Temperature-dependent profiles and kinetic analysis of oxidation of linoleic acid and glyceryl trilinoleate

Abstract

The square root autocatalytic equation used to describe the initial process of lipid oxidation was investigated from the viewpoint of the kinetic theory of radical polymerization. The oxidation processes of linoleic acid were investigated from 5 °C to 40 °C, and the oxidation rate constants of the equation were estimated. The Arrhenius plot of the oxidation rate constants of linoleic acid was compared with that of glyceryl trilinoleate, and these were parallel within the investigated concentration and temperature ranges. It showed that the rate constant of oxidation of linoleic acid was faster than that of glyceryl trilinoleate and suggested that the difference was mainly ascribed to the frequency factor.

Introduction

A characteristic of lipid oxidation is the complex and various oxidation products produced. Oxidation of purified single substrates, such as linoleic acid or its triacylglycerol, produces several hydroperoxides having a hydroperoxyl group and double bonds at various positions. These are further transformed into more complex secondary oxidation products, some of which are evaporated as gases or sedimented as solids.

These oxidation processes are sensitive to environmental conditions such as temperature and composition (Miyakawa, 1965), and the conditions of lipid oxidation affect the ratio and types of the products (Pratt et al., 2011). The existence of many methods for evaluating the oxidation process indicates its complexity and the variety of viewpoints used to estimate the quality of oils. The sensitivity of the oxidation process results in different profiles of lipid oxidation in vivo (Kaikkonen et al., 2004; Niki, 2021), in emulsified solutions (Miyashita et al., 1993), and in nanoparticles (Imai et al., 2008) compared with the bulk solution.

The ambiguity originating from these complexities has been partially unraveled through the innovation of analytical methods, especially liquid and gas chromatography (LC and GC) in combination with mass spectrometry (Chan et al., 1975). These methods identify various chemical compounds separately and sensitively by the improved separation principles, computing power, and sensitivity of the detection systems and reveal the complexities of the oxidation substances by their chemical structures (Frankel, 1983, 1984; Kato et al., 2018, 2022; Sakaino et al., 2022). These developments in analytical methods enabled prompt characterization of the stereo structures of the oxidation substances (Yoshinaga et al., 2014), and differences in the bioactivities of the stereo structures improved the appropriate recognition of the oxidative products, such as the bioreactivity of trans-fatty acids.

In this study, we investigated the oxidation process of linoleic acid at various temperatures from 5 °C to 40 °C in the dark during the initial period of oxidation using the quantitative evaluation method reported previously (Shima, 2021). The results were compared with the oxidation of glyceryl trilinoleate previously reported by Shima and Sakashita (2016). The detection method for lipid oxidation used in the previous report (Shima, 2021) was UV absorption of the conjugated diene structure, which was created by the rearrangement of double bonds during the oxidation of linoleic acid to hydroperoxide. The evaluation period was limited to the initial period of the oxidation process, during which the primary oxidation products were produced (Yamamoto et al., 1982; Yazu et al., 1996). However, the stereo structures of the resulting hydroperoxides differ depending on photo oxidation or thermal oxidation (Frankel, 1984; Kato et al., 2018). Since some of the hydroperoxides generated from the photo oxidation of linoleic acid have two double bonds located at the non-conjugated position that have lower UV absorption than the conjugated double bond, the oxidation of lipids was investigated in the dark.

Theoretical

Analogical inference with radical polymerization　　Lipid oxidation has been known as a kind of radical chain reaction. The square root autocatalytic equation (Eq. 1) was employed to describe the initial oxidation process of linoleic acid in the previous report (Shima, 2021).

  

where C_COOH is the concentration of hydroperoxide in the lipid, which is regarded as the concentration of the functional group of the conjugated diene structure, since only the early stage of lipid autoxidation is observed; C_CH,0 is the concentration of hydrocarbon at the bis-allylic position of the unoxidized lipid, k′ is the rate constant, and t is time. The integral equation of Eq. 1 is also available (Shima, 2021).

On the other hand, the radical reaction has been investigated in polymer science as radical polymerization. According to the reaction kinetics of radical polymerization (Flory, 1953), the rate of polymerization, R_p expressed as the consumption rate of monomer, is described as follows:

  

where [M] is the concentration of monomer, [P ·] is the total concentration of propagating radical substances, k_p is the rate constant of the polymerization, k_d is the rate constant of the decomposition of initiator, k_t is the rate constant of the termination reaction including the coupling reaction and the disproportionation reaction, [I₂] is the concentration of the initiator, and f is the initiator efficiency, which represents the efficiency of the initiator by multiplying its concentration.

In a typical radical polymerization, a polymer molecule is a radical that grows by the successive addition of non-radical monomers. Polymer growth is inhibited by some reactions, including chain transfer reaction. This reaction is known as the transfer of a radical from radical A to a non-radical B, resulting in the non-radical A and radical B. If A is a propagating polymer and B is a monomer, the elongation of polymer A is stopped, and the radical monomer B becomes the seed of a novel polymer. If this chain-transfer reaction is the only reaction in the system, the radical reaction proceeds, however, no polymer is generated. The early period of lipid oxidation appears to be a radical reaction in which the chain transfer reaction mainly occurs. In this case, polymers of the lipid molecules are not generated, and the radical is transferred to the unoxidized fatty acid and reacts with oxygen to produce hydroperoxide, which accumulates in the system. As lipid oxidation proceeds, secondary oxidation products are generated, and the polymerization reaction may be increased instead of the chain transfer reaction.

In Eq. 1, which describes the oxidation process, the square root of the hydroperoxide concentration was included instead of the square root of the initiator concentration. This could be explained by the fact that hydroperoxide might have supplied the radical instead of the initiator. The steady-state approximation is applied to the derivation of Eq. 2, which is hypothesized based on the equilibrium state.

  

where R_i is the initiation reaction rate and, R_t is the termination reaction rate. After the system immediately reached an equilibrium state, the concentration of the radical compounds was in equilibrium with the concentration of the initiator. Therefore, the concentration of the radical compound increases with the concentration of the initiator.

  

Frankel (1984) explained that the lipid radical is in equilibrium with the lipid hydroperoxide oxidized from unsaturated fatty acids, referring to the exchange of oxygen of the hydroperoxide for atmospheric oxygen using isotopes, and changes in the steric isomers generated by the oxidation of lipids (Chan et al., 1979). If the equilibrium between the radical and the hydroperoxide is established in the lipid oxidation process by a steady-state approximation, the concentration of the radical would increase with the concentration of the lipid hydroperoxide, resulting in the acceleration of oxidation, which has been experimentally observed during the initial lipid oxidation process.

Walling (1957) discussed this radical chain reaction from the perspective of reaction kinetic analysis, and the effect of the initiation by decomposed hydroperoxide was verified by kinetic analysis of the experimental results of oxygen uptake in several oxidation experiments of olefinic systems. These results suggest that the acceleration of the reaction during the early stages of autoxidation could be due to hydroperoxide, which decomposes and serves as an initiator of novel chains (Cheves et al., 1957). The previous discussion by Frankel (1984) originated from stereochemical changes in oxidized substrates; therefore, these discussions seemed to elucidate an identical phenomenon from different standpoints.

This hypothesis indicates that the kinetic analysis of the autoxidation of lipid would resemble the kinetic analysis established in radical polymerization. The radical polymerization is affected by various characteristics of the reaction system, such as the steric hinderance, pH, and stereoelectronic effects. Lipid oxidation is also sensitive to these characteristics of the system (Porter, 2013). Hence, further experimental and theoretical investigations are required to reveal the details of lipid oxidation.

Materials and Methods

Materials　　Linoleic acid was obtained from Tokyo Chemical Industry (Tokyo, Japan) with 99.3 % purity (GC) according to the supplier’s information. Glyceryl trilinoleate was obtained from Sigma-Aldrich (St. Louis, MO, USA) with 98 % purity (TLC and GC) according to the supplier’s information. n-Hexane was obtained from Nacalai Tesque (Kyoto, Japan), and was specially prepared reagent grade for HPLC.

Time course of the concentration of the conjugated diene structure　　Linoleic acid or glyceryl trilinoleate (approximately 10 mg) was spotted on the bottom of each test tube (18 mm outer diameter and 165 mm length) and was weighed precisely using an analytical electronic balance. The test tubes were then covered with aluminum foil and stored in an aluminum block in a block heater (DTU-1C, TAITEC, Saitama, Japan) maintained at 20, 30, or 40 °C. Otherwise, the test tubes were stored at 5 °C in the aluminum block located in a pharmaceutical refrigerator with a freezer (MPR-414F, Sanyo Electric, Osaka, Japan). The test tube containing these lipids at time 0 h was not stored in the aluminum block and was directly provided as a sample for analysis. After the first sample at 0 h, the test tube was removed at appropriate intervals, and the partially oxidized lipid was diluted with n-hexane to an appropriate concentration and then poured into a quartz cell (1 cm light path length). The absorbance at 234 nm was measured using a UV spectrophotometer (UVmini-1240, Shimadzu, Kyoto, Japan), with n-hexane as a reference solution at 30 °C. Each data point in the figures represents a single run.

Densities of linoleic acid and glyceryl trilinoleate were obtained from Shima (2021) and Shima and Sakashita (2016), respectively. These densities were used to calculate the concentrations of the conjugated diene structures in these lipids.

Estimation of parameters　　The procedures followed were almost the same as previously reported (Shima, 2021). Briefly, Eq. 1 contains three parameters to be determined: k′, t_v, and C_COOH,v (Shima, 2021). t_v is the time of the imaginary origin at which lipids were not oxidized and C_COOH,V is a value represented by the concentration calculated from the absorbance at 234 nm, which originates from functional groups other than the conjugated diene (Shima, 2021). These parameters were estimated by minimizing the sum of adaptability, which is the absolute value of the relative error between the theoretical C_{234 nm} value, which is the sum of C_COOH and C_COOH,V, and the experimental value for each experimental data point in the time course using the direct search method (Sannomiya, 1983) with some modifications. These procedures were processed using Microsoft Excel^® 2016 and Microsoft Visual C++^® 2019 (Microsoft, Redmond, WA, USA).

Results and Discussion

Estimation of oxidation rate constants　　Three parameters (k′, t_V, and C_COOH,v) for the oxidation of linoleic acid at various temperatures were estimated using Eq. 1. Fig. 1 shows t_V, C_COOH,v, and k′ for the oxidation of linoleic acid and glyceryl trilinoleate. The parameters of glyceryl trilinoleate were estimated employing the experimental data published previously (Shima and Sakashita, 2016), except TL 5 °C in Fig. 1 that was obtained in this research. Because the initial concentration of hydroperoxide was evaluated by t_V and C_COOH,v, k′ was theoretically independent from the initial oxidation state. The lipids used in this research were not refined after being obtained and were slightly oxidized during the storage period. Therefore, t_V usually became a negative value, and the length of t_V was determined by the temperature of the lipid oxidation experiment, because the lengths were virtually calculated as if the oxidation occurred backward until the lipid was not oxidized. On the other hand, C_COOH,v is theoretically zero or a positive value and depends on the batch of lipids used for the experiments. For example, C_COOH,v of the experiments in this research (i.e., LA 5 °C to LA 30 °C) mainly resembled about 0.01 mol/L.

Fig. 1

Estimated t_v (A), C_COOH,v (B), and k′ (C) of the oxidation processes of linoleic acid (LA) and glyceryl trilinoleate (TL), which were experimented or referred in this research. (a) and (b) mean the references to Shima (2021) and Shima and Sakashita (2016), respectively.

t_V and C_COOH,v of TL 5 °C (b) in Fig. 1A and 1B, respectively, show a different tendency from those of the other temperatures. One reason for this phenomenon might be that t_V was large compared to the experimental period of this sample (t = 0−160 h), partially because of the initial oxidation condition of the lipid. Since t_V was estimated from a relatively short experimental period, the fluctuation of the experimental results might have affected the C_COOH,v. Therefore, we measured again the oxidation of glyceryl trilinoleate at 5 °C and obtain proper values (TL 5 °C in Figs. 1A and 1B), and the results of the newer experiment were employed in the Arrhenius plot discussed in the later section.

Fig. 1C shows k′ of these experiments. Temperature dependencies of k′ of linoleic acid and glyceryl trilinoleate were specified. C_CH,0 values were calculated from the densities of linoleic acid (Shima, 2021) and the specific gravities of glyceryl trilinoleate (Shima and Sakashita, 2016), respectively.

Using these estimated parameters, theoretical curves were drawn as solid lines in Figs. 2A–2B, and the experimental results are shown as symbols. The vertical axes of these figures are significantly different because of the difference in the concentration of the over all absorbance, C_{234 nm}.

Fig. 2

Oxidation time courses of linoleic acid at 5–40 °C.

Oxidation process of linoleic acid at 5–40 °C　　Oxidation time courses of linoleic acid at 5–40 °C are shown in Figs. 2A–2B, and the theoretical curves represent the experimental values. According to Prett et al. (2011), stereochemical fidelity was less and incorporation of atmospheric oxygen was more when the temperature was raised to 40 °C, which is about the oxidation process of oleate hydroperoxide. Several experimental conditions in their report differed from this research, however, their results suggest that a perturbing effect of the heat seemed obvious at approximately this temperature. The hydroperoxide produced in our experiments would also not exist permanently at 40 °C. It would change to secondary oxidation products and disappear if stored at the same temperature for an extended period. For example, Chan et al. (1979) reported that the linoleate hydroperoxides generated at 40 °C diminished by half after 160 h.

Arrhenius　plot Fig. 3 shows the Arrhenius plot of the oxidation rate constant of linoleic acid at 5–40 °C and that of glyceryl trilinoleate at 5–50 °C. These results suggest that the same Arrhenius activation energy can explain the temperature dependence of linoleic acid oxidation until 40 °C. The experimental result at 5 °C of this research was selected from two experimental results at about 5 °C to obtain the Arrhenius plot because of the validity of the estimated values of t_v and C_COOH,v. The two approximation lines in Fig. 3 seemed almost parallel, and the upper line represents the oxidation of linoleic acid having Arrhenius activation energy E_A = 67.6 kJ/mol and frequency factor A = 6.11 × 10⁹ L^0.5/(mol^0.5 h). The lower line represents the oxidation of glyceryl trilinoleate having E_A = 75.2 kJ/mol and A = 5.89 × 10¹⁰ L^0.5/(mol^0.5 h). Therefore, the oxidation rate constant of linoleic acid was higher than that of glyceryl trilinoleate at the same temperature. The difference between the two compounds was the frequency factor within the examined temperature range. The slight difference of E_A between them changes the order of A of the two lines. However, the practically important range shown in Fig. 3 is currently the focus. As the molecular mass of glyceryl trilinoleate is approximately three times larger than that of linoleic acid, and covalent bonds constrain its linoleoyl groups to the glycerol group, these differences between linoleic acid and glyceryl trilinoleate are suggested to have affected the oxidation rate constants.

Fig. 3

Arrhenius plots of linoleic acid (○) and glyceryl trilinoleate (□). ● represents the experimental results for linoleic acid (Shima, 2021). ■ represents the experimental results for glyceryl trilinoleate in this research.

Details of the oxidation time courses at 5, 30, and 40 °C were examined, including several independently obtained experimental results. First, oxidations of linoleic acid and glyceryl trilinoleate at 5 °C are shown in Fig. 4. One of the time courses of linoleic acid was obtained by Shima (2021) independently of the other one. The time-course trends clearly show that the oxidation rates of the two linoleic acids are faster than those of glyceryl trilinoleate. The oxidation processes of the two fatty acids seemed different, but the oxidation rate constants were similar (Fig. 1C). As the square root autocatalytic equation (Eq. 1) was obtained by the kinetic analysis of the oxidation of partially oxidized linoleic acids (Shima, 2021), the difference of the two time courses of the oxidation of linoleic acid was analyzed as the difference of the initial concentration of oxidized products represented by the absolute value of t_v (Fig. 1A), and then the oxidation rate constants seemed to be not primarily affected by the initial oxidation level of the sample oils. The oxidation processes of glyceryl trilinoleate at 5 °C in Fig. 4 are observed to resemble except the initial oxidation level, but the estimated t_v and C_COOH,v were obviously different, which was discussed previously in the Estimation of oxidation rate constants section.

Fig. 4

Oxidation time courses of linoleic acid and glyceryl trilinoleate at 5 °C.. Symbols □ and ■ represent glyceryl trilinoleate obtained in this research and from Shima and Sakashita (2016), respectively. Symbols ○ and ● represent linoleic acid obtained in this research and from reference Shima (2021), respectively. ○ is the same result in Fig. 2A.

Oxidation of glyceryl trilinoleate at 30 °C, which was cited from our previous results (Shima and Sakashita, 2016), was compared with that of linoleic acid at the same temperature (Fig. 5), and the inset figure shows the period mainly focused on the oxidation process of linoleic acid. An intuitive comparison indicated that the two oxidation processes were complex because of the difference in their measurement periods: however, the rate constants of linoleic acid were shown to be larger than those of glyceryl trilinoleate (Fig. 1C). The oxidation time courses of glyceryl trilinoleate and linoleic acid at 40 °C are shown in Fig. 6. The rate constants are also shown in Fig. 1C. These results also indicate that the oxidation rate of linoleic acid was higher than that of glyceryl trilinoleate.

Fig. 5

Oxidation time courses of linoleic acid and glyceryl trilinoleate at 30 °C. Insert graph focuses on the initial 10 h. Symbols □ and ○ represent the oxidation of glyceryl trilinoleate (Shima and Sakashita, 2016) and linoleic acid, respectively. ○ is the same results at 30 °C in Fig. 2B.

Fig. 6

Oxidation time courses of linoleic acid and glyceryl trilinoleate at 40 °C. Symbols □ and ○ represent the oxidation of glyceryl trilinoleate (Shima and Sakashita, 2016) and linoleic acid, respectively. ○ is the same results at 40 °C in Fig. 2B.

The values obtained in this research and other researches are shown in Fig. 3. Despite the origin of the experimental results, the Arrhenius plots of linoleic acid and glyceryl trilinoleate appeared adequately to describe them.

Steric effect on lipid oxidation　　The steric effect on lipid oxidation has been investigated for the oxidation of triacylglycerols composed of unsaturated fatty acids. Glycerol has three sequentially aligned hydroxyl groups, and researchers have focused on the difference in the oxidation of unsaturated fatty acids at the second position of the hydroxyl group (sn-2) and compared it with that of the first and third hydroxyl groups (sn-1, 3). Oxidation of docosahexaenoic acid (DHA) at sn-2 is suppressed compared to that at sn-1(3) (Wijesundera et al., 2008). Wada and Koizumi (1983) investigated the effects of the position of unsaturated fatty acids esterified with glycerol on oxidation. They prepared two types of triacylglycerol mixtures consisting of unsaturated and saturated fatty acids: a mixture of monoacid triacylglycerols of unsaturated fatty acids and saturated fatty acids, and random inter-esterified triacylglycerols. They concluded that randomized triacylglycerols were more stable than those with the same quantities of a simple mixture of two types of monoacid triacylglycerols. They further investigated the effect of the esterified position of unsaturated fatty acids, and unsaturated fatty acids at sn-2 were more stable than those at sn-1 and sn-3. They also investigated the effect of the length of the saturated fatty acid accompanied by esterification of the unsaturated fatty acid on the same glycerol. They concluded that the chain length of the saturated fatty acid did not influence the oxidation of unsaturated fatty acids. Wijesundera et al. (2008) also investigated the effect of fatty acids on the oxidation of DHA and reported that oleic acid suppressed the oxidation of the accompanying DHA compared with palmitic acid. These results suggest that the bent structure of oleic acid at the C9 double bonds of cis arrangements affects the oxidation of DHA, however, the length of the saturated fatty acid has a negligible effect, and oxidation is affected by the molecular structure of the lipids. The reason for the difference in the oxidation rate constant between linoleic acid and glyceryl trilinoleate has not been elucidated; however, the effect of the stereo structure of triacylglycerol on the oxidation process suggests that the difference in molecular structure affects the oxidation process of linoleic acid and its triacylglycerol.

Conclusion

The theoretical similarity of the square root autocatalytic equation is discussed as the radical chain reaction derived from the radical polymerization process. The accelerated progress of the initial lipid oxidation was described by the radical concentration equilibrated with lipid hydroperoxide, which was generated as the primary oxidation product. Linoleic acid oxidation was examined from 5 °C to 40 °C. The Arrhenius plots of linoleic acid and glyceryl trilinoleate were almost parallel and showed that the rate constant for the oxidation of linoleic acid was faster than that of glyceryl trilinoleate at the same temperature; the difference between them seemed to be mainly described by the difference in the frequency factor.

Nomenclature

C_COOH

Concentration of hydroperoxide in the lipid

C_CH,O

Concentration of hydrocarbon at the bis-allylic position of the unoxidized lipid in the lipid

k′

Rate constant of lipid oxidation

t

Time

R_p

Rate of polymerization

[M]

Concentration of monomer

[P ·]

Total concentration of propagating radical substances

k_p

Rate constant of the polymerization

k_d

Rate constant of the decomposition of initiator

k_t

Rate constant of the termination reaction

[I₂]

Concentration of the initiator

f

Initiator efficiency

R_i

Initiation reaction rate

R_t

Termination reaction rate

t_v

Time of the imaginary origin at which lipids were not oxidized

C_COOH,v

A value represented by the concentration calculated from the absorbance at 234 nm, originating from functional groups other than the conjugated diene

C_{234 nm}

Sum of C_COOH and C_COOH,v

E_A

Arrhenius activation energy

A

Frequency factor

Conflict of interest　　There are no conflicts of interest to declare.

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