}$ = net hepatic blood flux of a metabolite $j'$ determined in blood (mmol/min); $H$ = Hematocrit; this parameter is only considered in the calculation of the net hepatic blood flux of a given metabolite ($G$); $N_{PV, HV \ or \ MA}$ = metabolite concentration in PV, HV or MA (mmol/L); $T_{inf}$ = time of para-aminohippuric acid infusion (min); $u_c(F \ or \ G)$ = combined standard uncertainty of an input ($F$ or $G$); $W_{inf}$ = total weight of infused volume of each syringe (expressed as mL considering that the density of the solution is 1)

<figure><img src="image_3.png" /></figure>
Fig. 3. Empirical uncertainty function for a given plasma or blood metabolite measured for each lactating Jersey cow (n=5) and each treatment diet [(starch vs fiber rich diet) x (low vs normal protein diet)]. Equation 1 represents the relationship between the overall measurement uncertainty at each theoretical concentration level of a metabolite.

Abbreviations: u(C<sub>th</sub>) = overall measurement uncertainty for a given theoretical concentration of a plasma or blood metabolite (C<sub>th</sub>); a = slope of the equation; b = y-intercept of the equation

<figure><img src="image_4.png" /></figure>

567