High Resolution NMR Spectroscopy as a Structural and Analytical Tool for Unsaturated Lipids in Solution

Mono- and polyunsaturated lipids are widely distributed in Nature, and are structurally and functionally a diverse class of molecules with a variety of physicochemical, biological, medicinal and nutritional properties. High resolution NMR spectroscopic techniques including 1H-, 13C- and 31P-NMR have been successfully employed as a structural and analytical tool for unsaturated lipids. The objective of this review article is to provide: (i) an overview of the critical 1H-, 13C- and 31P-NMR parameters for structural and analytical investigations; (ii) an overview of various 1D and 2D NMR techniques that have been used for resonance assignments; (iii) selected analytical and structural studies with emphasis in the identification of major and minor unsaturated fatty acids in complex lipid extracts without the need for the isolation of the individual components; (iv) selected investigations of oxidation products of lipids; (v) applications in the emerging field of lipidomics; (vi) studies of protein-lipid interactions at a molecular level; (vii) practical considerations and (viii) an overview of future developments in the field.


Introduction
Lipids are a broad and diverse group of naturally occurring biomolecules with numerous physicochemical and biological properties. They play diverse and important roles in nutrition and health [1][2][3][4]. Lipids have important functional roles as major constituents of cellular membranes (e.g., brain consists mainly of fats [4]), signaling molecules, and as energy source for metabolic processes. Lipids due to their hydrophobic chemical structures are incompatible with an aqueous medium, therefore, their circulation through the blood stream to reach peripheral tissues is achieved through the formation of macromolecular complexes with lipoproteins. Fatty acids (FAs) are the major lipid building blocks of complex lipids, such as glycerolipids, i.e., monoacylglycerols (MAGs), diacylglycerols (DAGs), and triacylglycerols (TAGs, Figure 1). These neutral lipids have a glycerol backbone with FA chains attached to the glycerol group, most commonly with an ester bond, but ether bonded FAs can be also found in minor amounts.
Lipids are widely distributed in plants and animals. In plants, they are found in seeds (e.g., sunflower, papeseed, cottonseed and soybean), fruits (e.g., olive, palm fruit and avocado), Table 2. Common ω-3 fatty acids found in Nature.

The Pleiotropic Role of Unsaturated Fatty Acids
Unsaturated fatty acids (UFAs) exert their physiological effects from specific locations in phospholipid pools in which they can be esterified. The movement of UFAs into phospholipid pools is catalyzed by fatty acid carrier proteins [30]. The acyl compositions of membranes and specific phospholipid pools are mediated by the specification of these enzymes. Two common functions of unsaturated fatty acids are protein-lipid interactions for enzyme targeting and messenger signaling [31]. A protein domain can recognize a membrane lipid and be targeted to a specific location in the cell for specific protein function. Lipids may also act as signaling molecules. For example, diacyglycerol (DAG) is a lipid second messenger that can modulate the function of protein kinase C (PKC) [32], while lysophosphatidic acid (PLA) is involved in the regulation of cell proliferation, migration and survival [33].
There is considerable evidence that the unsaturated fatty content of membranes can modify the structure and functionality of membrane enzymes [34]. Unsaturated fatty acids into membranes are confined, with few exceptions, in the sn-2 position of phospholipids ( Figure 2). The occurrence of unsaturated and saturated fatty acids in the same phospholipid molecule can have important implications in membrane structure and function. First, the two types of acyl chains cannot demix in the membrane. Second, high degree of cis unsaturation implies less ability for rotation around the double bonds and, thus, greatly influences membrane acyl packing. Third, the position of the cis    Conjugated linoleic acids (CLAs) have been extensively investigated using 1 H-NMR (Table 4) including the (cis-9, trans-12) 18:2 isomer, which is the dominant species in dairy products, and several other positional and geometric isomers [55,56] which may have different biological functions. Figure 5 illustrates that the 1 H-NMR spectrum of CLAs in the lipid fraction of milk exhibit highly diagnostic resonances due to the -CH= protons of the conjugated double bonds in the region of 6.35 to 5.50 ppm. Some of these resonances are clearly shifted to higher frequencies with respect to protons of isolated double bonds, thus, illustrating the increased delocalization of conjugated double bonds. The "inner" olefinic protons of C10 and C11 are deshielded with respect the olefinic protons of C9 and C12. Furthermore, in the mixed cis/trans isomers the signals of the cis bonds are deshielded with respect to those of the trans bonds. In the case of identical bond configuration, the signals of the two "inner" protons overlap as well as the two signals of the "outer" protons.  Conjugated linolenic acids (CLnAs) is a group of positional (8, 10, 12-18:3; 9, 11, 13-18:3; 10, 12, 14-18:3; etc.) and geometric (trans-trans-trans, cis-trans-trans, cis-trans-cis etc.) [57,58] isomers which occur in significant amounts in some seed oils such as tung oil, catalpa and cherry seed oil. NMR studies of CLnAs are limited to 13 C-NMR [57] and 1 H and 13 C-NMR [58] data of α-eleostearic acid: (9cis, 11-trans, 13-trans) 18:3, β-eleostearic acid: (9-trans, 11-trans, 13-trans) 18:3 and punicic acid: (9-cis, 11-trans, 13-cis) 18:3 (Table 5). Due to extensive overlap of the 1 H-NMR signals, homonuclear 1 H decoupling techniques were extensively used for the simplification of the 1 H-NMR spectra and calculation of the 3 J coupling constants. In the all-trans β-eleostearic acid, three multiplets at 6.10(2H) ppm, 6.04(2H) ppm, and 5.66(2H) ppm were found due to near magnetic equivalence of the protons Figure 6. Computer simulated 1 H-NMR signals for alkenyl and allylic protons in isolated cis and trans double bonds. Adopted, with permission, from [54]. Copyright 1975, North-Holland Publishing Company.

Protons of the Glycerol Moiety
The location of acyl chain esterification on the glycerol backbone was assigned as sn-1, sn-2 and sn-3 ( Figure 2). NMR spectroscopy can be used to provide information on the regiospecific distribution of fatty acids of triacylglycerols (TAGs) and phospholipids. 1,3-triglycerides (TAG), 1-and 2-monoacylglycerides (MAG) and 1,2-diacylglycerides (DAG) can be identified on the basis of the chemical shifts of the protons attached to glycerol carbons ( Table 6). The proton signal at 5.26 ppm (m, J 1a ,2 = 5.88 Hz) was assigned to H2 of the glycerol backbone of TAG. The H1 and H3 protons of the glycerol moiety in TAG appear at 4.15 and 4.30 ppm. The 2 -CH-OCO-and HO-CH 2 -CH resonances of sn-1/2,3 DAG, the 1 b-CH 2 -OCO-and 1 a-CH 2 -OCO-resonances of sn-1,2 DAG and the 1 b, 3 b-CH 2 -OCO-, 1 a, 3 a-CH 2 -OCO-and -CH 2 -OCO resonances of sn-1,3 DAG have also been assigned in oils. The 3 a-CH 2 -OCO-resonance of 1-MAG appears at 3.59 ppm.  [59,60].   The bis-allylic protons, =HC-CH 2 -CH=, in polyenoic fatty acids and esters are in a characteristic region of 2.60-2.85 ppm due to the effect of the magnetic anisotropy of the double bonds. The chemical shifts appear to be related to the number and the geometric configuration of the double bonds (Table 7). Thus, the bis-allylic protons of DHA, α-linolenic acid and linoleic acid appear at 2.85, 2.82 and 2.78 ppm, respectively. The bis-allylic protons of α-linolenic acid are more deshielded (δ = 2.82 ppm) than in linoleic acid (δ = 2.78 ppm) due to a larger number of double bonds in the former case. The cis-cis configuration results in a stronger deshielding effect with respect to cis-trans and trans-trans configuration. Table 7. 1 H-NMR features of some characteristic groups in polyenoic fatty acids and esters (in CC1 4 ). Reprinted, with permission, from [54]. Copyright 1975, North-Holland Publishing Company.

Group
δ-Value ical shifts appear to be related to the number and the geometric configuration of the double s (Table 7). Thus, the bis-allylic protons of DHA, α-linolenic acid and linoleic acid appear at 2.85, and 2.78 ppm, respectively. The bis-allylic protons of α-linolenic acid are more deshielded (δ = ppm) than in linoleic acid (δ = 2.78 ppm) due to a larger number of double bonds in the former The cis-cis configuration results in a stronger deshielding effect with respect to cis-trans and -trans configuration. The deshielding effect in polyyonic fatty acids and esters is stronger than that observed in enoic fatty acids and esters (Table 8). This may be attributed to the position of the allylic protons e deshielding region of the magnetic anisotropy of the triple bond. mical shifts appear to be related to the number and the geometric configuration of the double nds (Table 7). Thus, the bis-allylic protons of DHA, α-linolenic acid and linoleic acid appear at 2.85, 2 and 2.78 ppm, respectively. The bis-allylic protons of α-linolenic acid are more deshielded (δ = 2 ppm) than in linoleic acid (δ = 2.78 ppm) due to a larger number of double bonds in the former e. The cis-cis configuration results in a stronger deshielding effect with respect to cis-trans and ns-trans configuration. The deshielding effect in polyyonic fatty acids and esters is stronger than that observed in lyenoic fatty acids and esters (Table 8). This may be attributed to the position of the allylic protons the deshielding region of the magnetic anisotropy of the triple bond. emical shifts appear to be related to the number and the geometric configuration of the double nds (Table 7). Thus, the bis-allylic protons of DHA, α-linolenic acid and linoleic acid appear at 2.85, 82 and 2.78 ppm, respectively. The bis-allylic protons of α-linolenic acid are more deshielded (δ = 82 ppm) than in linoleic acid (δ = 2.78 ppm) due to a larger number of double bonds in the former se. The cis-cis configuration results in a stronger deshielding effect with respect to cis-trans and ans-trans configuration. The deshielding effect in polyyonic fatty acids and esters is stronger than that observed in lyenoic fatty acids and esters (Table 8). This may be attributed to the position of the allylic protons the deshielding region of the magnetic anisotropy of the triple bond. emical shifts appear to be related to the number and the geometric configuration of the double nds (Table 7). Thus, the bis-allylic protons of DHA, α-linolenic acid and linoleic acid appear at 2.85, 2 and 2.78 ppm, respectively. The bis-allylic protons of α-linolenic acid are more deshielded (δ = 2 ppm) than in linoleic acid (δ = 2.78 ppm) due to a larger number of double bonds in the former e. The cis-cis configuration results in a stronger deshielding effect with respect to cis-trans and ns-trans configuration. The deshielding effect in polyyonic fatty acids and esters is stronger than that observed in lyenoic fatty acids and esters (Table 8). This may be attributed to the position of the allylic protons the deshielding region of the magnetic anisotropy of the triple bond. mical shifts appear to be related to the number and the geometric configuration of the double nds (Table 7). Thus, the bis-allylic protons of DHA, α-linolenic acid and linoleic acid appear at 2.85, 2 and 2.78 ppm, respectively. The bis-allylic protons of α-linolenic acid are more deshielded (δ = 2 ppm) than in linoleic acid (δ = 2.78 ppm) due to a larger number of double bonds in the former e. The cis-cis configuration results in a stronger deshielding effect with respect to cis-trans and ns-trans configuration. The deshielding effect in polyyonic fatty acids and esters is stronger than that observed in lyenoic fatty acids and esters (Table 8). This may be attributed to the position of the allylic protons the deshielding region of the magnetic anisotropy of the triple bond. emical shifts appear to be related to the number and the geometric configuration of the double nds (Table 7). Thus, the bis-allylic protons of DHA, α-linolenic acid and linoleic acid appear at 2.85, 2 and 2.78 ppm, respectively. The bis-allylic protons of α-linolenic acid are more deshielded (δ = 2 ppm) than in linoleic acid (δ = 2.78 ppm) due to a larger number of double bonds in the former e. The cis-cis configuration results in a stronger deshielding effect with respect to cis-trans and ns-trans configuration. The deshielding effect in polyyonic fatty acids and esters is stronger than that observed in lyenoic fatty acids and esters (Table 8). This may be attributed to the position of the allylic protons the deshielding region of the magnetic anisotropy of the triple bond. The deshielding effect in polyyonic fatty acids and esters is stronger than that observed in polyenoic fatty acids and esters (Table 8). This may be attributed to the position of the allylic protons in the deshielding region of the magnetic anisotropy of the triple bond.

Group
δ-Value region of 2.60-2.85 ppm due to the effect of the magnetic anisotropy of the double bonds. The chemical shifts appear to be related to the number and the geometric configuration of the double bonds (Table 7). Thus, the bis-allylic protons of DHA, α-linolenic acid and linoleic acid appear at 2.85, 2.82 and 2.78 ppm, respectively. The bis-allylic protons of α-linolenic acid are more deshielded (δ = 2.82 ppm) than in linoleic acid (δ = 2.78 ppm) due to a larger number of double bonds in the former case. The cis-cis configuration results in a stronger deshielding effect with respect to cis-trans and trans-trans configuration. The deshielding effect in polyyonic fatty acids and esters is stronger than that observed in polyenoic fatty acids and esters (Table 8). This may be attributed to the position of the allylic protons in the deshielding region of the magnetic anisotropy of the triple bond. region of 2.60-2.85 ppm due to the effect of the magnetic anisotropy of the double bonds. The chemical shifts appear to be related to the number and the geometric configuration of the double bonds (Table 7). Thus, the bis-allylic protons of DHA, α-linolenic acid and linoleic acid appear at 2.85, 2.82 and 2.78 ppm, respectively. The bis-allylic protons of α-linolenic acid are more deshielded (δ = 2.82 ppm) than in linoleic acid (δ = 2.78 ppm) due to a larger number of double bonds in the former case. The cis-cis configuration results in a stronger deshielding effect with respect to cis-trans and trans-trans configuration. The deshielding effect in polyyonic fatty acids and esters is stronger than that observed in polyenoic fatty acids and esters (Table 8). This may be attributed to the position of the allylic protons in the deshielding region of the magnetic anisotropy of the triple bond. region of 2.60-2.85 ppm due to the effect of the magnetic anisotropy of the double bonds. The chemical shifts appear to be related to the number and the geometric configuration of the double bonds (Table 7). Thus, the bis-allylic protons of DHA, α-linolenic acid and linoleic acid appear at 2.85, 2.82 and 2.78 ppm, respectively. The bis-allylic protons of α-linolenic acid are more deshielded (δ = 2.82 ppm) than in linoleic acid (δ = 2.78 ppm) due to a larger number of double bonds in the former case. The cis-cis configuration results in a stronger deshielding effect with respect to cis-trans and trans-trans configuration. The deshielding effect in polyyonic fatty acids and esters is stronger than that observed in polyenoic fatty acids and esters (Table 8). This may be attributed to the position of the allylic protons in the deshielding region of the magnetic anisotropy of the triple bond. The bis-allylic protons, =HC-CH2-CH=, in polyenoic fatty acids and esters are in a characteristic region of 2.60-2.85 ppm due to the effect of the magnetic anisotropy of the double bonds. The chemical shifts appear to be related to the number and the geometric configuration of the double bonds (Table 7). Thus, the bis-allylic protons of DHA, α-linolenic acid and linoleic acid appear at 2.85, 2.82 and 2.78 ppm, respectively. The bis-allylic protons of α-linolenic acid are more deshielded (δ = 2.82 ppm) than in linoleic acid (δ = 2.78 ppm) due to a larger number of double bonds in the former case. The cis-cis configuration results in a stronger deshielding effect with respect to cis-trans and trans-trans configuration. The deshielding effect in polyyonic fatty acids and esters is stronger than that observed in polyenoic fatty acids and esters (Table 8). This may be attributed to the position of the allylic protons in the deshielding region of the magnetic anisotropy of the triple bond.  The bis-allylic protons, =HC-CH2-CH=, in polyenoic fatty acids and esters are in a characteristic region of 2.60-2.85 ppm due to the effect of the magnetic anisotropy of the double bonds. The chemical shifts appear to be related to the number and the geometric configuration of the double bonds (Table 7). Thus, the bis-allylic protons of DHA, α-linolenic acid and linoleic acid appear at 2.85, 2.82 and 2.78 ppm, respectively. The bis-allylic protons of α-linolenic acid are more deshielded (δ = 2.82 ppm) than in linoleic acid (δ = 2.78 ppm) due to a larger number of double bonds in the former case. The cis-cis configuration results in a stronger deshielding effect with respect to cis-trans and trans-trans configuration. The deshielding effect in polyyonic fatty acids and esters is stronger than that observed in polyenoic fatty acids and esters (Table 8). This may be attributed to the position of the allylic protons in the deshielding region of the magnetic anisotropy of the triple bond. The CH 2 -CH 2 -COOH protons of DHA result in a composite signal at 2.46 ppm due to the combined deshielding effect of the COOH group and the ω-3 double bond (Table 9). This chemical shift is highly diagnostic for the presence of DHA in mixture analysis especially in fish oils (Section 5.1). The -OOC-CH 2 -CH 2 -protons of all fatty acids appear at 2.33 ppm. The double bond configuration influences the chemical shift of the -CH 2 -CH=CH-protons of UFA. In particular, the methylene protons adjacent to a cis double bond is deshielded by~0.05 ppm with respect to that adjacent to a trans bond. The -CH 3 group of α-linolenic acid appears at 0.98 ppm (triplet, 3 J = 7.5 Hz), the -CH 3 group of butyric acid at 0.94 ppm ( 3 J = 7.4 Hz), and the -CH 3 terminal groups of the rest of the fatty acids in a narrow range of chemical shifts of 0.885 to 0.87 ppm (triplets, 3 J = 6.9 to 7.3 Hz). α-linolenic acid (18:3, ω-3) contains a double bond close to the terminal -CH 3 group that causes a shift to higher ppm values from 0.89 to 0.98 ppm. Figure 7 illustrates that ω-3 fatty acids can be clearly identified from the other lipids on the basis of the chemical shifts of the terminal methyl group. Interestingly, the apparently quartet at~0.88 ppm is due to superposition of three triplets which results in the identification of the ω-6 and ω-9 fatty acids from the saturated FA. This demonstrates the significant long range effect of the double bond on the chemical shifts of the terminal CH 3 groups. It should be emphasized, however, that sufficient separation of the triplets would require either the use of ultra-high magnetic fields or advanced 2D 1 H-13 C HSQC-TOCSY (Section 4.6) and band selective 1 H-13 C HMBC (Section 4.7) experiments. The CH2-CH2-COOH protons of DHA result in a composite signal at 2.46 ppm due to the combined deshielding effect of the COOH group and the ω-3 double bond (Table 9). This chemical shift is highly diagnostic for the presence of DHA in mixture analysis especially in fish oils (Section 5.1). The -OOC-CH2-CH2-protons of all fatty acids appear at 2.33 ppm. The double bond configuration influences the chemical shift of the -CH2-CH=CH-protons of UFA. In particular, the methylene protons adjacent to a cis double bond is deshielded by ~0.05 ppm with respect to that adjacent to a trans bond. The -CH3 group of α-linolenic acid appears at 0.98 ppm (triplet, 3 J = 7.5 Hz), the -CH3 group of butyric acid at 0.94 ppm ( 3 J = 7.4 Hz), and the -CH3 terminal groups of the rest of the fatty acids in a narrow range of chemical shifts of 0.885 to 0.87 ppm (triplets, 3 J = 6.9 to 7.3 Hz). α-linolenic acid (18:3, ω-3) contains a double bond close to the terminal -CH3 group that causes a shift to higher ppm values from 0.89 to 0.98 ppm.  Figure 7 illustrates that ω-3 fatty acids can be clearly identified from the other lipids on the basis of the chemical shifts of the terminal methyl group. Interestingly, the apparently quartet at

1 H-NMR Relaxation Times
In order to obtain quantitative NMR data and avoid differential saturation effects, the protons should be fully relaxed. This demands recycling time i.e., acquisition time + relaxation delay of at least 5 × T 1 , where T 1 is the longitudinal relaxation time of the slowest relaxing nuclei. The longitudinal relaxation times (T 1 ) of the 1 H nuclei of the acyl chains of triglycerides in oils were found to be sufficiently short, the longest being that of the terminal CH 3 group (1.51 s) (Table 10), and substantially shorter than those of the 13 C nuclei (see Section 3.2). This implies that very good S/N ratio and, thus, quantitative results can be obtained even for minor analytes within relatively short period of time.

13 C-NMR Spectroscopy
The 13 C nucleus with I = 1/2 has become a very useful analytical and structural tool in lipid research despite its low gyromagnetic ratio (6.726 × 10 7 rad T −1 s −1 ), its low natural abundance (1.108%) and the low receptivity with respect to that of 1 H (1.7 × 10 −4 ). This may be attributed to the fact that 13 C has a large chemical shift range (~200 ppm) with respect to that of 1 H (~10 ppm), the significant advances in NMR instrumentation, the use of versatile pulse sequences, polarization transfer experiments and sophisticated 2D 1 H-13 C NMR experiments. High resolution 13 C-NMR, therefore, has emerged as a versatile technique for the analysis of lipids, since the pioneering work of Shoolery [61], Gunstone [19,62] and Wollenberg [63], which allows the characterization of the isomeric distribution of omega-3 PUFA in lipid fractions. 13 C-NMR was demonstrated to be an excellent method in determining the distribution of triacylglycerols and the position of the fatty acids on the glycerol backbone and in obtaining quantitative information about the fatty acid composition of vegetable oils, vegetable seeds and other lipid extracts, as will be analyzed below.
The 13 C-NMR chemical shifts of lipids can be grouped in four regions: the carbonyl and carboxyl carbons in the region of 172-178 ppm, unsaturated carbons of 124-134 ppm, the glycerol backbone carbons of 60-72 ppm and aliphatic carbons of 10-35 ppm.

Carbonyl and Carboxyl Carbon Region
The carboxyl carbon atoms of the free fatty acids appear in a narrow but distinct region of 177.5 to 180 ppm. The resonances are shifted to high frequency with respect to ethyl esterified derivatives bỹ 4 ppm (Table 11 and Figure 8). This high frequency shift is sufficient for the quantification of free fatty acids with respect to esterified lipids. For accurate quantification results, however, caution should be exercised since the relaxation times of carboxyl and carbonyl carbon atoms (Table 12) are significantly longer than those of 1 H-NMR (Table 10). To obtain quantitative data, the relaxation problem can be resolved by adding a relaxation reagent, such as chromium acetonylacetonoate (Cr(acac) 3 ), or by recording proton decoupled NOE suppressed 13 C-NMR spectra with sufficiently long interpulse delay (~5 T 1 , where T 1 is the longest relaxation time of a lipid mixture).
The carboxyl carbon atoms of the free fatty acids appear in a narrow but distinct region of 177.5 to 180 ppm. The resonances are shifted to high frequency with respect to ethyl esterified derivatives by ~4 ppm (Table 11 and Figure 8). This high frequency shift is sufficient for the quantification of free fatty acids with respect to esterified lipids. For accurate quantification results, however, caution should be exercised since the relaxation times of carboxyl and carbonyl carbon atoms (Table 12) are significantly longer than those of 1 H-NMR (Table 10). To obtain quantitative data, the relaxation problem can be resolved by adding a relaxation reagent, such as chromium acetonylacetonoate (Cr(acac)3), or by recording proton decoupled NOE suppressed 13 C-NMR spectra with sufficiently long interpulse delay (~5 T1, where T1 is the longest relaxation time of a lipid mixture).  Table 11. 13 C-NMR peak assignments of the carboxyl and the ester carbonyl region of UFAs in CDCl3.

Compound
Carbon Functional Group δ (ppm) (9-cis, 11-trans)-CLA, (9-trans, 11-cis)-CLA,  The carbonyl carbons of long chain saturated and unsaturated acyl groups in sn-1,3 TAG appear at 172.8-172.7 ppm while those in sn-2 TAG at 172.41-172.38 ppm. Saturated and unsaturated acyl groups in sn-1,3 DAG appear at 173.35-173.32 ppm. Acyl chains in the external position in sn-1,2/-2,3 DAG appear at 173.18 ppm while those in sn-2 at 173.08 ppm. It should be emphasized that the 13 C-NMR carbonyl and carboxyl signals enable the selective identification of different ∆ type fatty acids i.e., DHA which is a ∆ 4 and EPA which is a ∆ 5 fatty acid ( Figure 8). The carbonyl signals can also be used for the integration of the position of unsaturated fatty acids within the glycerol moiety (sn-1,3 and sn-2). Thus, 13 C-NMR enables the identification and, thus, quantification of sn-1 saturated with respect to sn-1 ∆ 9 18:1 and the sn-2 distribution of ∆ 9 18:1, ∆ 9 18:2, ∆ 5 and ∆ 4 without the need for the isolation of the individual lipid components (Figure 9).  The carbonyl carbons of fatty acids of TAG appear as two sets of resonances: the high frequency group which includes the chains esterified at 1(3)-glycerol positions and the low frequency group which includes the 2-glycerol position chains. The chemical shift difference of about 0.42 ppm was explained by the effect of two γ-gauche interactions on the C=O group of 2-position with respect to one interaction of the carbonyls of 1(3) chains [64].
The carbonyl carbons of long chain saturated and unsaturated acyl groups in sn-1,3 TAG appear at 172.8-172.7 ppm while those in sn-2 TAG at 172.41-172.38 ppm. Saturated and unsaturated acyl groups in sn-1,3 DAG appear at 173.35-173.32 ppm. Acyl chains in the external position in sn-1,2/-2,3 DAG appear at 173.18 ppm while those in sn-2 at 173.08 ppm. It should be emphasized that the 13 C-NMR carbonyl and carboxyl signals enable the selective identification of different Δ type fatty acids i.e., DHA which is a Δ 4 and EPA which is a Δ 5 fatty acid ( Figure 8). The carbonyl signals can also be used for the integration of the position of unsaturated fatty acids within the glycerol moiety (sn-1,3 and sn-2). Thus, 13 C-NMR enables the identification and, thus, quantification of sn-1 saturated with respect to sn-1 Δ 9 18:1 and the sn-2 distribution of Δ 9 18:1, Δ 9 18:2, Δ 5 and Δ 4 without the need for the isolation of the individual lipid components ( Figure 9).

Olefinic Carbon Region
The 13 C-NMR chemical shift range of the olefinic carbons (124-134 ppm) is wider than that of the carbonyl and carboxyl carbons (Tables 13 and 14). Nevertheless, the olefinic carbon region is usually the most complex part of the spectrum in lipid mixture analysis. The unsaturated carbons were resolved according to the position of the double bond with respect to the C=O carbons and the

Olefinic Carbon Region
The 13 C-NMR chemical shift range of the olefinic carbons (124-134 ppm) is wider than that of the carbonyl and carboxyl carbons (Tables 13 and 14). Nevertheless, the olefinic carbon region is usually the most complex part of the spectrum in lipid mixture analysis. The unsaturated carbons were resolved according to the position of the double bond with respect to the C=O carbons and the double bond number. The non-equivalence of the 13 C chemical shifts of olefinic carbons has been investigated in a number of mono-unsaturated fatty acids with different number of C-C bonds separating the double bond and the ester group. The unsaturated carbon nearest to the chain of the ester group is shifted to lower frequency from the unsaturated carbon nearest to the chain methyl end. This allows the shift differences of the double bond pair to be used as a criterion of the number of C-C bonds intervening between the C=O and the C=C bonds [64][65][66]. The carbon of the double bond closer to the carbonyl C=O bond in the sn-2 position is shielded with respect to that in the 1(3)-position. The opposite trend was observed for the carbon which is further from the C=O bond. The chemical shift differences were explained in terms of a linear electric field effect of the C=O group [67]. Davis et al. [68] suggested the use of shift increments to predict the configuration of an unknown CLA geometric and positional isomer. For a number of (7-cis, 9-trans), (8-cis, 10-trans), (9-cis, 11-trans), (10-cis, 12-trans) and (11-cis, 13-trans) 18:2 positional isomers, the differential chemical shift, ∆δ, between C 1ol (the olefinic carbon closest to the carboxyl group) and C 4ol (the olefinic carbon most remote from the carboxyl group) shows a gradual and significant shift as the conjugated system becomes more remote from the carboxyl function (Table 15).

Glycerol Carbons
The 13 C-NMR signals of the glycerol carbon occur in the region of 60-72 ppm (Table 16). 2-monoacylglycerols, 1,3-diacyglycerols and triacylglycerols result in two signals for the glycerol moiety with intensity rations 1:2. The asymmetrical 1-monoacyglycerols and 1,2-diacyglycerols result in three signals. The resonances of the glycerol C-2 of all glycerides are shifted to higher frequencies with respect to those of the glycerol 1(3)-carbons. The length and degree of unsaturation of the acyl chains has been shown to influence the chemical shifts of the glycerol carbons (see Section 5.6.3).

Aliphatic Carbons
The 13 C-NMR chemical shift range of the aliphatic carbons (Table 17) is very wide and has been utilized extensively for the identification and quantification of lipids. The mixed geometric (9-cis, 11-trans) 18:2 and (9-trans, 11-cis) 18:2 CLA isomers were identified on the basis of the carbon chemical shifts of the allylic methylene groups. Resonances at δ( 13 C) ≈ 27.6 ppm are characteristic of an adjacent cis-double bond and signals at δ( 13 C) ≈ 32.8 ppm to methylene carbons adjacent to the trans-bond.
The length of saturated FA and acyl chains and the proximity of the last double bond to the methyl end, strongly affects the 13 C chemical shift which can be utilized for the classification and quantification of ω-3, ω-6 and ω-7 fatty acids ( Figure 10). The 13 C resonance of the CH 3 groups of ω-3 fatty acids is deshielded by 0.15 ppm with respect to the CH 3 group of saturated fatty acids. Separation of the ω-6, ω-7 and ω-9 UFA can also be achieved, however, the chemical shift do not follow a regular pattern with respect to the number of intervening CH 2 bonds ( Figure 10). The methylene C-2 carbons demonstrate a clear separation of the ω-3 EPA (δ = 20.41 ppm) and DHA (δ = 20.40 ppm) ( Figure 11).
The length of saturated FA and acyl chains and the proximity of the last double bond to the methyl end, strongly affects the 13 C chemical shift which can be utilized for the classification and quantification of ω-3, ω-6 and ω-7 fatty acids ( Figure 10). The 13 C resonance of the CH3 groups of ω-3 fatty acids is deshielded by 0.15 ppm with respect to the CH3 group of saturated fatty acids. Separation of the ω-6, ω-7 and ω-9 UFA can also be achieved, however, the chemical shift do not follow a regular pattern with respect to the number of intervening CH2 bonds ( Figure 10). The methylene C-2 carbons demonstrate a clear separation of the ω-3 EPA (δ = 20.41 ppm) and DHA (δ = 20.40 ppm) ( Figure 11).  Combination, therefore, of the -CH3 and methylene C-2 spectral regions results in chromatographic like NMR methodology for the identification and quantification of various PUFA, even when using a medium strength spectrometer (500 MHz for 1 H).

31 P-NMR Spectroscopy
The 31 P nucleus has I = 1/2, high gyromagnetic ratio (10.829 × 10 9 rad T −1 s −1 ) and a wide range of chemical shifts, 100% natural abundance and, thus, high sensitivity, which is only 15 times less than that of the 1 H nucleus [23]. 31 P-NMR has been shown to be a powerful method in phospholipid analysis. 31 P-NMR spectra show separate signals depending on the fatty acid distribution of the phospholipids. In soybean lecithin ~20% of the fatty acids are saturated and nearly 100% of them are distributed in the sn-1 position. The unsaturated fatty acids are distributed in the sn-1 and sn-2 positions. 31 P-NMR was able to distinguish between double unsaturated and mixed saturated/unsaturated phospholipids. Similarly, the 31 P of phosphatidic acid (PA) shows two unequal signals due to the presence of the mixed saturated / unsaturated (40%) and unsaturated/unsaturated (60%) lipids [21,69]. 31 P-NMR has been applied in the analysis of olive oil and other vegetable oils [59,[70][71][72] and, especially, in cases where strong signal overlap and dynamic range problems in 1 H-NMR spectra and/or long relaxation times of the insensitive 13 C nuclei make the analysis of oils a difficult task. Application of 31 P-NMR in the analysis of olive oil and other vegetable oils was achieved by derivatization of the labile hydrogens of functional groups, such as hydroxyl and carboxyl groups of the oil constituents with the phosphorus reagent 2-chloro-4,4,5,5-tetramethyldioxaphospholane (I) and the use of 31 P chemical shifts to identify labile groups (compound II). The phosphitylation reaction (Scheme 1) is quantitative, takes place under mild conditions (within the NMR tube) and is completed in less than 15 min. Using this reaction, it was possible to quantify DAG and MAG species and free glycerol in oils. Quantitative 31 P requires the use of the inverse gated decoupling technique in combination with the paramagnetic chemical shift reagent Cr(acac)3 and a relaxation delay 5T1 ≈ 4.6 s, where T1 is the relaxation time of the internal standard. The disadvantage of the 31 P-NMR methodology is the destruction of the analytes. Combination, therefore, of the -CH 3 and methylene C-2 spectral regions results in chromatographic like NMR methodology for the identification and quantification of various PUFA, even when using a medium strength spectrometer (500 MHz for 1 H).

31 P-NMR Spectroscopy
The 31 P nucleus has I = 1/2, high gyromagnetic ratio (10.829 × 10 9 rad T −1 s −1 ) and a wide range of chemical shifts, 100% natural abundance and, thus, high sensitivity, which is only 15 times less than that of the 1 H nucleus [23]. 31 P-NMR has been shown to be a powerful method in phospholipid analysis. 31 P-NMR spectra show separate signals depending on the fatty acid distribution of the phospholipids.
In soybean lecithin~20% of the fatty acids are saturated and nearly 100% of them are distributed in the sn-1 position. The unsaturated fatty acids are distributed in the sn-1 and sn-2 positions. 31 P-NMR was able to distinguish between double unsaturated and mixed saturated/unsaturated phospholipids. Similarly, the 31 P of phosphatidic acid (PA) shows two unequal signals due to the presence of the mixed saturated / unsaturated (40%) and unsaturated/unsaturated (60%) lipids [21,69]. 31 P-NMR has been applied in the analysis of olive oil and other vegetable oils [59,[70][71][72] and, especially, in cases where strong signal overlap and dynamic range problems in 1 H-NMR spectra and/or long relaxation times of the insensitive 13 C nuclei make the analysis of oils a difficult task. Application of 31 P-NMR in the analysis of olive oil and other vegetable oils was achieved by derivatization of the labile hydrogens of functional groups, such as hydroxyl and carboxyl groups of the oil constituents with the phosphorus reagent 2-chloro-4,4,5,5-tetramethyldioxaphospholane (I) and the use of 31 P chemical shifts to identify labile groups (compound II). The phosphitylation reaction (Scheme 1) is quantitative, takes place under mild conditions (within the NMR tube) and is completed in less than 15 min. Using this reaction, it was possible to quantify DAG and MAG species and free glycerol in oils. Quantitative 31 P requires the use of the inverse gated decoupling technique in combination with the paramagnetic chemical shift reagent Cr(acac) 3 and a relaxation delay 5T 1 ≈ 4.6 s, where T 1 is the relaxation time of the internal standard. The disadvantage of the 31 P-NMR methodology is the destruction of the analytes.

Selective Suppression of Major Signals
1 H-NMR spectroscopy has found limited application in the identification and quantification of minor species in lipid extracts. This is due to the fact that the equilibrium magnetization of e.g., the olefinic (CH2)n 1 H spins of the major constituents of the lipids is 10 2 -10 4 greater than the equilibrium magnetization of the 1 H spins of the minor species. The problem is particularly severe in two dimensional experiments in which changes in the phase of the strong signals during various increments can lead to severe t1 noise. A straightforward method of reducing major resonances is the saturation of selective resonances by the use of variable frequency presaturation. Figure 12 illustrates that a S/N ratio increase by a factor of ~10 was achieved after multiple suppression of dominating lipid signals due to increase in the receiver gain of the spectrometer [73]. Similarly, selective suppression of the two major lipid resonances at 0.90 and 1.20 ppm in the lipid fraction of a lyophilized milk resulted in an increase in the S/N ratio of the minor CLA resonances by a factor of ~3 which allowed the identification and quantification of minor CLA isomers [56].

Selective Suppression of Major Signals
1 H-NMR spectroscopy has found limited application in the identification and quantification of minor species in lipid extracts. This is due to the fact that the equilibrium magnetization of e.g., the olefinic (CH 2 ) n 1 H spins of the major constituents of the lipids is 10 2 -10 4 greater than the equilibrium magnetization of the 1 H spins of the minor species. The problem is particularly severe in two dimensional experiments in which changes in the phase of the strong signals during various increments can lead to severe t 1 noise. A straightforward method of reducing major resonances is the saturation of selective resonances by the use of variable frequency presaturation. Figure 12 illustrates that a S/N ratio increase by a factor of~10 was achieved after multiple suppression of dominating lipid signals due to increase in the receiver gain of the spectrometer [73]. Similarly, selective suppression of the two major lipid resonances at 0.90 and 1.20 ppm in the lipid fraction of a lyophilized milk resulted in an increase in the S/N ratio of the minor CLA resonances by a factor of~3 which allowed the identification and quantification of minor CLA isomers [56].

Selective Suppression of Major Signals
1 H-NMR spectroscopy has found limited application in the identification and quantification of minor species in lipid extracts. This is due to the fact that the equilibrium magnetization of e.g., the olefinic (CH2)n 1 H spins of the major constituents of the lipids is 10 2 -10 4 greater than the equilibrium magnetization of the 1 H spins of the minor species. The problem is particularly severe in two dimensional experiments in which changes in the phase of the strong signals during various increments can lead to severe t1 noise. A straightforward method of reducing major resonances is the saturation of selective resonances by the use of variable frequency presaturation. Figure 12 illustrates that a S/N ratio increase by a factor of ~10 was achieved after multiple suppression of dominating lipid signals due to increase in the receiver gain of the spectrometer [73]. Similarly, selective suppression of the two major lipid resonances at 0.90 and 1.20 ppm in the lipid fraction of a lyophilized milk resulted in an increase in the S/N ratio of the minor CLA resonances by a factor of ~3 which allowed the identification and quantification of minor CLA isomers [56]. Signal-to-noise (SNR) increase by a factor of ~10 was obtained after suppression of multiple dominating lipid signals due to the increase of the receiver gain. Number of scans and total experimental time were kept constant, i.e., NS = 32 and 4 min, respectively. Adopted, with permission, from [73]. Copyright 2011, Elsevier Ltd.

Figure 12.
Signal-to-noise (SNR) increase by a factor of~10 was obtained after suppression of multiple dominating lipid signals due to the increase of the receiver gain. Number of scans and total experimental time were kept constant, i.e., NS = 32 and 4 min, respectively. Adopted, with permission, from [73]. Copyright 2011, Elsevier Ltd.

Selective 1D TOCSY Experiments
The selective 1D TOCSY experiment is an important NMR technique for establishing 1 H-1 H connectivity via scalar coupling in small and medium size molecules [74,75]. However, the method has found limited applications in complex mixtures and, more specific, in natural products and food extracts [76][77][78][79]. Figure 13 illustrates a series of selective 1D TOCSY spectra of the (9-cis, 11-trans) 18:2 CLA isomer. The H11 olefinic proton (δ = 6.27 ppm) was selected for excitation using mixing times τ m of 33 ms, 70 ms, 200 ms and 400 ms. For mixing times of τ m = 200 ms and 400 ms the complete assignment and structure of the compound can be achieved with very good resolution. In mixture analysis what is required, is an isolated target peak to be used as the magnetization transfer source. This is the case e.g., of CLA olefinic resonances which provided a means to distinguish a lipid in complex lipid fractions not only at a class level, with reference to molecular fragments (saturated, monounsaturated, bis-allylic, and polyunsaturated), but also at the level of individual compounds (Section 5.2).

Selective 1D TOCSY Experiments
The selective 1D TOCSY experiment is an important NMR technique for establishing 1 H-1 H connectivity via scalar coupling in small and medium size molecules [74,75]. However, the method has found limited applications in complex mixtures and, more specific, in natural products and food extracts [76][77][78][79]. Figure 13 illustrates a series of selective 1D TOCSY spectra of the (9-cis, 11-trans) 18:2 CLA isomer. The H11 olefinic proton (δ = 6.27 ppm) was selected for excitation using mixing times τm of 33 ms, 70 ms, 200 ms and 400 ms. For mixing times of τm = 200 ms and 400 ms the complete assignment and structure of the compound can be achieved with very good resolution. In mixture analysis what is required, is an isolated target peak to be used as the magnetization transfer source. This is the case e.g., of CLA olefinic resonances which provided a means to distinguish a lipid in complex lipid fractions not only at a class level, with reference to molecular fragments (saturated, monounsaturated, bis-allylic, and polyunsaturated), but also at the level of individual compounds (Section 5.2). The asterisk denotes the selected H11 resonance that was excited. For panels (b-e), the magnetization transfer network is illustrated. Adopted, with permission, from [78]. Copyright 2015, American Chemical Society. [80][81][82] The 1 H-NMR spectrum of the caproleic acid ( Figure 14) shows the resonances due to the protons of the -CH=CH2 proton at 5.79 ppm (multiplet), the =CH2 protons at 4.98 ppm (H10b, dq) and 4.92 ppm (H10a, dq), the -CH2-COOH protons at 2.35 ppm (triplet), the -CH2-CH=CH2 protons at 2.05 ppm (multiplet), the -CH2-CH2-COOH protons at 1.64 ppm (multiplet) and all -CH2-protons at 1.25 ppm (multiplet). Figure 15 illustrates a selected region of the 2D 1 H-1 H TOCSY spectrum of the caproleic acid. The use of mixing time τm = 100 ms cause magnetization transfer throughout the whole The asterisk denotes the selected H11 resonance that was excited. For panels (b-e), the magnetization transfer network is illustrated. Adopted, with permission, from [78]. Copyright 2015, American Chemical Society.

Homonuclear 2D 1 H-1 H COSY and 2D 1 H-1 H TOCSY Experiments [80-82]
The 1 H-NMR spectrum of the caproleic acid ( Figure 14) shows the resonances due to the protons of the -CH=CH 2 proton at 5.79 ppm (multiplet), the =CH 2 protons at 4.98 ppm (H10b, dq) and 4.92 ppm (H10a, dq), the -CH 2 -COOH protons at 2.35 ppm (triplet), the -CH 2 -CH=CH 2 protons at 2.05 ppm (multiplet), the -CH 2 -CH 2 -COOH protons at 1.64 ppm (multiplet) and all -CH 2 -protons at 1.25 ppm (multiplet). Figure 15 illustrates a selected region of the 2D 1 H-1 H TOCSY spectrum of the caproleic acid. The use of mixing time τ m = 100 ms cause magnetization transfer throughout the whole number of protons of caproleic acid. The H9 (5.79 ppm) correlates with the H8 (2.05 ppm) and the H7 (1.35 ppm). The red peaks show the weak correlations between H9 (5.79 ppm)-H2 (2.35 ppm) and H9 (5.79 ppm)-H3 (1.65 ppm). This also provides unequivocal assignment of the H9 with respect to H10a,b and H2 for the given mixing time.  . This also provides unequivocal assignment of the H9 with respect to H10a,b and H2 for the given mixing time.   The 1D 1 H-NMR and 2D 1 H-1 H NMR spectra of the (9-cis, 11-trans) 18:2 CLA isomer are illustrated in Figures 16 and 17, respectively. Again the use of mixing time τ m = 100 ms cause the polarization to spread out the whole number of protons. Thus, the olefinic H9 proton demonstrates cross peaks, at lower contour level, with both H2 and H18 protons (Table 18). The assignment, however, of the composite signals at 1.25-1.35 ppm due to H4-H7 and H14-H17 protons would require the use of several 2D 1 H-1 H TOCSY or selective 1D 1 H TOCSY with various mixing times. The 1D 1 H TOCSY experiment has the following advantages: (i) significantly increases the digital resolution while in the 2D TOCSY it is limited by the number of points taken in the indirect dimension, (ii) removes dynamic range issues and detects cross peaks even in regions with strong signal overlap of lipid extracts and (iii) decreases significantly the experimental time [78]. The 1D 1 H-NMR and 2D 1 H-1 H NMR spectra of the (9-cis, 11-trans) 18:2 CLA isomer are illustrated in Figures 16 and 17, respectively. Again the use of mixing time τm = 100 ms cause the polarization to spread out the whole number of protons. Thus, the olefinic H9 proton demonstrates cross peaks, at lower contour level, with both H2 and H18 protons (Table 18). The assignment, however, of the composite signals at 1.25-1.35 ppm due to H4-H7 and H14-H17 protons would require the use of several 2D 1 H-1 H TOCSY or selective 1D 1 H TOCSY with various mixing times. The 1D 1 H TOCSY experiment has the following advantages: (i) significantly increases the digital resolution while in the 2D TOCSY it is limited by the number of points taken in the indirect dimension, (ii) removes dynamic range issues and detects cross peaks even in regions with strong signal overlap of lipid extracts and (iii) decreases significantly the experimental time [78].  The 1D 1 H-NMR and 2D 1 H-1 H NMR spectra of the (9-cis, 11-trans) 18:2 CLA isomer are illustrated in Figures 16 and 17, respectively. Again the use of mixing time τm = 100 ms cause the polarization to spread out the whole number of protons. Thus, the olefinic H9 proton demonstrates cross peaks, at lower contour level, with both H2 and H18 protons ( Table 18). The assignment, however, of the composite signals at 1.25-1.35 ppm due to H4-H7 and H14-H17 protons would require the use of several 2D 1 H-1 H TOCSY or selective 1D 1 H TOCSY with various mixing times. The 1D 1 H TOCSY experiment has the following advantages: (i) significantly increases the digital resolution while in the 2D TOCSY it is limited by the number of points taken in the indirect dimension, (ii) removes dynamic range issues and detects cross peaks even in regions with strong signal overlap of lipid extracts and (iii) decreases significantly the experimental time [78].    [83][84][85]. This method results in one cross peak per pair of coupled nuclei whose two coordinates are the chemical shifts of 1 H (observed nucleus) and 13 C (indirectly detected nucleus). This experiment enables: (i) proton assignments to be mapped directly into their bonded carbons and, thus, may be used to spread complex 1 H-NMR spectra, as in the case of lipids, according to the greater dispersion of the carbon resonances and (ii) quantification of minor lipids even in complex mixtures (see Section 5.2). Identification and quantification of minor lipids in complex mixtures with the use of 1 H-13 C gHSQC experiment suffers from low resolution in the 13 C dimension. A significant increase in the digital resolution can be achieved with the use of either reduced 13 C spectra width (Section 5.2) or band selected 1 H-13 C gHSQC experiment [86]. Dais et al. [60] utilized band selected 1 H-13 C gHSQC experiment to identify the terminal methyl protons of minor trans fatty acids in fish oil supplements which indicated a cross peak at δ = 13.72 ppm ( Figure 18). This low frequency chemical shift is characteristic of trans fatty acids [87]. The achievable resolution was found to be comparable to that of the 1D 13 C-NMR spectrum in addition to much higher sensitivity due to indirect detection.

1 H-13 C Heteronuclear Single-Quantum Correlation Spectroscopy ( 1 H-13 C HSQC)-Band Selective 1 H-13 C HSQC [80-83]
1 H-13 C HSQC spectroscopy detects correlations between 1 H-13 C nuclei which are separated by one bond. 1 J ( 1 H-13 C) couplings are typically optimized for 145 Hz, being an average value for one bond couplings [83][84][85]. This method results in one cross peak per pair of coupled nuclei whose two coordinates are the chemical shifts of 1 H (observed nucleus) and 13 C (indirectly detected nucleus). This experiment enables: (i) proton assignments to be mapped directly into their bonded carbons and, thus, may be used to spread complex 1 H-NMR spectra, as in the case of lipids, according to the greater dispersion of the carbon resonances and (ii) quantification of minor lipids even in complex mixtures (see Section 5.2).
Identification and quantification of minor lipids in complex mixtures with the use of 1 H-13 C gHSQC experiment suffers from low resolution in the 13 C dimension. A significant increase in the digital resolution can be achieved with the use of either reduced 13 C spectra width (Section 5.2) or band selected 1 H-13 C gHSQC experiment [86]. Dais et al. [60] utilized band selected 1 H-13 C gHSQC experiment to identify the terminal methyl protons of minor trans fatty acids in fish oil supplements which indicated a cross peak at δ = 13.72 ppm (Figure 18). This low frequency chemical shift is characteristic of trans fatty acids [87]. The achievable resolution was found to be comparable to that of the 1D 13 C-NMR spectrum in addition to much higher sensitivity due to indirect detection.

Multiplicity Edited 1 H-13 C HSQC
This is a variant HSQC method which combines both spectra editing (i.e., DEPT-135) and HSQC into one experiment [81,86,88]. The correlation cross peaks are phase coded according to DEPT-135 multiplicity e.g., CH and CH 3 are of the same positive phase, whereas CH 2 groups are of negative sign. The method has been successfully applied for the assignment of the 13 C signals of the glycerol backbone protons of diacylglycerol (DAG) oil ( Figure 19). The same experiment was also utilized to assign the methyl, allylic and bis-allylic carbons of linoleic and linolenic acids [59].

Multiplicity Edited 1 H-13 C HSQC
This is a variant HSQC method which combines both spectra editing (i.e., DEPT-135) and HSQC into one experiment [81,86,88]. The correlation cross peaks are phase coded according to DEPT-135 multiplicity e.g., CH and CH3 are of the same positive phase, whereas CH2 groups are of negative sign. The method has been successfully applied for the assignment of the 13 C signals of the glycerol backbone protons of diacylglycerol (DAG) oil ( Figure 19). The same experiment was also utilized to assign the methyl, allylic and bis-allylic carbons of linoleic and linolenic acids [59].

2D 1 H-13 C HSQC-TOCSY-Band Selective Experiments
2D 1 H-13 C HSQC-TOCSY is a hybrid NMR experiment which combines the HSQC and TOCSY pulse sequences in order to relay the magnetization along with a proton network, using the greater dispersion of the 13 C chemical shifts. This experiment is very useful to elucidate assignments in overcrowded 1 H-NMR spectra since its row, for a particular 13 C chemical shift, contains a 1 H TOCSY sub-spectrum of the molecular fragment. The 2D 1 H-13 C HSQC-TOCSY experiment has been successfully employed to correlate carbon signals with the adjacent allylic protons of unsaturated fatty acids [89,90] and to analyze the positional distribution of unsaturated chains in TAG model compounds [91]. Of particular interest is the application of gHSQC-TOCSY experiment for mixture analysis in DAG oils [59]. Carbon -proton pairs connected over two bonds were observed for the allylic and bis-allylic carbons of the unsaturated chains which resulted in the unambiguous assignment of several carbons of the acyl chains of oleic, linoleic and linolenic acids ( Figure 20). For example, with the use of the pairs H7, C17 of linolenic acid (LN) direct assignment of the allylic Figure 19. 600 MHz HSQC-DEPT NMR spectrum of DAG olive oil in CDCl 3 solution, showing one bond correlations between the glycerol backbone protons and carbons; negative (blue color) signals for the CH 2 carbons and positive (red color) signals for the CH carbons. Adopted, with permission, from [59]. Copyright 2011, Springer AOCS.

2D 1 H-13 C HSQC-TOCSY-Band Selective Experiments
2D 1 H-13 C HSQC-TOCSY is a hybrid NMR experiment which combines the HSQC and TOCSY pulse sequences in order to relay the magnetization along with a proton network, using the greater dispersion of the 13 C chemical shifts. This experiment is very useful to elucidate assignments in overcrowded 1 H-NMR spectra since its row, for a particular 13 C chemical shift, contains a 1 H TOCSY sub-spectrum of the molecular fragment. The 2D 1 H-13 C HSQC-TOCSY experiment has been successfully employed to correlate carbon signals with the adjacent allylic protons of unsaturated fatty acids [89,90] and to analyze the positional distribution of unsaturated chains in TAG model compounds [91]. Of particular interest is the application of gHSQC-TOCSY experiment for mixture analysis in DAG oils [59]. Carbon -proton pairs connected over two bonds were observed for the allylic and bis-allylic carbons of the unsaturated chains which resulted in the unambiguous assignment of several carbons of the acyl chains of oleic, linoleic and linolenic acids ( Figure 20). For example, with the use of the pairs H7, C17 of linolenic acid (LN) direct assignment of the allylic carbons C17, C16, C14, C11 and C8 could be achieved with a mixing time of 80 ms (for the notation system for 1 H resonances see the original article). A significant increase in the digital resolution in the 13 C dimension can be achieved with the use of band selective 1 H-13 C HSQC-TOCSY experiment. The method has been successfully applied by Willker et al. [86] to investigate multiple 13 C labeled biofluids and to identify and quantify blood plasma lipids [89] (see Section 5.6.4). carbons C17, C16, C14, C11 and C8 could be achieved with a mixing time of 80 ms (for the notation system for 1 H resonances see the original article). A significant increase in the digital resolution in the 13 C dimension can be achieved with the use of band selective 1 H-13 C HSQC-TOCSY experiment. The method has been successfully applied by Willker et al. [86] to investigate multiple 13 C labeled biofluids and to identify and quantify blood plasma lipids [89] (see Section 5.6.4).

1 H-13 C Heteronuclear Multiple-Bond Correlation ( 1 H-13 C HMBC) Experiments-Band Selective Constant Time 1 H-13 C HMBC [80-83]
The 1 H-13 C HMBC experiment detects correlations due to n J( 1 H-13 C) couplings, where n = 2-4 (possibly n > 4 for favorable extended conjugated systems). The method can provide correlations across C-C and C-X fragments, thus, providing one of the most powerful tools for investigating connectivities within extensive molecular skeletons. Due to the variety of n J( 1 H-13 C) couplings, the pulse sequence is usually optimized for ~8 Hz. Figure 21 illustrates selected regions of the 1 H- 13 C HMBC experiments of the (cis-9, trans-11) 18:2 CLA isomer in CDCl3. The 1 H signals at 6.28 and 5.93 ppm have been assigned to the protons involved in the olefinic bonds. Μore specifically, the proton at 6.28 ppm correlates with the carbon at 125.3 ppm that was assigned to C11 (Table 19). Similarly, the proton at 5.93 ppm correlates with the carbon The 1 H-13 C HMBC experiment detects correlations due to n J( 1 H-13 C) couplings, where n = 2-4 (possibly n > 4 for favorable extended conjugated systems). The method can provide correlations across C-C and C-X fragments, thus, providing one of the most powerful tools for investigating connectivities within extensive molecular skeletons. Due to the variety of n J( 1 H-13 C) couplings, the pulse sequence is usually optimized for~8 Hz. Figure 21 illustrates selected regions of the 1 H- 13 C HMBC experiments of the (cis-9, trans-11) 18:2 CLA isomer in CDCl 3 . The 1 H signals at 6.28 and 5.93 ppm have been assigned to the protons involved in the olefinic bonds. More specifically, the proton at 6.28 ppm correlates with the carbon at 125.3 ppm that was assigned to C11 (Table 19). Similarly, the proton at 5.93 ppm correlates with the carbon at 128.4 ppm (C10). Proton at 5.33 ppm correlates with carbon at 129.6 ppm and, thus, was assigned to the C9. In addition, the H11 (6.28 ppm) shows correlations with the C13 ( [59] provided cross-peaks between protons of the glycerol moiety with the ester CO carbons of the attached fatty acid chain. This allowed the unequivocal identification of the fatty acid which was previously based on additive properties of inductive effects of the double bonds [92]. The authors were able to classify the carbonyl signals into three groups corresponding to     13 C peak assignments of the (9-cis, 11-trans) 18:2 CLA isomer in CDCl 3 (solution conditions the same as in Figure 16).

H
δ H (ppm) 13 [93,94] provide a significantly enhanced digital resolution in the 13 C dimension compared to that of the 1 H-13 C gHMBC experiments. Figure 22 illustrates a band selective constant time 1 H-13 C HMBC experiment of a fish oil sample using a selective 2 ppm 13 C spectral width. The excellent resolution of the resulting cross peaks between the carbonyl carbons of various FAs with the glyceridic sn-1, sn-3 and sn-2 positions can provide unequivocal determination of the positional distribution of ω-3, ω-6 and ω-9 fatty acids in the glycerol moiety, including the ω-3 docosapentaenoic acid (DPA) which is an elongated metabolite of EPA (Table 2).   Figure 16). 13 [93,94] provide a significantly enhanced digital resolution in the 13 C dimension compared to that of the 1 H-13 C gHMBC experiments. Figure  22 illustrates a band selective constant time 1 H-13 C HMBC experiment of a fish oil sample using a selective 2 ppm 13 C spectral width. The excellent resolution of the resulting cross peaks between the carbonyl carbons of various FAs with the glyceridic sn-1, sn-3 and sn-2 positions can provide unequivocal determination of the positional distribution of ω-3, ω-6 and ω-9 fatty acids in the glycerol moiety, including the ω-3 docosapentaenoic acid (DPA) which is an elongated metabolite of EPA (Table 2).

DOSY Experiments
Diffusion-ordered spectroscopy (DOSY) [95] is a sensitive technique that allows the determination of self-diffusion coefficients which are due to random translational motions of molecules as a consequence of their thermal energy. The self-diffusion coefficients, D(m 2 s −1 ), depend upon molecular properties (size, shape, molecular weight) but, also, on concentration, solvent, temperature and aggregation state. With the DOSY method each component of a mixture can be separated according to its apparent diffusion coefficient and, thus, has found several applications in mixture analysis [96], combinatorial chemistry [95], food chemistry [59,97] and natural products [98][99][100]. In the field of lipid research, the signals of the glycerol segment of TAG were separated relative to those of TAG on the basis of their different diffusion coefficients obtained from the DOSY NMR spectrum of DAG oil [59,60]. The TAG, with larger molecular weight, showed smaller diffusion coefficient (4.5 × 10 −10 m 2 s −1 ) than that of the DAG components (5.4 × 10 −10 m 2 s −1 ). DOSY experiments were also utilized to obtain qualitative information about the degree of glycerol esterification by the n-acyl and trans acyl chains [60]. Diffusion-edited NMR techniques, which enhance NMR signals of lipoproteins and remove signals from low molecular weight analytes, have found several applications in body fluids and lipoprotein analysis. This subject will be discussed in Section 5.6.4.

Chemical shift Reagents (CSR)
Lipid derivatives generally afford NMR spectra that preclude a simple first order interpretation, especially in the case of olefinic, allylic and (CH2)n protons (Figures 5 and 6). It has been demonstrated that NMR chemical shift reagents (CSR) such as Eu(fod)3 [tris-(1,1,1,2,2,3,3-heptafluoro-7,7-dimethyl-4,6-octanedionate)-europium(III)] can increase considerably the amount of structural information obtained from NMR studies [101]. The effect of chemical shift reagents can be considered to be mainly due to dipolar interaction and has been reported to depend on the Lewis basicity of the functional group [102,103]. Thus, the strength of interaction decreases in the order: amines > alcohols > ketones ≥ aldehydes ≥ ethers > esters > nitriles.

DOSY Experiments
Diffusion-ordered spectroscopy (DOSY) [95] is a sensitive technique that allows the determination of self-diffusion coefficients which are due to random translational motions of molecules as a consequence of their thermal energy. The self-diffusion coefficients, D(m 2 s −1 ), depend upon molecular properties (size, shape, molecular weight) but, also, on concentration, solvent, temperature and aggregation state. With the DOSY method each component of a mixture can be separated according to its apparent diffusion coefficient and, thus, has found several applications in mixture analysis [96], combinatorial chemistry [95], food chemistry [59,97] and natural products [98][99][100]. In the field of lipid research, the signals of the glycerol segment of TAG were separated relative to those of TAG on the basis of their different diffusion coefficients obtained from the DOSY NMR spectrum of DAG oil [59,60]. The TAG, with larger molecular weight, showed smaller diffusion coefficient (4.5 × 10 −10 m 2 s −1 ) than that of the DAG components (5.4 × 10 −10 m 2 s −1 ). DOSY experiments were also utilized to obtain qualitative information about the degree of glycerol esterification by the n-acyl and trans acyl chains [60]. Diffusion-edited NMR techniques, which enhance NMR signals of lipoproteins and remove signals from low molecular weight analytes, have found several applications in body fluids and lipoprotein analysis. This subject will be discussed in Section 5.6.4.

Chemical Shift Reagents (CSR)
Lipid derivatives generally afford NMR spectra that preclude a simple first order interpretation, especially in the case of olefinic, allylic and (CH 2 ) n protons (Figures 5 and 6). It has been demonstrated that NMR chemical shift reagents (CSR) such as Eu(fod) 3 [tris-(1,1,1,2,2,3,3-heptafluoro-7,7-dimethyl-4,6-octanedionate)-europium(III)] can increase considerably the amount of structural information obtained from NMR studies [101]. The effect of chemical shift reagents can be considered to be mainly due to dipolar interaction and has been reported to depend on the Lewis basicity of the functional group [102,103]. Thus, the strength of interaction decreases in the order: amines > alcohols > ketones ≥ aldehydes ≥ ethers > esters > nitriles.
Halides, indoles and double bonds are generally considered to be inactive. Chemical shift studies of methyl oleate revealed that at the optimum [Eu(fod) 3 ]/[methyl oleate] ratio of~1.8, discrete proton signals could only be obtained from C-1 up to C-5 which are near to the coordination site. No induced chemical shifts were observed for the olefinic protons [103]. Information for unsaturated lipid derivatives can be obtained by the introduction of additional functional groups which are CSR active. Thus, successful CSR studies were published on methyl ricinoleate (methyl 12-hydroxy-cis-∆ 9,10 -octadecenoate) and methyl 12-hydroxy stearate (methyl 12-hydroxy-9,10-octadecanoate) [104]. For methyl ricinoleate, individual signals were observed for each of the olefinic protons 9 and 10 and their induced shifts were related to the proximity of the OH group. Yb(fod) 3 has been utilized to identify and discriminate side chain isomers of phytosterols even when using a 90 MHz instrument [105]. For unambiguous assignment of overlapping proton signals it was necessary to perform an incremental CSR study, the construction of proton plots and the calculation of induced shift values.
Despite the original promising results, the CSR method has found limited application in lipid research presumably due to extensive use of high magnetic fields. Nevertheless, Agiomyrgianaki et al. [106] exploited the use of a shift reagent in order to distinguish cis and trans unsaturation in oils and fats. The method is based on the ability of silver ions to form weak charge-transfer complexes with the olefinic double bonds and the fact that cis-unsaturated fatty acids form stronger complexes than the trans geometric isomers. The authors were able to differentiate cis and trans unsaturation in mixtures of cis and trans methyl esters of monoene aliphatic acids and unsaturated triacylglycerol mixtures, using a low magnetic field instrument (300 MHz for 1 H). For a mixture of 0.2 M in CDCl 3 of methyl oleate and methyl elaidate, which have single cis and trans bonds respectively, very good separation of the mono allylic and olefinic protons at δ = 2.02 ppm and δ = 5.34 ppm was achieved with a silver shift reagent/substrate molar ratio of 0.5. However, attempts to differentiate lipid molecules with different degree of unsaturation and positional distribution of cis double bonds were unsuccessful.

Database Matching Approach-Resolving NMR Signals Using Multivariate Data Analysis
Extracts of natural sources consist of complex mixtures of compounds which cannot be effectively and rapidly detected without considerable effort and extensive workup. Thus, the general availability of natural product databases containing experimental data and bioinformatics navigation tolls can greatly facilitate the identification of natural products from complex mixtures [107]. Several NMR databases have been published [108,109]. In the database matching approach, the NMR analysis relies on the spectral comparison using databases of NMR spectra. With this method automatic compound identification can be achieved or the number of possible candidates can be significantly reduced. Among the various data bases, the most popular are the various versions of the Chenomx NMR Suit library (Chenomx, Inc., Edmonton, AB, Canada). Unfortunately, the number of fatty acid standards is, at present, rather limited which precludes unambiguous identification. It should be emphasized that chemical shift variations can occur in lipid extracts with respect to model compounds, due to complex interactions that may occur in the former case and differences in concentration, temperature, solvent etc.
Multivariate data analysis (MDA) has been extensively used to reduce information contained in complex NMR spectra with strongly overlapped peaks. Among the variety of algorithms, the principal component analysis (PCA) has been extensively utilized in order to deconvolute the signals and convert complex systems to simplified and reduced processed information. Recently Pereira et al. [110] applied an unsupervised component analysis to resolve and identify the NMR signals of 3 short-chain fatty acids: acetic acid, propionic acid and butyric acid. The principal object analysis was able to identify the number of independent contributions present in the mixture. The method, however, was applied to a relatively simple mixture, therefore, its utility in complex lipid extracts has yet to be thoroughly investigated.

Identification and Quantification of Unsaturated Fatty Acids in Complex Mixtures
Omega-3 fatty acids are widely distributed in nature and can be found in walnuts, flaxseed, soybean oil, canola oil, shellfish, salmon, herring, sardins, anchovies, trout, etc. (Table 20 [111]). Omega-6 fatty acids can be found in soybean oil, safflower oil and other liquid vegetable oils. The fatty acid profiles of a variety of fats and oils with emphasis on unsaturated and polyunsaturated fatty acids have been extensively quantified using 1 H-and 13 C-NMR [19][20][21][22]25,62,63,[112][113][114][115][116][117][118][119][120][121][122]. The 1 H-NMR method utilizes the integration area per proton and provides equations for determining the mol amounts of the unsaturated fatty acids. Although some modified equations have been suggested depending on the particular fat/oil to be investigated, there is a general consensus that 1 H-NMR can provide an excellent method for obtaining quantitative results on TAG, 1,2-DAG, DHA, α-linolenic acid, linoleic acid and UFA. Table 20. ω-3 content (%) of α-linolenic acid (ALA) in seed oils. Reprinted with permission from [111]. Evaluation of the total amount (%) of triacylglycerides (TAG) can be based on the integrals of the signals due to -CH 2 -OOC-protons of the glycerol moiety at~4.30 ppm (I 4.30 ) using the following equation [123]: Evaluation of the degree of total unsaturation in oils and fats with 1 H-NMR (Equations (9) and (10)) has distinct advantages with the respect to the classical iodine value since it is more rapid and can provide information on the different types of unsaturated fatty acids [124]. Quantification of ω-6 and ω-3 polyunsaturated fatty acids can also be carried out by 1 H-NMR using the above equations in a simple and efficient way compared to classical analytical methods which involve trans-esterification of the oil or fat to produce methyl esters and the identification and quantification by gas chromatography [125]. The conversion of 1 H-NMR data from mol % to wt % can be achieved [124] with the hypothesis that the average chain lengths of mono-and poly-unsaturated are C 18 and by estimating the average number of protons in unsaturated and saturated chains from the integrals of given resonances in the spectrum. Figure 23 illustrates the 1 H-NMR spectrum of a salmon oil. The amount of total ω-3 can be easily calculated using the integral of the triplet at 0.97 ppm. Quantification of the individual DHA and EPA fatty acid can also be obtained on the basis of the integrals at 2.40 ppm, due to CH 2 -CH 2 -COOR protons of DHA, and, at 1.7 ppm, due to CH 2 -CH=CH protons of EPA.
estimating the average number of protons in unsaturated and saturated chains from the integrals of given resonances in the spectrum. Figure 23 illustrates the 1 H-NMR spectrum of a salmon oil. The amount of total ω-3 can be easily calculated using the integral of the triplet at 0.97 ppm. Quantification of the individual DHA and EPA fatty acid can also be obtained on the basis of the integrals at 2.40 ppm, due to CH2-CH2-COOR protons of DHA, and, at 1.7 ppm, due to CH2-CH=CH protons of EPA.  Figure 24 illustrates the 1 H-NMR spectra of TAG and phospholipid fractions from krill oil after preparative separation. The identification and quantification of ω-3 from ω-6, ω-9 and saturated fatty acids can be achieved. Interestingly, the branched phytanic acid can also be quantified.  Figure 24 illustrates the 1 H-NMR spectra of TAG and phospholipid fractions from krill oil after preparative separation. The identification and quantification of ω-3 from ω-6, ω-9 and saturated fatty acids can be achieved. Interestingly, the branched phytanic acid can also be quantified.

Identification and Quantification of Minor Lipids in Complex Mixtures
The analysis of minor lipids is extremely challenging and complex because it can be very slow and laborious using the classical chromatographic analytical methods. Tsiafoulis et al. [56] reported direct identification and quantification of four minor geometric (9-cis, 11-trans) 18:2, (9-trans, 11-cis) 18:2, (9-cis, 11-cis) 18:2 and (9-trans, 11-trans) 18:2 conjugated linoleic acid (CLA) isomers ( Figure 25) in lipid fractions of lyophilized milk samples with the combined use of 2D 1 H-1 H TOCSY ( Figure 26) and 2D 1 H-13 C HSQC (Figure 27). Selective saturation of major lipid signals, resulted in an increase in the S/N of the CLA resonances by a factor of three due to the significantly higher receiver gain of the spectrometer (Section 4.1). This allowed the identification of both the (9-cis, 11-trans) 18:2 CLA and the minor (9-trans, 11-trans) 18:2 CLA.
Further confirmation of the above assignments was achieved with the use of 1 H-13 C HSQC experiment ( Figure 27). Thus, the near generated H10 and H11 protons at 5.97 ppm of (9-trans, 11trans) 18:2 CLA isomer indicated a 13 C cross peak at 130.51 ppm which should be compared with the literature 13

Identification and Quantification of Minor Lipids in Complex Mixtures
The analysis of minor lipids is extremely challenging and complex because it can be very slow and laborious using the classical chromatographic analytical methods. Tsiafoulis et al. [56] reported direct identification and quantification of four minor geometric (9-cis, 11-trans) 18:2, (9-trans, 11-cis) 18:2, (9-cis, 11-cis) 18:2 and (9-trans, 11-trans) 18:2 conjugated linoleic acid (CLA) isomers ( Figure 25) in lipid fractions of lyophilized milk samples with the combined use of 2D 1 H-1 H TOCSY ( Figure 26) and 2D 1 H-13 C HSQC (Figure 27). Selective saturation of major lipid signals, resulted in an increase in the S/N of the CLA resonances by a factor of three due to the significantly higher receiver gain of the spectrometer (Section 4.1). This allowed the identification of both the (9-cis, 11-trans) 18:2 CLA and the minor (9-trans, 11-trans) 18:2 CLA.
Further confirmation of the above assignments was achieved with the use of 1 H-13 C HSQC experiment ( Figure 27). Thus, the near generated H10 and H11 protons at 5.97 ppm of (9-trans, 11-trans) 18:2 CLA isomer indicated a 13 C cross peak at 130.51 ppm which should be compared with the literature 13 C values of 130.37 and 130.51 ppm for carbons, respectively. Moreover, the H10 and H11 resonances at 6.22 ppm that correlate to the C10 and C11 carbons at 123.74 ppm are most likely due to the presence of (9-cis, 11-cis) 18:2 CLA isomer. Decrease of the spectral width in the 13 C dimension from~143 ppm to~30 ppm resulted in a significant increase in the digital resolution. Thus, in addition to the major resonance at 6.27 ppm with a cross peak at 125.58 ppm, due to (9-cis, 11-trans) 18:2 isomer, the minor resonance at 6.29 ppm with a cross peak at 125.85 ppm was tentatively designed to H10-C10 connectivities of the (9-trans, 11-cis) 18:2 isomer.     The determination of the concentration of the CLA isomers was based on the combination of 1D 1 H-NMR and 2D 1 H-13 C HSQC described by Lewis et al. [126] on the basis of calibration curves from known concentrations of the geometric isomers. The integral of each isomer was normalized with the respect to the signal of the reference compound TSP-d 4 in DMSO-d 6, of known concentration, in a coaxial arrangement.
Although the reduced 13 C spectra width is a useful method to increase digital resolution in the 13 C dimension in 2D 1 H-13 C HSQC experiments, complications may arise due to folding resonances.
As demonstrated by Dais et al. [60] band-selective 1 H-13 C HSQC and 1 H-13 C HMBC experiments can provide excellent resolution in the 13 C dimension comparable to that obtain with 1D 13 C-NMR (Figures 18 and 22).
Recently the direct identification of six minor species in the lipid fraction of milk and halloumi cheese, (9 cis, 11-trans) 18:2 and (9-trans, 11-trans) 18:2 CLA isomers, caproleic acid (CA), glycerol in 1,2-diacylglyceride (1,2 DAG), 1-monoacylglyceride (1-MAG), and 2-monoacylglyceride (2-MAG), was achieved with the use of selective one-dimensional total correlation spectroscopy (1D-TOCSY). Figure 28 illustrates a 500 MHz 1 H-NMR spectrum of the lipid fraction of a lyophilized halloumi cheese sample in CDCl 3 . Selective 1D TOCSY experiment, with 400 mixing time of the H11 proton of the (9-cis, 11-trans) 18:2 CLA isomer illustrates an effective magnetization transfer throughout the full spin system, although the signals of the H2 to H8 and H12 to H18 were completely hidden in the conventional 1D 1 H-NMR spectrum under the resonances of the abundant TAG analytes with signal intensities stronger by a factor of 4 × 10 2 to 3 × 10 3 . Similar experiments were performed with the selective excitation of the H10a H10b protons at 4.97 ppm of caproleic acid (Figure 28c) and at 3.72 ppm of the 3 -CH 2 OH proton of the glycerol moiety in 1,2 DAG (Figure 28d).
In all cases the 1D TOCSY experiment allows the complete identification of minor lipids in a time-efficient manner and with excellent resolution. The 1D TOCSY quantification was based on the standard addition method of Sandusky et al. [127]. More specific successive amounts of e.g., 0.5, 1.0 and 2.0 mM of caproleic acid were added and the resulting linear correlation was utilized for the estimation of the concentration of caproleic acid. Table 21 provides the quantification data which are in agreement with those obtained with the use of the GC-MS method of analysis (ISO 15884: 2002) [128].
Selective 1D TOCSY excitation of the bis-allylic protons at 2.82 ppm demonstrated the effective magnetization transfer to the proton of methyl group at 0.98 ppm. Similar results were obtained with selective 1D TOCSY excitation of the -CH 3 group at 0.98 ppm which demonstrated the effective magnetization transfer to the bis-allylic protons at 2.82 ppm with complete elimination of the bis-allylic protons of linoleic acid at 2.78 ppm. This provided assignment that the resonances at 2.82 and 0.98 ppm should be attributed to the α-linolenic acid [123].
A selective 1D TOCSY excitation for the assignment of the weak bis-allylic protons at 2.85 ppm demonstrated not only an effective magnetization transfer to the -CH 3 group at 0.98 ppm and, thus, its assignment as an ω-3 lipid, but also to a very characteristic complex resonance at 2.46 ppm. This provided an unequivocal assignment that the ω-3 lipid is the docasahexaenoic acid (DHA). These experiments clearly demonstrated that the 1D TOCSY allows for the unequivocal assignment and structure elucidation of ω-3 and ω-6 lipids in a time-efficient manner and with excellent spectral resolution [123].    Figure 30 illustrates an apparent triplet at 5.92 ppm ( 3 J = 10.9 Hz) of the H10 olefinic proton of the (9-cis, 11-trans) 18:2 CLA which is strongly overlapped with a minor peak at 5.97 ppm which has been assigned to the composite signal of the H10 and H11 protons of the (9-trans, 11-trans)    Figure 30 illustrates an apparent triplet at 5.92 ppm ( 3 J = 10.9 Hz) of the H10 olefinic proton of the (9-cis, 11-trans) 18:2 CLA which is strongly overlapped with a minor peak at 5.97 ppm which has been assigned to the composite signal of the H10 and H11 protons of the (9-trans, 11-trans) 18:2 CLA isomer. Selective excitation of the minor peak at 5.97 ppm clearly demonstrates magnetization transfer to the composite signal of the H9 and H12 resonances at 5.54 ppm which are not overlapped with other resonances of the lipid milk fraction.   In (b) τm = 400 ms was used for magnetization transfer from H11 to H9 of the (9-cis, 11-trans) 18:2 CLA. In (c) τm = 70 ms was used in order to optimize magnetization transfer from H10, 11 to H9, 12 of the (9-trans, 11-trans) 18:2 CLA. The asterisks denote the resonances that were excited with the use of a selective pulse.

Identification and Quantification of Free Fatty Acids
Free fatty acids (FFAs) in oils, waxes and various pharmaceutical excipients [129] arise from several processes including: (i) the hydrolysis of triacylglycerides (TAGs) during production and storage of the oil, (ii) handling of the row material and (iii) secondary oxidation of unsaturated aldehydes or other oxidation products originating from the cleavage of lipid hydroperoxides resulting in the formation of short chain FFAs [130].
Satyarthi et al. [131] utilized the integration of the α-CH2 methylene protons to quantify free fatty acids in non-edible lipids and biodiesel. The method is not sufficiently sensitive to detect small content of FFA in lipids due to the presence of a strong signal from the α-CH2 protons of esterified groups. Recently, Skiera et al. [129,132] utilized the integration of the free carboxylic group which is extremely deshielded. The method was applied to 305 oil and fat samples. Application to castor oil was not successful due to extensive line broadening which may be attributed to exchange with the OH protons of alcohol groups. It was, therefore, necessary to use mixtures of CDCl3/DMSO-d6 to reduce exchange rates and, thus, line widths. Non-protic hydrogen bonding organic solvents, especially DMSO-d6, have been extensively utilized in the reduction of proton exchange rates of OH groups in natural products [133][134][135][136]. 31 P-NMR has been utilized to investigate FFA content in lipids, however, the method requires the derivatization of FFAs prior to 31 P-NMR analysis [137][138][139]. It In (b) τ m = 400 ms was used for magnetization transfer from H11 to H9 of the (9-cis, 11-trans) 18:2 CLA. In (c) τ m = 70 ms was used in order to optimize magnetization transfer from H10, 11 to H9, 12 of the (9-trans, 11-trans) 18:2 CLA. The asterisks denote the resonances that were excited with the use of a selective pulse.

Identification and Quantification of Free Fatty Acids
Free fatty acids (FFAs) in oils, waxes and various pharmaceutical excipients [129] arise from several processes including: (i) the hydrolysis of triacylglycerides (TAGs) during production and storage of the oil, (ii) handling of the row material and (iii) secondary oxidation of unsaturated aldehydes or other oxidation products originating from the cleavage of lipid hydroperoxides resulting in the formation of short chain FFAs [130].
Satyarthi et al. [131] utilized the integration of the α-CH 2 methylene protons to quantify free fatty acids in non-edible lipids and biodiesel. The method is not sufficiently sensitive to detect small content of FFA in lipids due to the presence of a strong signal from the α-CH 2 protons of esterified groups. Recently, Skiera et al. [129,132] utilized the integration of the free carboxylic group which is extremely deshielded. The method was applied to 305 oil and fat samples. Application to castor oil was not successful due to extensive line broadening which may be attributed to exchange with the OH protons of alcohol groups. It was, therefore, necessary to use mixtures of CDCl 3 /DMSO-d 6 to reduce exchange rates and, thus, line widths. Non-protic hydrogen bonding organic solvents, especially DMSO-d 6 , have been extensively utilized in the reduction of proton exchange rates of OH groups in natural products [133][134][135][136]. 31 P-NMR has been utilized to investigate FFA content in lipids, however, the method requires the derivatization of FFAs prior to 31 P-NMR analysis [137][138][139]. It should be emphasized that the most successful method for the identification and quantification of FFAs is 13 C-NMR in the carboxyl and ester carbonyl region (Section 3.2.1) despite the long experimental times required [140,141].

Investigation of Oxidation Products
The problem of oxidative deterioration is of great economic importance in the production of lipid containing foods. Oxidation of unsaturated lipids not only produces offensive odours and flavours but can also decrease the nutritional quality and safety due to the formation of secondary reaction products. Even for a simple monounsaturated lipid, such as oleate, the autoxidation may lead to a variety of hydroperoxides and terminal products. NMR spectroscopy is regarded as one of the most reliable methods to study lipid peroxidation for two reasons: (i) it can investigate changes in the starting materials as well as the evolution of various oxidation products during the process, and (ii) does not require any chemical reaction, contrary to various spectrophotometric techniques [26,28,29]. 1 H-NMR spectroscopy has been extensively utilized to elucidate the structures of primary and secondary products of lipid peroxidation [26,28,29]. Chan et al. [142] investigated the oxidation of methyl linoleate for 48-72 h at 30 • C and elucidated, after HPLC analysis, the structures of four major oxidized products by using a low field (90 MHz) NMR spectrometer. Similarly, Neff et al. [143], elucidated the structures of oxidized products from photoxidation of methyl linoleate ( Figure 31). It should be emphasized that the six membered epidioxides undergo hydrogen abstraction, loss of O 2 and rearrangement of double bonds to form other oxidized products of methyl linoleate. 1 H-NMR was used by Saito [144] to determine the extent of lipid peroxidation of fish oil stored at 40 • C. A significant difference in the peak area of olefinic protons compared to the aliphatic protons was observed, which is a strong indication of oxidation. The ratios of aliphatic to olefinic protons and aliphatic to diallylmethylene protons were found to gradually increase during the oxidation of lipids and may serve as an index of oxidative degradation of oil samples [145]. Grootveld et al. [146][147][148] investigated in detail lipid oxidation products in autoxidized culinary oils rich in PUFAs which were subjected to standard frying/cooking practices. With the use of various 2D 1 H-1 H and 2D 1 H-13 C-NMR techniques the detection and quantification of trans-2-alkenals, trans-trans, and cis-trans-alka-2,4-dienals and n-alkanals were achieved.
Goicoechea and Guillen [149], have reported a detailed study of primary and secondary oxidized products of corn oil being oxidized at room temperature and provided chemical shifts and splitting patterns for a variety of oxidation products which are of importance in analysing lipid oxidation. For example, the aldehyde proton resonates at 9.3-10 ppm and a doublet signal indicates an adjacent CH group. Therefore, the doublet signal at 9.49 ppm can be regarded as (E)-2-alkenal. On the other hand, the triplet signal at 9.75 indicates an adjacent CH 2 group and may be regarded as the aldehyde proton from alkanals.
Guillen et al. [26] comprehensively reviewed the use of NMR techniques to study the thermal oxidation of food lipids. In addition to thermal oxidation, the concentration and nature of the compounds formed were also described. Table 22 presents chemical shifts and multiplicities of the 1 H-NMR signals in CDCl 3 of some primary and secondary (or further) oxidation compounds generated in edible oils and model lipid compounds submitted to different degradative conditions [149][150][151][152][153][154][155][156][157][158][159][160][161][162][163]. These include various types of aldehydes, ketones, alcohols and epoxides. The formation of these secondary oxidized compounds depends upon composition of the original food lipid and thermooxidation conditions used.   Figure 31. Oxidized products of methyl linoleate. Adopted, with permission, from [143]. Copyright 1983, Oil Chemists' Society (AOCS).  It is worth noticing that aldehydes are, generally, considered to be the secondary oxidation products, all α,β-unsaturated aldehydes have conjugated double bonds and few of them have hydroperoxy groups as well. This indicates that neither conjugated diene nor the hydroperoxy group are exclusive primary oxidation products. Figure 32 illustrates some primary oxidation products derived from unsaturated oleic and linolenic acyl groups. Figure 33 illustrates secondary and further oxidation products derived from linolenic acyl groups.
Skiera et al. [164] suggested a 1 H-NMR method for the quantification of hydroperoxides in edible oils. Proton transfer line width broadening of the hydroperoxide (OOH) signal was significantly eliminated using a mixture of CDCl 3 and DMSO-d 6 (5:1 v:v) and, thus, accurate integration could be obtained. The method was applied to 200 edible oil samples and the analytical performance was compared with the commonly used method of peroxide value (PV). Significant discrepancies between the two methods for some oil varieties were observed. The low hydroperoxide values in the case of olive oils compared with the NMR values were attributed to the high content of specific phenolic compounds which exhibit strongly deshielded 1 H-NMR chemical shifts in the region of hydroperoxide signals [165][166][167].  Lachenmeier et al. [166] utilized the aldehyde proton resonances in the region of 9-10 ppm for quality control of vegetable oils and decorative cosmetics. The method was used to analyze 72 oil and 38 cosmetic samples in order to investigate their compliance with food and cosmetics regulations. 22 samples (31%) from the vegetable oil, contained detectable levels of aldehydes. Only two samples contained levels above 100 mg kg −1 (Figure 34). 26 samples (68%) from the analyzed 38 lipsticks were found to contain aldehydes above the detection limits and 15 had levels above 100 mg kg −1 . One sample, which was characterized by a rancid state, was found to contain over 2000 mg kg −1 of total aldehydes ( Figure 35). It was concluded that lipsticks are problematic with regard to oxidative  Lachenmeier et al. [166] utilized the aldehyde proton resonances in the region of 9-10 ppm for quality control of vegetable oils and decorative cosmetics. The method was used to analyze 72 oil and 38 cosmetic samples in order to investigate their compliance with food and cosmetics regulations. 22 samples (31%) from the vegetable oil, contained detectable levels of aldehydes. Only two samples contained levels above 100 mg kg −1 (Figure 34). 26 samples (68%) from the analyzed 38 lipsticks were found to contain aldehydes above the detection limits and 15 had levels above 100 mg kg −1 . One sample, which was characterized by a rancid state, was found to contain over 2000 mg kg −1 of total aldehydes ( Figure 35). It was concluded that lipsticks are problematic with regard to oxidative Figure 33. Some of the secondary or further oxidation compounds derived from linoleic acyl groups that can be detected by 1 H-NMR. Adopted, with permission, from [26]. Copyright 2014, Institute of Food Technologists.
Lachenmeier et al. [166] utilized the aldehyde proton resonances in the region of 9-10 ppm for quality control of vegetable oils and decorative cosmetics. The method was used to analyze 72 oil and 38 cosmetic samples in order to investigate their compliance with food and cosmetics regulations. 22 samples (31%) from the vegetable oil, contained detectable levels of aldehydes. Only two samples contained levels above 100 mg kg −1 (Figure 34). 26 samples (68%) from the analyzed 38 lipsticks were found to contain aldehydes above the detection limits and 15 had levels above 100 mg kg −1 . One sample, which was characterized by a rancid state, was found to contain over 2000 mg kg −1 of total aldehydes ( Figure 35). It was concluded that lipsticks are problematic with regard to oxidative stability presumably due to relatively high temperatures (>75 • C) used and the presence of pro-oxidants, such as iron oxides, which may be contained as pigments. stability presumably due to relatively high temperatures (>75 °C) used and the presence of prooxidants, such as iron oxides, which may be contained as pigments.   stability presumably due to relatively high temperatures (>75 °C) used and the presence of prooxidants, such as iron oxides, which may be contained as pigments.

LC-NMR
LC-NMR is one of the most powerful methods for separation and structural elucidation of unknown compounds in mixtures [169][170][171][172][173]. LC-NMR, thus, represents a potentially interesting complementary technique to LC-MS in analysis of complex biological matrices for the detailed on-line structural analysis of products. However, there is a very limited number of recent publications about applications that can demonstrate the usefulness of this technique in lipid analysis.
LC-NMR was used for the quantification of αand γ-linolenic free fatty acids resulting from blackcurrant (Ribes nigrum) hydrolysis reaction [174]. A 2D reverse phase HPLC method with two HPLC columns, C 8 and C 18 in a series, was utilized. The results were found to be in agreement with the GC method on FAME.

Lipidomics
Lipidomics is a subfield of metabolomics that focuses on the study of molecular lipids within a cell, tissue, and biofluids, including the analysis of lipid species and their abundance as well as studies of their biological activities, subcellular localization, and tissue distribution [175][176][177]. The most commonly applied analytical methods for lipidomics are based on MS, often combined with chromatographic separation methods such as LC and GC. Several hundreds of lipids can be separated with the UPLC-MS methodologies in the profiling studies of various biological matrices. For sufficiently volatile lipids, GC-MS and GC coupled to flame ionization detection is the most widely used method for the analysis of FAs, both for FFAs and esterified FAs. Nevertheless, a significant number of studies have used NMR in the field of lipidomics including composition and authenticity of oils, quality and identification of dairy products and their provenance and geographical origin quality, and lipoprotein analysis in serum/plasma. Some representative examples will be analyzed below.

Authentication and Quality Assessment of Oils
Extra virgin olive oil is the most investigated oil due to its high quality nutritional and sensorial properties and, thus, high commercial value. This frequently leads to adulterations with low quality oils of different botanical origin or refined olive oils. Furthermore, the analysis and monitoring of olive oils of specific protected geographical origin is a challenging analytical problem for NMR spectroscopy because there is no single physicochemical parameter which allows a comprehensive investigation [178,179]. Therefore, emphasis has been given to food fingerprinting with the intrinsic aim to detect as many compounds in the metrics as possible. Mannina and Sobolev provided a comprehensive overview of high resolution NMR characterization of Mediterranean olive oils in terms of quality, authenticity and geographical characterization [180]. Dais and Hatzakis investigated, with the use of NMR, the geographical and varietal classification of extra virgin oil [181] and provided a comprehensive overview of NMR methods for quality control and authentication of olive oil through metabolic profiling or fingerprinting [182]. 1

H-NMR investigations of a large number of oil samples and subsequent PLS-DA statistical
analysis demonstrated the correct, up to 90%, sample classification/prediction [183][184][185]. 1 H NMR was utilized to predict the geographical origin of olive oil samples (three regions from Italy and four regions from Greece) with a use of data bucketing and PSA and by a Monte Carlo embedded cross-validation [73]. Due to the rather limited number of samples which were investigated, correct prediction probabilities of 78% were achieved with region specific correct predictions of 53% to 100%. 1 H-NMR and isotopic fingerprinting were utilized to investigate the geographical origin or protected designation origin (PDO) of 125 virgin olive oils from five Mediterranean countries, using a variety of supervised or unsupervised statistical tools [186]. Mannina et al. [187] investigated by 1 H NMR the presence of refined hazelnut oil in admixtures with refines olive oils. Analysis of 92 samples with multiple regression models predicted, with R 2 >0.9984, contamination of hazelnut oil in olive oil at concentrations as low as 10%.

Authentication and Quality Assessment of Dairy Products
1 H-NMR was used to characterize the lipid fraction of buffalo and cow milk samples [188].
Multivariate statistical analysis of the quantification results permitted buffalo and cow milk to be differentiated. The total concentration of saturated and unsaturated FAs were eliminated from the data since they were found to be highly correlated with the MUFA concentrations. Schievano et al. [189] utilized a combination of 1 H-NMR selective 1D TOCSY, 13 C and 1 H-13 C HMQC to discriminate Asiago d' Allevo cheese samples. The cheese, which is produced from raw dairy milk, has a protected denomination of origin (PDO) mark. Figure 36 illustrates selected regions of the 1 H-NMR spectrum of a representative cheese sample from an alpine farm and comparison with the spectrum from an industrial factory (insets in Figure 36). A higher amount of unsaturated fatty acids, both in the olefinic and bis-allylic regions, were observed in the cheese from alpine farms. A statistical analysis of the NMR spectra of the lipid fraction demonstrated that the cheese samples from alpine farms are clearly separated from the remaining ones and are clustered in the left side of the PCA plot. The loadings in Figure 37 demonstrate PC1 negative values for the olefinic and allylic protons, the methyl groups of linolenic acid and the bis-allylic protons in which case the higher contribution is from linolenic acid. On the contrary, PC1 loadings show positive values for the saturated fatty acids. It was concluded that cheeses produced in alpine farms are significantly different i.e., they contain higher amount of PUFA, from those produced in low land and mountain industrialized factories based on objective NMR metabolite parameters.   Figure 36). Adopted, with permission, from [189]. Copyright 2008, American Chemical Society.
Of particular interest is the application of 1 H-NMR to whole milk without any pre-treatment [190]. The 1 H-NMR signals of butyric acid, mono and polyunsaturated fatty chains and lecithin have been assigned using 2D NMR experiments.
Chemometric analysis of 1 H and 13 C-NMR, stable isotope-ratio mass spectrometry and GC data was utilized to differentiate organic and conventional milk [191]. Yang et al. [192] investigated metabolic biomarkers of the water soluble fraction of milk from Holstein cows and other minor dairy animals. Data of the lipid fraction, however, were not reported.

Authentication and Quality Assessment of Fish and Meat Lipids
The increasing production and consumption of fish products, has led to an increasing demand for analytical methods for the unequivocal determination of wild vs. farmed specimens, ecological products and geographical origins. The lipid variability and profile of fish is very large with about 20 fatty acids in relative amounts >1%.
Aursand et al. [193] utilized 13 C-NMR and pattern recognition techniques for the discrimination of farmed and wild Atlantic salmon (Salmo salar L.), different geographical origins and verification of the origin of market samples. Muscle lipids of 195 samples from seven different countries in addition to market samples, were analyzed. Excellent discrimination (98.5% to 100%) was achieved between wild and farmed salmon. Correct classification with respect to geographical origin was from 82.2% to 99.3%. The farmed fish was found to have a relatively high level of ω-6 fatty acids, abundant in vegetables oils, compared to the wild fish ( Figure 38). 13 C-NMR was used for the regiospecific analysis of TAG in fish oils [194]. Through PCA analysis, it was concluded that the chemical shifts of the sn-2 MUFAs and SFAs contribute mostly to the classification of different salmon species. 13 C-NMR was also applied for the classification of 112 commercial fish oil capsule products using unsupervised multivariate analysis, Kohonen neural networks and generative topographic mapping [195]. 1 H-NMR profiling of lipids extracts combined with PCA and LDA was used to classify wild and farmed samples of gilthead sea bream from the Mediterranean region [196] and to investigate the effect of various production practices.
Although the glycerol carbon atoms are usually considered to be less sensitive to individual asymmetric distribution, Diehl et al. [197] were able to investigate detailed regiospecific analysis of the FA distribution in neutral and polar lipids from krill oil. In contrast to fish oil where EPA and DHA are found in the TAG form, krill oil is characterized by lower amounts of TAG. Figure 39 illustrates the dominant presence of PUFAs and more specific of DHA and EPA in the sn-2 position of phosphatidylcholine (PC). 31 P-NMR was validated, with regard to major phospholipid species of krill oil, according to Good Laboratory Practice (GLP) and International Council for Harmonization (ICH) guidelines [197]. It was demonstrated that the method is highly accurate, sensitive, reproducible and robust regardless of the type of NMR spectrometer used by different laboratories. 1 H-NMR has also been used in meat authentication and determination of geographical origin and investigation of adulteration practice of mixing meat from different species or tissues. Al-Jowder et al. [198] reported that 1 H-NMR can be utilized to distinguish liver, kidney and muscle tissues of beef. Authentication of beef vs. horse meat was achieved using a very low frequency (60 MHz) instrument [199]. The analysis of 107 extracts was based on the 1 H-NMR signals of olefinic, bis-allylic, and terminal -CH 3 groups. 1 H-NMR fingerprinting of lipids with chemometric tools allowed the detection of irradiated vs. non irradiated beef samples [200]. NMR and isotope ratio mass spectrometry was used to characterize animal products according to geographic origin and feeding diet [201]. 13 C-NMR demonstrated that the degree of saturation of FAs and MUFAs was significantly higher (p < 0.005) for animals fed on maize silage than for grazing steers (vice versa for PUFAs and SFAs). was demonstrated that the method is highly accurate, sensitive, reproducible and robust regardless of the type of NMR spectrometer used by different laboratories. 1 H-NMR has also been used in meat authentication and determination of geographical origin and investigation of adulteration practice of mixing meat from different species or tissues. Al-Jowder et al. [198] reported that 1 H-NMR can be utilized to distinguish liver, kidney and muscle tissues of beef. Authentication of beef vs. horse meat was achieved using a very low frequency (60 MHz) instrument [199]. The analysis of 107 extracts was based on the 1 H-NMR signals of olefinic, bis-allylic, and terminal -CH3 groups. 1 H-NMR fingerprinting of lipids with chemometric tools allowed the detection of irradiated vs. non irradiated beef samples [200]. NMR and isotope ratio mass spectrometry was used to characterize animal products according to geographic origin and feeding diet [201]. 13 C-NMR demonstrated that the degree of saturation of FAs and MUFAs was significantly higher (p < 0.005) for animals fed on maize silage than for grazing steers (vice versa for PUFAs and SFAs).  . Selected 13 C regions of triacylglycerol (TAG) (B) and phosphatidylchorine (PC) (C). Adopted, with permission, from [197]. Copyright 2016, AOCS.

Serum/Plasma Lipoprotein Analysis
Several human diseases show abnormal patterns of unsaturated fatty acids especially due to insufficient capabilities for desaturation or chain elongation. Therefore, the assignment and quantification of individual unsaturated fatty acids in body fluids are of great importance. Willker and Leibfritz utilized a semi-selective 1 H-13 C HSQC experiment [86,89] to obtain ultra-high resolution in the 13 C double bond region (~0.7 Hz per point) and, thus, to assign and quantify individual Figure 39. 13 C-NMR spectrum of krill oil in the region of glycerol carbon atoms (A). Selected 13 C regions of triacylglycerol (TAG) (B) and phosphatidylchorine (PC) (C). Adopted, with permission, from [197]. Copyright 2016, AOCS.

Serum/Plasma Lipoprotein Analysis
Several human diseases show abnormal patterns of unsaturated fatty acids especially due to insufficient capabilities for desaturation or chain elongation. Therefore, the assignment and quantification of individual unsaturated fatty acids in body fluids are of great importance. Willker and Leibfritz utilized a semi-selective 1 H-13 C HSQC experiment [86,89] to obtain ultra-high resolution in the 13 C double bond region (~0.7 Hz per point) and, thus, to assign and quantify individual unsaturated fatty acids, such as 18:1, 18:2 and 20:4 in body fluids (blood plasma and cerebrospinal fluid) and pig brain (grey and white matter). Additional 1 H-13 C HSQC-TOCSY experiments allowed the direct correlation between the olefinic 13 C signals with the adjacent allylic 1 H signals. Figure 40 illustrates selective 800 MHz 1 H-13 C HSQC-TOCSY spectrum of the double bond region of blood plasma lipids. In the C=C-CH 2 -C=C region the 18:2 signals are well separated from 18:3 and 20:4 polyunsaturated fatty acids. In the C=C-CH 2 -region the 18:1 and 20:4 signals are well separated from the rest of the lipids [89].  NMR spectroscopy has been extensively utilized for the qualitative and quantitative determination of lipoproteins, cholesterol and triacylglycerides ( Figure 41 [202]) and the number of sub fraction articles and their size [203,204]. Numerous studies have been reported to monitor changes in the organization of lipids within particle subclasses [205], to investigate the effects of exercise on lipoprotein profile [206], changes in lipids induced by diet therapies [207], lipoprotein analysis in the study of diabetes and related diseases [208], in assessing CVD risk [202] and in investigating the progression of coronary heart disease [209]. Readers should consult a recent comprehensive review article [203]. NMR spectroscopy has been extensively utilized for the qualitative and quantitative determination of lipoproteins, cholesterol and triacylglycerides ( Figure 41 [202]) and the number of sub fraction articles and their size [203,204]. Numerous studies have been reported to monitor changes in the organization of lipids within particle subclasses [205], to investigate the effects of exercise on lipoprotein profile [206], changes in lipids induced by diet therapies [207], lipoprotein analysis in the study of diabetes and related diseases [208], in assessing CVD risk [202] and in investigating the progression of coronary heart disease [209]. Readers should consult a recent comprehensive review article [203]. A diffusion-edited NMR spectrum enhances the NMR signal of lipoproteins and removes signals from small metabolites [210]. This allows the composition of the constituent lipids of lipoproteins to be assigned and analyzed, through the acquisition of a set of diffusion-edited NMR spectra with an increasing strength in gradient, which enables the translational diffusion coefficients to be calculated.
For the quantification of cholesterol and triacylglycerides in several sub fractions and the calculation of particle number, the decomposition of the CH3 groups and/or correlation statistical methods have been utilized [211][212][213]. Peak overlapping, however, is very severe which makes the lineshape fitting to individual sub fractions problematic and prone to finding multiple solutions [204].

Investigation of Lipid-Derived Molecules
Lipid-derived molecules play a pivotal role in many biological processes including cellular signaling, secretion and cellular proliferation [214]. Brash et al. [215] isolated and characterized two geometric allene isomers synthesized from natural 9S-hydroperoxylinoleic acid by allene oxide synthese cytochrome P450 CYB74C3. The obtained results, especially of a novel 10 cis isomer, provided insights into the mechanisms of allene oxide cyclization and the double bond geometry in naturally occurring allene oxides.
For the quantification of cholesterol and triacylglycerides in several sub fractions and the calculation of particle number, the decomposition of the CH 3 groups and/or correlation statistical methods have been utilized [211][212][213]. Peak overlapping, however, is very severe which makes the lineshape fitting to individual sub fractions problematic and prone to finding multiple solutions [204].

Investigation of Lipid-Derived Molecules
Lipid-derived molecules play a pivotal role in many biological processes including cellular signaling, secretion and cellular proliferation [214]. Brash et al. [215] isolated and characterized two geometric allene isomers synthesized from natural 9S-hydroperoxylinoleic acid by allene oxide synthese cytochrome P450 CYB74C3. The obtained results, especially of a novel 10 cis isomer, provided insights into the mechanisms of allene oxide cyclization and the double bond geometry in naturally occurring allene oxides.

Protein-Lipid Interactions
Large amounts of free fatty acids, FFA, circulate in mammalian plasma and play significant role in a variety of physiological activities, as substrates for complex protein-lipid interactions and in important signaling events [219,220]. FFA are present in blood at concentration from about 100 µM to more than 0.1 mM. The pool of circulating FFA is composed of approximately forty distinct molecular species. The FFA profile is expected to reflect the physiological state and changes in the profile have been correlated with diseases [221].
Many FFA are bound to serum albumin. Under normal physiological conditions 0.1-2 moles of fatty acids are bound to albumin. The fatty acid ligands are in rapid exchange between solution and their binding sites in the protein. Human serum albumin (HSA) is a monomeric protein of 585 amino acids with a molecular weight of 66.4 kDa. The X-ray structure determination [222,223] demonstrated that the protein is 67% α-helical, without β-sheets, with three homologous domains (labeled I-III) and 17 intra-subdomain disulphide bridges which are conserved across species and contribute to the high thermostability of the protein. Each domain is comprised of two subdomains. The X-ray structure of the complex of HSA with myristate revealed six fatty acid binding sites [224]. Five of the sites (numbers 1-5 in Figure 42) are characterized by a strong electron density of the ligand [225]. The sixth ligand was tentatively assigned at the interface between the subdomains IIA and IIB. The binding sites 1, 4 and 5 are within a single subdomain in IB, IIIA and IIIB, respectively. The binding sites 2 and 3 incorporate residues from different domains [225].
A number of biochemical labeling and NMR experiments [226][227][228] implicated domains I and III in fatty acid binding. In particular, NMR studies using fatty acids selectively labeled with 13 C demonstrated that the carboxylate group of the fatty acid ligand was bound more tightly in the binding site due to electrostatic interactions, than the flexible hydrophobic methylene chain [229,230]. Subsequent NMR studies with 13 C-labeled laurate, myristate, palmitate, stearate and oleate were interpreted with the existence of at least five distinct chemical shifts for the carboxylate carbon due to five distinct binding sites with BSA [231][232][233]. Variation of the pH revealed that four of the five binding sites are involved in electrostatic interactions in the pH range of 4-8 due to ionic hydrogen bonds between the carboxylate group of the fatty acid and side chain of basic aminoacids, such as arginine or lycine. It should be noticed that the X-ray structure demonstrates ionic hydrogen bond interactions for all six binding sites. Comparative NMR studies of intact and proteolitic fragments of BSA identified three high-affinity sites of oleic acid [226], one in domain I and two in domain II. Detailed NMR studies of the binding of 13 C-carboxyl labelled palmitate to HSA in the presence of competitor ligands and drugs, for specific binding sites, allowed the location of high and low affinity fatty acid and the correlation of specific binding site from the X-ray structures to specific 13 C-NMR signals.

Protein-Lipid Interactions
Large amounts of free fatty acids, FFA, circulate in mammalian plasma and play significant role in a variety of physiological activities, as substrates for complex protein-lipid interactions and in important signaling events [219,220]. FFA are present in blood at concentration from about 100 μM to more than 0.1 mM. The pool of circulating FFA is composed of approximately forty distinct molecular species. The FFA profile is expected to reflect the physiological state and changes in the profile have been correlated with diseases [221].
Many FFA are bound to serum albumin. Under normal physiological conditions 0.1-2 moles of fatty acids are bound to albumin. The fatty acid ligands are in rapid exchange between solution and their binding sites in the protein. Human serum albumin (HSA) is a monomeric protein of 585 amino acids with a molecular weight of 66.4 kDa. The X-ray structure determination [222,223] demonstrated that the protein is 67% α-helical, without β-sheets, with three homologous domains (labeled I-III) and 17 intra-subdomain disulphide bridges which are conserved across species and contribute to the high thermostability of the protein. Each domain is comprised of two subdomains. The X-ray structure of the complex of HSA with myristate revealed six fatty acid binding sites [224]. Five of the sites (numbers 1-5 in Figure 42) are characterized by a strong electron density of the ligand [225]. The sixth ligand was tentatively assigned at the interface between the subdomains IIA and IIB. The binding sites 1, 4 and 5 are within a single subdomain in IB, IIIA and IIIB, respectively. The binding sites 2 and 3 incorporate residues from different domains [225].
A number of biochemical labeling and NMR experiments [226][227][228] implicated domains I and III in fatty acid binding. In particular, NMR studies using fatty acids selectively labeled with 13 C demonstrated that the carboxylate group of the fatty acid ligand was bound more tightly in the binding site due to electrostatic interactions, than the flexible hydrophobic methylene chain [229,230]. Subsequent NMR studies with 13 C-labeled laurate, myristate, palmitate, stearate and oleate were interpreted with the existence of at least five distinct chemical shifts for the carboxylate carbon due to five distinct binding sites with BSA [231][232][233]. Variation of the pH revealed that four of the five binding sites are involved in electrostatic interactions in the pH range of 4-8 due to ionic hydrogen bonds between the carboxylate group of the fatty acid and side chain of basic aminoacids, such as arginine or lycine. It should be noticed that the X-ray structure demonstrates ionic hydrogen bond interactions for all six binding sites. Comparative NMR studies of intact and proteolitic fragments of BSA identified three high-affinity sites of oleic acid [226], one in domain I and two in domain II.
Detailed NMR studies of the binding of 13 C-carboxyl labelled palmitate to HSA in the presence of competitor ligands and drugs, for specific binding sites, allowed the location of high and low affinity fatty acid and the correlation of specific binding site from the X-ray structures to specific 13 C-NMR signals.    Figure 43 illustrates a strategy of resolving and identifying peaks by drug competition. FA site 1 appears as a well-resolved peak and FA site 2 with enhanced resolution. The propofol (PFL), site II drug, displaces FA from sites 3 and 4 and, thus, 4 attenuates the NMR peaks corresponding to those sites. Displacement of FA from these sites leads to enhancement of the signal from site 1 [234]. It was demonstrated that fatty acid sites 2,4 and 5 bind FA with high affinity, while sites 1, 3, 6 and 7 exhibit low affinity to FA. More recently, the enhanced sensitivity and resolution of 1 H-13 C HSQC experiments using [ 13 C]-methyl-labeled oleic acid 18:1 provided evidence of nine distinct binding sites to HSA (Figure 44) [235]. Individual binding sites were detected in the NMR spectra since the binding sites are structurally distinct and the binding site exchange rates are slow in the NMR time scale. Detailed analysis of competition experiments, with a wide range of drugs, provided evidence for site-specific characterization of the mutual effects of FA and ligand binding [235,236].  [224] (PDB ID, 1bj5). Both crystal structures have been fully refined to 2.5 Å resolution. The six myristate molecules are numbered 1-6 and shown in a space-filling representation. Adopted, with permission, from [225]. Copyright 1999, Elsevier Science B.V. Figure 43 illustrates a strategy of resolving and identifying peaks by drug competition. FA site 1 appears as a well-resolved peak and FA site 2 with enhanced resolution. The propofol (PFL), site II drug, displaces FA from sites 3 and 4 and, thus, 4 attenuates the NMR peaks corresponding to those sites. Displacement of FA from these sites leads to enhancement of the signal from site 1 [234]. It was demonstrated that fatty acid sites 2,4 and 5 bind FA with high affinity, while sites 1, 3, 6 and 7 exhibit low affinity to FA. More recently, the enhanced sensitivity and resolution of 1 H-13 C HSQC experiments using [ 13 C]-methyl-labeled oleic acid 18:1 provided evidence of nine distinct binding sites to HSA ( Figure 44) [235]. Individual binding sites were detected in the NMR spectra since the binding sites are structurally distinct and the binding site exchange rates are slow in the NMR time scale. Detailed analysis of competition experiments, with a wide range of drugs, provided evidence for site-specific characterization of the mutual effects of FA and ligand binding [235,236].   [224] (PDB ID, 1bj5). Both crystal structures have been fully refined to 2.5 Å resolution. The six myristate molecules are numbered 1-6 and shown in a space-filling representation. Adopted, with permission, from [225]. Copyright 1999, Elsevier Science B.V. Figure 43 illustrates a strategy of resolving and identifying peaks by drug competition. FA site 1 appears as a well-resolved peak and FA site 2 with enhanced resolution. The propofol (PFL), site II drug, displaces FA from sites 3 and 4 and, thus, 4 attenuates the NMR peaks corresponding to those sites. Displacement of FA from these sites leads to enhancement of the signal from site 1 [234]. It was demonstrated that fatty acid sites 2,4 and 5 bind FA with high affinity, while sites 1, 3, 6 and 7 exhibit low affinity to FA. More recently, the enhanced sensitivity and resolution of 1 H-13 C HSQC experiments using [ 13 C]-methyl-labeled oleic acid 18:1 provided evidence of nine distinct binding sites to HSA ( Figure 44) [235]. Individual binding sites were detected in the NMR spectra since the binding sites are structurally distinct and the binding site exchange rates are slow in the NMR time scale. Detailed analysis of competition experiments, with a wide range of drugs, provided evidence for site-specific characterization of the mutual effects of FA and ligand binding [235,236].       NMR studies have not been published using isotopic labeling of specific protein aminoacids with 13 C and 15 N to investigate the effect of pH on fatty acid binding. Furthermore, to the best of our knowledge, saturation transfer difference (STD) [237][238][239] and Tr-NOESY [240,241] experiments for

Preparation of Solid and Liquid Samples
The sample preparation includes sampling, concentration and homogenation. In the case of dairy products specific methods of conservation should be used in order to preserve the quality and the composition of nutrients. For animal tissues, rapid metabolic changes can be quenched by a rapid freezing in liquid nitrogen after slaughter [24]. Lyophlization is a common method for long-term stability of samples which increases the efficiency of extraction of lipids due to disruption of cellular membranes [242,243] and increased surface area, and provides a convenient method for a normalization of metabolites per sample dry weight [24]. Some volatile analytes may be lost during the freeze-drying process although, compared to other drying methods, the loss of these compounds may not be a major concern [244]. In the case of oils, the analysis does not involve any pretreatment although, due to high viscosity, dilution is necessary as a preliminary step [114]. The significant effect of concentration on the chemical shifts, should also be taken into account (see discussion below).

Lipid Extraction Methods
Sample preparation is one of the most important steps in the analysis of lipids since it can affect analyte concentration and, thus, the accuracy of quantitative results. The Folch et al. [245] and Bligh-Dyer [246] methods and their variants have been widely used. The method relies upon partitioning the lipid matrix into two immiscible layers, as upper water-methanol and a chloroform one. Optimization of the extraction process can involve several parameters such as agiation or sonication assisted, time duration and temperature of the extraction, the lipid content extracted and the optimum chloroform volume [56]. Figure 45 illustrates a comparison of the efficiency of various extraction methods with respect to unsaturated fatty acids in lyophilized milk samples. The concentration of the extracted analytes deviates strongly from linearity for lyophilized milk above 250 mg, presumably due to progressive saturation of the solution. The extracted solution, after a centrifiguration step, can be evaporated or dried under vacuum and subsequently dissolved in deuterated solvent.  Comparison of various extraction methods in respect to the total (9-cis, 11-trans), (9-trans, 11-cis) and (9-cis, 11-cis) 18:2 CLA isomers and caproleic acid integrals. (B) Efficiency of the extraction of the milk lipid fraction using the Bligh and Dyer 1:2 method in respect to mg of lyophilized milk sample; ( ), the relative integrals of the composite (9-cis, 11-trans), (9-trans, 11-cis) and (9-cis, 11-cis) 18:2 CLA isomers in respect to the standard reference compound as above. ( ), the amount of the extracted composite (9-cis, 11-trans), (9-trans, 11-cis) and (9-cis, 11-cis) 18:2 CLA isomers expressed in mg g −1 of lyophilized milk sample. Adopted, with permission, from [56]. Copyright 2014, by the Elsevier B.V.

NMR Solvent, Referenicng and Quantification Methods
Deuterated chloroform has been widely used in 1 H-and 13 C NMR since it is an excellent solvent for most lipids. For specific applications, mixtures of CDCl 3 and DMSO-d 6 have also been utilized [132,164]. DMSO-d 6 induces significant chemical shift changes with respect to those in CDCl 3 which should be taken into consideration when comparing literature data. The chemical shift of the residual 1 H-NMR signal of CDCl 3 and the 13 C signal of CDCl 3 have been commonly utilized for referencing.
Quantification of unsaturated fatty acids can be achieved in 1 H-NMR using Equations (1) to (10) without the use of internal standard. As previously emphasized, the conversion of 1 H-NMR data from mol % to wt % can be achieved with the hypothesis that the average chain lengths of unsaturated fatty acids are C 18 and by estimating the average number of protons in unsaturated and saturated chains from the integrals of given resonances in the spectrum [124]. An alternative method for quantification is the ERETIC method which provides a reference signal synthesized by an electronic device [247]. Quantification in 13 C-NMR can be obtained by integration of the appropriate carbonyl and olefinic signals [20,92].
For 31 P-NMR, pyridine-chloroform solutions have been utilized (1.6:1.0 volume ratio) containing 0.165 µM of Cr(acac) 3 . Integration of the signal was obtained with respect to cyclohexanol as an internal standard [23,59].

Effects of Temperature and Conentration
Most 1 H-, 13 C-and 31 P-NMR spectra have been acquired in the range of 296 to 298 K, therefore, no significant changes in the chemical shifts of literature data due to temperature variation are expected.
The effect of concentration on chemical shifts is an important aspect which should be considered in lipid analysis. The use of high concentrated solutions in 1 H NMR results: (i) in broadening of the NMR signals and, thus, poor resolution, (ii) baseline distortions and spurious signals due to receiver overload, (iii) saturation of analytes and, thus, unreliable quantification results and (iv) chemical shift variation. Vlahov et al. [92] investigated in detail the effect of sample concentration (200 mg and 50 mg) on the 13 C NMR chemical shifts of lampante olive oils. In most cases, chemical shift variations below 0.2 ppm were observed, however, the large chemical shift variations of the methylene C-2 and C-3 carbons prevented an unequivocal assignment.

Conclusions and Future Prospects
The research work summarized in this article provides sufficient evidence that 1 H-, 13 C-and 31 P-NMR spectroscopy has been a valuable structural and analytical tool for unsaturated lipids The quantitative analysis performed by integration of the appropriate signals is greatly facilitated by the unequivocal assignment of the signals using a variety of 1D and 2D NMR techniques, such as 1 H-1 H TOCSY, 1 H-13 C HSQC, 1 H-13 C HMBC, 1 H-13 C HSQC-DEPT, etc. Further, the latest developments with respect to sensitivity, and the introduction of cryogenerated micro-NMR probes have greatly facilitated the rapid de novo identification of specific polyunsaturated fatty acids.
NMR spectroscopy will undoubtedly continue to be developed as a primary structural and analytical spectroscopic method in the field of unsaturated lipid research. It should be emphasized, however, that it appears unlikely that any single NMR technique will be a panacea for the complete structural analysis of lipids. Cited below are selected current and potential areas where further research could be fruitful: (1) The excellent resolution and sensitivity advantages of the selective 1D TOCSY and band selective 1 H-13 C HSQC, 1 H-13 C HSQC-TOCSY and 1 H-13 C HMBC experiments show great potential in deciphering complex lipid extracts and oxidation products, even though such methods are still not frequently used in lipid research. (2) Application of broadband 1 H homonuclear decoupled techniques will result in highly resolved 1 H-NMR spectra with collapsed singlets, thus minimizing overlap and expediting spectral analysis [248,249]. Several novel 1D and 2D selective experiments and improved slice-selective experiments have been proposed which can provide ultra-highly resolved NMR spectra with great potentialities for accurate determination of very small chemical shift differences, coupling constants, and relaxation times [250][251][252][253][254]. (3) Development of comprehensive NMR databases combined with prediction software will greatly improve the amount of structural information that can be extracted from 1 H, 13 C, 1 H-1 H COSY, 1 H-1 H TOCSY, 1 H-13 C HSQC, and 1 H-13 C HMBC NMR data and would accelerate the dereplication process [255,256]. (4) Application of hyperpolarizable techniques will greatly improve sensitivity since they are capable of generating spin population levels that are~5 × 10 4 times higher than the Boltzman equilibrium at room temperature [257]. Particularly promising results can be obtained in solution state by dissolution dynamic nuclear polarization (DNP), where the sample to be analyzed is mixed with free radicals in a solution frozen to liquid helium temperatures and hyperpolarized by irradiating in the vicinity of the ESR of the unpaired electrons of the radicals [258,259]. (5) Development of automated hyphenated LC-SPE-NMR-MS platforms [260]. (6) More comprehensive and systematic comparisons between NMR and other analytical methods, such as GC-MS, should be performed in order to investigate their limitations, strengths and weaknesses as well as the advantages of their combined use. (7) Development of officially recognized NMR methodologies for fats and oils through collaboration of various NMR groups. (8) Application of STD and Tr-NOESY techniques would allow the analysis of interactions of chemically unmodified fatty acids with full-length proteins and, thus, provide further understanding of fatty acid conformational changes upon binding to lipoproteins even at a cellular level [240,241]. (9) Further developments in DOSY (Diffusion Order Spectroscopy) can make it special powerful tool for the analysis of unsaturated fatty acids and lipids [248].
It is hoped that this review will provide some guidance and stimulus for future NMR applications in the field of unsaturated lipid research.