# Quantification of “Cold-Hot” Medicinal Properties of Chinese Medicines Based on Primary Metabolites and Fisher’s Analysis

Authors: Xian-rui Wang; Ting-ting Cao; Xue-mei Tian; Hui Wang; Yun Wang
Journal: Computational and Mathematical Methods in Medicine
 (2022)

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## Abstract

Background. Chinese medicinal properties (CMP) are an important part of the basic theory of traditional Chinese medicines (TCMs). Quantitative research on the properties of TCMs is of great significance to deepen the understanding and application of the theory of drug properties and promoting the modernization of TCMs. However, these studies are limited to strong subjectivity or distinguish different drug properties based on certain indicators since CMP studies are diverse. Objective. To realize quantitative comparison of same medicinal properties of different Chinese medicines. Method. To solve the above problem, we proposed and explored quantification of Chinese medicinal properties (QMP) and the quantification value of medicinal properties “R”. The correlation between primary metabolites and “cold-hot” medicinal properties was explored on the premise of material basis of Chinese herbal medicines and Fisher’s analysis. Based on indicators related to “cold-hot” medicinal properties, we utilized quantitative values “R” to characterize the strength or weakness of “cold-hot” medicinal properties. Results. According to QMP, the same medicinal properties were quantified and compared by quantification value of medicinal properties that expressed by alphabet “R”. The general theoretical formula of “R” deduced is R=l×cosθ/L=∑i=1njipi/∑i=1npi2, in which n≥1. In the light of formula of “R” and indicators related to “cold-hot” medicinal properties, we got “R” value of “cold-cool” and “warm-hot” medicinal properties. “R” values of “cold-cool” medicinal properties of Phellodendri chinensis cortex, Coptidis rhizoma, and Menthae haplocalycis herba were 0.63, 1.00, and 0.49, respectively. The result showed that Coptidis rhizoma is the most “cold-cool”, followed by Phellodendri chinensis cortex, with Menthae haplocalycis herba is the weakest in the three Chinese medicines, consistent with cognition of TCM theory. Conclusion. QMP has certain guiding significance for the quantification of “cold and hot” drug properties. “R” is feasible to realize the quantitative comparison of the same drug properties of different traditional Chinese medicine, which is helpful to promote process of modern Chinese medicine construction.


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## Body

## 1. Introduction

The theory of medicinal properties is an important part of basic theory of traditional Chinese medicines (TCMs), which is one of the significant guidelines to guide clinical use of TCMs [1]. The theory of medicinal properties mainly includes four natures, five flavors, channel tropism, toxicity, and ascending-descending-floating-sinking [2]. The four natures refer to four properties of TCMs that are cold, hot, warm, and cool [3], which can also be mainly classified into two categories: one is hot-warm and the other is cold-cool. The five flavors contain five basic tastes that are pungent, sweet, sour, bitter, and salty [4]. Four natures and five flavors are core of theory of medicinal properties of Chinese medicines. In particular, the study of four natures of Chinese medicines was highly sought after by researchers.Four natures of Chinese medicines that were summarized in long-term medical practice have characteristics of abstractness, ambiguity, subjectivity, etc. [5]. Because of above characteristics, it is difficult to carry out quantitative analysis of “cold-hot” medicinal properties, which is one of the significant difficulties that impede the modernization of TCM. Quantitative analysis of “cold-hot” medicinal properties is to quantify the abstract concepts of Chinese medicinal properties “four qi” to compare the strength or weakness of “hot” or “cold” medicinal properties. Quantification of Chinese medicinal properties (CMP) that contains quantitative analysis of “cold-hot” medicinal properties is becoming a common trend in the research of TCMs [6]. The outline of strategic plan for development of TCMs had stressed that the scientific research on drug properties of TCMs should be strengthened through current scientific and technological methods. The realization of quantification of medicinal properties can strengthen people’s understanding for theory of TCMs and enhance the persuasion of TCMs, which is more conducive to the modernization of TCM. To this end, relevant scholars carried out a series of exploratory research. According to Fu et al., the higher the molecular energy state and the lower the average molecular weight, the greater the correlation with the hot-warm properties of TCMs; on the other hand, the lower the molecular energy state, the greater the correlation with the cold-cool properties of TCMs [7]. Wei et al. have proposed a novel method of multisolvent similarity measure to distinguish cold-cool and hot-warm medicinal properties [8]. In addition, a research method of expert assessment has been established to quantify “cold-hot” properties of TCMs and so on [9–11].Recently, it has become an important and urgent task for modern scientific research to identify and explain the theory of TCMs which have been applied in China for more than 4000 years. Due to the little contribution to the understanding of traditional Chinese medicine theory, the action mechanism of drugs with cold and heat characteristics is not clear. In previous quantitative study of “cold-hot” medicinal properties, however, there are some limitations in above quantitative study of “cold-hot” medicinal properties [6, 8]. For example, in the process of quantification of “cold-hot” medicinal properties, researchers adopted the subjective approach of evaluation and numerical size assignment of medicinal properties. Subjectivity is too strong to quantify medicinal properties objectively and scientifically. Moreover, most research only discriminated “cold-hot” medicinal properties based on certain indicators, rather than comparing the strong or weakness of medicinal properties [7, 10, 11]. CMP play a vital role in theoretical research and clinical practice. However, the traditional CMP system is subjective, qualitative, fixed, inconsistent, and obscured [2, 5]. Additionally, we are still short of an objective and scientific method that could realize the quantitative comparison of “cold-hot” medicinal properties of Chinese medicines. Nowadays, quantifying CMP research achieved a notable progress. We presented and analyzed quantification of Chinese medicinal properties (QMP) and the quantification value of Chinese medicinal properties “R”. From the perspective that the medicinal properties of TCMs are related to their material basis, we explored the correlation between primary metabolites and “cold-hot” medicinal properties. Further, based on indicators related to “cold-hot” medicinal properties, we utilized quantitative values “R” to characterize the strength or weakness of “cold-hot” medicinal properties and to realize quantitative comparison of the same “cold-hot” properties of different Chinese medicines.


## 2. Methods

### 2.1. Quantification of Medicinal Properties and Basic Rationale

#### 2.1.1. Quantification of Chinese Medicinal Properties

In this paper, we came up with a new concept—QMP. QMP proposed in this article referred to quantitative comparison of same medicinal properties of different Chinese medicines through quantification value of Chinese medicinal properties “R”, which was based on vector representation of medicinal properties and operation rules of vector and linear algebra.


#### 2.1.2. Based Rationale of Quantitative Analysis for Medicinal Properties of Chinese Medicines

In this section, we introduced the basic rationale of quantitative analysis for medicinal properties of Chinese medicines and the quantification value of Chinese medicinal properties “R”.As shown in Figure1, vectors e1 and e2 represent the medicinal properties of reference drug and test drug, respectively, where θ is the angle between the two vectors. The codirectional ray where vector e1 is located was taken as the evaluation axis of medicinal properties (EAMP). At the same time, the modulus of vector e1 was taken as the metrical unit of drug properties, with the metrical unit is expressed by “a”. Then, through the modulus of vector e2 and cosine value of angle θ to calculate vertical projection of vector e2 on EAMP, the vertical projection of vector e2 was denoted by “b”. On the basis of above information, we define “b/a” as the quantification value of medicinal properties of traditional Chinese medicines, which was indicated by the alphabet “R”. According to the rule of vectors [12], “R” can be strictly defined as follows:
(1)R=ba,a=e1,b=e2×cosθ,soR=e2×cosθe1.Figure 1
Based rationale of quantitative analysis for medicinal properties with reference drug, in which EAMP is the evaluation axis of medicinal properties.The modulus of vectore1 was denoted as ∣e1∣; at the same time, the modulus of vector e2 was denoted as e2.In addition, because the module of a vector and cosθ is a real number that has only size, so “R” is real number with no units.There was another case where there was no clear reference drug. As shown in Figure2, vectors e1 and e2 represented the medicinal properties of test drug A and test drug B, respectively, with vector e3 was the summation vector of e1 and e2. The codirectional ray where vector e3 located was taken as the evaluation axis of medicinal properties (EAMP); meanwhile, the vertical projections of vectors e1 and e2 on EAMP were denoted as “b” and “a”, respectively. In addition, the modulus of vector e3 was taken as a metrical unit of drug properties that was expressed by “c”. In the same way, we defined “b/c” and “a/c” as the quantification values of medicinal properties of test drug “A” and that of test drug “B”, respectively. Suppose that the angle between e1 and e3 is θ1, with the angle between e2 and e3 is θ2, and the moduli of vectors e1, e2, and e3 were denoted as e1, e2, and e3. In accordance with the rule of vectors, we can obtain that
(2)e3=e1+e2,c=e3,b=e1×cosθ1,a=e2×cosθ2,RA=bc=e1×cosθ1e3,RB=ac=e2×cosθ2e3,where RA and RB represented the quantification values of medicinal properties of test drug “A” and that of test drug “B”, respectively.Figure 2
Based rationale of quantification of medicinal properties with no reference drug, in which EAMP is the evaluation axis of medicinal properties.On the basis of the above fundamentals, the quantification value of Chinese medicinal properties “R” was defined to realize the quantitative comparison of same medicinal properties of different traditional Chinese medicines, which can avoid the influence of subjective factors such as evaluation of experts and weight assignment of drug properties to some extent. However, a key problem to solve was how to use vectors to represent the same medicinal properties of different Chinese medicines. In the following chapters, we analyzed the question of making use of vectors to denote Chinese medicinal properties.


### 2.2. Vector Representation of Medicinal Properties

The completion of quantification of medicinal properties was on the basis of its basic rationale, but the vector representation of medicinal properties was the premise of quantification of drug properties. There are two important factors that use vectors to represent Chinese medicinal properties. One is characterization indexes of medicinal properties, and the other is coordinate representation of vector.


#### 2.2.1. Characterization Indexes of Chinese Medicinal Properties

Characterization indicator of drug properties is an “attribute index” to measure medicinal properties. Based on some “attribute index”, different drug properties of traditional Chinese medicines can be distinguished. In addition, quantifiable attribute indicators that are related to the nature of TCMs could provide a basis for quantitative comparison of medicinal properties.More and more scientific technologies such as spectroscopy technology [13–15], high-throughput technology [16, 17], data mining [18, 19], and big data [20, 21] have been widely used in macroanalysis and microanalysis of TCMs, which provide us with a great deal of information. As far as quantitative comparison of drug properties is concerned, it is vital to select suitable characterization indexes of medicinal properties from numerous information. Therefore, when selecting the suitable characterization indicators, we should analyze the properties of characterization indexes and the connection of drug properties and indicators according to specific situation, rather than haphazard selection. The selection of characterization indicators of medicinal properties should pay attention to the following aspects:
(1)
There is a direct or potential connection between characterization indicators and medicinal properties(2)
Characterization indicators of medicinal properties should be able to obtain corresponding indicator values rather than only described qualitatively(3)
The number of characterization indicators is not less than one(4)
Characterization indicators can reflect in different herbal medicines


#### 2.2.2. Coordinate Representation of Vectors

The coordinate representation of vectors is another mathematical representation of vector, which connects mathematics with vectors [22].Supposing in theN-dimensional space defined as V, ξ1,ξ2,ξ3,⋯,ξn−2,ξn−1,ξn∈V, in which ξ1~n are the unit vectors with different directions;
(3)ξ1=ξ2=ξ3=⋯=ξn−1=ξn=1.Ifλ⟶⊆V and OA⟶=λ⟶, based on the rule of summation of vectors, we can obtain the following:
(4)λ⟶=a1⋅ξ1+a2⋅ξ2+a3⋅ξ3+⋯+an−1⋅ξn−1+an⋅ξn,OA⟶=a1⋅ξ1+a2⋅ξ2+a3⋅ξ3+⋯+an−1⋅ξn−1+an⋅ξn−1,in which ξ1,ξ2,ξ3,⋯,ξn−2,ξn−1,ξn are the unit vectors fixed in V and point “O” is the origin of coordinates;
(5)OA⟶=λ⟶=a1,a2,a3,⋯,an−1,an.Since the unit vectors are fixed inV, for any vector in V, there is only one set of ordered sequence (a1,a2,a3,⋯,an−1,an) to make OA⟶=a1⋅ξ1+a2⋅ξ2+a3⋅ξ3+⋯+an−1⋅ξn−1+an⋅ξn set up. Then, the set of ordered sequence (a1,a2,a3,⋯,an−1,an) is recorded as the coordinates of OA⟶, in which the sequence is the coordinate of point “A”.On the basis of the above analysis, if there are two points “M” and “N” in V:
(6)M=m1,m2,m3,⋯,mn−1,mn,N=n1,n2,n3,⋯,nn−1,nn,ξ1,ξ2,ξ3,⋯,ξn−2,ξn−1,ξn∈V,in which ξ1~n are the unit vectors with different directions.OM⟶ and ON⟶ can be deduced as follows:
(7)OM⟶=m1⋅ξ1+m2⋅ξ2+m3⋅ξ3+⋯+mn−1⋅ξn−1+mn⋅ξn,ON⟶=n1⋅ξ1+n2⋅ξ2+n3⋅ξ3+⋯+nn−1⋅ξn−1+nn⋅ξn,MN⟶=ON⟶−OM⟶,MN⟶=n1−m1⋅ξ1+n2−m2⋅ξ2+⋯+nn−1−mn−1⋅ξn−1+nn−mn⋅ξn,MN⟶=n1,n2,n3,⋯,nn‐1,nn−m1,m2,m3,⋯,mn‐1,mn=n1−m1,n2−m2,n3−m3,⋯,nn‐1−mn‐1,nn−mn.For the vector that takes “M” as the starting point and point “N” as the ending point, MN⟶=n1−m1,n2−m2,n3−m3,⋯,nn−1−mn−1,nn−mn can be obtained. That is to say, the coordinate of MN⟶ is the coordinate of “N” minus that of “M”.Based on “attribute indexes” related to medicinal properties, we can analyze the “attribute indexes” of “Blank” and Chinese medicines to obtain corresponding blank values and attribute indicator values of Chinese medicines.Then, in theN-dimensional space composed of attribute indexes, we record the ordered array of blank values as “blank spot” coordinates; at the same time, we take the ordered array of attribute indicator values of Chinese medicines as “medicinal properties spot” coordinates. In that way, the vector from “blank spot” to “medicinal properties point” is a vector that can represent medicinal properties of a Chinese medicine, whose coordinate is the coordinate of “medicinal properties spot” minus that of “blank spot”.For example, when the medicinal properties of Chinese medicine “H” are characterized by attribute indexes I1, I2, and I3, the corresponding blank values a0, b0, and c0 can be obtained by analysis of attribute indexes I1, I2, and I3 of the blank group. In the same way, the attribute index values a1, b1, and c1 can also be obtained by analysis of attribute indexes I1, I2, and I3 of drug “H”. Then, in a three-dimensional space formed by attribute indexes I1, I2, and I3, blank values arranged in the order of (I1, I2, and I3) are taken as “blank spot” coordinates, which are recorded as (a0, b0, and c0). Moreover, the ordered array of attribute indicator values is taken as “medicinal properties spot” that is recorded as (a1, b1, and c1). Therefore, we can obtain that the vector from “blank point” to “medicinal point” is a vector that can represent medicinal properties of Chinese medicine “H”. The coordinate of the above vector can be expressed as follows:H=a1,b1,c1−a0,b0,c0=a1−a0,b1−b0,c1−c0, in which H represents the medicinal properties of Chinese medicine “H”.On the premise of same “attribute index”, different Chinese medicines have different attribute index values. Therefore, through the vector representation of medicinal properties, different vectors can represent the same medicinal properties of different traditional Chinese medicines. Further, according to the basic rationale of quantification of medicinal properties, the quantification of same medicinal properties of different Chinese medicines was carried out to obtain the quantitative value of medicinal properties that is represented by “R”, which can realize the quantitative comparison of same medicinal properties of different Chinese medicines. In the following part, we deduced the general theoretical formula of “R”.


### 2.3. Quantitative Value of Medicinal Properties “R”

The general theoretical formula of “R” was deduced based on basic rationale of quantification of medicinal properties and coordinate representation of vector.Suppose that the two Chinese medicines with the same medicinal properties were drug “A” and drug “B”, respectively. There are “n” characterization indexes selected to characterize medicinal properties, which are recorded as (I1, I2, I3,…,In−1, In). Through analysis of each attribute index of blank, drug “A”, and drug “B”, the “medicinal properties spots” of drug “A”, drug “B”, and the “blank spot” are as follows:
(i)
Blank spot:a1,a2,a3,⋯,an−1,anT(ii)
Medicinal properties spot of drug “A”: b1,b2,b3,⋯,bn−1,bnT(iii)
Medicinal properties spot of drug “B”: c1,c2,c3,⋯,cn−1,cnTa1~an, b1~bn, and c1~cn are all different attribute index values that correspond to indexes I1~In, respectively.Based on the vector representation of medicinal properties, we got the vector coordinates of drug properties of traditional Chinese medicines “A” and “B”, which are represented by “α” and “β”, respectively.
(8)α=x1,x2,x3,⋯,xn−1,xnT=b1,b2,b3,⋯,bn−1,bnT−a1,a2,a3,⋯,an−1,anT=b1−a1,b2−a2,b3−a3,⋯,bn−1−an−1,bn−anT,β=y1,y2,y3,⋯,yn−1,ynT=c1,c2,c3,⋯,cn−1,cnT−a1,a2,a3,⋯,an−1,anT=c1−a1,c2−a2,c3−a3,⋯,cn−1−an−1,cn−anT.For vectors “α” and “β”, through vector coordinate operation, we obtained the following information [23]:
(1)
Modulus of vectorsα and β are α and β(9)α=∑i=1nxi2=x12+x22+⋯+xn−12+xn2,β=∑i=1nyi2=y12+y22+⋯+yn−12+yn2.Scalar product of vectorsα and β is recorded as α,β.
(10)α,β=∑i=1nxiyi=x1y1+x2y2+x3y3+⋯+xn−1yn−1+xnyn.(2)
Cosine value of angleθα,β=α⋅β⋅cosθ, in which θ is the angle between vectors α and β, so cosθ could be deduced that
(11)cosθ=α,βα⋅β.(3)
Based on above formula, we got that(12)cosθ=α,βα⋅β=∑i=1nxiyi∑i=1nxi2⋅∑i=1nyi2=x1y1+x2y2+⋯+xn−1yn−1+xnynx12+x22+⋯+xn−12+xn2⋅y12+y22+⋯+yn−12+yn2.When Chinese medicine “B” was the reference drug, the codirectional ray where vector β is located was taken as EAMP. At the same time, β was taken as the metrical unit of medicinal properties. In addition, the vertical projection of vector α on EAMP is α⋅cosθ. According to the basic principles of quantification of medicinal properties, we obtained the quantitative value of drug properties of Chinese medicine “A” compared to drug “B”, with the quantitative value of drug properties represented by RA,B.
(13)RA,B=α⋅cosθβ=∑i=1nxiyi∑i=1nyi2=x1y1+x2y2+⋯+xn−1yn−1+xnyny12+y22+⋯+yn−12+yn2.When Chinese medicines “A” and “B” were not specified as reference drugs, we took the codirectional ray where vector γ was located as EAMP, with the vector γ was the resultant vector of vector α and vector β. Moreover, γ was taken as the metrical unit of drug properties to quantify the drug properties of Chinese medicines “A” and “B”:
(14)γ=α+β,γ=z1,z2,z3,⋯,zn−1,znT=x1,x2,x3,⋯,xn−1,xnT+y1,y2,y3,⋯,yn−1,ynT=x1+y1,x2+y2,x3+y3,⋯,xn−1+yn−1,xn+ynT,γ=∑i=1nzi2=z12+z22+⋯+zn−12+zn2.Suppose that the angle betweenα and γ is θ1, with the angle between γ and β is θ2:
(15)cosθ1=α,γα⋅β=∑i=1nxizi∑i=1nxi2⋅∑i=1nzi2=x1z1+x2z2+⋯+xn−1zn−1+xnznx12+x22+⋯+xn−12+xn2⋅z12+z22+⋯+zn−12+zn2,cosθ2=β,γβ⋅γ=∑i=1nyizi∑i=1nyi2⋅∑i=1nzi2=y1z1+y2z2+⋯+yn−1zn−1+ynzny12+y22+⋯+yn−12+yn2⋅z12+z22+⋯+zn−12+zn2.Similarly, the quantitative value of medicinal properties of drugs “A” and “B” represented by RA and RB, respectively, can be deduced according to the basic rationale of quantification of medicinal properties.
(16)RA=α⋅cosθ1γ=∑i=1nxizi∑i=1nzi2=x1z1+x2z2+⋯+xn−1zn−1+xnznz12+z22+⋯+zn−12+zn2,RB=β⋅cosθ2γ=∑i=1nyizi∑i=1nzi2=y1z1+y2z2+⋯+yn−1zn−1+ynznz12+z22+⋯+zn−12+zn2.Based on the derivation of formulasRA,B, RA, and RB, we have summarized the general theoretical formula of quantitative value of drug properties that is denoted by “R”.
(17)R=l⋅cosθL=∑i=1njipi∑i=1npi2n≥1.In above general theoretical formula,l is the modulus of vector l that denotes medicinal properties of test Chinese medicine. L is the length of metrical unit of drug properties, with vector L is a vector representing medicinal properties of reference Chinese medicine or a resultant vector that is synthesized by all vectors representing medicinal properties of test drugs. “θ” is the angle between l and L. “ji” is the i-th component of vector l coordinate. “pi” is the i-th component of vector L coordinate.Combining mathematical vectors with linear algebra and Chinese medicinal properties, we proposed the QMP metric model and deduced the general theoretical formula of quantitative value of medicinal properties “R”. Theoretically based on QMP and “R” formula, we can analyze abstract medicinal properties such as the four natures and five flavors. In the following sections, to verify the feasibility of QMP, based on analysis of correlation between primary metabolites and “cold-hot” medicinal properties, we carried out quantitative analysis of “cold-hot” medicinal properties of traditional Chinese medicines.


## 2.1. Quantification of Medicinal Properties and Basic Rationale

### 2.1.1. Quantification of Chinese Medicinal Properties

In this paper, we came up with a new concept—QMP. QMP proposed in this article referred to quantitative comparison of same medicinal properties of different Chinese medicines through quantification value of Chinese medicinal properties “R”, which was based on vector representation of medicinal properties and operation rules of vector and linear algebra.


### 2.1.2. Based Rationale of Quantitative Analysis for Medicinal Properties of Chinese Medicines

In this section, we introduced the basic rationale of quantitative analysis for medicinal properties of Chinese medicines and the quantification value of Chinese medicinal properties “R”.As shown in Figure1, vectors e1 and e2 represent the medicinal properties of reference drug and test drug, respectively, where θ is the angle between the two vectors. The codirectional ray where vector e1 is located was taken as the evaluation axis of medicinal properties (EAMP). At the same time, the modulus of vector e1 was taken as the metrical unit of drug properties, with the metrical unit is expressed by “a”. Then, through the modulus of vector e2 and cosine value of angle θ to calculate vertical projection of vector e2 on EAMP, the vertical projection of vector e2 was denoted by “b”. On the basis of above information, we define “b/a” as the quantification value of medicinal properties of traditional Chinese medicines, which was indicated by the alphabet “R”. According to the rule of vectors [12], “R” can be strictly defined as follows:
(1)R=ba,a=e1,b=e2×cosθ,soR=e2×cosθe1.Figure 1
Based rationale of quantitative analysis for medicinal properties with reference drug, in which EAMP is the evaluation axis of medicinal properties.The modulus of vectore1 was denoted as ∣e1∣; at the same time, the modulus of vector e2 was denoted as e2.In addition, because the module of a vector and cosθ is a real number that has only size, so “R” is real number with no units.There was another case where there was no clear reference drug. As shown in Figure2, vectors e1 and e2 represented the medicinal properties of test drug A and test drug B, respectively, with vector e3 was the summation vector of e1 and e2. The codirectional ray where vector e3 located was taken as the evaluation axis of medicinal properties (EAMP); meanwhile, the vertical projections of vectors e1 and e2 on EAMP were denoted as “b” and “a”, respectively. In addition, the modulus of vector e3 was taken as a metrical unit of drug properties that was expressed by “c”. In the same way, we defined “b/c” and “a/c” as the quantification values of medicinal properties of test drug “A” and that of test drug “B”, respectively. Suppose that the angle between e1 and e3 is θ1, with the angle between e2 and e3 is θ2, and the moduli of vectors e1, e2, and e3 were denoted as e1, e2, and e3. In accordance with the rule of vectors, we can obtain that
(2)e3=e1+e2,c=e3,b=e1×cosθ1,a=e2×cosθ2,RA=bc=e1×cosθ1e3,RB=ac=e2×cosθ2e3,where RA and RB represented the quantification values of medicinal properties of test drug “A” and that of test drug “B”, respectively.Figure 2
Based rationale of quantification of medicinal properties with no reference drug, in which EAMP is the evaluation axis of medicinal properties.On the basis of the above fundamentals, the quantification value of Chinese medicinal properties “R” was defined to realize the quantitative comparison of same medicinal properties of different traditional Chinese medicines, which can avoid the influence of subjective factors such as evaluation of experts and weight assignment of drug properties to some extent. However, a key problem to solve was how to use vectors to represent the same medicinal properties of different Chinese medicines. In the following chapters, we analyzed the question of making use of vectors to denote Chinese medicinal properties.


## 2.1.1. Quantification of Chinese Medicinal Properties

In this paper, we came up with a new concept—QMP. QMP proposed in this article referred to quantitative comparison of same medicinal properties of different Chinese medicines through quantification value of Chinese medicinal properties “R”, which was based on vector representation of medicinal properties and operation rules of vector and linear algebra.


## 2.1.2. Based Rationale of Quantitative Analysis for Medicinal Properties of Chinese Medicines

In this section, we introduced the basic rationale of quantitative analysis for medicinal properties of Chinese medicines and the quantification value of Chinese medicinal properties “R”.As shown in Figure1, vectors e1 and e2 represent the medicinal properties of reference drug and test drug, respectively, where θ is the angle between the two vectors. The codirectional ray where vector e1 is located was taken as the evaluation axis of medicinal properties (EAMP). At the same time, the modulus of vector e1 was taken as the metrical unit of drug properties, with the metrical unit is expressed by “a”. Then, through the modulus of vector e2 and cosine value of angle θ to calculate vertical projection of vector e2 on EAMP, the vertical projection of vector e2 was denoted by “b”. On the basis of above information, we define “b/a” as the quantification value of medicinal properties of traditional Chinese medicines, which was indicated by the alphabet “R”. According to the rule of vectors [12], “R” can be strictly defined as follows:
(1)R=ba,a=e1,b=e2×cosθ,soR=e2×cosθe1.Figure 1
Based rationale of quantitative analysis for medicinal properties with reference drug, in which EAMP is the evaluation axis of medicinal properties.The modulus of vectore1 was denoted as ∣e1∣; at the same time, the modulus of vector e2 was denoted as e2.In addition, because the module of a vector and cosθ is a real number that has only size, so “R” is real number with no units.There was another case where there was no clear reference drug. As shown in Figure2, vectors e1 and e2 represented the medicinal properties of test drug A and test drug B, respectively, with vector e3 was the summation vector of e1 and e2. The codirectional ray where vector e3 located was taken as the evaluation axis of medicinal properties (EAMP); meanwhile, the vertical projections of vectors e1 and e2 on EAMP were denoted as “b” and “a”, respectively. In addition, the modulus of vector e3 was taken as a metrical unit of drug properties that was expressed by “c”. In the same way, we defined “b/c” and “a/c” as the quantification values of medicinal properties of test drug “A” and that of test drug “B”, respectively. Suppose that the angle between e1 and e3 is θ1, with the angle between e2 and e3 is θ2, and the moduli of vectors e1, e2, and e3 were denoted as e1, e2, and e3. In accordance with the rule of vectors, we can obtain that
(2)e3=e1+e2,c=e3,b=e1×cosθ1,a=e2×cosθ2,RA=bc=e1×cosθ1e3,RB=ac=e2×cosθ2e3,where RA and RB represented the quantification values of medicinal properties of test drug “A” and that of test drug “B”, respectively.Figure 2
Based rationale of quantification of medicinal properties with no reference drug, in which EAMP is the evaluation axis of medicinal properties.On the basis of the above fundamentals, the quantification value of Chinese medicinal properties “R” was defined to realize the quantitative comparison of same medicinal properties of different traditional Chinese medicines, which can avoid the influence of subjective factors such as evaluation of experts and weight assignment of drug properties to some extent. However, a key problem to solve was how to use vectors to represent the same medicinal properties of different Chinese medicines. In the following chapters, we analyzed the question of making use of vectors to denote Chinese medicinal properties.


## 2.2. Vector Representation of Medicinal Properties

The completion of quantification of medicinal properties was on the basis of its basic rationale, but the vector representation of medicinal properties was the premise of quantification of drug properties. There are two important factors that use vectors to represent Chinese medicinal properties. One is characterization indexes of medicinal properties, and the other is coordinate representation of vector.


### 2.2.1. Characterization Indexes of Chinese Medicinal Properties

Characterization indicator of drug properties is an “attribute index” to measure medicinal properties. Based on some “attribute index”, different drug properties of traditional Chinese medicines can be distinguished. In addition, quantifiable attribute indicators that are related to the nature of TCMs could provide a basis for quantitative comparison of medicinal properties.More and more scientific technologies such as spectroscopy technology [13–15], high-throughput technology [16, 17], data mining [18, 19], and big data [20, 21] have been widely used in macroanalysis and microanalysis of TCMs, which provide us with a great deal of information. As far as quantitative comparison of drug properties is concerned, it is vital to select suitable characterization indexes of medicinal properties from numerous information. Therefore, when selecting the suitable characterization indicators, we should analyze the properties of characterization indexes and the connection of drug properties and indicators according to specific situation, rather than haphazard selection. The selection of characterization indicators of medicinal properties should pay attention to the following aspects:
(1)
There is a direct or potential connection between characterization indicators and medicinal properties(2)
Characterization indicators of medicinal properties should be able to obtain corresponding indicator values rather than only described qualitatively(3)
The number of characterization indicators is not less than one(4)
Characterization indicators can reflect in different herbal medicines


### 2.2.2. Coordinate Representation of Vectors

The coordinate representation of vectors is another mathematical representation of vector, which connects mathematics with vectors [22].Supposing in theN-dimensional space defined as V, ξ1,ξ2,ξ3,⋯,ξn−2,ξn−1,ξn∈V, in which ξ1~n are the unit vectors with different directions;
(3)ξ1=ξ2=ξ3=⋯=ξn−1=ξn=1.Ifλ⟶⊆V and OA⟶=λ⟶, based on the rule of summation of vectors, we can obtain the following:
(4)λ⟶=a1⋅ξ1+a2⋅ξ2+a3⋅ξ3+⋯+an−1⋅ξn−1+an⋅ξn,OA⟶=a1⋅ξ1+a2⋅ξ2+a3⋅ξ3+⋯+an−1⋅ξn−1+an⋅ξn−1,in which ξ1,ξ2,ξ3,⋯,ξn−2,ξn−1,ξn are the unit vectors fixed in V and point “O” is the origin of coordinates;
(5)OA⟶=λ⟶=a1,a2,a3,⋯,an−1,an.Since the unit vectors are fixed inV, for any vector in V, there is only one set of ordered sequence (a1,a2,a3,⋯,an−1,an) to make OA⟶=a1⋅ξ1+a2⋅ξ2+a3⋅ξ3+⋯+an−1⋅ξn−1+an⋅ξn set up. Then, the set of ordered sequence (a1,a2,a3,⋯,an−1,an) is recorded as the coordinates of OA⟶, in which the sequence is the coordinate of point “A”.On the basis of the above analysis, if there are two points “M” and “N” in V:
(6)M=m1,m2,m3,⋯,mn−1,mn,N=n1,n2,n3,⋯,nn−1,nn,ξ1,ξ2,ξ3,⋯,ξn−2,ξn−1,ξn∈V,in which ξ1~n are the unit vectors with different directions.OM⟶ and ON⟶ can be deduced as follows:
(7)OM⟶=m1⋅ξ1+m2⋅ξ2+m3⋅ξ3+⋯+mn−1⋅ξn−1+mn⋅ξn,ON⟶=n1⋅ξ1+n2⋅ξ2+n3⋅ξ3+⋯+nn−1⋅ξn−1+nn⋅ξn,MN⟶=ON⟶−OM⟶,MN⟶=n1−m1⋅ξ1+n2−m2⋅ξ2+⋯+nn−1−mn−1⋅ξn−1+nn−mn⋅ξn,MN⟶=n1,n2,n3,⋯,nn‐1,nn−m1,m2,m3,⋯,mn‐1,mn=n1−m1,n2−m2,n3−m3,⋯,nn‐1−mn‐1,nn−mn.For the vector that takes “M” as the starting point and point “N” as the ending point, MN⟶=n1−m1,n2−m2,n3−m3,⋯,nn−1−mn−1,nn−mn can be obtained. That is to say, the coordinate of MN⟶ is the coordinate of “N” minus that of “M”.Based on “attribute indexes” related to medicinal properties, we can analyze the “attribute indexes” of “Blank” and Chinese medicines to obtain corresponding blank values and attribute indicator values of Chinese medicines.Then, in theN-dimensional space composed of attribute indexes, we record the ordered array of blank values as “blank spot” coordinates; at the same time, we take the ordered array of attribute indicator values of Chinese medicines as “medicinal properties spot” coordinates. In that way, the vector from “blank spot” to “medicinal properties point” is a vector that can represent medicinal properties of a Chinese medicine, whose coordinate is the coordinate of “medicinal properties spot” minus that of “blank spot”.For example, when the medicinal properties of Chinese medicine “H” are characterized by attribute indexes I1, I2, and I3, the corresponding blank values a0, b0, and c0 can be obtained by analysis of attribute indexes I1, I2, and I3 of the blank group. In the same way, the attribute index values a1, b1, and c1 can also be obtained by analysis of attribute indexes I1, I2, and I3 of drug “H”. Then, in a three-dimensional space formed by attribute indexes I1, I2, and I3, blank values arranged in the order of (I1, I2, and I3) are taken as “blank spot” coordinates, which are recorded as (a0, b0, and c0). Moreover, the ordered array of attribute indicator values is taken as “medicinal properties spot” that is recorded as (a1, b1, and c1). Therefore, we can obtain that the vector from “blank point” to “medicinal point” is a vector that can represent medicinal properties of Chinese medicine “H”. The coordinate of the above vector can be expressed as follows:H=a1,b1,c1−a0,b0,c0=a1−a0,b1−b0,c1−c0, in which H represents the medicinal properties of Chinese medicine “H”.On the premise of same “attribute index”, different Chinese medicines have different attribute index values. Therefore, through the vector representation of medicinal properties, different vectors can represent the same medicinal properties of different traditional Chinese medicines. Further, according to the basic rationale of quantification of medicinal properties, the quantification of same medicinal properties of different Chinese medicines was carried out to obtain the quantitative value of medicinal properties that is represented by “R”, which can realize the quantitative comparison of same medicinal properties of different Chinese medicines. In the following part, we deduced the general theoretical formula of “R”.


## 2.2.1. Characterization Indexes of Chinese Medicinal Properties

Characterization indicator of drug properties is an “attribute index” to measure medicinal properties. Based on some “attribute index”, different drug properties of traditional Chinese medicines can be distinguished. In addition, quantifiable attribute indicators that are related to the nature of TCMs could provide a basis for quantitative comparison of medicinal properties.More and more scientific technologies such as spectroscopy technology [13–15], high-throughput technology [16, 17], data mining [18, 19], and big data [20, 21] have been widely used in macroanalysis and microanalysis of TCMs, which provide us with a great deal of information. As far as quantitative comparison of drug properties is concerned, it is vital to select suitable characterization indexes of medicinal properties from numerous information. Therefore, when selecting the suitable characterization indicators, we should analyze the properties of characterization indexes and the connection of drug properties and indicators according to specific situation, rather than haphazard selection. The selection of characterization indicators of medicinal properties should pay attention to the following aspects:
(1)
There is a direct or potential connection between characterization indicators and medicinal properties(2)
Characterization indicators of medicinal properties should be able to obtain corresponding indicator values rather than only described qualitatively(3)
The number of characterization indicators is not less than one(4)
Characterization indicators can reflect in different herbal medicines


## 2.2.2. Coordinate Representation of Vectors

The coordinate representation of vectors is another mathematical representation of vector, which connects mathematics with vectors [22].Supposing in theN-dimensional space defined as V, ξ1,ξ2,ξ3,⋯,ξn−2,ξn−1,ξn∈V, in which ξ1~n are the unit vectors with different directions;
(3)ξ1=ξ2=ξ3=⋯=ξn−1=ξn=1.Ifλ⟶⊆V and OA⟶=λ⟶, based on the rule of summation of vectors, we can obtain the following:
(4)λ⟶=a1⋅ξ1+a2⋅ξ2+a3⋅ξ3+⋯+an−1⋅ξn−1+an⋅ξn,OA⟶=a1⋅ξ1+a2⋅ξ2+a3⋅ξ3+⋯+an−1⋅ξn−1+an⋅ξn−1,in which ξ1,ξ2,ξ3,⋯,ξn−2,ξn−1,ξn are the unit vectors fixed in V and point “O” is the origin of coordinates;
(5)OA⟶=λ⟶=a1,a2,a3,⋯,an−1,an.Since the unit vectors are fixed inV, for any vector in V, there is only one set of ordered sequence (a1,a2,a3,⋯,an−1,an) to make OA⟶=a1⋅ξ1+a2⋅ξ2+a3⋅ξ3+⋯+an−1⋅ξn−1+an⋅ξn set up. Then, the set of ordered sequence (a1,a2,a3,⋯,an−1,an) is recorded as the coordinates of OA⟶, in which the sequence is the coordinate of point “A”.On the basis of the above analysis, if there are two points “M” and “N” in V:
(6)M=m1,m2,m3,⋯,mn−1,mn,N=n1,n2,n3,⋯,nn−1,nn,ξ1,ξ2,ξ3,⋯,ξn−2,ξn−1,ξn∈V,in which ξ1~n are the unit vectors with different directions.OM⟶ and ON⟶ can be deduced as follows:
(7)OM⟶=m1⋅ξ1+m2⋅ξ2+m3⋅ξ3+⋯+mn−1⋅ξn−1+mn⋅ξn,ON⟶=n1⋅ξ1+n2⋅ξ2+n3⋅ξ3+⋯+nn−1⋅ξn−1+nn⋅ξn,MN⟶=ON⟶−OM⟶,MN⟶=n1−m1⋅ξ1+n2−m2⋅ξ2+⋯+nn−1−mn−1⋅ξn−1+nn−mn⋅ξn,MN⟶=n1,n2,n3,⋯,nn‐1,nn−m1,m2,m3,⋯,mn‐1,mn=n1−m1,n2−m2,n3−m3,⋯,nn‐1−mn‐1,nn−mn.For the vector that takes “M” as the starting point and point “N” as the ending point, MN⟶=n1−m1,n2−m2,n3−m3,⋯,nn−1−mn−1,nn−mn can be obtained. That is to say, the coordinate of MN⟶ is the coordinate of “N” minus that of “M”.Based on “attribute indexes” related to medicinal properties, we can analyze the “attribute indexes” of “Blank” and Chinese medicines to obtain corresponding blank values and attribute indicator values of Chinese medicines.Then, in theN-dimensional space composed of attribute indexes, we record the ordered array of blank values as “blank spot” coordinates; at the same time, we take the ordered array of attribute indicator values of Chinese medicines as “medicinal properties spot” coordinates. In that way, the vector from “blank spot” to “medicinal properties point” is a vector that can represent medicinal properties of a Chinese medicine, whose coordinate is the coordinate of “medicinal properties spot” minus that of “blank spot”.For example, when the medicinal properties of Chinese medicine “H” are characterized by attribute indexes I1, I2, and I3, the corresponding blank values a0, b0, and c0 can be obtained by analysis of attribute indexes I1, I2, and I3 of the blank group. In the same way, the attribute index values a1, b1, and c1 can also be obtained by analysis of attribute indexes I1, I2, and I3 of drug “H”. Then, in a three-dimensional space formed by attribute indexes I1, I2, and I3, blank values arranged in the order of (I1, I2, and I3) are taken as “blank spot” coordinates, which are recorded as (a0, b0, and c0). Moreover, the ordered array of attribute indicator values is taken as “medicinal properties spot” that is recorded as (a1, b1, and c1). Therefore, we can obtain that the vector from “blank point” to “medicinal point” is a vector that can represent medicinal properties of Chinese medicine “H”. The coordinate of the above vector can be expressed as follows:H=a1,b1,c1−a0,b0,c0=a1−a0,b1−b0,c1−c0, in which H represents the medicinal properties of Chinese medicine “H”.On the premise of same “attribute index”, different Chinese medicines have different attribute index values. Therefore, through the vector representation of medicinal properties, different vectors can represent the same medicinal properties of different traditional Chinese medicines. Further, according to the basic rationale of quantification of medicinal properties, the quantification of same medicinal properties of different Chinese medicines was carried out to obtain the quantitative value of medicinal properties that is represented by “R”, which can realize the quantitative comparison of same medicinal properties of different Chinese medicines. In the following part, we deduced the general theoretical formula of “R”.


## 2.3. Quantitative Value of Medicinal Properties “R”

The general theoretical formula of “R” was deduced based on basic rationale of quantification of medicinal properties and coordinate representation of vector.Suppose that the two Chinese medicines with the same medicinal properties were drug “A” and drug “B”, respectively. There are “n” characterization indexes selected to characterize medicinal properties, which are recorded as (I1, I2, I3,…,In−1, In). Through analysis of each attribute index of blank, drug “A”, and drug “B”, the “medicinal properties spots” of drug “A”, drug “B”, and the “blank spot” are as follows:
(i)
Blank spot:a1,a2,a3,⋯,an−1,anT(ii)
Medicinal properties spot of drug “A”: b1,b2,b3,⋯,bn−1,bnT(iii)
Medicinal properties spot of drug “B”: c1,c2,c3,⋯,cn−1,cnTa1~an, b1~bn, and c1~cn are all different attribute index values that correspond to indexes I1~In, respectively.Based on the vector representation of medicinal properties, we got the vector coordinates of drug properties of traditional Chinese medicines “A” and “B”, which are represented by “α” and “β”, respectively.
(8)α=x1,x2,x3,⋯,xn−1,xnT=b1,b2,b3,⋯,bn−1,bnT−a1,a2,a3,⋯,an−1,anT=b1−a1,b2−a2,b3−a3,⋯,bn−1−an−1,bn−anT,β=y1,y2,y3,⋯,yn−1,ynT=c1,c2,c3,⋯,cn−1,cnT−a1,a2,a3,⋯,an−1,anT=c1−a1,c2−a2,c3−a3,⋯,cn−1−an−1,cn−anT.For vectors “α” and “β”, through vector coordinate operation, we obtained the following information [23]:
(1)
Modulus of vectorsα and β are α and β(9)α=∑i=1nxi2=x12+x22+⋯+xn−12+xn2,β=∑i=1nyi2=y12+y22+⋯+yn−12+yn2.Scalar product of vectorsα and β is recorded as α,β.
(10)α,β=∑i=1nxiyi=x1y1+x2y2+x3y3+⋯+xn−1yn−1+xnyn.(2)
Cosine value of angleθα,β=α⋅β⋅cosθ, in which θ is the angle between vectors α and β, so cosθ could be deduced that
(11)cosθ=α,βα⋅β.(3)
Based on above formula, we got that(12)cosθ=α,βα⋅β=∑i=1nxiyi∑i=1nxi2⋅∑i=1nyi2=x1y1+x2y2+⋯+xn−1yn−1+xnynx12+x22+⋯+xn−12+xn2⋅y12+y22+⋯+yn−12+yn2.When Chinese medicine “B” was the reference drug, the codirectional ray where vector β is located was taken as EAMP. At the same time, β was taken as the metrical unit of medicinal properties. In addition, the vertical projection of vector α on EAMP is α⋅cosθ. According to the basic principles of quantification of medicinal properties, we obtained the quantitative value of drug properties of Chinese medicine “A” compared to drug “B”, with the quantitative value of drug properties represented by RA,B.
(13)RA,B=α⋅cosθβ=∑i=1nxiyi∑i=1nyi2=x1y1+x2y2+⋯+xn−1yn−1+xnyny12+y22+⋯+yn−12+yn2.When Chinese medicines “A” and “B” were not specified as reference drugs, we took the codirectional ray where vector γ was located as EAMP, with the vector γ was the resultant vector of vector α and vector β. Moreover, γ was taken as the metrical unit of drug properties to quantify the drug properties of Chinese medicines “A” and “B”:
(14)γ=α+β,γ=z1,z2,z3,⋯,zn−1,znT=x1,x2,x3,⋯,xn−1,xnT+y1,y2,y3,⋯,yn−1,ynT=x1+y1,x2+y2,x3+y3,⋯,xn−1+yn−1,xn+ynT,γ=∑i=1nzi2=z12+z22+⋯+zn−12+zn2.Suppose that the angle betweenα and γ is θ1, with the angle between γ and β is θ2:
(15)cosθ1=α,γα⋅β=∑i=1nxizi∑i=1nxi2⋅∑i=1nzi2=x1z1+x2z2+⋯+xn−1zn−1+xnznx12+x22+⋯+xn−12+xn2⋅z12+z22+⋯+zn−12+zn2,cosθ2=β,γβ⋅γ=∑i=1nyizi∑i=1nyi2⋅∑i=1nzi2=y1z1+y2z2+⋯+yn−1zn−1+ynzny12+y22+⋯+yn−12+yn2⋅z12+z22+⋯+zn−12+zn2.Similarly, the quantitative value of medicinal properties of drugs “A” and “B” represented by RA and RB, respectively, can be deduced according to the basic rationale of quantification of medicinal properties.
(16)RA=α⋅cosθ1γ=∑i=1nxizi∑i=1nzi2=x1z1+x2z2+⋯+xn−1zn−1+xnznz12+z22+⋯+zn−12+zn2,RB=β⋅cosθ2γ=∑i=1nyizi∑i=1nzi2=y1z1+y2z2+⋯+yn−1zn−1+ynznz12+z22+⋯+zn−12+zn2.Based on the derivation of formulasRA,B, RA, and RB, we have summarized the general theoretical formula of quantitative value of drug properties that is denoted by “R”.
(17)R=l⋅cosθL=∑i=1njipi∑i=1npi2n≥1.In above general theoretical formula,l is the modulus of vector l that denotes medicinal properties of test Chinese medicine. L is the length of metrical unit of drug properties, with vector L is a vector representing medicinal properties of reference Chinese medicine or a resultant vector that is synthesized by all vectors representing medicinal properties of test drugs. “θ” is the angle between l and L. “ji” is the i-th component of vector l coordinate. “pi” is the i-th component of vector L coordinate.Combining mathematical vectors with linear algebra and Chinese medicinal properties, we proposed the QMP metric model and deduced the general theoretical formula of quantitative value of medicinal properties “R”. Theoretically based on QMP and “R” formula, we can analyze abstract medicinal properties such as the four natures and five flavors. In the following sections, to verify the feasibility of QMP, based on analysis of correlation between primary metabolites and “cold-hot” medicinal properties, we carried out quantitative analysis of “cold-hot” medicinal properties of traditional Chinese medicines.


## 3. Quantitative Analysis of “Cold-Hot” Medicinal Properties

### 3.1. Correlation Analysis between Primary Metabolites and “Hot-Cold” Medicinal Properties

According to theory of traditional Chinese medicines, “four natures” that contain cold, hot, warm, and cool can be mainly divided into two categories: “hot-warm” and “cold-cool”. On the other hand, relevant research shows that the “hot-warm” and “cold-cool” properties of traditional Chinese medicines have a certain correlation with their material basis [7, 8, 23]. From this perspective, through data mining and literature collation, we have obtained some primary metabolite information of Chinese medicines with different drug properties, including the total sugar (TS), polysaccharide (PS), monosaccharide (MS), total lipid (TL), total protein (TP), and amino acid (AA). Based on above indicators and relevant data (Table 1) [24–26], we analyzed the correlation between primary metabolites and “hot-cold” medicinal properties based on Fisher’s analysis.Table 1
Content results of relevant components in 49 traditional Chinese medicines (%).
TCMTSPSMSTLTPAACold-coolAnemarrhenae rhizoma27.836.425.251.214.026.73Gardeniae fructus22.093.105.6911.673.035.23Lophatherum herba20.852.362.061.382.657.07Phellodendri chinensis cortex24.512.792.213.419.274.68Coptidis rhizoma38.592.546.960.735.7711.26Fraxini cortex31.550.701.970.611.421.55Lonicerae japonicae flos16.174.3310.382.098.739.34Isatidis folium14.721.144.583.157.9215.32Taraxaciherba20.467.647.613.508.459.69Menthae haplocalycis herba18.550.604.542.813.276.56Platycladi cacumen12.931.485.794.062.775.65Bupleuri radix23.220.842.743.233.674.75Plantaginis semen18.511.092.145.021.7310.40Kochiae fructus29.912.402.728.1814.2114.39Puerariae lobatae radix39.575.704.491.016.443.58Sargassum9.462.063.270.300.243.91Dianthi herba23.610.047.132.585.565.83Trichosanthis fructus23.770.6213.927.7610.7315.99Gentianae radix et rhizoma39.421.547.862.201.528.14Aloe9.180.1716.410.203.441.96Trachelospermi caulis et folium24.101.426.481.527.634.57Ecliptae herba11.861.053.881.041.377.91Siegesbeckiae herba13.051.307.036.334.194.88Arnebiae radix13.360.433.251.863.433.28Hot-warmFuzi92.454.241.010.580.471.96Cinnamomi cortex45.875.751.205.2213.471.11Zingiberis rhizoma65.034.1411.074.7215.325.40Euodiae fructus17.282.5411.357.3113.995.32Alpiniae officinarum rhizoma43.996.1214.022.8912.211.86Piperis fructus55.485.532.916.610.478.60Piperis longi fructus57.124.026.365.772.719.23Curculiginis rhizoma74.684.2912.431.5363.0810.87Eucommiae cortex26.521.227.334.251.092.79Sinapis semen20.120.752.0025.0521.1924.26Pinelliae rhizoma77.7126.671.020.263.844.14Psoraleae fructus19.730.249.1115.0639.8623.35Atractylodis rhizoma26.5916.2817.736.730.332.62Alpiniae katsumadai semen52.483.172.988.700.846.20Citri reticulatae pericarpium37.903.6024.751.301.333.96Chuanxiong rhizoma44.252.523.298.8335.6511.11Magnollae officinalis cortex28.230.967.576.061.852.30Ephedrae herba27.371.4711.163.212.993.65Chaenomelis fructus22.312.9018.861.704.503.66Aucklandiae radix17.9233.2218.905.572.984.05Notopthrygii rhizoma et radix29.942.223.519.773.885.48Arisaematis rhizoma93.8212.952.240.480.644.31Clematidis radix et rhizoma34.721.488.130.661.595.29Asari radix et rhizoma71.775.095.671.314.404.97Corydalis rhizoma93.2511.503.960.511.018.34On the basis of above indicators TS, PS, MS, TL, TP, and AA, we established the identification model of medicine properties through Fisher’s linear analysis for exploring correlation between primary metabolites and “cold-hot” medicinal properties.As shown in Figure3, blue represents “cold-cool” Chinese medicines; meanwhile, red represents “hot-warm” Chinese medicines. Based on Fisher’s discriminant function: Y=0.45×AA−0.05×TP−0.87×TL−0.41×MS−0.06×PS−0.19×TS−10.58, we could correctly distinguish the drug properties of traditional Chinese medicines in Table 1 and the correct rate of discrimination reaches up to 93.88%. When Y>0, the corresponding traditional Chinese medicines are classified as “cold-cool” medicines; if Y<0, it could be classified as “hot-warm” Chinese medicines. The Fisher’s discriminant results are shown in Table 2, in which the medicinal properties of Gardeniae fructus, Eucommiae cortex, and Clematidis radix et rhizoma were misjudged.Figure 3
The diagram of Fisher’s linear discriminant.Table 2
Fisher’s discriminant results of 49 traditional Chinese medicines.
TCMYDrug propertiesTest classificationAnemarrhenae rhizoma4.63Cold-coolCold-coolGardeniae fructus-4.03Cold-coolHot-warm∗∗Lophatherum herba7.54Cold-coolCold-coolPhellodendri chinensis cortex3.61Cold-coolCold-coolCoptidis rhizoma4.51Cold-coolCold-coolFraxini cortex3.90Cold-coolCold-coolLonicerae japonicae flos5.05Cold-coolCold-coolIsatidis folium9.68Cold-coolCold-coolTaraxaciherba4.12Cold-coolCold-coolMenthae haplocalycis herba5.56Cold-coolCold-coolPlatycladi cacumen4.59Cold-coolCold-coolBupleuri radix4.20Cold-coolCold-coolPlantaginis semen6.40Cold-coolCold-coolKochiae fructus2.39Cold-coolCold-coolPuerariae lobatae radix1.40Cold-coolCold-coolSargassum8.84Cold-coolCold-coolDianthi herba3.35Cold-coolCold-coolTrichosanthis fructus0.35Cold-coolCold-coolGentianae radix et rhizoma1.55Cold-coolCold-coolAloe2.72Cold-coolCold-coolTrachelospermi caulis et folium3.70Cold-coolCold-coolEcliptae herba9.31Cold-coolCold-coolSiegesbeckiae herba1.68Cold-coolCold-coolArnebiae radix6.42Cold-coolCold-coolFuzi-7.14Hot-warmHot-warmCinnamomi cortex-3.57Hot-warmHot-warmZingiberis rhizoma-8.82Hot-warmHot-warmEuodiae fructus-2.07Hot-warmHot-warmAlpiniae officinarum rhizoma-6.02Hot-warmHot-warmPiperis fructus-3.28Hot-warmHot-warmPiperis longi fructus-3.99Hot-warmHot-warmCurculiginis rhizoma-8.21Hot-warmHot-warmEucommiae cortex0.04Hot-warmCold-cool∗∗Sinapis semen-5.96Hot-warmHot-warmPinelliae rhizoma-4.55Hot-warmHot-warmPsoraleae fructus-1.33Hot-warmHot-warmAtractylodis rhizoma-7.28Hot-warmHot-warmAlpiniae katsumadai semen-5.53Hot-warmHot-warmCitri reticulatae pericarpium-6.24Hot-warmHot-warmChuanxiong rhizoma-3.61Hot-warmHot-warmMagnollae officinalis cortex-2.20Hot-warmHot-warmEphedrae herba-0.49Hot-warmHot-warmChaenomelis fructus-1.50Hot-warmHot-warmAucklandiae radix-5.56Hot-warmHot-warmNotopthrygii rhizoma et radix-2.84Hot-warmHot-warmArisaematis rhizoma-7.26Hot-warmHot-warmClematidis radix et rhizoma2.39Hot-warmCold-cool∗∗Asari radix et rhizoma-4.65Hot-warmHot-warmCorydalis rhizoma-5.99Hot-warmHot-warm∗∗ represents a wrong judgment of drug properties.Through the quantitative discriminant function composed of indexes TS, PS, MS, TL, TP, and AA, the “cold-hot” medicinal properties of 46 different traditional Chinese medicines can be correctly distinguished, except Gardeniae fructus, Eucommiae cortex, and Clematidis radix et rhizoma. In other words, there was a correlation between above six indicators and “cold-hot” medicinal properties to a certain extent. On the basis of quantitative discrimination, in the system composed of 46 kinds of traditional Chinese medicines except Gardeniae fructus, Eucommiae cortex, and Clematidis radix et rhizoma, TS, PS, MS, TL, TP, and AA could be used as characterization indexes of drug properties.


### 3.2. Quantification of “Cold-Cool” Medicinal Properties

On the premise of characterization indexes determined in Section3.1, we carried out quantitative comparison of “cold-cool” drug properties of different traditional Chinese medicines. At the same time, we took the quantitative comparison of “cold-cool” drug properties of Phellodendri chinensis cortex, Coptidis rhizoma, and Menthae haplocalycis herba as an example to explain in detail.


#### 3.2.1. Vector Expression of “Cold-Cool” Drug Properties

Based on TS, PS, MS, TL, TP, and AA, we used different vectors to represent the “cold-cool” drug property of Phellodendri chinensis cortex, Coptidis rhizoma, and Menthae haplocalycis herba. Since the attribute of index is the content of a certain component in the traditional Chinese medicines, moreover, the control blank did not contain the component to be tested, and the blank values of TS, PS, MS, TL, TP, and AA are all “0”. As can be seen from Table1, the Phellodendri chinensis cortex’s indicator values of TS, PS, MS, TL, TP, and AA were 24.51, 2.79, 2.21, 3.41, 9.27, and 4.68, respectively. Then, in the six-dimensional space formed by attribute indexes TS, PS, MS, TL, TP, and AA, blank values arranged in order of (TS, PS, MS, TL, TP, AA) were taken as “blank spot” whose coordinates were recorded as (0, 0, 0, 0, 0, 0). The same ordered array of attribute indicator values was taken as “medicinal properties spot” whose coordinate is (24.51, 2.79, 2.21, 3.41, 9.27, 4.68). Therefore, vector A from “blank point” to “medicinal properties point” is a vector that can represent “cold-cool” drug properties of Phellodendri chinensis cortex.
(18)A=24.51,2.79,2.21,3.41,9.27,4.68−0,0,0,0,0,0=24.51,2.79,2.21,3.41,9.27,4.68.In the same way, vectorsB and C represent “cold-cool” drug properties of Menthae haplocalycis herba and Coptidis rhizoma, respectively, as follows:
(19)B=18.55,0.60,4.54,2.81,3.27,6.56−0,0,0,0,0,0=18.55,0.60,4.54,2.81,3.27,6.56,C=38.59,2.54,6.96,0.73,5.77,11.26−0,0,0,0,0,0=38.59,2.54,6.96,0.73,5.77,11.26.In the light of vector coordinate ofA, B, and C, we quantitatively compared “cold-cool” drug properties of Phellodendri chinensis cortex, Menthae haplocalycis herba, and Coptidis rhizoma through the calculation of “R”.


#### 3.2.2. Quantitative Comparison of “Cold-Cool” Drug Properties Based on “R”

When performing quantitative comparison of “cold-cool” drug properties, we used Coptis chinensis as a reference drug. At this time, the quantitative values of medicinal properties of Phellodendri chinensis cortex and Menthae haplocalycis herba compared to that of Coptidis rhizoma were recorded asRA,C and RB,C, respectively. According to the general theoretical formula of quantitative value of drug properties, it can be calculated that
(20)RA,C=∑i=1njipi∑i=1npi2=24.51×38.59+2.79×2.54+⋯+9.27×5.77+4.68×11.2638.592+2.542+⋯+5.772+11.262=0.63,RB,C=∑i=1njipi∑i=1npi2=18.55×38.59+0.60×2.54+⋯+3.27×5.77+6.56×11.2638.592+2.542+⋯+5.772+11.262=0.49.Coptidis rhizoma is the reference drug, the quantitative value of whose medicinal properties “RC” can be obtained by self-comparison.
(21)RC=1.00.According to the calculation of quantitative value of drug properties, we obtained thatRC>RB,C>RA,C. That is to say, in the comparison of “cold-cool” medicinal properties, Coptidis rhizoma is the most “cold-cool”, followed by Phellodendri chinensis cortex, with Menthae haplocalycis herba is the weakest. Above results are consistent with the cognition of traditional Chinese medicine theory to Coptidis rhizoma, Phellodendri chinensis cortex, and Menthae haplocalycis herba. The theory of TCM holds that Coptidis rhizoma, Scutellariae radix, and Phellodendri chinensis cortex are all “cold” in drug properties, with Coptis chinensis being the most especially [27], while Menthae haplocalycis herba is classified as “cool” in drug properties which is weaker than “cold” [28].In addition, based on characterization indexes and relevant data, taking Coptis rhizoma as reference drug and through the calculation of formula “R”, the quantitative values of drug properties of other “cold-cool” traditional Chinese medicines have been also obtained. The results of quantitative values of “cold-cool” drug properties are shown in Table 3.Table 3
The results of quantitative values of “cold-cool” drug properties.
TCMRTCMRAnemarrhenae rhizoma0.72Kochiae fructus0.84Lophatherum herba0.54Puerariae lobatae radix0.97Phellodendri chinensis cortex0.63Sargassum0.26Coptidis rhizoma∗∗1.00Dianthi herba0.62Fraxini cortex0.74Trichosanthis fructus0.74Lonicerae japonicae flos0.51Gentianae radix et rhizoma0.99Isatidis folium0.48Aloe0.30Taraxaciherba0.60Trachelospermi caulis et folium0.63Menthae haplocalycis herba0.49Ecliptae herba0.34Platycladi cacumen0.37Siegesbeckiae herba0.38Bupleuri radix0.58Arnebiae radix0.35Plantaginis semen0.51——Coptidis rhizoma∗∗ was taken as the reference drug.


### 3.3. Quantification of “Hot-Warm” Medicinal Properties

Using the same method as quantifying “cold-cool” medicinal properties, we quantified “hot-warm” drug properties. When making quantitative comparisons, we took “Fuzi” as the reference drug to calculate. The results are shown in Table4.Table 4
The results of quantitative values of “hot-warm” drug properties.
TCMRTCMRFuzi∗∗1.00Alpiniae katsumadai semen0.57Cinnamomi cortex0.50Citri reticulatae pericarpium0.41Zingiberis rhizoma0.71Chuanxiong rhizoma0.48Euodiae fructus0.19Magnollae officinalis cortex0.31Alpiniae officinarum rhizoma0.48Ephedrae herba0.30Piperis fructus0.60Chaenomelis fructus0.25Piperis longi fructus0.62Aucklandiae radix0.21Curculiginis rhizoma0.82Notopthrygii rhizoma et radix0.33Sinapis semen0.23Arisaematis rhizoma1.02Pinelliae rhizoma0.85Asari radix et rhizoma0.78Psoraleae fructus0.22Corydalis rhizoma1.01Atractylodis rhizoma0.30——As shown in Table4, for example, RFuzi=1.00, RCurculiginisrhizoma=0.82, and RAucklandiaeradix=0.21. The results showed that “hot-warm” properties of Fuzi are greater than those of Curculiginis rhizoma and Aucklandiae radix, which are also in line with the theoretical perception of traditional Chinese medicine. In addition, The R values in Table 4 allowed us to compare the strength or weakness of “hot-warm” drug properties of different Chinese medicines mentioned above.


## 3.1. Correlation Analysis between Primary Metabolites and “Hot-Cold” Medicinal Properties

According to theory of traditional Chinese medicines, “four natures” that contain cold, hot, warm, and cool can be mainly divided into two categories: “hot-warm” and “cold-cool”. On the other hand, relevant research shows that the “hot-warm” and “cold-cool” properties of traditional Chinese medicines have a certain correlation with their material basis [7, 8, 23]. From this perspective, through data mining and literature collation, we have obtained some primary metabolite information of Chinese medicines with different drug properties, including the total sugar (TS), polysaccharide (PS), monosaccharide (MS), total lipid (TL), total protein (TP), and amino acid (AA). Based on above indicators and relevant data (Table 1) [24–26], we analyzed the correlation between primary metabolites and “hot-cold” medicinal properties based on Fisher’s analysis.Table 1
Content results of relevant components in 49 traditional Chinese medicines (%).
TCMTSPSMSTLTPAACold-coolAnemarrhenae rhizoma27.836.425.251.214.026.73Gardeniae fructus22.093.105.6911.673.035.23Lophatherum herba20.852.362.061.382.657.07Phellodendri chinensis cortex24.512.792.213.419.274.68Coptidis rhizoma38.592.546.960.735.7711.26Fraxini cortex31.550.701.970.611.421.55Lonicerae japonicae flos16.174.3310.382.098.739.34Isatidis folium14.721.144.583.157.9215.32Taraxaciherba20.467.647.613.508.459.69Menthae haplocalycis herba18.550.604.542.813.276.56Platycladi cacumen12.931.485.794.062.775.65Bupleuri radix23.220.842.743.233.674.75Plantaginis semen18.511.092.145.021.7310.40Kochiae fructus29.912.402.728.1814.2114.39Puerariae lobatae radix39.575.704.491.016.443.58Sargassum9.462.063.270.300.243.91Dianthi herba23.610.047.132.585.565.83Trichosanthis fructus23.770.6213.927.7610.7315.99Gentianae radix et rhizoma39.421.547.862.201.528.14Aloe9.180.1716.410.203.441.96Trachelospermi caulis et folium24.101.426.481.527.634.57Ecliptae herba11.861.053.881.041.377.91Siegesbeckiae herba13.051.307.036.334.194.88Arnebiae radix13.360.433.251.863.433.28Hot-warmFuzi92.454.241.010.580.471.96Cinnamomi cortex45.875.751.205.2213.471.11Zingiberis rhizoma65.034.1411.074.7215.325.40Euodiae fructus17.282.5411.357.3113.995.32Alpiniae officinarum rhizoma43.996.1214.022.8912.211.86Piperis fructus55.485.532.916.610.478.60Piperis longi fructus57.124.026.365.772.719.23Curculiginis rhizoma74.684.2912.431.5363.0810.87Eucommiae cortex26.521.227.334.251.092.79Sinapis semen20.120.752.0025.0521.1924.26Pinelliae rhizoma77.7126.671.020.263.844.14Psoraleae fructus19.730.249.1115.0639.8623.35Atractylodis rhizoma26.5916.2817.736.730.332.62Alpiniae katsumadai semen52.483.172.988.700.846.20Citri reticulatae pericarpium37.903.6024.751.301.333.96Chuanxiong rhizoma44.252.523.298.8335.6511.11Magnollae officinalis cortex28.230.967.576.061.852.30Ephedrae herba27.371.4711.163.212.993.65Chaenomelis fructus22.312.9018.861.704.503.66Aucklandiae radix17.9233.2218.905.572.984.05Notopthrygii rhizoma et radix29.942.223.519.773.885.48Arisaematis rhizoma93.8212.952.240.480.644.31Clematidis radix et rhizoma34.721.488.130.661.595.29Asari radix et rhizoma71.775.095.671.314.404.97Corydalis rhizoma93.2511.503.960.511.018.34On the basis of above indicators TS, PS, MS, TL, TP, and AA, we established the identification model of medicine properties through Fisher’s linear analysis for exploring correlation between primary metabolites and “cold-hot” medicinal properties.As shown in Figure3, blue represents “cold-cool” Chinese medicines; meanwhile, red represents “hot-warm” Chinese medicines. Based on Fisher’s discriminant function: Y=0.45×AA−0.05×TP−0.87×TL−0.41×MS−0.06×PS−0.19×TS−10.58, we could correctly distinguish the drug properties of traditional Chinese medicines in Table 1 and the correct rate of discrimination reaches up to 93.88%. When Y>0, the corresponding traditional Chinese medicines are classified as “cold-cool” medicines; if Y<0, it could be classified as “hot-warm” Chinese medicines. The Fisher’s discriminant results are shown in Table 2, in which the medicinal properties of Gardeniae fructus, Eucommiae cortex, and Clematidis radix et rhizoma were misjudged.Figure 3
The diagram of Fisher’s linear discriminant.Table 2
Fisher’s discriminant results of 49 traditional Chinese medicines.
TCMYDrug propertiesTest classificationAnemarrhenae rhizoma4.63Cold-coolCold-coolGardeniae fructus-4.03Cold-coolHot-warm∗∗Lophatherum herba7.54Cold-coolCold-coolPhellodendri chinensis cortex3.61Cold-coolCold-coolCoptidis rhizoma4.51Cold-coolCold-coolFraxini cortex3.90Cold-coolCold-coolLonicerae japonicae flos5.05Cold-coolCold-coolIsatidis folium9.68Cold-coolCold-coolTaraxaciherba4.12Cold-coolCold-coolMenthae haplocalycis herba5.56Cold-coolCold-coolPlatycladi cacumen4.59Cold-coolCold-coolBupleuri radix4.20Cold-coolCold-coolPlantaginis semen6.40Cold-coolCold-coolKochiae fructus2.39Cold-coolCold-coolPuerariae lobatae radix1.40Cold-coolCold-coolSargassum8.84Cold-coolCold-coolDianthi herba3.35Cold-coolCold-coolTrichosanthis fructus0.35Cold-coolCold-coolGentianae radix et rhizoma1.55Cold-coolCold-coolAloe2.72Cold-coolCold-coolTrachelospermi caulis et folium3.70Cold-coolCold-coolEcliptae herba9.31Cold-coolCold-coolSiegesbeckiae herba1.68Cold-coolCold-coolArnebiae radix6.42Cold-coolCold-coolFuzi-7.14Hot-warmHot-warmCinnamomi cortex-3.57Hot-warmHot-warmZingiberis rhizoma-8.82Hot-warmHot-warmEuodiae fructus-2.07Hot-warmHot-warmAlpiniae officinarum rhizoma-6.02Hot-warmHot-warmPiperis fructus-3.28Hot-warmHot-warmPiperis longi fructus-3.99Hot-warmHot-warmCurculiginis rhizoma-8.21Hot-warmHot-warmEucommiae cortex0.04Hot-warmCold-cool∗∗Sinapis semen-5.96Hot-warmHot-warmPinelliae rhizoma-4.55Hot-warmHot-warmPsoraleae fructus-1.33Hot-warmHot-warmAtractylodis rhizoma-7.28Hot-warmHot-warmAlpiniae katsumadai semen-5.53Hot-warmHot-warmCitri reticulatae pericarpium-6.24Hot-warmHot-warmChuanxiong rhizoma-3.61Hot-warmHot-warmMagnollae officinalis cortex-2.20Hot-warmHot-warmEphedrae herba-0.49Hot-warmHot-warmChaenomelis fructus-1.50Hot-warmHot-warmAucklandiae radix-5.56Hot-warmHot-warmNotopthrygii rhizoma et radix-2.84Hot-warmHot-warmArisaematis rhizoma-7.26Hot-warmHot-warmClematidis radix et rhizoma2.39Hot-warmCold-cool∗∗Asari radix et rhizoma-4.65Hot-warmHot-warmCorydalis rhizoma-5.99Hot-warmHot-warm∗∗ represents a wrong judgment of drug properties.Through the quantitative discriminant function composed of indexes TS, PS, MS, TL, TP, and AA, the “cold-hot” medicinal properties of 46 different traditional Chinese medicines can be correctly distinguished, except Gardeniae fructus, Eucommiae cortex, and Clematidis radix et rhizoma. In other words, there was a correlation between above six indicators and “cold-hot” medicinal properties to a certain extent. On the basis of quantitative discrimination, in the system composed of 46 kinds of traditional Chinese medicines except Gardeniae fructus, Eucommiae cortex, and Clematidis radix et rhizoma, TS, PS, MS, TL, TP, and AA could be used as characterization indexes of drug properties.


## 3.2. Quantification of “Cold-Cool” Medicinal Properties

On the premise of characterization indexes determined in Section3.1, we carried out quantitative comparison of “cold-cool” drug properties of different traditional Chinese medicines. At the same time, we took the quantitative comparison of “cold-cool” drug properties of Phellodendri chinensis cortex, Coptidis rhizoma, and Menthae haplocalycis herba as an example to explain in detail.


### 3.2.1. Vector Expression of “Cold-Cool” Drug Properties

Based on TS, PS, MS, TL, TP, and AA, we used different vectors to represent the “cold-cool” drug property of Phellodendri chinensis cortex, Coptidis rhizoma, and Menthae haplocalycis herba. Since the attribute of index is the content of a certain component in the traditional Chinese medicines, moreover, the control blank did not contain the component to be tested, and the blank values of TS, PS, MS, TL, TP, and AA are all “0”. As can be seen from Table1, the Phellodendri chinensis cortex’s indicator values of TS, PS, MS, TL, TP, and AA were 24.51, 2.79, 2.21, 3.41, 9.27, and 4.68, respectively. Then, in the six-dimensional space formed by attribute indexes TS, PS, MS, TL, TP, and AA, blank values arranged in order of (TS, PS, MS, TL, TP, AA) were taken as “blank spot” whose coordinates were recorded as (0, 0, 0, 0, 0, 0). The same ordered array of attribute indicator values was taken as “medicinal properties spot” whose coordinate is (24.51, 2.79, 2.21, 3.41, 9.27, 4.68). Therefore, vector A from “blank point” to “medicinal properties point” is a vector that can represent “cold-cool” drug properties of Phellodendri chinensis cortex.
(18)A=24.51,2.79,2.21,3.41,9.27,4.68−0,0,0,0,0,0=24.51,2.79,2.21,3.41,9.27,4.68.In the same way, vectorsB and C represent “cold-cool” drug properties of Menthae haplocalycis herba and Coptidis rhizoma, respectively, as follows:
(19)B=18.55,0.60,4.54,2.81,3.27,6.56−0,0,0,0,0,0=18.55,0.60,4.54,2.81,3.27,6.56,C=38.59,2.54,6.96,0.73,5.77,11.26−0,0,0,0,0,0=38.59,2.54,6.96,0.73,5.77,11.26.In the light of vector coordinate ofA, B, and C, we quantitatively compared “cold-cool” drug properties of Phellodendri chinensis cortex, Menthae haplocalycis herba, and Coptidis rhizoma through the calculation of “R”.


### 3.2.2. Quantitative Comparison of “Cold-Cool” Drug Properties Based on “R”

When performing quantitative comparison of “cold-cool” drug properties, we used Coptis chinensis as a reference drug. At this time, the quantitative values of medicinal properties of Phellodendri chinensis cortex and Menthae haplocalycis herba compared to that of Coptidis rhizoma were recorded asRA,C and RB,C, respectively. According to the general theoretical formula of quantitative value of drug properties, it can be calculated that
(20)RA,C=∑i=1njipi∑i=1npi2=24.51×38.59+2.79×2.54+⋯+9.27×5.77+4.68×11.2638.592+2.542+⋯+5.772+11.262=0.63,RB,C=∑i=1njipi∑i=1npi2=18.55×38.59+0.60×2.54+⋯+3.27×5.77+6.56×11.2638.592+2.542+⋯+5.772+11.262=0.49.Coptidis rhizoma is the reference drug, the quantitative value of whose medicinal properties “RC” can be obtained by self-comparison.
(21)RC=1.00.According to the calculation of quantitative value of drug properties, we obtained thatRC>RB,C>RA,C. That is to say, in the comparison of “cold-cool” medicinal properties, Coptidis rhizoma is the most “cold-cool”, followed by Phellodendri chinensis cortex, with Menthae haplocalycis herba is the weakest. Above results are consistent with the cognition of traditional Chinese medicine theory to Coptidis rhizoma, Phellodendri chinensis cortex, and Menthae haplocalycis herba. The theory of TCM holds that Coptidis rhizoma, Scutellariae radix, and Phellodendri chinensis cortex are all “cold” in drug properties, with Coptis chinensis being the most especially [27], while Menthae haplocalycis herba is classified as “cool” in drug properties which is weaker than “cold” [28].In addition, based on characterization indexes and relevant data, taking Coptis rhizoma as reference drug and through the calculation of formula “R”, the quantitative values of drug properties of other “cold-cool” traditional Chinese medicines have been also obtained. The results of quantitative values of “cold-cool” drug properties are shown in Table 3.Table 3
The results of quantitative values of “cold-cool” drug properties.
TCMRTCMRAnemarrhenae rhizoma0.72Kochiae fructus0.84Lophatherum herba0.54Puerariae lobatae radix0.97Phellodendri chinensis cortex0.63Sargassum0.26Coptidis rhizoma∗∗1.00Dianthi herba0.62Fraxini cortex0.74Trichosanthis fructus0.74Lonicerae japonicae flos0.51Gentianae radix et rhizoma0.99Isatidis folium0.48Aloe0.30Taraxaciherba0.60Trachelospermi caulis et folium0.63Menthae haplocalycis herba0.49Ecliptae herba0.34Platycladi cacumen0.37Siegesbeckiae herba0.38Bupleuri radix0.58Arnebiae radix0.35Plantaginis semen0.51——Coptidis rhizoma∗∗ was taken as the reference drug.


## 3.2.1. Vector Expression of “Cold-Cool” Drug Properties

Based on TS, PS, MS, TL, TP, and AA, we used different vectors to represent the “cold-cool” drug property of Phellodendri chinensis cortex, Coptidis rhizoma, and Menthae haplocalycis herba. Since the attribute of index is the content of a certain component in the traditional Chinese medicines, moreover, the control blank did not contain the component to be tested, and the blank values of TS, PS, MS, TL, TP, and AA are all “0”. As can be seen from Table1, the Phellodendri chinensis cortex’s indicator values of TS, PS, MS, TL, TP, and AA were 24.51, 2.79, 2.21, 3.41, 9.27, and 4.68, respectively. Then, in the six-dimensional space formed by attribute indexes TS, PS, MS, TL, TP, and AA, blank values arranged in order of (TS, PS, MS, TL, TP, AA) were taken as “blank spot” whose coordinates were recorded as (0, 0, 0, 0, 0, 0). The same ordered array of attribute indicator values was taken as “medicinal properties spot” whose coordinate is (24.51, 2.79, 2.21, 3.41, 9.27, 4.68). Therefore, vector A from “blank point” to “medicinal properties point” is a vector that can represent “cold-cool” drug properties of Phellodendri chinensis cortex.
(18)A=24.51,2.79,2.21,3.41,9.27,4.68−0,0,0,0,0,0=24.51,2.79,2.21,3.41,9.27,4.68.In the same way, vectorsB and C represent “cold-cool” drug properties of Menthae haplocalycis herba and Coptidis rhizoma, respectively, as follows:
(19)B=18.55,0.60,4.54,2.81,3.27,6.56−0,0,0,0,0,0=18.55,0.60,4.54,2.81,3.27,6.56,C=38.59,2.54,6.96,0.73,5.77,11.26−0,0,0,0,0,0=38.59,2.54,6.96,0.73,5.77,11.26.In the light of vector coordinate ofA, B, and C, we quantitatively compared “cold-cool” drug properties of Phellodendri chinensis cortex, Menthae haplocalycis herba, and Coptidis rhizoma through the calculation of “R”.


## 3.2.2. Quantitative Comparison of “Cold-Cool” Drug Properties Based on “R”

When performing quantitative comparison of “cold-cool” drug properties, we used Coptis chinensis as a reference drug. At this time, the quantitative values of medicinal properties of Phellodendri chinensis cortex and Menthae haplocalycis herba compared to that of Coptidis rhizoma were recorded asRA,C and RB,C, respectively. According to the general theoretical formula of quantitative value of drug properties, it can be calculated that
(20)RA,C=∑i=1njipi∑i=1npi2=24.51×38.59+2.79×2.54+⋯+9.27×5.77+4.68×11.2638.592+2.542+⋯+5.772+11.262=0.63,RB,C=∑i=1njipi∑i=1npi2=18.55×38.59+0.60×2.54+⋯+3.27×5.77+6.56×11.2638.592+2.542+⋯+5.772+11.262=0.49.Coptidis rhizoma is the reference drug, the quantitative value of whose medicinal properties “RC” can be obtained by self-comparison.
(21)RC=1.00.According to the calculation of quantitative value of drug properties, we obtained thatRC>RB,C>RA,C. That is to say, in the comparison of “cold-cool” medicinal properties, Coptidis rhizoma is the most “cold-cool”, followed by Phellodendri chinensis cortex, with Menthae haplocalycis herba is the weakest. Above results are consistent with the cognition of traditional Chinese medicine theory to Coptidis rhizoma, Phellodendri chinensis cortex, and Menthae haplocalycis herba. The theory of TCM holds that Coptidis rhizoma, Scutellariae radix, and Phellodendri chinensis cortex are all “cold” in drug properties, with Coptis chinensis being the most especially [27], while Menthae haplocalycis herba is classified as “cool” in drug properties which is weaker than “cold” [28].In addition, based on characterization indexes and relevant data, taking Coptis rhizoma as reference drug and through the calculation of formula “R”, the quantitative values of drug properties of other “cold-cool” traditional Chinese medicines have been also obtained. The results of quantitative values of “cold-cool” drug properties are shown in Table 3.Table 3
The results of quantitative values of “cold-cool” drug properties.
TCMRTCMRAnemarrhenae rhizoma0.72Kochiae fructus0.84Lophatherum herba0.54Puerariae lobatae radix0.97Phellodendri chinensis cortex0.63Sargassum0.26Coptidis rhizoma∗∗1.00Dianthi herba0.62Fraxini cortex0.74Trichosanthis fructus0.74Lonicerae japonicae flos0.51Gentianae radix et rhizoma0.99Isatidis folium0.48Aloe0.30Taraxaciherba0.60Trachelospermi caulis et folium0.63Menthae haplocalycis herba0.49Ecliptae herba0.34Platycladi cacumen0.37Siegesbeckiae herba0.38Bupleuri radix0.58Arnebiae radix0.35Plantaginis semen0.51——Coptidis rhizoma∗∗ was taken as the reference drug.


## 3.3. Quantification of “Hot-Warm” Medicinal Properties

Using the same method as quantifying “cold-cool” medicinal properties, we quantified “hot-warm” drug properties. When making quantitative comparisons, we took “Fuzi” as the reference drug to calculate. The results are shown in Table4.Table 4
The results of quantitative values of “hot-warm” drug properties.
TCMRTCMRFuzi∗∗1.00Alpiniae katsumadai semen0.57Cinnamomi cortex0.50Citri reticulatae pericarpium0.41Zingiberis rhizoma0.71Chuanxiong rhizoma0.48Euodiae fructus0.19Magnollae officinalis cortex0.31Alpiniae officinarum rhizoma0.48Ephedrae herba0.30Piperis fructus0.60Chaenomelis fructus0.25Piperis longi fructus0.62Aucklandiae radix0.21Curculiginis rhizoma0.82Notopthrygii rhizoma et radix0.33Sinapis semen0.23Arisaematis rhizoma1.02Pinelliae rhizoma0.85Asari radix et rhizoma0.78Psoraleae fructus0.22Corydalis rhizoma1.01Atractylodis rhizoma0.30——As shown in Table4, for example, RFuzi=1.00, RCurculiginisrhizoma=0.82, and RAucklandiaeradix=0.21. The results showed that “hot-warm” properties of Fuzi are greater than those of Curculiginis rhizoma and Aucklandiae radix, which are also in line with the theoretical perception of traditional Chinese medicine. In addition, The R values in Table 4 allowed us to compare the strength or weakness of “hot-warm” drug properties of different Chinese medicines mentioned above.


## 4. Analysis and Discussion

### 4.1. QMP and Quantification Value “R”

In this paper, we defined QMP as quantitative comparison of same medicinal properties of different Chinese medicines through quantification value of Chinese medicinal properties “R”. Why is a quantitative comparison of the same medicinal properties rather than different medicinal properties? Just as Newton’s laws have their own conditions of applicability, many of theory may be deviated or even erroneous when they exceeded scope of application. QMP is achieved by means of quantification value of Chinese medicinal properties “R”. Theoretically, since “cold-cool” and “hot-warm” are opposing medicinal properties, their quantification value “R” should be a negative value. However, in practice, as medicinal property indicators are objective and specific, they have their corresponding indicator values rather than subjective assignments. Therefore, there are basically no cases where the metric is negative. In order to ensure that the metric model is accurate and reliable, we define QMP as quantitative comparison of same medicinal properties.The quantification value “R” was derived based on vector representation of medicinal properties and rules of vector operations, which has a solid theoretical foundation in mathematics. It can be used to quantify and compare the strength or weakness of medicinal properties such as four natures, five flavors, and toxicity, which provide a scientific and objective method for quantitative comparison of medicinal properties. It is worth noting that QMP is actually a relative metric comparison. For example, in Section 3.2.2, we used Coptidis rhizoma as the reference drug for comparison of medicinal properties. In other words, when the reference drugs are different, we can obtain different “R” values. However, what “R” stands for is the same; it is a relative comparison of the strength or weakness of medicinal properties. Such that RA,B and RA,C represent the strength or weakness of medicinal properties of drug “A” in relation to that of drug “B” and drug “C”, respectively.


### 4.2. Discussion of Quantification for “Cold-Hot” Medicinal Properties

The “cold-hot” medicinal properties have characteristics of abstractness, ambiguity, subjectivity, etc. [5]. Researchers have carried out analyses from a number of perspectives with some success [7, 8, 24, 25]. Wang et al. studied on the differentiation of “cold-hot” medicinal properties based on primary metabolites [29]. Wang and Li constructed the identification model of “cold-hot” medicinal properties based on the GC-MS chromatogram of lipid components [30]. All of these are indicative of the relevance of primary metabolites to medicinal properties to some extent. In addition, a single main ingredient or active ingredient is not sufficient to characterize medicinal properties of TCMs. Therefore, we integrated information on primary metabolites for correlation analysis of medicinal properties.For correlation analysis between primary metabolites and drug properties, we used Fisher’s linear analysis. Firstly, primary metabolites TS, PS, MS, TL, TP, and AA were highly correlated, nonlinearity, and unclear statistical distribution, which may not make the data suitable for statistical testing. Secondly, Fisher’s linear analysis can turn the dimension of high-dimensional data with nonlinearity, high correlation, and unclear statistical distribution characteristics into low-dimensional linear space for discriminant analysis, which is suitable for data analysis. Based on primary metabolites TS, PS, MS, TL, TP, and AA, the “cold-hot” medicinal properties can be well distinguished, which proves that above indicators are in connection with “cold-hot” medicinal properties of 46 Chinese medicines (except Gardeniae fructus, Eucommiae cortex and Clematidis radix et rhizoma). In this process, the correlation was based on discriminatory analysis of “cold-hot”, which is currently the commonly used and recognized method. In this context, we proposed the QMP and the quantification value “R”. It is expected to provide a reference for quantitative comparison of medicinal properties.From point of view of material base of medicinal properties, based on correlation indicators of medicinal properties of primary metabolites TS, PS, MS, TL, TP, and AA, we completed a quantitative comparison of “cold-hot” medicinal properties of 46 Chinese medicines. A few results contradicted the perception of TCM theory, such asREuodiaefructus=0.19 and RCorydalisrhizoma=1.01. Above R values indicated that Corydalis rhizoma is more “hot-warm” than Euodiae fructus, which was at odds with TCM theory. This may be due to errors in experimental measurements. However, most of the results of quantitative comparison are basically in line with the perception of TCM theory. It demonstrates that QMP has certain guiding significance for quantitative comparison of “cold-hot” medicinal properties. It is feasibility for “R” to achieve quantitative comparison of same drug properties of different Chinese medicines, which is helpful to promote process of modern Chinese medicine construction. In addition, the QMP has a highly flexible character. Based on the choice of indicators, it can be applied to many areas of analysis related to drug properties to quantify medicinal properties of TCMs or to integrate multiple fields of analysis related to medicinal properties to evaluate the strength or weakness of medicinal properties, which is in line with the trend in medicinal properties research [31]. However, the current research studies have obvious shortages. The quality of research methods used to analyze the relationship between material composition and CMP varies. Many studies use subjective analysis methods that rely too much on the personal experience of experts and lack credible standards. It is difficult to solve the complex nonlinear and diversity problems in CMP discrimination, prediction, and quantification by using difference analysis methods such as standard deviation and t-test.


## 4.1. QMP and Quantification Value “R”

In this paper, we defined QMP as quantitative comparison of same medicinal properties of different Chinese medicines through quantification value of Chinese medicinal properties “R”. Why is a quantitative comparison of the same medicinal properties rather than different medicinal properties? Just as Newton’s laws have their own conditions of applicability, many of theory may be deviated or even erroneous when they exceeded scope of application. QMP is achieved by means of quantification value of Chinese medicinal properties “R”. Theoretically, since “cold-cool” and “hot-warm” are opposing medicinal properties, their quantification value “R” should be a negative value. However, in practice, as medicinal property indicators are objective and specific, they have their corresponding indicator values rather than subjective assignments. Therefore, there are basically no cases where the metric is negative. In order to ensure that the metric model is accurate and reliable, we define QMP as quantitative comparison of same medicinal properties.The quantification value “R” was derived based on vector representation of medicinal properties and rules of vector operations, which has a solid theoretical foundation in mathematics. It can be used to quantify and compare the strength or weakness of medicinal properties such as four natures, five flavors, and toxicity, which provide a scientific and objective method for quantitative comparison of medicinal properties. It is worth noting that QMP is actually a relative metric comparison. For example, in Section 3.2.2, we used Coptidis rhizoma as the reference drug for comparison of medicinal properties. In other words, when the reference drugs are different, we can obtain different “R” values. However, what “R” stands for is the same; it is a relative comparison of the strength or weakness of medicinal properties. Such that RA,B and RA,C represent the strength or weakness of medicinal properties of drug “A” in relation to that of drug “B” and drug “C”, respectively.


## 4.2. Discussion of Quantification for “Cold-Hot” Medicinal Properties

The “cold-hot” medicinal properties have characteristics of abstractness, ambiguity, subjectivity, etc. [5]. Researchers have carried out analyses from a number of perspectives with some success [7, 8, 24, 25]. Wang et al. studied on the differentiation of “cold-hot” medicinal properties based on primary metabolites [29]. Wang and Li constructed the identification model of “cold-hot” medicinal properties based on the GC-MS chromatogram of lipid components [30]. All of these are indicative of the relevance of primary metabolites to medicinal properties to some extent. In addition, a single main ingredient or active ingredient is not sufficient to characterize medicinal properties of TCMs. Therefore, we integrated information on primary metabolites for correlation analysis of medicinal properties.For correlation analysis between primary metabolites and drug properties, we used Fisher’s linear analysis. Firstly, primary metabolites TS, PS, MS, TL, TP, and AA were highly correlated, nonlinearity, and unclear statistical distribution, which may not make the data suitable for statistical testing. Secondly, Fisher’s linear analysis can turn the dimension of high-dimensional data with nonlinearity, high correlation, and unclear statistical distribution characteristics into low-dimensional linear space for discriminant analysis, which is suitable for data analysis. Based on primary metabolites TS, PS, MS, TL, TP, and AA, the “cold-hot” medicinal properties can be well distinguished, which proves that above indicators are in connection with “cold-hot” medicinal properties of 46 Chinese medicines (except Gardeniae fructus, Eucommiae cortex and Clematidis radix et rhizoma). In this process, the correlation was based on discriminatory analysis of “cold-hot”, which is currently the commonly used and recognized method. In this context, we proposed the QMP and the quantification value “R”. It is expected to provide a reference for quantitative comparison of medicinal properties.From point of view of material base of medicinal properties, based on correlation indicators of medicinal properties of primary metabolites TS, PS, MS, TL, TP, and AA, we completed a quantitative comparison of “cold-hot” medicinal properties of 46 Chinese medicines. A few results contradicted the perception of TCM theory, such asREuodiaefructus=0.19 and RCorydalisrhizoma=1.01. Above R values indicated that Corydalis rhizoma is more “hot-warm” than Euodiae fructus, which was at odds with TCM theory. This may be due to errors in experimental measurements. However, most of the results of quantitative comparison are basically in line with the perception of TCM theory. It demonstrates that QMP has certain guiding significance for quantitative comparison of “cold-hot” medicinal properties. It is feasibility for “R” to achieve quantitative comparison of same drug properties of different Chinese medicines, which is helpful to promote process of modern Chinese medicine construction. In addition, the QMP has a highly flexible character. Based on the choice of indicators, it can be applied to many areas of analysis related to drug properties to quantify medicinal properties of TCMs or to integrate multiple fields of analysis related to medicinal properties to evaluate the strength or weakness of medicinal properties, which is in line with the trend in medicinal properties research [31]. However, the current research studies have obvious shortages. The quality of research methods used to analyze the relationship between material composition and CMP varies. Many studies use subjective analysis methods that rely too much on the personal experience of experts and lack credible standards. It is difficult to solve the complex nonlinear and diversity problems in CMP discrimination, prediction, and quantification by using difference analysis methods such as standard deviation and t-test.


## 5. Conclusion

In this paper, we present quantification of Chinese medicinal properties (QMP) and the quantification value of medicinal properties “R”. Through the calculation of quantitative value of drug properties “R”, we can realize the quantitative comparison of “cold-hot” medicinal properties of TCMs; that is to say, it is feasible for QMP to achieve the quantitative comparison of same drug properties of different Chinese medicines. In addition, QMP has certain guiding significance for the quantification of Chinese medicinal properties. It is beneficial to promote the process of modern Chinese medicine construction.



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*Source: 5790893-2022-01-22.xml*