50.0 mg powder of flavonoids from D. dao was dissolved in 10 mL of LB culture medium. After filtration through millipore filter (pore size: 0.45 μm), sample solution was conducted at the concentration of 5.0 mg/mL for microcalorimetric measurements.

This experiment was performed using the ampoule method and the microcalorimeter was thermostated at 37°C. One 20 mL sterilized glass ampoule was filled with 10 mL LB culture medium. while others were filled with 0.5 mL LB culture medium containing E. coli at a cell density of 1 × 10⁶ colony forming units (CFU)/ml (Kong et al., 2011) and different weight of flavonoids were added into each ampoule with a final volume of 10 ml. Eventually, each ampoule was sealed up and put into the eight-channel calorimeter block. When the temperature of ampoules reached 37°C, the P-t curves were recorded at an interval of 1 s until the recorder returned to the baseline. All data were collected continuously using the dedicated software package.

The standard solutions were prepared by accurately weighing. 20.0 mg of Cianidanol, L-Epicatechin, Quercetin, or Luteolin was added respectively into 10 mL of methanol to prepare the solutions with a concentration of 2 mg/ml, and then filtered through millipore filter with the pore size of 0.22 μm.

The chromatographic separation was performed using a Waters Acquity BEH C₁₈ column (50 × 2.1 mm, 1.7 μm) with Column temperature of 30°C. The mobile phase composed of solvent A (Chromatographic grade methanol) and solvent B [water solution of 0.15% (V/V) formic acid] was performed with a linear gradient: 0–3.8 min (5%, A), 3.8–4 min (5–30%, A), 4–14.8 min (30%, A), 14.8–15 min (30–50%, A), 15–18.8 min (50%, A), 18.8–19 min (50–95%, A), 19–20 min (95%, A) at a rate of 0.2 mL/min. The detection wavelength was set at 280, 350, 360 nm and the sample injection volume was designated as 2.0 μl, based on the Chinese Pharmacopoeia 2015 edition.

When the suspensions of E. coli are introduced into the ampoules with LB culture medium, the heat-output signals are recorded to form the normal metabolic P-t curves of E. coli (Figure 1). The heat of bacteria represents its metabolic strength. The curve in Figure 1 shows the typical growth characteristics of E. coli and could be divided into five phases: the lag phase (from point A to point B in Figure 1), the first exponential growth phase (from B to C), the transition phase (from C to D), the second exponential growth phase (from D to E), and the decline phase (from E to F).

When the suspensions of E. coli are introduced into the ampoules with different concentrations of flavonoids, there exists corresponding changes in the P-t curve. As could be seen in Figure 2, Table 1, the P-t curves of low concentration flavonoids on E. coli had slight changes compared with control group. The P-t curves and quantitative thermo-kinetic parameters had obvious changes in high concentration, such as the peak of the second exponential growth phase reducing, the time of peak postponing, the slope of curves diminishing and the area of curves lowering. Besides, curves and parameters changed with the concentration increasing. All these demonstrated that the growth of E. coli was influenced by flavonoids in different degrees.

The influence of flavonoids on the growth of E. coli could be quantitatively reflected from the changes of eight thermo-kinetic parameters in Figure 2. The P-t curve of E. coli growth could be fitted by two exponential functions. They both obey the following equation.

In this equation, P₀ and P_t are the power at time 0 and t. Using this equation, the quantitative thermo-kinetic parameters such as the power of the first and second peak (P₁ and P₂) represent the strength of E. Coli metabolism.

The growth rate constants (k₁ and k₂) of the first and second exponential phase for E. coli growth at 37°C represent the rate of E. coli metabolism which is always a thermo-kinetic parameter. The heat outputs in stage 1 and stage 2 (Q₁ and Q₂) are obtained from the P-t curve of E. coli growth affected by different concentrations of flavonoids. The growth rate constant k₁ and k₂ and the correlation coefficient R (not listed, R > 0.9) are also calculated.

Based on the IC₅₀ of sample, S2 exhibited favorable anti-bacterial effect. The content of Luteolin, L-Epicatechin, Cianidanol, and Quercetin was defined as 0-code, and Luteolin (X₁), L-Epicatechin (X₂), Cianidanol (X₃), and Quercetin (X₄) were chosen as the four factor. The general quaternary quadratic designs of rotary combination statistical model (1/2 implement) was introduced to investigate the combined effect of four flavonoids with the use of microcalorimeter figuring out the antibacterial rate (Y-value) on different code level. The content of four flavonoids on different code level was illustrated on Table 5 with Table 6 and Figure 4 displaying experimental design scheme and the analysis result in Table 7.

The regression equations of antibacterial rate were obtained from statistical model of quaternary quadratic general rotary unitized design. That was

The result (Table 7) of variance analysis with this model showed that F₁ = 2.85323 (testing of lack of fit for regression equation of antibacterial rate) was < F_0.05(5, 3) = 9.01, which suggested that the X factor had little influence on experimental result. Moreover, the test result for significance was that F₂ = 6.98973 > F_0.01(11, 8) = 5.74, demonstrating that the regression equation had significant difference. The mathematic model with good fitting degree could reflect the experimental file from the two aspects. Hence, the parameters calculated from the model had favorable confidence level.

In single-factor analysis procedure, the P-values of X₁ (Luteolin) and X₃ (Cianidanol) were < 0.01. Surprisingly, the P-values of (L-Epicatechin) and X₄ (Quercetin) were >0.05. Moreover, the simplified four quaternary regression equation was calculated out without no-significance items of α = 0.10. That was

The four flavonoids had independent anti-bacterial effect with Luteolin and Cianidanol showing the main and better anti-bacterial effect from the analysis of variance table. In addition, the P-value of X₁ (Luteolin) was less than X₃ (Cianidanol) and the concentration range of X₁ was 296–1061 ng·ml⁻¹ far less than that of X₃ (4482–17,506 ng·ml⁻¹).

The diagram of single factor effect for S1–S3 was rationally calculated from the rotational combination design model. The single factor under different code level was predicted to make out the antibacterial rate (Y-value) with others factors as 0-code in this method.

The effect of different factors on bacteria could be observed via the range of each factor (the difference of Y-value for the highest code between the lowest one) and change tend single factor in the analysis of single factor effect. The result showed that X₁ (Luteolin) mainly contributed to the antibacterial rate (Y-value) with X₃ (Cianidanol) and X₄ (Quercetin) contributing only marginally. Unexpectedly, X₂ (L-Epicatechin) had little influence on antibacterial rate. Based on the range result, the sequence of antimicrobial activity was X₁ (Luteolin) > X₃ (Cianidanol) > X₄ (Quercetin) > X₂ (L-Epicatechin) consistent with the P-value of analysis of variance model, further validating the different anti-bacteria effect among the four individual compounds (Figure 5).

Analysis of the effect of two-factor interaction that defined other factor as 0-code for the four flavonoids was obtained from the statistical model of quaternary quadratic general rotary unitized design. The changes of different factors on Y-value as well as the relationship between two factors could be found out via Y-value of two factors under different levels of code by mathematical model. The results showed that there were two couple of factors obvious and similar, such as the pair of Quercetin and Luteolin between Cianidanol and Luteolin (Figure 6).

The diagram of two-factor interaction effect for X₁ (Luteolin) and X₃ (Cianidanol) was rationally calculated from the rotational combination design model. When X₁ and X₃ factor were in high code level, the synergistic activity was obvious between X₁ and X₃ with the antibacterial rate (Y-value) in the top level, which suggested that there was a positive effect between high concentration of X₁ (Luteolin) and X₃ (Cianidanol) and antibacterial rate (Y-value). With the decline of code of Luteolin and Cianidanol, Y-value (antibacterial rate) decreased rapidly with a smaller degree. When the X₁ code number was −1 to −1.6820, the Y-value decreased at first and increased later. When the X₁ code number was −1.3410 and the X₃ code number was −1.6818, the Y-value was 27.5466, which is the lowest point in this analysis model. Therefore, we predicted that there existed positive and synergistic effect between Luteolin and Cianidanol. When Luteolin and Cianidanol was in a higher concentration, there existed obvious synergistic effect between them. But when Luteolin and Cianidanol in low concentration, no marked synergistic effect was observed, even presenting slight antagonistic effects similar with the relationship of X₁ (Luteolin) and X₄ (Quercetin).

Obviously, the analysis showed that there existed both single factor effect and interaction among two factors. So it was difficult to find out the best antibacterial concentration and combinations from the results of the single factor effect and interaction analysis, and quaternary quadratic regression mathematical model did not have the maximum value of bacterial inhibition rate. The analysis method of frequency domain was performed to analyze and confirm this regression model and the combined optimum concentration (Table 8).

Table 8 showed the frequency distribution of 325 cases with antibacterial rate exceeding 39.87%. when antibacterial rate was over 39.87%, most cases could be obtained, verifying the mathematical regression model. Code value of factors was that X₁: 0.633–0.864, X₂: −0.135–0.135, X₃: 0.374–0.627, X₄: 0.200–0.460 under the condition that the antibacterial rate >39.87 within 95% confidence limits. In other words, Luteolin was 822.32–874.99 ng·ml⁻¹, L-Epicatechin was 215.74–236.26 ng·ml⁻¹, Cianidanol was 12,597.62–13,547.13 ng·ml⁻¹, and Quercetin was 5674.6–6138.18 ng·ml⁻¹.

To minimize the error for this experiment, the combined range was defined as Luteolin 850 ng·ml⁻¹ (Code = 0.754), L-Epicatechin 220 ng·ml⁻¹(Code = −0.079), Cianidanol 13,000 ng·ml⁻¹ (Code = 0.481), and Quercetin 6,000 ng·ml⁻¹ (Code = 0.382). The actual antibacterial rate was 45.96% according to the best combination close to the predicted value (46.22%) which further verified the rationality of regression model.

Finally, with the use of validated mathematical model, we finally obtained the combination that Luteolin was 1,061.00–1,061.00 ng·ml⁻¹, L-Epicatechin was 189.14–262.86 ng·ml⁻¹, Cianidanol was 15,990.33–16,973.62 ng·ml⁻¹, Quercetin was 6,799.67–7662.64 ng·ml⁻¹ with Y-value (inhibition rate) >60.00 within 95% confidence limits.

To verify the result that antibacterial activity of the four major components from the leaves of D. dao is Luteolin > Cianidanol > Quercetin > L-Epicatechin based on the quadratic general rotary unitized design model, we determined the anti-bacterial activity of the four flavonoid independently using the microcalorimetry method (Figure 7) with the same parameter as above. The Probit regression with SPSS statistical analysis software was conducted to calculate the half-inhibitory concentration (IC₅₀) after antibacterial rate counted. IC₅₀ representing the sensitivity of bacteria to flavonoids was one of the most important indexes in evaluating the anti-bacterial activity of flavonoids. Table 9 showed the 95% confidence limit of IC₅₀ for each flavonoid. The result showed that Luteolin (15.642 μg·ml⁻¹), Cianidanol (17.584 μg·ml⁻¹), and Quercetin (19.002 μg·ml⁻¹) had lower IC₅₀ values, except for L-Epicatechin. When the concentration of L-Epicatechin was increased to 32 μg/ml, the inhibition rate of L-Epicatechin was still < 50%. In the final calculation, only Probit regression can be used to predict the IC₅₀ of L-Epicatechin (44.247 μg·ml⁻¹). The exact IC₅₀ of L-Epicatechin remains to be further analyzed yet, but that the antibacterial activity of L-Epicatechin is much weaker than that of Luteolin, and Cianidanol and Quercetin can be confirmed. By comparing the IC₅₀ values, we can confirm that antibacterial activity of the four major components from the leaves of D. dao (Luteolin > Cianidanol > Quercetin > L-Epicatechin) based on the quadratic general rotary unitized design model is correct.

In the quadratic general rotary unitized design model, we analyzed two factors interaction effect: Luteolin and Cianidanol, Quercetin, and Luteolin had synergistic effects on antibacterial activity at high doses. In order to verify this result, we independently measured the antimicrobial activity of the two combinations. We referred to the proportion of flavonoids the anti-bacterial rate > 39.87 within 95% confidence limits from the quadratic general rotary unitized design model to determine the ratio of Luteolin and Cianidanol was 1:15, and the ratio of Luteolin and Quercetin was 1:7. microcalorimetry determination of half inhibition rate was also conducted to determine the anti-bacterial activity of flavonoids with the same anti-microbial activity indicators as above (Figure 8). The Probit regression with SPSS statistical analysis software was conducted to calculate the half-inhibitory concentration (IC₅₀) after antibacterial rate counted. IC₅₀ representing the sensitivity of bacteria to flavonoids was one of the most important indexes in evaluating the anti-bacterial activity of flavonoids. Table 9 showed the 95% confidence limit of IC₅₀ for Luteolin and Cianidanol, Quercetin and Luteolin. The result showed that the IC₅₀ values of the combination of Luteolin and Cianidanol was 11.566 μg/ml (722.9 ng·ml⁻¹ for Luteolin, 10,843.1 ng·ml⁻¹ for Cianidanol), and that of the combination of Luteolin and Quercetin was 14.721 μg·ml⁻¹ (1840.1 ng·ml⁻¹ for Luteolin, 12,880.9 ng·ml⁻¹ for Cianidanol) within 95% confidence limits. The ratio of their anti-microbial activity P (in IC₅₀ value) through the concentration ratio weighted average method based on the IC₅₀ values of the four flavonoids alone and two combinations of two flavonoids was calculated. The results displayed that the IC₅₀ value for the combination of Luteolin and Cianidanol was increased to 1.425-fold than the theoretical antibacterial activity of the same concentration of the compound alone and the IC₅₀ value for the combination of Luteolin and Quercetin was 1.129-fold as much as the theoretical antibacterial activity of the same concentration of the compound alone. The synergistic effect of Luteolin and Cianidanol (P_L+C = 1.425), Quercetin and Luteolin (P_L+Q = 1.129) on anti-microbial activity could be confirmed, since the P-values of which were >1.

Cianidanol (C), Luteolin (L), Quercetin (Q).