Often, two or more clinical drugs are used in combination. Chinese medicine treatment adheres to the basic theory of Chinese medicine with regard to the compatibility of compounds. Therefore, to clarify the mechanism of Chinese herbal medicine, it is necessary to establish the role of traditional Chinese medicine active ingredients by using effective research methods ^[1]. These should be established to examine the original composition of the original group of Chinese herbal compounds (static methods), their metabolism in the body (dynamic methods), and the validity of these methods. To study the effectiveness of a formulation compared with single components, four complicated issues must first be addressed ^[2]: Determination of the effect coefficient of each component; multi-component single targets to establishment the dose-effect relationship; multi-target multi-component scale-free networks to establish relationship dynamics; and an integration factor for the individual components: these constitute the overall pharmacodynamic effect of the total spectrum of the kinetic parameters of relationship between the components. In the establishment of these relationships, the use of Hill's dose-effect relationship between the linear curves to achieve targets superimposed between the effects of various building components into the overall effect and the quantitative relationship between the core issue is key ^[3]. This article describes the role of the drug and receptor relationships with Michaelis-Menten kinetics ^[4], compares dose-effect relationship with the concentration-time relationship characterized by dynamics, presents the first discovery of a dose-effect relationship into the speed (the concentration of drug with reference to the effect of changes in receptor speed)-effect relationship that can be achieved from the linear rate of change, in order to achieve the single-target multi-component linear superposition. This article presents the first creation of mathematical models of in vivo pharmacodynamics, and uses the muscarinic M receptor agonist acetylcholine, α adrenergic receptor agonist adrenaline, and their mixtures as model drugs, and the in vitro intestinal tension to verify the created mathematical model.

1.   The basic idea

To compare Michaelis-Menten receptor kinetics with Hill dose pharmacokinetic characteristics of the mathematical model, which are proposed to correct the metabolic rates of the drug effect and dose-effect model of Hill, and to establish a linear quick effect model.

1.1   Interaction of drug effects and metabolic rate to establish a linear relationship

1.1.1   Single-ingredient drug effect and dose dose-response curves

Based on the receptor kinetics model from the Hill equation (1):

where formula D is the dose, E_m is the maximum efficacy value, H is the index of curve shape, α is the effect of the strength coefficient, and K_D is half the maximum effect of the drug concentration, (1) is the quantitative relationship of the drug-dose intensity for most of the drug dose-effect relationships ^{[5, 6]}.

1.1.2   Single-component mathematical model of drug metabolism

According to Michaelis-Menten receptor kinetics and the rules of drug action, receptors at the target drug concentration follow the dynamic relationship given by equation (2) ^[6]:

In equation (2), K₁, K₂, K₃, V_m, K_m, the equilibrium constant ^{[7, 8]} of the Michaelis-Menten equation, K_m, is $E = \frac{{\alpha {E_{\text{m}} }{{[D]}^H}}}{{{{\left( {{K_D}} \right)}^H} + {{[D]}^H}}} = \frac{{\alpha '{V_{\text{m}} }{{[D]}^H}}}{{{{\left( {{K_m}} \right)}^H} + {{[D]}^H}}} = \alpha '\left( {\frac{{dD}}{{dt}}} \right)$; the maximum speed is also half of the concentration.

As the concentration of drug effect and the rate of change are equivalent, $E = \frac{{\alpha {E_{\text{m}} }{{[D]}^H}}}{{{{\left( {{K_D}} \right)}^H} + {{[D]}^H}}} = \frac{{\alpha '{V_{\text{m}} }{{[D]}^H}}}{{{{\left( {{K_m}} \right)}^H} + {{[D]}^H}}} = \alpha '\left( {\frac{{dD}}{{dt}}} \right)$. The comparison of (1) and (2) shows that the concentration changes and drug effect strength have a linear relationship, but speed has a non-linear relationship with concentration; which can be shown by equation (3):

The values α and α' are different coefficients, therefore:

If the effective threshold is E₀, equation (3) becomes:

Equation (4), an important linear equation for our drug dose, is also the basis for drug superposition.

1.1.3   Multi-component single-target effects of the linear mathematical model of stack

Based on equation (4), according to traditional Chinese medicine to move from a single-component formulation to a multiple-component formulation, two sub-effects and toxicity are three effects for which modeling can be divided into four cases: non-toxic effects of an increase; decreased non-toxic effects; toxic effects of an increase; and reduced toxic effects; if the efficacy and toxicity are considered separately, the actual increase and decrease only two cases, those effects increase the coefficient of expression have a positive sign, and a negative sign indicates decreased efficacy, the multi-component single target effects of competition (both reflected in the effect on the coefficient α), non-competition (reflected in the effect of a factor α, and another is reflected in the threshold, but also on the constant E₀) allowed superimposition of the Hill dose-effect curve. There are two cases: one is independent of the drug competition, and in the other, two kinds of drug interactions occur ^[9].

Independent competition stacked linear mathematical model: Separate effects of each component are also represented by a linear superposition; the total effect of the rate of change with the concentration of each component can be obtained from the linear regression coefficient of the effects in equation (5):

Equation (5) describe multi-component single-target effects with the most simple superposition.

A mathematical model of the interaction of linear stack: there is also a mutual interaction between the various components of the linear superposition, the total effect of the rate of change in the concentration of each component, and its interaction term effects can be obtained for the linear regression coefficient ${\alpha '_i}$, as shown in equation (6):

Equation (6) describes the superposition of multi-component single-target effects.

Equations (5) and (6) show that the drug effect to study linearization, the metabolic rate must be controlled by receptors.

1.2   Receptor (body effect) to determine the speed of change in drug concentration

Receptors change the body drug concentrations and the in vitro and in vivo pharmacokinetics in two ways. The body's rate of change can be calculated from a concentration-time curve function; then, the time derivative can for in vitro receptors (effect on the body) on the rate of change of drug concentration in the dosing rate can be controlled to set a target. Following the in vivo analysis, the in vitro rate of change of the drug concentration is calculated.

1.2.1   Rate of change of drug concentration in vivo receptor calculation

The pharmacokinetics of drugs in the body are affected by quantitative changes in the central chamber ^[10], as shown in Figure 1.

Figure  1.  In vivo pharmacokinetic model of receptor sites

下载: 全尺寸图片 幻灯片

From Figure 1: Effect of room and room differential equations for the type of drug:

Where k_m is the receptor metabolism constant, equation (7) describes the efficacy of the role of general quantitative relationship between the room type, for three cases:

1) When k_m≫X_c, drugs can reach receptor saturation and the equation (7) becomes linear:

The above equation for the Laplace transformation is:

For the n-compartment model in terms of the center compartment of the drug, substituted into equation (9) for the inverse Laplace transformation, is:

For equation (10), the derivative is:

Therefore, the pharmacodynamics of a single component general equation are described by:

When the metabolism of drugs in the target position did not occur, then equation (11) becomes:

Therefore, the multi-component single-target single-pharmacodynamic target is represented by the general equation:

For metabolism occurring outside of the target position, then the formula is:

2) When km≪Xc, drugs do not reach receptor saturation, equation (7) with constants becomes:

The above equation for the Laplace transformation is:

(17) for the inverse Laplace transformation:

For equation (18), the derivative is:

Therefore, the pharmacodynamics of a single component general equation are represented by:

When the metabolism of drugs in the target position does not occur, then equation (11) becomes:

Therefore, the m multi-component single-target saturation pharmacodynamics is presented by the general equation:

For metabolism occurring outside of the target position, then the formula is:

From (20)-(23) we can see that the time of drug effect has nothing to do with where the contents are metabolized, only the metabolic constants associated with the receptor, whereas when the receptor metabolic constant is zero, then the effect is a constant at a maximum.

3) When km≈Xc, drug receptor saturation is nearly half, the performance of nonlinear equations, (7) becomes:

in the original function of Xe is not easy to find, but from (12)-(13) single-component values ${\alpha ^\prime }\frac{{{k_{1e}}}}{{{k_m}}}$ can be obtained, from equation (20)-(21) various types of single-component values ${\alpha ^\prime }{k_{1e}}$ can be obtained. Then, the comparison of the two equations of each component can be obtained for K_m, and the measured the concentration effect compartment concentration-time can be used to find ${\alpha ^\prime }$ and then to calculate ${k_{1e}}$from equation (10), (12), (18), and (20) can be considered${k_{e0}}$, so that all single-ingredient pharmacodynamic parameter estimates will not interact. For multi-component analysis according to equation (14)-(15) the value of each component can be obtained ${\alpha ^\prime }\frac{{{k_{1e}}}}{{{k_m}}}$, from equation (22)-(23), various values of the components can be obtained ${\alpha ^\prime }{k_{1e}}$. A comparison of the two equations can be obtained for the components of K_m, and then measured for the concentration effect of the compartment on the concentration-time, to find ${\alpha ^\prime }$, and then calculated${k_{1e}}$from equation (14); (22) can be considered ${k_{e0}}$. Therefore, a multi-component estimate of all pharmacodynamic parameters can be obtained. Nonlinear efficacy can be expressed as either single-component or multi-component.

Single component:

When k_e0 is zero, then (25) becomes:

Multi-component:

When ke0 is zero, then (27) becomes:

(27), (28) for the dynamics of multi-component spectral efficiency based on the kinetic equation. These equations are in two parts: part of the overall multi-component single-target pharmacodynamic equation, in various formats; the other part is the overall efficacy and pharmacodynamic effect of multi-target model, which is specifically described in another paper.

1.2.2   Calculation of rate of change of receptor drug concentration in vitro

You can also change the receptor in vitro drug concentration, the receptor changes by the time effect, which allows experimental Hill dose-response curve linearization. The compartment of the in vitro receptor changes in drug concentration are shown in Figure 2.

Figure  2.  Receptor sites in the in vitro pharmacokinetic model

下载: 全尺寸图片 幻灯片

The drug concentration of C_a in the first preparations made is shown in Figure 2, along with the equilibrium constant of drug elimination K₁, and then the speed V_e on the effect of chamber volume administration, the discharge rate of drug, the drug concentration of C_e, the drug effects the equilibrium constant for the elimination compartment K₂, the drugs from the effects of compartment transfer into the target receptor chamber rate constants for the K_a, the target receptor in the elimination chamber equilibrium constant is K, which produces the following effects. The receptor pharmacokinetic effects are differential equations of the type ^[11]:

Kinetic equations for the same efficacy in vivo can be divided into three cases.

1) When the dosage is small, the receptor expression of the linear kinetic equation is:

The above equation for the Laplace transformation when Laplace was X_e as a function of:

(32) for the inverse Laplace transformation:

Similarly, equation (33) becomes equation (36):

Similarly, equation (34) transforms to:

When the receptor is not involved in metabolism, K=0, then:

From equation (37), the derivative was:

From equation (38), the derivative was ${c_r}^\prime = \frac{{{k_a}}}{{{k_m}}}{c_e}$

Combined with equation (25), we have determined the single-target multi-component in vitro efficacy kinetic equation:

When the drug is heavy, with receptor saturation, the constant term reflects the dynamic equation:

The above equation for the Laplace transformation, when Laplace was Xe, as a function of:

(41) for the inverse Laplace transformation:

Of equation (42), the derivative was the type:

When k is zero,

Combined with equation (25), we have determined the in vitro efficacy of single-target multi-component kinetic equation:

When the amount of drug receptor capacity by nearly half, reflecting the nonlinear dynamic equations for the type (31), C_r cannot be found in the original function ^[12], but from (45) to obtain the components of the$\alpha '\frac{{{k_a}}}{k}$; then from equation (42) and (44) to obtain k, k_a; the combination allows the determination of $\alpha '$, from (40), which was eventually considered to be$\frac{{\alpha '}}{{{k_m}}}$, so that the pharmacodynamic parameters of each component was completely considered; ${k_m}$is a multi-component efficacy dynamic mathematical model of the general formula:

When K is equal to zero, then equation (46) becomes

Equation (46) can be expressed in vitro multi-component single-target non-linear pharmacodynamic behavior, this paper its experimental verification.

2.   Verification Experiment

2.1   Equipment, materials, and methods

Instruments: constant smooth groove (HN-400E, Chengdu Taimeng Technology Co., Ltd., batch number: TM052-0904-01-030-019); muscle tension sensor (model JH-2, Beijing Institute of Space Medico-Engineering); intravenous drip, note the use of infusion, flask, reagent bottles, beakers, pipettes, and syringes.

Reagents: acetylcholine (Pharmacology Laboratory, Hunan Medical University of 1:1000 solution provided by the teacher); adrenal hydrochloride injection (1 mg/mL, Tianjin Jinhui Amino Acid Co., Ltd., batch number: 0902272); sodium chloride, chlorinated potassium, sodium dihydrogen phosphate, sodium bicarbonate, calcium chloride, and glucose, were all of analytical grade.

Experimental animals: three male guinea pigs of average weight provided by the laboratory animal center of Hunan University of Chinese Medicine.

2.2   Methods

2.2.1   Preparation of test solution and reagent

Tyrode's solution was prepared from: NaCl, 8 g; KCl, 0. 2 g; MgSO₄·7H₂O, 0.26 g; NaH₂PO₄, 0.065 g, NaHCO_3, 1 g; CaCl₂, 0.2 g; glucose, 1 g; and distilled water to 1000 mL.

Reagent preparation: preparation of 0.5×10^-6 mg/mL of both acetylcholine and adrenaline solutions; and a preparation of a mixture of equal concentrations of the two solutions.

2.2.2   Preparation of isolated guinea pig intestine

Immediately after the guinea pigs were sacrificed by a broken neck, the abdominal cavity was cut open, the ileum was detected, the ileum was clipped, Tyrode's solution was placed into a beaker, the syringe containing intestinal content was rinsed with 20 mL of warm Tyrode's solution, and the small intestine was cut in sections of approximately 1.5 cm in length.

2.2.3   Connection to the device and data acquisition

A small section of intestine was ligated at both ends with a thin, short ring fixed at one end to make a dish in the desire and the other end of the tie line was connected to a tension sensor. The small intestine segments were incubated in a bath at temperature 37℃. A total volume of 20 mL was used, with adjustment for inflation. The whole process could avoid intestinal exposure to the air.

The computer acquisition system should be started by the BL-420F icon and the tension sensor is connected to the channel. The tie line and the sensor should be adjusted so that the bowel movements can be freely detected by the sensor. The gain and scanning speed should be adjusted, and the bowel movement curves will be clearly displayed on the monitor to record the bowel activity curve.

2.2.4   Design of experiments

Experimental and control sub-quantitative instilled directly into the two types directly into the bath is added directly to the two drugs, the concentration of 0.5×10^-6 mg/mL; quantitative trickle-down approach is based on Figure 2, to 0.05 mL/s with a uniform rate of infusion 0.5×10^-6 mg/mL of the two drugs, or other concentrations of the mixture in the bath, while the bottom to 0.05 mL/s speed exhaust the bath solution, 20 mL volume of the solution remains unchanged, However, the concentration increased with the increase over time, while real-time observation and recording tension curve values.

3.   Results

3.1   Pharmacodynamics calculation changes

The above formulation is the in vitro calculation, but this will change in specific cases. In this experiment, with shorter drug stability, the k1 and k2 is zero, then (37) and (39) become:

The effect of:

Equation (50) m is a single component in the mixture to take 2. By equation (43), $k$ and $\alpha '{k_a}$ may be fitted; then by (49), (50) to obtain k, ka; known c0, h, Ve, obtained by the calculation of $\alpha '$ and ${k_m}$.

3.2   Pharmacodynamic parameters of acetylcholine and adrenaline as single components

Direct accession into the sub-saturated and quantitative infusion. The saturation measured directly after the entry of acetylcholine is shown in Figure 3 and for adrenaline is shown in Figure 4.

Figure  3.  The relationship between the time and tension of saturated acetylcholine solution

下载: 全尺寸图片 幻灯片

Figure  4.  The relationship between time and tension of saturated adrenaline solution

下载: 全尺寸图片 幻灯片

According to equations (50) and (43), with lnE t to give the values^-1, $\alpha '{k_a}$ was 26.73, and R was -0.9108; the $k$ for adrenaline was 1.203×10^-5 s^-1, $\alpha '{k_a}$ was 9.513, and R was 0.9105.

Measured by infusion of acetylcholine in Figure 5; adrenaline shown in Figure 6.

Figure  5.  The relationship between time and tension of acetylcholine determined by the drip method

下载: 全尺寸图片 幻灯片

Figure  6.  The relationship between time and tension of adrenaline determined by the drip method

下载: 全尺寸图片 幻灯片

According to equation (50), (49), with Et for non-linear regression was of acetylcholine, adrenaline pharmacodynamic parameters, the results are shown in Table 1.

Table  1.  Measured pharmacodynamic parameters of in vitro infusions of acetylcholine and adrenaline

Parameters	C0 (mg·mL-1)	k1 (s-1)	k2 (s-1)	Ve mL	h mL·s-1	K (s-1)	Ka (s-1)	km (s-1)	α (张 s·m g -1)	E0 (张)	R	n	F	P
acetylcholine	5.000×10-7	0	0	20	0.05	2.675×10-3	5.786×10-9	2.500×10-7	4.619×109	13	0.7655	1322	621.9	< 0.01
adrenaline	5.000×10-7	0	0	20	0.05	1.415×10-3	5.846×10-9	2.300×10-7	-1.627×109	9.2	0.6501	1013	246.0	< 0.01
Notes: F0.05(3, ∞)=2.60;F0.01(3, ∞)=3.78.

下载: 导出CSV 

| 显示表格

3.3   Pharmacodynamic parameters of acetylcholine/ adrenaline mixture

Quantitative determination of trickle-down and its time relationship with the tension is shown in Figure 7. The pharmacodynamic parameters in Table 1, according to equation (49) calculated by acetylcholine and adrenaline in the body's metabolic rate and concentration, as shown in Figure 8 to 11.

Figure  7.  The relationship between the time and tension of the mixture of acetylcholine and adrenaline

下载: 全尺寸图片 幻灯片

Figure  8.  The relationship between the time and concentration of acetylcholine on the receptor in the mixture

下载: 全尺寸图片 幻灯片

Figure  9.  The relationship between the time and metabolic rate of acetylcholine in the mixture

下载: 全尺寸图片 幻灯片

Figure  10.  The relationship between the time and concentration of adrenaline at the receptor in the mixture

下载: 全尺寸图片 幻灯片

Figure  11.  The relationship between the time and metabolic rate of adrenaline in the mixture

下载: 全尺寸图片 幻灯片

The comparison of Figures 7, 9, and 11 shows that there is a high degree of consistency. In equation (50), with E on the target receptor on acetylcholine metabolism, the metabolic rate of speed and adrenaline linear regression results are shown in Table 2.

Table  2.  Measured in vitro infusion of acetylcholine, adrenaline mixture pharmacodynamic parameters

Parameters	C0 (mg·mL-1)	k1 (s-1)	k2 (s-1)	Ve mL	h mL·s-1	K (s-1)	Ka (s-1)	km (s-1)	α (张 s·m g -1)	E0 (张)	R	n	F	P
acetylcholine	5.000×10-7	0	0	20	0.05	2.675×10-3	5.786×10-9	2.500×10-7	1.375×1010	7.082	0.9230	2000	5703	< 0.01
adrenaline	5.000×10-7	0	0	20	0.05	1.415×10-3	5.846×10-9	2.300×10-7	-6.150×109	7.082	0.9230	2000	5703	< 0.01
Notes: F0.05(3, ∞)=2.60;F0.01(3, ∞)=3.78.

下载: 导出CSV 

| 显示表格

4.   Discussion

4.1   Hill is a linear dose-effect relationship between the pharmacokinetics determined by the receptor

It is known that a single component Hill equation can represent a dose-effect relationship, but this curve is nonlinear. In single-component studies, the pharmacokinetic parameters are clear; the effects and the concentration are directly related, one to one, so non-linear fitting of the concentration can obtain, the pharmacodynamic parameters. However, for multi-component systems of medicine, a must exist to establish the suitability of linear superposition of the multi-component effects of the problem. Previous authors have studied the pharmacokinetics of traditional Chinese medicine ^[12] and the dose-effect model comparing the Hill and nonlinear Michaelis-Menten models. The first dose found in Hill's model is based on the Michaelis-Menten receptor; both have the same dynamics and thermodynamics. From the perspective of dynamics, the role of the drug effect is the combined result of multiple receptors: changes in the rate of drug metabolism result in biochemical changes in the strength of its micro-performance, just as the intensity of chemical reaction rate equilibrium constant can be expressed; for example, when the rate of drug metabolism and biological effects of the changes in speed are equal, the biochemical effects of balance, when the drug metabolites are completely eliminated, the biological effects stop completely. From a thermodynamic perspective, the unit drug effects on the human body must involve a fast metabolic rate, short duration, and intensity per unit time to produced efficacy: the drug effect strength and metabolic rate were positively correlated with the drug concentration, its strength is mainly due to its metabolism in intensity caused by the body when drugs do not participate in metabolism, the concentration did not change. For no metabolic rate and a high concentration, the drug effects were not reflected, such as an inert material placed in the body does not produce a fixed effect and reflects the mechanical and supportive role.

4.2   Hill equation describes a linear dose-effect relationship between the pharmacodynamics on the basis of traditional Chinese medicine

To establishment a linear mathematical model of drug effect, you can expand the overall dose-effect relationship of traditional Chinese medicine. Chinese medicine has many forms of PK-PD model to address the key issues of the traditional Chinese Medicine (spectrum): 1) the overall effect and to determine the validity of the synergistic effect among; 2) the effectiveness of stacking multiple components. For example, in multi-component medicines, the overall effect of traditional Chinese medicine and the components of the metabolic rate of return of target receptors to obtain the effect of composition on the target contribution to solve the overall effect and validity between components. Subsequently, to create the overall effect and target the relationship between the various components of the overlay target efficacy, to establish the efficacy of Chinese herbal compound dynamics, and also to develop a spectrum efficiency kinetics mathematical model to solve the overall effect of the problems with multi-targets superimposed ^[13], and to clarify more than medicine; for example, find the time-effect relationship, and define this clearly.

4.3   Hill dose-effect relationship can be linearized in vivo experiments

Pharmacodynamics and pharmacokinetics are generally associated with the pharmacodynamic experiments for single-component, direct experiments. However, the pharmacokinetic and pharmacodynamic parameters can be associated by the Hill model, and sometimes also in vitro experiments. For Chinese medicines, in the case of target receptors to allow the best in vitro experiments, the first component is used to determine the validity of the original parties, and then in vivo pharmacokinetics (spectrum) efficient kinetic experiments to determine the original composition and possible metabolites effectiveness of traditional Chinese medicine spectral efficiency gain of kinetic parameters.

4.4   In vitro acetylcholine and adrenaline kinetics

For typical drugs, the acetylcholine M receptor agonist and the α adrenergic receptor agonist act in opposition; the former increases the smooth muscle tone of the digestive tract, the latter does the opposite. This set of isolated guinea pig intestine solution experiments simulated the in vivo environment and dynamic liquid trickle-down approach. The drug concentration in the bath was dynamic, and the experimental results obtained in an experimental simulation environment for in vivo pharmacodynamics, to some extent, may reflect the in vivo effects of drugs.

In Figure 9, Figure 3, and Table 2, the parameters obtained by fitting the two drugs to a credible mathematical model are shown (P < 0.05); especially Figure 7, Figure 9, and Figure 11, show the efficacy and metabolic rate of the two drugs, with a linear regression with R = 0.9230 (F = 5703, P < 0.05), which shows a strong correlation. Acetylcholine intestinal tension increased role of the obvious effect coefficient, resulting in a large peak, whereas the adrenaline of intestinal relaxation is weak, the effect coefficient in the large contraction of the peak produced on the basis of a small relaxation peak. The large peak did not bury the small peak, which explained the role of the two drugs of different receptors, whereas the two drugs target receptors by the metabolic rate and by the time when the effects of consistent, while the drug concentration in the bath conditions was very different (see Figure 7, Figure 8, and Figure 10).

The acetylcholine in vitro pharmacodynamic parameters were: k, 2.675×10^-3 s^-1;; k_a, 5.786×10^-9 s^-1; k_m, 2.500×10^-7 s^-1; α is 4.619×10⁹张 s·mg^-1; E₀, 13 (P < 0.01). The adrenaline pharmacodynamic parameters were: k, 1.415×10^-3 s^-1; k_a, 5.846×10^-9 s^-1; k_m, 2.300×10^-7 s^-1; α, -1.627×10⁹张 s· mg^-1; E₀, 9.2 (P < 0.01); after mixing the two drugs, the values were 1.375×10¹⁰ α张 s·mg^-1, -6.150×10⁹张 s·mg ^-1, and E₀, 7.08; the other parameters did not change (P < 0.01).

5.   Conclusion

In summary, the relationship can be linearized by using the quick dose Hill equation and the validity of traditional Chinese medicine can be confirmed by using the model of the quick in vivo model. However, during real experiments it should be noted that the in vitro and in vivo relevance of in vitro experimental conditions, control, data processing should be strictly controlled in vitro and that the construction of mathematical models should use the currently available relevant statistical software for data processing; however, because no related software has been developed, data processing is not easy and this issue should be studied.

Acknowledgements

We thank for the funding support from the National Natural Science Foundation of China (No. 81073142 and No. 30901971).

Competing Interests

The authors declare no conflict of interest.