Degradation kinetics of vitamins in premixes for pig: effects of choline, high concentrations of copper and zinc, and storage time

Objective The present work was undertaken to evaluate the effects of storage time, choline chloride, and high concentrations of Cu and Zn on the kinetic behavior of vitamin degradation during storage in two vitamin premixes and four vitamin-trace mineral (VTM) premixes. Methods Two vitamin premixes (with or without 160,000 mg/kg of choline) were stored at 25°C and 60% humidity. Besides, four VTM premixes were used to evaluate the effects of choline (0 vs 40,000 mg/kg) and trace minerals (low CuSO4+ZnO vs high CuSO4+ZnO) on vitamin stability in VTM premixes stored in room, and the VTM premixes were stored in room temperature at 22°C. Subsamples from each vitamin and VTM premix were collected at 0, 1, 2, 3, 6, and 12 months. The retention of vitamin A (VA), vitamin D3 (VD3), vitamin E (VE), vitamin K3 (VK3), vitamin B1 (VB1), vitamin B2 (VB2), vitamin B3 (VB3), vitamin B5 (VB5), and vitamin B6 (VB6) in vitamin premixes and VTM premixes during storage was determined. The stability of vitamins in vitamin premixes and VTM premixes was determined and reported as the residual vitamin activity (% of initial) at each sampling point. Results The effect of choline on VK3 retention was significant in vitamin premixes (p<0.05). The negative effect of storage time was significant for the retentions of VD3, VK3, VB1, VB2, VB5, and VB6 in vitamin premix (p<0.05). For VTM premixes, negative effect of storage time was significant (p<0.05) for the losses of vitamin in VTM premixes. Choline and high concentrations of Cu and Zn significantly increased VA, VK3, VB1, and VB2 loss during storage (p<0.05). The supplementation of high concentrations of Cu and Zn significantly decreased the concentrations of VD3 and VB6 (p<0.05) in VTM premixes at extended storage time. Conclusion The maximum vitamin stability was detected in vitamin and VTM premixes containing no choline or excess Cu and Zn. The results indicated that extended storage time increased degradation of vitamin in vitamin or VTM premixes. These results may provide useful information for vitamin and VTM premixes to improve the knowledge of vitamin in terms of its stability.


INTRODUCTION
Vitamin and vitamintrace mineral (VTM) premixes are designed for supplemental nu tritional support to animals who are unable to ingest adequate amounts of natural feedstuffs [1,2]. Choline serves some essential biological functions in young animals [3,4], such as improving fat transport and metabolism in the liver, source of methyl donors for methio nine regeneration from homocysteine, building and maintaining cell wall structure, and supporting nervous system function.
In the postweaning period, the stress of being removed from the sow and mixing into a new environment results in perturbations of gut microbiota and lowered defenses against pathogen entry for piglets, which can lead to increased risk of disease [5,6]. Postweaning diarrhea is one of the most common causes of mortality for weanling pigs, and hence greatly impaired growth performance of pigs [5,6]. In practi cal application, the inclusion of high concentrations of zinc oxide (ZnO) and copper sulfate (CuSO 4 ) in weaned pig diets can improve the growth performance and decrease diarrhea incidence [57]. All of these treatments may affect the formu lation of the ingredients in premixes, leading to bioavailability loss of necessary nutrients. In addition, premixes are often not consumed immediately after manufacturing and can be degraded due to several factors, such as the length of storage and premix compositions. (e.g. choline chloride and high concentrations of metal ions) [3,811]. Numerous reports have discussed the stability of vitamins under various condi tions such as storage and processing [811]. Vitamins may be unstable to heat and light as well as exposure to acid, al kali, air, and moisture. The degradation of vitamin activity in premixes and complete feed during storage may result in hidden depressions in growth, feed efficiency, and disease resistance due to the subclinical vitamin deficiencies [3,8,11]. For this reason, the vitamin content should be evaluated after manufacturing and storage in order to ensure the amount provided.
However, studies on the stability of vitamins in vitamin premix and VTM premix are limited. In addition, these fac tors (choline chloride and high concentrations of CuSO 4 and ZnO) in premixes have received limited research attention, and it is unclear which vitamins in vitamin or VTM premix es are vulnerable when choline and high concentrations of Cu and Zn are present. Therefore, the objectives of this study were to i) determine the rate of vitamin loss in vitamin or VTM premixes and the effects of choline and high concen trations of Cu and Zn on the stability of vitamins during storage and ii) to develop vitamin retention prediction mod els based on storage time.

Experimental design
This study was conducted at the State Key Laboratory of Animal Nutrition at China Agricultural University (Beijing, China) and Ministry of Agriculture and Rural Affairs Feed Efficacy and Safety Evaluation Center (Beijing, China). Ap proval from the Animal Care and Use Committee was not obtained for this experiment because no animals were used.

Chemical reagents
Deionized water (18 MΩ·cm) from a Millipore MilliQ (Bed ford, MA, USA) water purification system was used to prepare all aqueous solutions. Standard for retinyl esters, cholecalcif erol, αtocopherol acetate, menadione, thiamine, riboflavin, pyridoxine, niacin and pantothenic acid were purchased from Sigma-Aldrich (Fluka, Sigma-Aldrich, Steinheim, Germany). The methanol and acetonitrile of highperformance liquid chromatography (HPLC) grade were used for HPLC analysis and were obtained from Fisher Scientific (Pittsburg, PA, USA). All the other chemicals used were analytical grade and pur chased from Sinopharm Chemical Reagent LTD (Beijing, China).

Premix formulation and treatments
Two vitamin premixes (containing no trace minerals) were formulated by commercial vitamins. The vitamin manu facturer is not disclosed in order to protect proprietary information. The manufacturing dates of all vitamins were obtained from the original suppliers to ensure that the prod ucts were within 6 months of manufacture and were not expired. The vitamin premixes were designed to be added at a rate of 2.5 g/kg of the diet. The specific vitamin com position and inclusion level were set to mimic common swine industry vitamin premixes. One of vitamin premixes contained choline, another vitamin premix without choline ( Table 1). The choline chloride concentration in vitamin premix was measured via chromatography [12].
Four VTM premixes were formulated to contain the same level of vitamins for weanling piglets. The VTM premixes were designed to be added at a rate of 10 g/kg of the diet, which is common in practice. Compositions of VTM pre mixes were shown in Table 1. Vitamin levels met or exceeded the requirement of NRC [13], which were chosen to repre sent the "typical" industry levels based on informal surveys of vitamin levels in commercially available premixes. The amounts of each vitamin used in each premix are shown in Table 2. Choline was added to VTM premixes 2 and 4. The choline chloride concentration in VTM premix was deter mined using chromatography [12]. The VTM premixes 1 to 4 were formulated to meet or exceeded NRC requirements for copper (Cu), iodine (I), iron (Fe), manganese (Mg), sele nium (Se), and zinc (Zn) for piglets [13]. The VTM premixes 3 and 4 contained 20,000 mg/kg of Cu added as CuSO 4 and 225,000 mg/kg per diet of Zn added as ZnO, which could provide 200 mg/kg of Cu and 2,250 mg/kg Zn in diet. The reason for choosing these levels of Cu and Zn is that wean ling pig premixes commonly have higher concentrations of Cu and Zn as an antimicrobial and improve growth perfor mance [57].

Premix preparation and storage
Vitamin and VTM mineral premixes were manufactured at a commercial vitamin premix plant. Each of the two vitamin Table 1. Composition of the vitamin and vitamin-trace mineral premixes 1)

Vitamin sampling, extraction and assays
Subsample of vitamin and VTM premixes were obtained from each of six replicates at 0, 1, 2, 3, 6, and 12 months. Samples were immediately sent to the Ministry of Agricul ture and Rural Affairs Feed Efficacy and Safety Evaluation Center (Beijing, China) used for vitamin analysis. The vita min A (VA) and E (VE) were determined by the method 2012.10 [14]. In brief, the sample (2 g) was mixed with pa pain solution until dispersed, placed in a 37°C±2°C water bath, and extracted by methanol. This extract was analyzed by HPLC (Agilent 1200 Series; Agilent Technologies Inc., Santa Clara, CA, USA). For the extraction of vitamin D 3 (VD 3 ) from samples, the method of 992.26 [14] was used.
In brief, 5 g sample was transferred to a centrifuge tube and anhydrous ethanol, ascorbic acid, and potassium hydroxide were added. Tubes were placed in a 75°C water bath. Sub samples were analyzed by HPLC followed by UV detection at 254 nm. For the determination of vitamin K 3 (VK 3 ), sam ples were extracted with trichloromethane. Extract filtered and injected into the HPLC system and UV detection was made at wavelength 251 nm [15].  [16] was used and modified. Five g of sample was weighed, extracted with phosphate buffer, heated in a water bath, and sonicated. The supernatants of the extracted samples were stored at -20°C until they were tested. These extracted samples were analyzed using a 250× 4.5 mm, 5 μm, Eclipse Plus C18 column (Agilent Technol ogies Inc., USA) on an Agilent liquid chromatograph. The stability of vitamins in vitamin premixes and VTM premixes during storage was determined and reported as the residual vitamin activity (% of initial) at each sampling point. This time was also convenient for us to compare with previous studies and for developing predicted equations to estimate the vitamin loss. The specific vitamin selected were based on the capacity to complete our respective lab analysis.

Data treatment and statistical analysis
Normality of the data was verified using the UNIVARIATE procedure of SAS (SAS Inst. Inc., Cary, NC, USA). The BOX PLOT procedure of SAS was used to check for outliers. Data were analyzed using the MIXED procedure of SAS (SAS Inst. Inc., USA) to determine the interactive and main effects of choline chloride, high concentrations of Zn and Cn, and storage time on the activity of vitamins in vitamin and VTM premixes. Results were considered significant at p≤0.05 and a tendency at p≤0.10. Diagrams were generated using the Excel 2016 (Microsoft Corporation, Redmond, WA, USA). Vitamin retention was modelled using linear regression and nonlinear regression. Linear regression to determine vitamin retentions was completed using the PROC REG procedure of SAS. Nonlinear regression was performed using PROC NLIN procedures of SAS with exponential model (Eq. (1)). The exponential model is flexible owing to the inclusion of a shape constant in addition to the rate constant and has been employed to describe vitamin degradation kinetics [17].
retentions was completed using the PROC REG procedure of SAS. Non 166 using PROC NLIN procedures of SAS with exponential model (Eq 167 flexible owing to the inclusion of a shape constant in addition to the rat 168 to describe vitamin degradation kinetics [17].

Effects of storage time and choline on stability of vitamins in vitam 189
There was no significant interactive effect of storage time and choline 190 VB5, and VB6 retention ( Table 3). The main effect of storage time 191 Where C t is the vitamin concentration at a time t, C 0 is the initial vitamin concentration, K aa is the rate constant. Mod elling and analysis of variance were performed using SAS 9.4 (SAS Inst. Inc., USA). The R 2 and the root mean square error of prediction (RMSEP) were used to define the bestfit equa tions.

Vitamin recovery method validation
Methods for vitamin analysis in samples were validated with repeatability betweenday precision, longterm precision, limits of quantitation, and linearity (data not shown) by the staff of the Ministry of Agriculture and Rural Affairs Feed Efficacy and Safety Evaluation Center (Beijing, China). Cal culated values (Table 1) were determined from the minimum declared vitamin concentrations as provided by each product' s manufacturer. The initial (d 0) analyzed vitamin concentra tions of the vitamin premix, or VTM premixes are reported in Table 2. The analyzed vitamin values in vitamin premix or VTM premixes were similar to calculated vitamin values in vitamin premix or VTM premixes.

Effects of storage time and choline on stability of vitamins in vitamin premixes
There was no significant interactive effect of storage time and choline on VA, VD 3 , VE, VB 1 , VB 2 , VB 3 , VB 5 , and VB 6 retention ( Table 3). The main effect of storage time was sig nificant (p<0.01) for the retentions of VD 3 , VB 1 , VB 2 , VB 5 , and VB 6 in vitamin premix (Figures 1 to 5). The retention of VK 3 was significantly influenced by storage time (p<0.01), choline (p<0.01) and the interaction between storage time and choline (p<0.01; Table 3; Figure 6). At 3 months, VA, VD 3 , VE, VK 3 , VB 1 , VB 2 , VB 3 , VB 5 , and VB 6 retained at least 96%, 92%, 97%, 78%, 95%, 94%, 98%, 94%, and 90% of their initial activity in vitamin premix with out choline, respectively. At 12 months, most vitamins retained 76% to 98% of the initial vitamin activity, but VK 3 was re tained 47.64% of its initial activity in vitamin premix without choline. With increased storage time, VA exhibited a tendency (p = 0.096) for decreased retention in vitamin premixes, but VA exhibited a tendency (p = 0.076) and VB 5 was margin ally significant (p = 0.053) for decreased retention during extended storage time in vitamin premixes containing cho line chloride.

Effects of storage time, choline, and Cu and Zn elements on stability of vitamins in VTM premixes
There were interactive effects among storage time, choline chloride and high concentrations of Cu and Zn on VK 3 , VB 1 , and VB 2 retentions (p<0.05) ( Table 4). Moreover, there were interactive effects between storage time and choline chloride on VA, VK 3 , VB 1 , and VB 2 retentions (p<0.05). There were    interactive effects between storage time and high concentra tions of Cu and Zn on VA, VD 3 , VK 3 , VB 1 , VB 2 , and VB 6 retentions (p<0.01). As well, there were interactive effects between choline chloride and high concentrations of Cu and Zn on VK 3 retention (p<0.01). The main effect of storage time on all tested vitamins was significant (p<0.01), the main effect of choline was significant for VA, VK 3 , VB 1 , and VB 2 reten tions (p<0.01) (Figures 2, 3, 6, and 7), and the main effect of high concentrations of Cu and Zn on VA, VD 3 , VK 3 , VB 1 , VB 2 , VB 6 retentions was significant (p<0.01) (Figures 1, 2, 3, 5, 6, and 7). Extended storage time had negative (p<0.01) effects on vitamin stability in VTM premix. When VTM premixes were stored, VE, VB 3 , and VB 5 activities decreased (p<0.05) (Figures 4, 8, and 9) as the duration of storage increased regardless of the choline chloride or high concentrations of Cu and Zn. Also, stability of VA, VK 3 , VB 1 , and VB 2 was decreased in VTM premix containing choline and high con centrations of Cu and Zn. However, the activity of VB 6 was rapidly decreased in VTM premix containing high concen trations of Cu and Zn ( Figure 5).

Kinetic properties of vitamin retention
The R 2 , RMSEP, and the prediction equations are presented ( Table 5). Analysis of kinetic data suggested that the degra dation follows a firstorder model. Degradation of VA, VD 3 , VK 3 , VB 1 , and VB 6 in VTM premix 1 could be suitably modeled based on high R 2 value (i.e. R 2 >0.90) of prediction equations. For premix containing chloride choline, equations for predicting retention of VA, VD 3 , VE, VK 3 , VB 3 , and VB 6 in VTM premix 2 were suitably modeled based on high R 2 value (i.e. R 2 >0.90), and those had high R 2 values compared

Extended storage time affected the stability of vitamins
Determination of vitamin stability before and after storing is necessary to assess the final amount of actual vitamin that will reach the enduser and to calculate what amount should be added to any feed matrix. Storing vitamins for long peri ods has been considered to negatively affect vitamin activity in vitamin or VTM premixes. However, the results of our study indicate that longterm storage of vitamin premixes had little influence upon VA, VE, and VB 3 concentrations. The results from our study agreed with previous studies on vitamin stability. Coelho [8] reported that the average loss per month of VA, VE, and VB 3 after storage was 2.9%, 2.7%, and 2.7%, respectively. Because most manufactures of VA producers stabilize VA using the method of sealing within a physical matrix, generally arabic gum or gelatin [2,18]. In addition, in the production of commerciallyavailable VA and VE, their hydroxy group is protected by the formation of an ester, as in αtocopherol acetate. The obtained αtoco pherol acetate is resistant to oxygen, since it lacks double bonds [3,9]. In the present study, the retention of niacin was more than 90% after 1 year of storage, which is consistent with Zhuge and Klopfenstein [19], who reported that the reten tion rate of VB 3 during storage was 91% to 96% during 27 weeks storage. This was not surprising to us because VB 3 has been reported to be the most stable among the B vitamins when added to feed or premixes [19] owing to its a stable molecular structure, which reduces its oxidation during stor age. Coelho [8] reported that the loss of commercial fatsoluble vitamins after one month of storage was less than 10%; after six months of storage, its loss rate was 10% to 60%. Shurson et al [20] reported that vitamin activity in vitamin and VTM premixes decreased with prolonged storage time, but stability of VE, VB 2 , VB 3 , VB 5 , and VB 6 are higher than that of other vitamins, which is in line with our results.

Addition of choline chloride affected vitamin stability
Choline chloride has been reported to significantly affect vi tamin activity [810]. Choline is considered a stress agent that affects vitamins that dissolve easily in water because it is hygroscopic, and can attract moisture to vitamin or VTM premixes [3]. The concentration of choline chloride in feed is usually higher than the microingredient level, and prob lems related to both physical and chemical properties can be expected when choline is added to vitamin or VTM pre mixes [810]. After six months of storage, the loss of vitamin in a vitamin premix without choline chloride was 1% to 5% [8]; with choline chloride in the premix, the vitamin loss up to 32% after six months of storage [8]. In addition, the negative effects of choline chloride on vitamins in a VTM premix were more significant. After six months of storage, the loss of vitamin in a VTM premix without choline chlo ride was 12% to 30% [8]. However, in a VTM premix with choline chloride, the loss after six months was 23% to 52% [8]. Vitamin K is known for its contribution to the blood clotting or coagulation process. The VK 3 was more stable in vitamin premix without choline than in the vitamin premix with choline during oneyear storage, which was consistent with TavčarKalcher and Vengušt [10]. Results from the present study suggest that loss of VK 3 activity was approxi mately 60% in two vitamin premixes. Our results are similar to the average monthly losses reported by Coelho [8]. In the current study, choline chloride is a significant factor af fecting the loss of VK 3 activity. Menadione (VK 3 ) is the form of vitamin K that is used in animal nutrition. It is not uti lized in pure form in premix plants but was formulated with sodium bisulfite and derivatives. The most common mena dione compound used in the industry is the watersoluble salt, menadione sodium bisulfite. It was reported that VK 3 was very sensitive to moisture and trace minerals, and choline chloride was particularly destructive to VK 3 [10]. Further more, supplemented choline chloride in vitamin or VTM premixes increased leaching of VK 3 and prolonged oxida tionreduction reactions [9,10]. The inclusion of choline chloride in a VTM premix contributes to VA, VK 3 , VB 1 , and VB 2 instability during storage. Stability data published by BASF 1994, cited by Whitehead [21], showed VA, VK 3 , VB 1 , and VB 2 loss of 15%, 36%, 30%, and 5% after one month and 42%, 100%, 73%, and 44% after six months of storage in VTM premixes containing choline chloride. Besides, we observed that loss of VA, VK 3 , VB 1 , and VB 2 was lower than that reported by Whitehead [21]. The reason may be that the vitamin manufacturing industry has developed prod ucts with improved stability. In the present study, we used thiamine mononitrate as VB 1 source, it is used more often in feed because of its higher stability compared to thiamine hydrochloride [3,8]. In addition, the commercial form of VA and VB 2 is spraydried processing, which usually pro vides improved stability during storage and transportation.

Excessive Cu and Zn elements in VTM premix affected vitamin stability
The VTM premixes are the most common dietary supple ments. In commercial conditions, feeding piglets with high concentrations of Zn and Cu stimulates their average daily gain, decreases the feed conversion ratio, improves the di gestibility of dietary nutrients and growth performance, and decreases the incidence of diarrhea [6,7]. However, minerals in premixes are usually in an inorganic form: sulfates, chlo rides, oxides, etc. Different metal compounds have different capability of catalytic oxidation reaction [8]. In the present study, high levels of CuSO 4 (more than 20,000 mg/kg of Cu in premix to promote growth) and ZnO (more than 225,000 mg/kg of Zn in premix to decrease the incidence of diarrhea) in VTM premixes resulted in the degradation of vitamins. Vitamin stability is reduced in the presence of certain trace minerals [8,9,20]. In our study, blending vitamins with trace minerals to form VTM premixes increased the loss of vita min activity during prolonged storage periods. These trace minerals in premix can catalyze the generation of free radi cals, thereby oxidizing antioxidants during storage. Certain metalcatalyzed destruction of vitamins in the feed matrix has been reviewed previously to a limited extent [22]. Trace minerals vary in their redox potential: Cu, Fe, and Zn are the most reactive, and Se, I, and Mg are less reactive minerals [8,22]. Reactive trace minerals reduce vitamin activity by oxidizing the vitamins. First, the metalliclike nature of trace minerals reduces the crystals of vitamins to smaller particles by eroding their protective coating. The smaller particles provide increased surface areas of vitamins for reactions be tween vitamin particles and trace mineral particles. Dove and Ewan [23] reported that a high concentration of Cu (250 mg/kg feed) or Zn (1,000 mg/kg feed) increased vitamin loss. Redoxactive transition metals, such as Cu, can serve as catalysts for the oxidation of organic compounds. Lu et al [24] reported that a high concentration of Cu sulfate promoted the undesirable oxidation of VE in feeds. Intrigu ingly, we did not find significant effects on VE content in the four VTM premixes during longterm storage. There are two significant factors that might contribute to achieve this posi tive characteristic. First, supplementation of VE are generally given in the form of allracαtocopheryl acetate in which the reactive hydroxyl group of αtocopherol is esterified; ren dering the molecule more stable than the free phenol form, and second, production of VE provides a physical barrier to reduce surface contact with prooxidant agents such as Zn or Cu. On the other hand, we observed longterm storage of VTM premix with high concentrations of Cu and Zn had no effect on VB 3 and VB 5 concentrations. The results from our study confirm previous studies on the stability of these vita mins. Shurson et al [20] reported recovery of VB 3 after 120 days of storage in a vitamin stock was 96.68%, 86.04% in vi tamin premix, and 87.04% in VTM premix. Zhuge and Klopfenstein [19] also reported that VB 3 was considerably more stable than other vitamins; at the end of 27 weeks stor age, VB 3 in premixes with or without mineral retained 91% and 96%, respectively. The VB 3 is probably the most stable of the watersoluble vitamins when added to feed or premixes, being little affected by heat, oxygen, moisture, or light [3,11]. However, there are no reports on the mechanism of resis tance to degradation or subsequent degradation products. The VB 5 , pantothenic acid, is a constituent of coenzyme A, which both act as carriers of acyl groups and activators of carbonyl groups in many metabolic processes [2,3]. Pure VB 5 is a viscous, hygroscopic, and chemicallyunstable oil. In premixes, this vitamin is commonly added as calcium pantothenate, a soluble and stable solid. The calcium salt is preferred to the sodium salt, as solid forms of the sodium salt are much more hygroscopic. Similar to niacin, there were no significant influences of choline and high concentrations of Cu and Zn on pantothenic acid retention in VTM premixes. But storage time was a significant factor affecting the loss of VB 5 under ambient temperature and relative humidity [3]. According to the previous results [20], there was no significant difference in the stability of VB 5 after 120 days of storage at vitamin stock, vitamin premix and vitamin inorganic trace minerals premix. A similar result was reported by Coelho [8]. Furthermore, it was reported that pantothenic acid was relatively stable to heat, oxygen, and light [8]. The stability of pantothenic acid is due to the presence of the carboxylic acid group to form two hydrogen bonds between a pair of molecules [25]. Furthermore, the amide group and two methyl groups in the aliphatic chain of pantothenic acid contribute to its stability.
In the current study, the supplementation of high concen trations of Cu and Zn significantly reduced the concentrations of VA, VD 3 , VK 3 , VB 1 , VB 2 , and VB 6 in VTM premixes dur ing storage. The reason can be explained that the presence of Zn and Cu in premix can speed up vitamin degradation [3,8,9], these minerals can catalyze the generation of free radicals which can oxidize vitamins in VTM premixes. Also, the re sults from our study confirm previous studies on vitamin stability in VTM premix. Shurson et al [20] reported that the stability of VA, VK 3 , VB 1 , and VB 6 in premixes was influ enced by the presence of trace minerals. These results were in line with previous study. Yang et al [9] reported that sta bility of VA, VB 1 , and VB 6 was affected by trace minerals, and the premixes containing high levels of Cu and Zn was more susceptible to oxidative reaction of vitamins. Factors that reduce VA activity are atmospheric oxygen, light, heat and other oxidizing agents [3]. Manan et al [26] looked at the stability of VA in the presence of Cu and Zn; the results showed that mineral fortification reduced VA stability by 36%. Pinkaew et al [27] reported the stability of VA in the presence of ZnO; the results showed that mineral fortifica tion reduced the VA stability by 13.4%. The chemical structure of VA is an unsaturated monohydric alcohol with 20 carbon atoms, consisting of a cyclohexane ring linked to a polyun saturated chain that terminates in an alcohol group. The five conjugated double bonds in the configuration of VA are easy points of attack for oxygen. The oxidation of the alcohol end group of VA results in the formation of retinal or alltrans retinaldehyde, which can be further oxidized to alltrans retinoic acid. Besides, the structure of VB 1 can help to un derstand its instability during storage. The methylene bridge connecting the pyrimidine and thiazole moiety can easily be broken down by oxidizing ingredients [25]. In addition, the VB 6 comprises a group of three related compounds: pyridoxine, pyridoxal, and pyridoxamine. Pyridoxine is commonly used for feed because pyridoxine is more stable than either pyridoxal or pyridoxamine [3,8], but pyridoxine was sensitive to light, particularly in neutral and alkaline solutions. The VB 6 can lose bioactivity, particularly when minerals in the form of carbonates or oxides are present [8,11]. In the current study, the supplementation of high concentrations of Cu and Zn significantly reduced the con centrations of VB 6 in VTM premixes during storage. The loss of VB 6 activity after three months of storage at room temperature was 24% [11], which was slightly higher than VB 6 loss in the present study. It may be that the degradation reaction of VB 6 was enhanced by metal ions in the previous study. Loss of VB 6 was lower when stored as vitamin pre mixes compared to VTM premixes, maybe the reason was that VTM premix contained more trace mineral. In VTM premixes, VB 6 can lose bioactivity, particularly when min erals in the form of carbonates or oxides are present [8,11]. We used pyridoxine hydrochloride in the present trial, which is a commercially available form. And pyridoxine hydro chloride is the main supplement used in feed, because it has good handling properties and stability. In addition, Coelho [8] reported the loss of VB 6 after six months of storage in a vitamin premix was 17%, and 32% in a VTM premix. Al though the retention rate of VB 6 in Coelho's study [8] was completely inconsistent with our results, our data also show that the stability of VB 6 is reduced in the premix contain ing inorganic trace minerals.
There are very limited stability data available for VD 3 and VB 2 in VTM premixes. The supplementation of high con centrations of Cu and Zn decreased the stability of VD 3 and VB 2 in VTM premixes in the present study. The VD 3 is a fun damentally unstable compound containing double bounds that can be altered by different stresses and prone to degrada tion due to oxidation [3,28]. The stability of VD to oxidation and its instability to trace minerals were also reported by pre vious studies; Mahmoodani et al [28] demonstrated catalyzed isomerization of VD 3 is liable via autoxidation to form a va riety of oxidation products. Further, Zhuge and Klopfenstein [19] reported that VB 2 was destroyed faster in the premix con taining minerals and 54% of VB 2 had been destroyed after 27 weeks of storage. In the last case, the loss of VB 2 after six months of storage was 44% cited by Whitehead [21]. The most wellcharacterized aspect of riboflavin reactivity is its sensitivity to light in an aerobic environment which may be one of the reasons for low VB 2 retention of previous studies. The rate of degradation can be promoted by complexation with some metal cations (e.g., Cu 2+ and Zn 2+ ) at the isoallox azine moiety [29]. Vitamin A, VD 3 , VK 3 , VB 1 , VB 2 , and VB 6 are relatively stable in vitamin premix, but degradation of vi tamin was potentiated by the chemical reaction caused by the presence of Cu and Zn elements.

Prediction equations for vitamin retention in premixes during storage
Prediction equations have been widely used to estimate val ues through regression analysis and can be a suitable proxy for conducting relevant experiments (i.e. loss in vitamin sta bility with time) and thus save time, reduce cost, and improve precision in diet formulation. To establish prediction equations of vitamin content in premix from storage time, regression analysis programming was used. The degradation of most of the vitamins followed firstorder kinetics that can be devel oped [9,30]. The degradation rate accelerated progressively with storage time in vitamin and VTM premixes. What is more, VA, VK 3 , VB 1 , VB 2 , and VB 6 degraded rapidly in VTM premix containing choline and high concentrations of Cu and Zn. When comparing the relative retention of vitamins, the data showed a significant deviation in different VTM premix. The VTM premix 4 has the most prominent sensi tivity, followed by VTM premix 3 and 2. These observations are in line with previous report [9], showing poor vitamin retention in VTM premix containing choline and trace min erals. This differing behavior regarding vitamin degradation can be attributed to difference premix formulation and the presence of more metal ions, such as Cu 2+ and Zn 2+ that act as catalysts. The degradation of vitamins does not always in crease linearly during storage, and the majority of predicted equations had good fit with the experimental data. This study is consistent with Giannakourou et al [30] who also found vitamin loss due to storage time was well predicted by expo nential models. For prediction of vitamin loss during storage with nonlinear kinetic models, this method has been proved effective to extract the kinetics parameters for vitamin deg radation [31]. To the best of our knowledge, the degradation kinetics of vitamin in VTM premixes had not been studied before. The purpose of present study was to establish kinetic equations for vitamin retention in different premixes during storage. Validated kinetic models of vitamin for VTM premix, can be used for evaluation, control and proper management of the premix, with the application of suitable time indica tors. Further, these results can serve for vitamin and VTM premixes production in order to improve the knowledge of vitamin its stability.

CONCLUSION
The present study has provided information on the kinetics of vitamin degradation in different premixes during storage. The degradation of vitamins in all the samples under all storage conditions followed the firstorder kinetics. Stability of VA, VK 3 , VB 1 , VB 2 , and VB 6 was higher in VTM premixes containing no choline or high concentrations of Cu and Zn. The high concentration of trace minerals in the VTM premix can negatively affect VD 3 stability. Our study also suggested that considering the potential losses of vitamins in formula tion, the time between the manufacturing and use of the vitamin premixes should be minimized, and vitamins and trace mineral premixes should be stored separately. This work could be used as a guideline for the fortification of vita min and VTM premixes.