Energy partition patterns and plasma metabolomics proles of modern growing pigs under different ambient temperatures: modelling and integrative analysis

Most of the studies focusing on energy partition patterns of growing pigs and the related mechanisms under different ambient temperatures were carried out during 1970s to early 2000s. With the rapid developments in pig breeding, research updates on such topics concerning modern growing pigs have been absent in the last decade. This study developed mathematical models to predict the energy partition patterns of modern growing pigs with different BWs at gradient-ambient temperatures, and investigated the underlying changes in plasma under such conditions based on the integrative analysis of indirect calorimetry and non-target metabolomics proling. their on revealed that the decreased energy intake and total heat production under 32 °C are associated with suppressed fatty acid oxidation and elevated lipogenesis and protein degradation, reected by biomarkers including up-regulated adrenic acid and down-regulated cortisol levels in plasma. Our ndings provide practical tools to precisely formulate diets for modern growing pigs under different ambient temperatures, and can help to improve our knowledge on potential mechanisms of thermoregulation in modern pig breeds.

The research on effects of ambient temperature on patterns of physiological changes in livestock started on 1940s, with the application of arti cial climate warehouse to mimic the environment in animal houses. In pigs, many studies were conducted from 1970s to early 2000s focusing on energy partition patterns under different temperatures using the climate-controlled open-circuit respiratory chamber [1][2][3][5][6][7][8][9]. With the development of animal breeding, modern pigs have great progress in productivity (e.g. quick weight gain and higher reproductivity), but their bodies become more sensitive to adverse environment such as changes in ambient temperatures [10]. Therefore, researches were carried out in recent years concerning about the alternations and alleviation strategies of modern pigs under heat or cold stress. However, there is few updates on patterns of energy balances in modern pigs at different ambient temperatures especially in the last decade.
Indirect calorimetry is the traditional non-invasion approach to determine the HP of the subjects, and has been widely used in livestock to monitor and model the energy partition patterns together with the analysis of feed intake and urine and feces outputs [11]. Moreover, the metabolic changes underlying the energy reactions has received more attention in recent years, which could directly re ect the regulation and adaptation of the animals to the surrounding conditions, and may provide novel diagnostic tools or biomarkers with high sensitivity towards the adverse effects [4]. The non-targeting metabolomics is an ideal approach to analyze the comprehensive changes in metabolites of the subjects, and has never been used to explore the relationships between metabolites alternation and the patterns of energy expenditure or substrate oxidation of growing pigs under various ambient temperatures.
Therefore, the objectives of this study were to determine and establish models for the energy partition patterns of modern growing pigs with different BWs at gradient-ambient temperatures, and to identify the underlying changes in energy metabolism under such conditions based on the integrative analysis of indirect calorimetry and non-target plasma metabolomics pro ling.

Methods
The Institutional Animal Care and Use Committee of China Agricultural University (Beijing, China) approved all protocols used in this experiment.

Equipment for indirect calorimetry
Six open-circuit respiration chambers (1.4 × 2.7 × 2.1 m 3 ) located in the FengNing Swine Research Unit of China Agricultural University (Academician Workstation in Chengdejiuyun Agricultural & Livestock Co., Ltd) were used to conduct the indirect calorimetry, which were described in details in previous studies [12,13] with the exception of temperature settings. The relative humidity was controlled at 70-75%, and the air velocity was controlled at 0.1 m/s. Oxygen content was measured with a paramagnetic differential analyzer (Oxymat 6E, Siemens, Munich, Germany), whereas CO 2 and CH 4 contents were measured with infrared analyzers (Ultramat 6E, Siemens). The analyzers had a range of 19.5-21.0% for O 2 , 0-1% for CO 2 , and 0-0.1% for CH 4 , with a sensitivity of 0.2%. Gas concentrations in each chamber were measured at 5-min intervals. The ethanol combustion experiment was used to check the accuracy of the chamber in measuring gaseous exchange.

Animals, diets and experiment design
Two animal trials were conducted in this study. In Trial 1, 36 healthy growing barrows (Duroc × Large White × Landrace) with initial BW of 26.4 ± 1.9 kg were allotted to a 6 × 6 Latin Square Design in 6 consecutive periods. In each period, 6 pigs were moved into 6 open-circuit respiration chambers with ambient temperatures setting as 18 °C, 21 °C, 23 °C, 27 °C, 30 °C, and 32 °C, respectively. In Trial 2, 24 healthy growing barrows (Duroc × Large White × Landrace) with initial BW of 64.2 ± 3.1 kg were allotted to a 4 × 6 Youden Square Design in 6 consecutive periods. In each period, 4 pigs were moved into 4 open-circuit respiration chambers (only 4 chambers were available during Trial 2) with ambient temperatures setting as 18 °C, 23 °C, 27 °C, and 32 °C, respectively.
Two diets based on corn-soybean meal were formulated to meet or exceed the nutrient requirements for growing pigs at 25 kg and 65 kg according to the recommendations by NRC [14], and were applied in Trial 1 and 2, respectively. The analyzed chemical compositions of those two diets were shown in Table 1. The speci c experiment procedures were kept the same in both animal trials. In each period, pigs were kept individually in stainless-steel metabolism crates (1.2 × 0.5 × 0.6 m 3 ) equipped with feeders and low-pressure nipple drinkers, and had a 7-d adaption period for crates and diets in the thermoneutrual-controlled room (24 ± 1 °C). On day 8, pigs were weighted and moved into the chambers for 5 days to measure the gases exchanges and calculate the total heat production (THP). Based on the feed intake during adaption, feed was supplied twice daily (08:30 and 15:30) ad libitum to pigs in chambers, and pigs had free access to water. For each pig, the total feces, urine output and wasted feed were collected twice daily from 08:00 to 08:30, and from 15:00 to 15:30, when the production of CO 2 , CH 4 and O 2 consumption were expelled in the calculation of daily HP, to determine the energy intakes of each day. On day 13, pigs were weighted in the morning and deprived of feed and fasted for 24 h, and the total urine output were collected during the fasting period to determine the fasting heat production (FHP), as an estimation of the energy used for maintenance [12]. On the morning of day 14, pigs were moved out the chambers and weighted again.

Sample collection
The daily urine output of each pig was collected into buckets with 50 mL 6 N HCl and sieved thereafter through multilayer gauze into plastic bottles and stored in -20 °C. The 5-day total urine collection and urine collection during the fasting period were quanti ed for each pig respectively, and a subsample of 50 mL for each pig was saved from the thoroughly mixed 5-day total collection for further analysis. The daily feces output of each pig was collected into plastic bags and immediately stored at -20 °C, then the 5-day total feces collection was thawed, mixed, and weighted, and a subsample of 350 g for each pig was oven-dried for 72 h at 65 °C to calculate the moisture content. Feed samples and subsamples of dried feces were nely ground through a 1 mm sieve prior to chemical analysis.
Blood samples of pigs in Trial 1 were collected from precaval vein into the heparinized tubes on day 13 morning during fasting, and then were centrifuged (Biofuge22R; Heraeus, Hanau, Germany) at 3,000 × g for 10 min at 4 °C. The supernatants were transferred to storage tubes, frozen in liquid nitrogen, and stored at -80 °C for further assays.

Chemical analysis and calculation
All chemical analysis of samples was conducted in duplicates and repeated if the duplicates differed by more than 5%. The gross energy (GE) in feed, feces, and urine samples was determined using an isoperibol calorimeter (Parr 6400 Calorimeter, Moline, IL, USA) with a standard reference of benzoic acid. For feed samples, the contents of dry matter (DM), crude protein (CP), ether extract (EE), and ash were determined following the methods of AOAC [15]. For fecal samples, the contents of DM and CP were determined. For urine samples, the nitrogen (N) content was measured according to Li et al. [13].
The dry matter intake (DMi) of each pig from day 8 to day 12 was calculated as the product of feed intake and the DM content of the diets. The GE intake was calculated as the product of actual DMi during the 5-day collection period and the GE values of the diets. The digestible energy (DE) intake and metabolizable energy intake (ME i ) was calculated as the difference between GE intake and the energy loss in feces, and the difference between DE intake and the energy loss in urine and methane, respectively. Methane energy was calculated using the methane volume and a conversion factor of 39.4 kJ/L [16].
The average daily THP was calculated according to the following equation based on the gas exchanges (O 2 consumption and productions of CO 2 and CH 4 ) during day 8 to day 12 recorded at 5-min intervals and then averaged and extrapolated to a 24-h period: HP (kJ) = 16.18 × O 2 (L) + 5.02 × CO 2 (L) − 2.17 × CH 4 (L) − 5.99 × urinary N (g) [16].
The FHP was calculated using the same equation, but the 24-h FHP was predicted from the 8-h HP after feed deprivation from 22:00 to 06:00 during the last day of each period, which was then extrapolated to the 24-h period [13]. The RE was calculated as the difference between ME i and THP, while the RE as protein (RE P ) was calculated as N retention (g/d) × 6.25 × 23.86 (kJ/g), and the RE as lipid (PE L ) was calculated as the difference between RE and RE P . The net energy (NE) intake was calculated as the sum of RE and maintenance energy estimated by FHP [17]. Moreover, the oxidation of carbohydrates (OXCHO) and fat (OXF) were calculated by the method described by The rates of DE:GE, ME:DE and NE:ME were then calculated based on the calculations of GE, DE, ME, and NE intakes. The respiratory quotient (RQ) was calculated as the ration between CO 2 production and O 2 consumption. All the energy balance indexes were present on the metabolic body weight (per kg BW 0.60 ) basis.

Hormone and biochemical marker assays in serum
The concentrations of cortisol, insulin, triiodothyronine (T 3 ) and thyroxine (T 4 ) in serum were analyzed using radioimmunoassay, while the activities of growth hormone (GH) and glucagon in serum were analyzed using commercial enzyme-linked immunosorbent assay (ELISA) kits (Nanjing Jiancheng Bioengineering Institute, Nanjing, China) following the manufacturer's guides. The levels of albumin, glutamicpyruvic transaminase (ALT), glutamic oxalacetic transaminase (AST), globulin, high density lipoprotein (HDL), low density lipoprotein (LDL), total cholesterol (TC), triglyceride (TG), total protein and urea in serum were determined using the automatic biochemical analyzer (7170, Hitachi Corp., Tokyo, Japan) with corresponding commercial kits (Nanjing Jiancheng Bioengineering Institute) following the manufacturer's guides.
Non-target metabolomics pro ling in plasma and data analysis Plasma samples from pigs kept under the ambient temperatures of 18 °C, 23 °C and 32 °C (de ned as low, neutral and high ambient temperature group, respectively) were used for non-target metabolomics pro ling assay, followed the procedures described by Liu et al.
Brie y, 100 µL plasma samples were added into 400 µL ice-cold extraction mix (methanol: acetonitrile = 1:1, v: v). After vortexing for 10 s, the mixture was centrifuged (Eppendorf, Germany) at 15,000 × g for 10 min at 4 °C to remove protein, and 400 µL supernatant was collected and evaporated to dryness using a vacuum concentrator (Concentrator PLUS, Eppendorf). The resulting dry residues were resuspended in 200 µL recovery solution (water: methanol = 4:1), vortexed and centrifuged again at 15,000 × g for 10 min at 4 °C. The supernatant was ltered through a 0.22 µm membrane and transferred to sampler vials to be analyzed on a UPLC

Statistical Analysis
For the metabolomics data, the software SIEVE 2.1 (Thermo Scienti c) and Progenesis QI (Nonlinear Dynamics, Waters Corporation) were used for raw data processing, including background subtraction, peak alignment, identi cation, and normalization with Pareto scaling to get the standardized relative abundance of the metabolites in different samples. Then principal components analysis (PCA) was conducted using SIMCA-P 13 software (Umetrics, Umea, Sweden), and one-way ANOVA was conducted using JMP Pro 14.3.0 (SAS Institute Inc., Carry, NC, USA) to compare the abundance of metabolites among different treatments. The metabolites with fold change > 1.5, CV < 20% and P < 0.05 were selected for further identi cation by comparison of the ion features in the experimental samples to the chemical standard entries in reference libraries (METLIN, HMDB and KEGG) that included retention time, molecular weight (m/z) as well as their associated MS/MS spectra. Boxplot was plotted using the ggplot2 package in R software (http://cran.r-project.org/, version 4.0.2) to illustrate the concentrations of the compounds that identi ed with signi cantly difference among the three treatments. Those compounds were then imported into the module of pathway analysis in Metaboanalyst 3.0 (https://www.metaboanalyst.ca/MetaboAnalyst/upload/PathUploadView.xhtml) to generate the pathway topology analysis. The metabolic pathway with impact value greater than 0.1 was characterized as the signi cantly relevant pathway [19].
For the other data, normality and homogeneity of variance were checked using the normal probability plot and residual plot from JMP Pro 14.3.0, and outliers were removed before further analysis. For N and energy balance data and serumal hormone and biochemical markers data collected in Trial 1, a statistical model including ambient temperature as the only xed effect and chamber as the random effect was tted using the Fit Model function in JMP Pro 14.3.0. Tukey's HSD test was used to separate the least square means among treatments with signi cantly different effects. Moreover, linear and quadratic effects of increased ambient temperature on responses were tested by polynomial contrast using the Fit Y by X function in JMP Pro 14.3.0. To better illustrate the comprehensive effects of ambient temperature and pig BW, the N and energy balance data collected in Trial 2 were combined with some corresponding data (those under the same temperature settings) in Trial 1 for analysis. A statistical model included the main effects of ambient temperature (18 °C, 23 °C, 27 °C, and 32 °C) and BW (25 kg and 65 kg), and their interaction effect as xed effects, and included the chamber as the random effect. The Fit Model function in JMP Pro 14.3.0 was used to conduct the two-way ANOVA, and Tukey's HSD test was used to separate the least square means among treatments with signi cantly different main effects only when the interaction effect was not signi cant. Moreover, equations were developed to predict the voluntary feed intake (VFI), ME i , RE P and RE L using metabolic body weight (BW 0.6 ) and ambient temperature as predictors based on some modi cations of the equations from Quiniou et al. [20]: All the data obtained in Trial 1 and 2 were combined and used for model development. Covariance analysis was used to further con rm the quadratic effects of BW and T on response variables, and coe cients were estimated by Gauss-Newton analysis using the Nonlinear Modelling function in JMP Pro 14.3.0. The predicted vs. actual plot and predicted vs. residuals plot were used to check the goodness of t of the models. For all the analysis, P < 0.05 was considered as signi cantly different.

Energy partition in pigs at 25 kg under different ambient temperatures
The energy partition of modern growing pigs at 25 kg kept at 18 °C, 21 °C, 23 °C, 27 °C, 29 °C and 32 °C were present in Table 2. As the ambient temperature increased from 18 °C to 32 °C, the DMi, N intake, fecal N output, N retention, ME i , THP and RE P of growing pigs at 25 kg all showed linearly and quadratically decreased pattern (P < 0.05). Speci cally, pigs raised at 18 °C had greater DMi, N intake, N retention, ME i , THP and RE P compared with those raised at 32 °C, while pigs kept at 18 °C also had greater THP compared with those kept at 29 °C (P < 0.05). Moreover, pigs raised at 18 °C and 21 °C exhibited greater fecal N output than those raised at 27 °C, and pigs kept at 23 °C also exhibited greater RE P than those kept at 32 °C (P < 0.05). On the other hand, as the ambient temperature increased from 18 °C to 32 °C, the OXCHO and RQ at fasting state linearly and quadratically increased, with pigs under 32 °C showed greater OXCHO and RQ during fasting compared with pigs under 18 °C, 21 °C and 23 °C (P < 0.05). Otherwise, no signi cant changes were observed on other parameters related to energy balance and utilization under different ambient temperatures (P > 0.05).  Table 3. There were signi cant interaction effects between BW and ambient temperature on DMi, N balance (including N intake, fecal N output, urine N output and N retention), ME i , THP adjusted to the same ME i , RE, RE P , RE L , RQ in fed state, NE/ME, RE/ME and RE L /ME (P < 0.05). However, the ME i , THP adjusted to the same ME i , RE, RE P , RE L , RE/ME and RE L /ME did not exhibit difference between pigs at 25 kg and those at 65 kg, and the NE/ME did not show difference among pigs under 18 °C, 23 °C, 27 °C, and 32 °C (P > 0.05). Table 3 Comparison between barrows at 25 kg and 65 kg on nitrogen and energy balance kept at different ambient temperatures 1 . Modelling the voluntary feed intake and energy partition considering pigs' BW and ambient temperature The quadratic effects of BW and T as well as their interaction effect on response variables were further con rmed. Models developed in the current study to predict VFI, ME i , RE P and RE L using both BW and ambient temperature (T) as predictors were: which were present in Table 4. The estimated VFI, ME i , RE P and RE L of pigs at 25 kg and 65 kg under ambient temperatures from 18 °C to 32 °C based on these models were plotted in Fig. 1A-D, which illustrated that feed intake and energy retention in pigs at 65 kg were more easily impaired by high temperatures than in pigs at 25 kg. Meanwhile, the models for VFI and ME i were compared with the below models developed previously ( Fig. 1A and 1B): Nearly parallel VFI curves were present between models in the current study and those built previously, but narrower gaps between ME i curves representing different BWs were found in our study compared with those from previous study especially under high ambient temperatures. Moreover, the goodness-of-t of those developed models were shown in Fig. 2

Metabolomics pro les in plasma of pigs at 25 kg under different ambient temperatures
The PCA score plot showed that the plasma samples from pigs stayed at low (18 °C), neutral (23 °C) and high (32 °C) ambient temperatures obviously clustered within the 95% con dence interval (Fig. 3). The PC1 and PC2 accounted for 41.9% and 9.98% of the total variance of the data, respectively, indicating there were major difference among the metabolomics pro les of the three treatment groups.
A total of 13 compounds were identi ed with different intensities among the three treatment groups by comparing to the standard entries in reference libraries (Table 6), which include categories of amino acid, fatty acid and steroid. To better illustrate the changes of those compounds in the treatment groups, data were visualized through boxplot in Fig. 4. Compared to pigs stayed at the neutral temperature (23 °C) or low temperature (18 °C), the concentrations of (2'E,4'Z,7'Z,8E)-colnelenic acid, 3-beta-hydroxy-5-cholestenoate, adrenic acid, dihydrocortisol and indoleacetic acid all dramatically up-regulated, while the concentrations of 20-hydroxyeicosatetraenoic acid, betasitosterol, cortisol, deoxyuridine, leukotriene C4, phenylacetylglycine and spermidine all greatly down-regulated in plasma of pigs stayed at the high temperature (32 °C). In addition, compared to pigs stayed at neutral temperature, the levels of beta-sitosterol markedly upregulated, while the levels of (2'E,4'Z,7'Z,8E)-colnelenic acid, cortisol, L-histidine, phenylacetylglycine and spermidine slightly downregulated in plasma of pigs stayed at the low temperature (18 °C). Effects of ambient temperature on voluntary feed intake and energy partition of modern growing pigs Most of the studies focusing on the VFI and energy partition patterns under different ambient temperatures in growing pigs were carried out in the second half of the 20th century. With the rapid developments in pig breeding, research updates on such topics concerning modern growing pigs have been absent in recent years.
Pig belongs to the warm-blooded animal. Under low ambient temperatures, the increased feed intake and heat production can facilitate the maintenance of a constant body temperature [22]. The criteria of "low" temperature is de ned according to the thermoneutrual zone and the LCT value, which is usually estimated by BW. NRC [14] used the following equations to estimate the LCT in growing pigs: LCT (°C) = 17.9-0.0375 × BW. Based on the temperature setting in the current study, all the pigs used in the animal trial were kept above the LCT. We observed an averaged 30 g/d/°C increase in DMI and 0.38 MJ/d/°C increase in ME i when the ambient temperature decreased from 27 °C to 18 °C for pigs with mean BW of 28 kg in the current study. Our results are similar to the VFI and energy intake patterns gained from Le Dividich et al. [23], who illustrated that the extra feed intake requirements were 32-33 g/d/°C and the additional DE required to compensate for 1 °C drop in temperature between 28 °C and 20 °C and between 20 °C and 12 °C were 0.20 and 0.44 MJ/d in 30 kg growing pigs individually housed, respectively, but are different from the results from other studies. For example, Lefaucheur et al. [24] reported that an extra feed intake of 25 g/d/°C was required to achieve similar rates of weight gain for individual pig at 30  As the ambient temperature keeps raising, the heat production of the pig body becomes a "burden", and pigs can keep the body temperature uctuate in a small range by increasing the evaporation heat loss and decreasing the heat production [22]. However, due to the degradation of the sweat gland, the capacity of heat dissipation through evaporation by pigs is limited [22]. Therefore, under high ambient temperatures, the feed intake of pigs will decrease dramatically to control their heat production [22]. For example, Collin et al. [25] showed that the VFI remained almost constant between 19 ºC and 25ºC, and proportionally decreased 33 g/day/ºC between 25ºC and 35ºC for pigs at 20 kg. In the current study, we observed an averaged 56 g/d/°C in DMI and 0.90 MJ/d/°C decrease in ME i when the ambient temperature increased from 29 °C to 32 °C for pigs with mean BW of 28 kg, but also observed an averaged 55 g/d/°C in DMI and 0.80 MJ/d/°C increase in ME i when the ambient temperature increased from 27 °C to 29 °C. The same pattern was also observed in THP adjusted into the same ME i level. Some previous studies also reported increased THP under high environmental temperatures, which could be attributed to the extra energy expenditure used for additional activity such as more frequent breathing and heart rating to facilitate the heat dissipation [9]. For instance, Close and Mount [26] illustrated that the THP was the lowest during 20 °C to 25 °C, and gradually increased when the temperature reached 30 °C. The above con ict in heat production results may rely on the speci c temperature range, BW and feeding level of the pigs [21]. Moreover, the increased consumption of dietary energy by pigs for heat dissipation in high temperature environment also leads to the decreased energy utilization e ciency.
The environmental temperature could affect the partition of ME i , speci cally, into maintenance energy, energy for thermoregulation, and energy for growth (the RE) in growing pigs. In the current study, no signi cant in uence of ambient temperatures on maintenance energy (ME m , estimated by FHP), RE and the partial energy utilization e ciency, including partial e ciency for digestion (DE/GE), metabolization (ME/DE), net utilization (NE/ME), retention (RE/ME) and maintenance (FHP/ME), were observed. However, the ambient temperature altered the OXCHO and RQ during fast state as well as the RE P , with OXCHO increased from ~ 200 to ~ 400 kJ/kg BW 0.75 /d, RE P decreased from 600 to ~ 430 kJ/kg BW 0.75 /d, and RQ increased from 0.80 to 0.87, when environment temperature increased from 18 °C to 32 °C, re ecting the enhanced maintenance energy partition at low ambient temperature and reduced protein synthesis at high ambient temperature. According to the previous study from Close [27], when the environmental temperature increased from 10 °C to 30 °C, the ME m decreased from 723 to 469 kJ/kg BW 0.75 /d, and the RE e ciency (RE/ME) decreased from 0.79 to 0.63, with a ME m of 440 kJ/kg BW 0.75 /d and a RE e ciency of 0.67 at the thermoneutral temperature of 25 °C. In addition, both the partial energy e ciency estimated for protein deposition and lipid deposition were similar at each environmental temperature and decreased from 0.78 at 10 °C to 0.63 at 30 °C [27]. The above results are somehow in according with our observations, indicating that under low ambient temperature, more energy intake were used to maintain the body temperature of pigs, while part of energy was used to dissipate the heat produced during protein and lipid synthesis under high ambient temperature, leading to the decreased partial energy e ciency. Due to the absence of dietary energy gradients settings, the changes of partial e ciency for protein and lipid synthesis under different temperatures were not tested in the current study.

Effects of ambient temperature on nitrogen balance of modern growing pigs
In the current study, we also focused on the effects of ambient temperatures on N balance. For pigs raised from 18 °C to 32 °C, the changing patterns of N intake and fecal N output were the same as that of the adjusted THP, which has been discussed previously.
Moreover, the ratio of fecal N output to total N intake ranged from 12.5-16.7%, and decreased from 18 °C to 29 °C, then increased from 29 °C to 32 °C. This range exactly matched the range of 16-12% for fecal N output to total N intake ratio reported by Guo [21] when temperature changed from 23 °C to 35 °C. Environmental temperature had no in uence on urine N output in our study, which was also supported by Guo [21] and Verstegen et al. [3]. The ratio of N retention to total N intake ranged from 68.7% (32 °C) to 76.0% (23 °C), and is quite different from those of Verstegen et al. [3], who reported a range of 50%-54% of N retention to dietary N intake ratio, and was independent with ambient temperatures. Those discrepancies in results of N balance could be mainly ascribed to the differences in pig breeds and experimental conditions. Modelling the energy partition of modern growing pigs with different BW under different ambient temperatures It has been widely proved that pigs at different growth stages have distinct patterns of energy partition as the ambient temperatures change, since the critical temperatures differ for pigs with different BW [14]. In the current study, we found signi cant interaction effects between BW and temperature on DMI, N balance, ME i , adjusted THP, RE and the partial e ciency for lipid deposition (RE L /ME), with pigs at 65 kg showed greater the above indexes except for RE P compared with pigs at 25 kg. Therefore, the quadratic models including the main effects of metabolic BW, ambient temperature and their interaction effects were used to t the raw data in the current study and to predict the VFI, ME i as well as RE P and RE L . Similar simulation equations have already been used to model the VFI [20], heat production and energy retention [1], and ME i [21] in pigs exposed to low or high ambient temperatures. Based on those curvilinear models developed in our study, it can be clearly see that pigs at heavier BW were more sensitive to high temperatures on VFI, ME i and protein and lipid deposition, which were partially supported by Renaudeau et al. [28], who analyzed the effects of high temperature on feed intake of pigs with different BW using meta-analysis based on 86 trials and 202 temperature treatments published from 1970 to 2009, and found that high temperature had a curvilinear effect on average daily feed intake, which was more pronounced in heavier pigs. In addition, the gaps between ME i curves representing different BWs in our study were narrower compared with those from previous studies using pigs with older genotypes, suggesting that modern genotypes could be more sensitive to heat stress than older genotypes of lesser growth potential. Similarly, Renaudeau et al. [28] also reported that the effect of increased temperature was greater in more contemporary publications.
However, one aw of the models developed in the current study is that the BW data collected for simulation only came from 2 growth stages, and the narrow range of BW may produce bias when predicting the responses on pigs with other BWs.
Effects of ambient temperature on hormone and biochemical markers in serum of modern growing pigs As the ambient temperature increased from 18 °C to 32 °C, there was linearly decreased cortisol, T 3 , T 4 , HDL and TC levels, linearly increased AST level, and quadratically changed glucagon level in serum of 25 kg pigs in the current study. Similar changes in physiological and biomedical parameters in plasma of growing pigs under heat stress were also reported previously [29,30]. The decreased cortisol content in plasma under low temperature may indicate improved protein degradation to provide amino acids for gluconeogenesis [30]. Moreover, the decreased cortisol level and increased glucagon and AST levels in plasma may also act as indicators for the stress reaction of pigs under extreme environmental conditions [30]. In addition, the depressed thyroid hormone (T 3 and T 4 ) levels have been associated with lowered metabolic heat production in pigs kept at high environmental temperature [29]. Meanwhile, a reduction in HDL and TC, indicating the decreased β-oxidation of fat for energy purpose and favored hepatic synthesis of triglycerides, could also support the depressed plasma thyroid hormone levels in pigs reared at high ambient temperature [29].
Effects of ambient temperature on plasma metabolomics pro les of modern growing pigs To simplify the analysis, only plasma samples from 18 °C, 23 °C and 32 °C were used for metabolomics analysis in the current study.
Among the 13 compounds identi ed, more compounds showed signi cant changes in pigs at high ambient temperature than those at low ambient temperature when compared to the thermoneutral condition, indicating that modern growing pigs are more sensitive to heat stress than cold stress re ected by the plasma metabolites. Another reason may be that the "low" temperature settings in the current study may not produce cold stress since it is above the LCT de ned by NRC [14].
Under high ambient temperature, most of the metabolites with up-regulated expressions belong to fatty acids ((2'E,4'Z,7'Z,8E)-colnelenic acid, 3-beta-hydroxy-5-cholestenoate and adrenic acid), or involve in pathways related to lipid metabolism or fatty acid metabolism (dihydrocortisol), indicating elevated lipogenic pathways and suppressed fatty acid oxidation, which were also re ected by the levels of hormone and biochemical markers in serum in the current study, and was supported by the reports of Qu and Ajuwon [31], who showed greater serum linoleic and total polyunsaturated fatty acids levels in pigs stayed at 35 °C. On the other hand, the metabolites with downregulated expressions at 32 °C are involved in amino acid metabolism (phenylacetylglycine and spermidine), or lipid metabolism (20-hydroxyeicosatetraenoic acid, beta-sitosterol and leukotriene C4), which may indicate the enhanced protein degradation and gluconeogenesis, as well as the depressed lipolysis. Interestingly, cortisol was also identi ed in the metabolomics analysis, with downregulated level at high temperature, supporting the results in the plasma hormone assay. Furthermore, most of the metabolites in plasma only exhibited slightly changes in pigs at 18 °C compared to that at 23 °C, suggesting less stress under this temperature setting.

Conclusion
The current study provided updated mathematical models to predict the voluntary feed intake and metabolizable energy intake as well as new models to estimate the energy requirements for protein and lipid deposition of growing pigs (25 to 65 kg) under ambient temperatures of 18 to 32 °C. It also suggested that pigs at heavier body weight were more sensitive to high temperatures on energy intake and partition, and pigs with modern genotypes could be more sensitive to heat stress than pigs with older genotypes. The integrative analysis of indirect calorimetry and metabolomics pro ling revealed that the decreased energy intake and total heat production under 32 °C are associated with suppressed fatty acid oxidation and elevated lipogenesis and protein degradation, re ected by biomarkers including up-regulated adrenic acid and down-regulated cortisol levels in plasma. Our ndings provide practical tools to precisely formulate diets for modern growing pigs under different ambient temperatures, and can help to improve our knowledge on potential mechanisms of thermoregulation in modern pig breeds.
(B) Modelling the metabolizable energy intake (dark curves) and comparison with models developed previously by Guo et al. [21]