A method for identifying the authenticity of donkey milk based on characteristic fatty acid fingerprinting

Abstract

This invention discloses a method for identifying the authenticity of donkey milk based on characteristic fatty acid fingerprinting, belonging to the field of food analysis technology. Based on seven characteristic fatty acids in donkey milk—C6:0, C18:0, C18:2 c9t11 (CLA n7), C10:0, C10:1 c9, C22:1 c13, and C18:2 c9c12 (LA)—this invention constructs a standard donkey milk fingerprint spectrum based on the ratios of C6:0 / C10:0, C6:0 / C10:1 c9, C6:0 / LA, C18:0 / C10:0, C18:0 / C22:1 c13, and CLA n7 / LA. The content of characteristic fatty acids in the test sample is measured, and the corresponding ratios are calculated and compared with the standard donkey milk fingerprint spectrum. If any ratio exceeds the characteristic range, the sample is determined to be not entirely donkey milk. This method for identifying the authenticity of donkey milk utilizes six ratios for multi-dimensional judgment, enabling rapid and accurate identification of donkey milk authenticity. It only requires measuring fatty acid content, making it simple and quick. Fingerprint spectroscopy can be used to detect not only raw milk samples but also processed dairy products, making it highly applicable. Historical and literature data can be used for sample-free determinations, providing strong traceability.

Description

Technical Field

[0001] This invention belongs to the field of food analysis technology, specifically relating to a method for identifying the authenticity of donkey milk. By measuring and calculating the ratio of six characteristic fatty acids and comparing it with the fingerprint spectrum of donkey milk, the authenticity of donkey milk samples can be effectively identified. Background Technology

[0002] my country possesses abundant donkey resources, and donkey milk, as a highly nutritious dairy substitute, has a long history of use. With the development of food science and technology, and the deepening research into the unique nutritional components, nutritional value, and health benefits of donkey milk, it has become a distinctive dairy industry with great development potential.

[0003] Donkey milk is nutritionally closest to human milk, rich in various bioactive substances, and has effects such as preventing and treating cardiovascular diseases, anti-fatigue, and anti-tumor properties. It also possesses antibacterial and bacteriostatic effects, enhances immunity, regulates intestinal flora, moisturizes and beautifies the skin, and serves as an adjunct to treatment and dietary therapy. Therefore, donkey milk has the potential for high nutritional added value and enormous market development potential. Currently, donkey milk production has not yet achieved large-scale and standardized production, and market prices vary widely, making it easy for counterfeit or adulterated products made from other animal milks (such as cow's milk or milk powder) to occur. Therefore, establishing accurate methods for analyzing the authenticity of donkey milk is crucial for ensuring the quality and safety of donkey milk products.

[0004] Existing methods for authenticating dairy products mainly include colorimetric methods (such as for starch, urea, hydrogen peroxide, etc.), precipitation methods (such as sodium sulfate), rapid test strip methods (antibiotics, melamine), and physical indicators (such as relative density, refractive index, etc.) for identifying known adulterants. However, these methods can only identify the characteristic properties of a specific known adulterant and cannot effectively identify unknown adulterants. For the identification of unknown exogenous proteins, DNA is often used as a biomarker or a differentially expressed protein from milk source to establish detection methods, mainly including PCR DNA sequencing, immunoassay, and chromatography.

[0005] PCR technology can be used to sequence DNA from somatic cells in milk. For example, De et al. (2011) used mitochondrial DNA circular fragments as target sequences and amplified 126bp and 226bp specific PCR products from cow's milk and buffalo milk, respectively. Using species-specific DNA sequences, they were able to identify cow's milk adulteration down to 0.01% in buffalo milk. my country's agricultural industry standard NY / T 3050-2016 also established a method for identifying cow's milk adulteration in goat's milk using PCR. However, the homogenization and heat treatment processes in dairy products are highly destructive to somatic cells or DNA, making the extraction of somatic cell DNA difficult, especially when adulterated with milk powder or soy flour. Therefore, DNA testing is only suitable for identifying the authenticity of raw milk and not for processed dairy products.

[0006] The authenticity of milk can also be determined by detecting proteins or immune responses in the milk. For example, Sharma et al. (2021) used non-immunoglobulin antigens in milk as indicators to identify milk adulteration as low as 5% in buffalo milk using immunoassay. Malo et al. (2018) used immunoglobulins in milk as indicators to identify milk adulteration as low as 1% in goat milk, sheep milk, and buffalo milk using immunoassay. Liu et al. (2019) used casein in milk as an indicator to identify milk adulteration as low as 0.07% in goat milk using immunoassay, while Ren et al. (2014) also used casein in milk to identify milk adulteration as low as 1% in donkey milk. Trimboli et al. (2019) used capillary electrophoresis to detect the content of α-lactalbumin in milk, and used α-lactalbumin as an indicator to identify milk adulteration as low as 1% in buffalo milk and quantify adulteration levels of more than 3.1% in buffalo milk. Chen et al. (2016) used a proteomics-based approach, employing β-lactoglobulin as an indicator, to qualitatively and quantitatively analyze cow's milk adulterated in goat's or sheep's milk. However, processing methods such as homogenization and heat treatment in dairy products are highly destructive to milk proteins, and the protein content varies widely among different types of milk, with numerous interfering factors. Therefore, protein-based immunoassay methods are only suitable for identifying the authenticity of raw milk, not dairy products, and have low sensitivity, making them prone to false positives.

[0007] The authenticity of milk can also be determined through cluster analysis of specific nutrients in the milk. For example, Pereira et al. (2020) determined the total fat and protein content in cow's milk and goat's milk using near-infrared spectroscopy and established a PLS-DA model that can identify cow's milk adulterated with a content as low as 1.0154 g / 100 g in goat's milk. Sen et al. (2021) determined the total fat, protein, lactose, and non-fat solids content in cow's milk, buffalo milk, and goat's milk using Fourier transform infrared spectroscopy and established an OPLS-DA model that can identify two types of milk mixtures with a mixing level higher than 5%: cow's milk-goat's milk and cow's milk-buffalo milk. The accuracy rates of the discriminant analysis were 93% and 91%, respectively. Zhang et al. (2018) determined the fatty acid content in cow's milk and mare's milk using gas chromatography and used PCA, SIMCA, and PLS models to analyze mixed samples of cow's milk and mare's milk. They demonstrated the feasibility of using fatty acid fingerprinting for the authenticity of specialty milk and were able to identify cow's milk adulteration in mare's milk with a content as low as 10%. Systematic research on analyzing fingerprint information from the breast is still very limited, and its application in authenticity verification is rare. Currently, it exhibits characteristics such as high technical threshold, low sensitivity, and poor applicability.

[0008] Milk contains a rich variety of fatty acids, with significant differences in their composition and content among different animal milks. Fatty acid fingerprinting refers to the overall composition and content characteristics of all fatty acids in milk. As a species-specific identification technique, it is more accurate and reliable for milk authenticity verification. However, due to the current state of detection technology, fatty acid determination results are mostly presented in the form of relative content, which requires area normalization quantification of all fatty acids in milk (Liu et al., 2018), significantly increasing analysis time. Selecting characteristic fatty acid ratios, on the other hand, only requires the determination of specific fatty acids, improving analytical efficiency and amplifying the specificity of different milks, thus enhancing the accuracy of authenticity verification. Studies have shown that the fatty acid ratios of C10:0 / C8:0, C12:0 / C10:0, C14:0 / C12:0, and C14:0 / C18:1 can be used to identify the adulteration of butter and lard in milk fat (Anmat, 2011). However, this method can only identify butter or lard adulterated with a content of more than 15% in milk fat, and its detection sensitivity is low (Rebechi, 2016).

[0009] The methods described above can identify adulterated dairy products to some extent, but their application to the authenticity of donkey milk has certain limitations. For example, pretreatment such as separation and extraction is required before testing, leading to cumbersome operation, long operation time, high analysis cost, low sensitivity, and poor applicability. There is limited research on existing methods for authenticating donkey milk, and no specific and traceable method exists for this purpose. Existing methods also cannot easily and quickly identify the authenticity of donkey milk. For example, Chinese patent CN 112378996 A discloses a method for rapidly detecting adulteration in donkey milk. This method involves preparing equal amounts of the test subject, control A, and control B; establishing standard data model A and B; establishing test subject data; and comparing the data: comparing ultrasonic attenuation data A and B with ultrasonic attenuation data D, and comparing ultrasonic velocity data A and B with ultrasonic velocity data D to determine whether ultrasonic attenuation data D is similar to ultrasonic attenuation data A and ultrasonic velocity data D is similar to ultrasonic velocity data A. If, after comparison, ultrasonic attenuation data D is similar to ultrasonic attenuation data A and ultrasonic velocity data D is similar to ultrasonic velocity data A, it can be determined that the test subject, i.e., the tested donkey milk, is not adulterated. However, this method is computationally cumbersome and time-consuming.

[0010] Therefore, there is an urgent need to develop a method for authenticating donkey milk and its products that is accurate, easy to operate, applicable, and traceable. Summary of the Invention

[0011] To overcome the shortcomings of existing methods for authenticating dairy products, particularly the lack of a suitable and traceable method for donkey milk, this invention aims to provide a set of characteristic ranges for the ratios of characteristic fatty acids in donkey milk. Another objective is to construct a fingerprint profile of donkey milk based on these characteristic fatty acid ratios and apply it to the authenticity identification of donkey milk and related products.

[0012] The invention's approach is as follows: Utilizing extensive experimental data and background investigation data from previous studies, various fatty acid ratios are statistically analyzed and screened. Several ratios with extremely low values ​​in donkey milk and significant differences from those in other animal milks are selected as characteristic fatty acid ratios. For each characteristic fatty acid ratio, its characteristic range in donkey milk is calculated using the method of AVG (mean) ± 2.58 × SD (standard deviation), achieving a confidence level of 99%. A radar chart is then created to form a fingerprint spectrum. The characteristic fatty acid ratios of the milk sample to be tested are measured and calculated, and then compared with the aforementioned fingerprint spectrum to verify authenticity.

[0013] The specific technical solution of this invention is as follows:

[0014] A method for authenticating donkey milk based on characteristic fatty acid fingerprinting includes the following steps:

[0015] S1: Construct a standard donkey milk fingerprint using the characteristic fatty acid ratios of donkey milk;

[0016] S2: Determine the content of characteristic fatty acids in the sample to be tested, calculate the corresponding fatty acid ratio, and compare it with the standard donkey milk fingerprint spectrum. If any characteristic fatty acid ratio exceeds the characteristic range of the standard donkey milk fingerprint spectrum, that is, outside the confidence range of the radar chart, the sample is determined to be not completely donkey milk and is counterfeit or adulterated.

[0017] Preferably, the characteristic fatty acids of the donkey milk are C6:0, C18:0, C18:2c9t11 (CLA n7), C10:0, C10:1c9, C22:1c13 and C18:2c9c12 (LA).

[0018] Preferably, the ratio range of the characteristic fatty acids in donkey milk is:

[0019] The feature range of C6:0 / C10:0 is 0.019 to 0.054;

[0020] The characteristic range of C6:0 / C10:1c9 is 0.030 to 0.343;

[0021] C6:0 / C18:2c9c12 Feature range 0~0.058;

[0022] The feature range of C18:0 / C10:0 is 0 to 0.293;

[0023] The characteristic range of C18:0 / C22:1c13 is 0.021 to 1.583;

[0024] The characteristic range of C18:2c9t11 / C18:2c9c12 is 0 to 0.056.

[0025] Preferably, the determination of the characteristic fatty acid content in the donkey milk sample to be tested in step S2 is performed by gas chromatography or gas chromatography-mass spectrometry.

[0026] Preferably, the results of calculating the corresponding fatty acid ratios in step S2 are expressed as relative values ​​(% of total fatty acids).

[0027] Preferably, the result of calculating the corresponding fatty acid ratio in step S2 is expressed as an absolute value (mg / L milk).

[0028] Compared with the prior art, the beneficial effects of this invention are as follows:

[0029] (1) Fingerprint characteristics (exclusivity): The characteristic fatty acid ratios selected in the donkey milk authenticity identification method based on characteristic fatty acid fingerprinting of this invention have obvious fingerprint characteristics. Compared with other animal milks, the above ratios are all extremely small. By using 6 indicators to judge from multiple dimensions, the authenticity of donkey milk can be quickly and accurately identified.

[0030] (2) Simple and fast: Compared with methods such as DNA sequencing and cluster analysis, the method for identifying the authenticity of donkey milk based on characteristic fatty acid fingerprinting of this invention is simpler in determining fatty acid content, and the determination can be completed in 2-4 hours. More importantly, fatty acids are a basic nutritional indicator and a commonly tested indicator for milk samples. Therefore, samples with existing fatty acid test results can be directly compared with fingerprints to obtain a conclusion on the authenticity of donkey milk, making the operation convenient.

[0031] (3) Strong applicability: Compared with DNA sequencing and immunoassay methods, the donkey milk authenticity identification method based on characteristic fatty acid fingerprinting of this invention can detect not only raw milk samples but also processed dairy products. Furthermore, the determination of fatty acid content has a low technical threshold and low cost. The results can be determined by gas chromatography or gas chromatography-mass spectrometry, or obtained by a rapid infrared determination device.

[0032] (4) Strong traceability: The donkey milk authenticity identification method based on characteristic fatty acid fingerprint spectrum of the present invention can be judged by data, and historical data, literature data, etc. can be judged without samples. Attached Figure Description

[0033] Figure 1 is a radar chart showing the range of characteristic fatty acid ratios in the donkey milk authenticity identification method based on characteristic fatty acid fingerprinting. Detailed Implementation

[0034] To enable those skilled in the art to better understand the present invention, it will now be further described in conjunction with specific embodiments. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0035] Example 1

[0036] Based on seven characteristic fatty acids in donkey milk (C6:0, C18:0, C18:2c9t11 (CLA n7), C10:0, C10:1c9, C22:1c13, and C18:2c9c12 (LA), a standard donkey milk fingerprint spectrum was constructed based on the ratios of six characteristic fatty acids in donkey milk: C6:0 / C10:0, C6:0 / C10:1c9, C6:0 / C18:2c9c12, C18:0 / C10:0, C18:0 / C22:1c13, and C18:2c9t11 (CLA n7) / C18:2c9c12 (LA). The range of these characteristic fatty acid ratios is shown in Table 1.

[0037] Table 1: Range of characteristic fatty acid ratios in donkey milk

[0038]

[0039]

[0040] The fingerprint spectrum of donkey milk was plotted according to the above-mentioned characteristic fatty acid ratio range, as shown in Figure 1.

[0041] Example 2

[0042] Fifty-four samples of Holstein cow milk were taken for verification analysis. The content of characteristic fatty acids in the samples was determined, the corresponding fatty acid ratios were calculated, and compared with the standard donkey milk fingerprint spectrum constructed in Example 1. If any characteristic fatty acid ratio exceeded the characteristic range, that is, outside the confidence range of the radar chart, the sample was determined to be not completely donkey milk and to be counterfeit or adulterated. The results are shown in Tables 2-1, 2-2, and 2-3.

[0043] Table 2-1 Characteristic fatty acid content (% total fatty acids, n=54) of Holstein cow milk adulterated with donkey milk

[0044]

[0045]

[0046]

[0047] Table 2-2 Characteristic fatty acid ratios of Holstein cow milk adulterated with donkey milk (n=54)

[0048]

[0049]

[0050]

[0051] Table 2-3 Results of the identification of genuine Holstein cow milk that was counterfeited or adulterated with donkey milk (n=54)

[0052]

[0053]

[0054] Test results showed that all milk samples were determined to be inconsistent with the characteristics of donkey milk, and 3.29% of Holstein cow milk could be identified as adulterated in donkey milk.

[0055] Example 3

[0056] Thirty-one samples of Jersey cow milk were taken for verification analysis. The content of characteristic fatty acids in the samples was determined, the corresponding fatty acid ratios were calculated, and compared with the standard donkey milk fingerprint spectrum constructed in Example 1. If any characteristic fatty acid ratio exceeded the characteristic range, that is, outside the confidence range of the radar chart, the sample was determined to be not completely donkey milk and to be counterfeit or adulterated. The results are shown in Tables 3-1, 3-2, and 3-3.

[0057] Table 3-1 Characteristic fatty acid content (% total fatty acids, n=31) of Jersey cow milk adulterated with donkey milk

[0058]

[0059]

[0060] Table 3-2 Characteristic fatty acid ratios of Jersey cow milk adulterated with or mixed with donkey milk (n=31)

[0061]

[0062]

[0063]

[0064] Table 3-3 Identification of the authenticity of Jersey cow milk that is counterfeit or adulterated with donkey milk (n=31)

[0065]

[0066] Test results showed that all milk samples were determined to be inconsistent with the characteristics of donkey milk, and 3.19% Jersey cow milk could be identified as adulterated in donkey milk.

[0067] Example 4

[0068] Eleven samples of buffalo milk were taken for verification analysis. The content of characteristic fatty acids in the samples was determined, the corresponding fatty acid ratios were calculated, and compared with the standard donkey milk fingerprint spectrum constructed in Example 1. If any characteristic fatty acid ratio exceeded the characteristic range, that is, outside the confidence range of the radar chart, the sample was determined to be not completely donkey milk and to be counterfeit or adulterated. The results are shown in Tables 4-1, 4-2, and 4-3.

[0069] Table 4-1 Characteristic fatty acid content (% total fatty acids, n=11) of buffalo milk adulterated with donkey milk

[0070]

[0071]

[0072] Table 4-2 Characteristic fatty acid ratios of buffalo milk adulterated with donkey milk (n=11)

[0073]

[0074] Table 4-3 Identification of the Authenticity of Buffalo Milk Counterfeited or Adulterated with Donkey Milk (n=11)

[0075]

[0076]

[0077] The test results showed that all milk samples could be determined to be inconsistent with the characteristics of donkey milk, and that 3.55% buffalo milk could be identified as adulterated in donkey milk.

[0078] Example 5

[0079] Twenty-four samples of yak milk were taken for verification analysis. The content of characteristic fatty acids in the samples was determined, the corresponding fatty acid ratios were calculated, and the samples were compared with the standard donkey milk fingerprint spectrum constructed in Example 1. If any characteristic fatty acid ratio exceeded the characteristic range, that is, outside the confidence range of the radar chart, the sample was determined to be not completely donkey milk and to be counterfeit or adulterated. The results are shown in Tables 5-1, 5-2, and 5-3.

[0080] Table 5-1 Characteristic fatty acid content (% total fatty acids, n=24) of yak milk adulterated with donkey milk

[0081]

[0082]

[0083] Table 5-2 Characteristic fatty acid ratios of yak milk adulterated with donkey milk (n=24)

[0084]

[0085]

[0086] Table 5-3 Identification of Authenticity of Yak Milk Counterfeited or Adulterated with Donkey Milk (n=24)

[0087]

[0088] Test results showed that all milk samples were determined to be inconsistent with the characteristics of donkey milk, and 4.11% of yak milk was identified as adulterated in the donkey milk.

[0089] Example 6

[0090] Thirty-six samples of goat milk were taken for verification analysis. The content of characteristic fatty acids in the samples was determined, the corresponding fatty acid ratios were calculated, and the samples were compared with the standard donkey milk fingerprint spectrum constructed in Example 1. If any characteristic fatty acid ratio exceeded the characteristic range, that is, outside the confidence range of the radar chart, the sample was determined to be not completely donkey milk and to be counterfeit or adulterated. The results are shown in Tables 6-1, 6-2, and 6-3.

[0091] Table 6-1 Characteristic fatty acid content (% total fatty acids, n=36) of goat milk adulterated with donkey milk

[0092]

[0093]

[0094] Table 6-2 Characteristic fatty acid ratios of sheep milk adulterated with donkey milk (n=36)

[0095]

[0096]

[0097] Table 6-3 Identification of Authenticity of Goat Milk Counterfeited or Adulterated with Donkey Milk (n=36)

[0098]

[0099] Test results showed that all milk samples were determined to be inconsistent with the characteristics of donkey milk, and 4.69% of sheep milk was identified as adulterated in donkey milk.

[0100] Example 7

[0101] Twenty-three camel milk samples were taken for verification analysis. The content of characteristic fatty acids in the samples was determined, the corresponding fatty acid ratios were calculated, and the samples were compared with the standard donkey milk fingerprint spectrum constructed in Example 1. If any characteristic fatty acid ratio exceeded the characteristic range, that is, outside the confidence range of the radar chart, the sample was determined to be not completely donkey milk and was counterfeit or adulterated. The results are shown in Tables 7-1, 7-2, and 7-3.

[0102] Table 7-1 Characteristic fatty acid content (% total fatty acids, n=23) of camel milk adulterated with donkey milk

[0103]

[0104]

[0105] Table 7-2 Characteristic fatty acid ratios of camel milk adulterated with or counterfeited donkey milk (n=23)

[0106]

[0107]

[0108] Table 7-3 Identification of Camel Milk Counterfeiting or Adulteration with Donkey Milk (n=23)

[0109]

[0110] The test results showed that all milk samples could be determined to be inconsistent with the characteristics of donkey milk, and 0.37% camel milk could be identified as adulterated in donkey milk.

[0111] Example 8

[0112] Thirty human milk samples were taken for verification analysis. The content of characteristic fatty acids in the samples was determined, the corresponding fatty acid ratios were calculated, and the samples were compared with the standard donkey milk fingerprint spectrum constructed in Example 1. If any characteristic fatty acid ratio exceeded the characteristic range, that is, outside the confidence range of the radar chart, the sample was determined to be not completely donkey milk and to be counterfeit or adulterated. The results are shown in Tables 8-1, 8-2, and 8-3.

[0113] Table 8-1 Characteristic fatty acid content (% total fatty acids, n=30) of human milk adulterated with donkey milk

[0114]

[0115]

[0116] Table 8-2 Characteristic fatty acid ratios of human milk adulterated with or mixed with donkey milk (n=30)

[0117]

[0118]

[0119] Table 8-3 Identification of the Authenticity of Human Milk Counterfeited or Adulterated with Donkey Milk (n=30)

[0120]

[0121]

[0122] Test results showed that all milk samples could be determined to be inconsistent with the characteristics of donkey milk, and 8.9% human milk could be identified as adulterated in donkey milk.

[0123] In summary, the method for authenticating donkey milk based on characteristic fatty acid fingerprinting, as described in this paper, was used to verify 54 samples of Holstein cow milk, 31 samples of Jersey cow milk, 11 samples of buffalo milk, 24 samples of yak milk, 36 samples of sheep milk, 23 samples of camel milk, and 30 samples of human milk. All 209 other animal milk samples showed characteristic fatty acid ratios exceeding the characteristic range of donkey milk, achieving a 100% difference identification rate. Furthermore, the method effectively identified donkey milk adulterated with 0.37%–8.9% or more of other animal milk.

Claims

1. A method for identifying the authenticity of donkey milk based on characteristic fatty acid fingerprinting, characterized in that... Includes the following steps: S1: Construct a standard donkey milk fingerprint using the characteristic fatty acid ratios of donkey milk; S2: Determine the content of characteristic fatty acids in the test sample and calculate the corresponding fatty acid ratio; S3: Compare the corresponding fatty acid ratios calculated in step S2 with the standard donkey milk fingerprint spectrum constructed in step S1. If any characteristic fatty acid ratio exceeds the characteristic range of the standard donkey milk fingerprint spectrum, that is, outside the confidence range of the radar chart, it is determined that the sample is not completely donkey milk and is counterfeit or adulterated. The characteristic fatty acids of donkey milk mentioned therein are: C6:0, C18:0, C18:2 c9t11, C10:0, C10:1 c9, C22:1 c13 and C18:2 c9c12; The ratio range of the characteristic fatty acids in donkey milk mentioned therein is: The feature range of C6:0 / C10:0 is 0.019 to 0.054; The characteristic range of C6:0 / C10:1 c9 is 0.030~0.343; C6:0 / C18:2 c9c12 Feature range 0~0.058; The feature range of C18:0 / C10:0 is 0 to 0.293; The characteristic range of C18:0 / C22:1 c13 is 0.021 to 1.583; The characteristic range of C18:2 c9t11 / C18:2 c9c12 is 0 to 0.

056.

2. The method for identifying the authenticity of donkey milk based on characteristic fatty acid fingerprinting as described in claim 1, characterized in that: The determination of the characteristic fatty acid content in the donkey milk sample to be tested in step S2 is performed by gas chromatography or gas chromatography-mass spectrometry.

3. The method for identifying the authenticity of donkey milk based on characteristic fatty acid fingerprinting as described in claim 1, characterized in that: The results of calculating the corresponding fatty acid ratios in step S2 are presented as relative values.

4. The method for identifying the authenticity of donkey milk based on characteristic fatty acid fingerprinting as described in claim 1, characterized in that: The results of calculating the corresponding fatty acid ratios in step S2 are expressed in absolute values.

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