The experimental treatment comprised varying concentrations of 6-BA (0, 20, 40, 60, and 80 mg/L), GA₃ (0, 50, 100, 150, and 200 mg/L), and NAA (0, 10, 20, 30, and 40 mg/L), respectively. Each treatment was replicated three times. The seedlings’ pseudobulbs were irrigated with 10 mL of the respective treatment solution once weekly, resulting in a total of eight applications. The emergence of lateral buds was documented at 30, 60, and 90 d, while leaf length, leaf width, and plant height were measured at 90 d mark.

The experimental design employed was a response surface methodology with a Box-Benhken design, encompassing a total of 17 experimental runs, including four replicates at the center points. The variables selected for optimization were 6-BA, GA₃, and NAA, coded as A, B, and C, respectively, with their range and levels detailed in Table 1. The sprouting was recorded at 30, 60, and 90 d, and leaf length, leaf width, and plant height were measured at 90 d.

6-BA is a typical cell division agent that predominantly stimulates stem and leaf development, bud proliferation, and cell division. After 90 d of experimental treatment, the data illustrated in Figs. 1A,B and 2. reveal that as the concentration of 6-BA increments, the number of lateral buds initially increases and subsequently decreases. When the 6-BA concentration was 60 mg/L, the number of lateral bud peaks at 3.29; conversely, at 80 mg/L, the number of lateral bud drops to a low of just 1.29. The trends in the line chart between 20 and 40 mg/L were relatively flat and not significantly different, but when the concentration of 6-BA concentration was 60 mg/L, there was a significant difference with other levels. Excessively high levels of 6-BA may inhibit lateral bud development while concurrently promoting overall plant growth. A concentration of 6-BA that is optimal and suitable for lateral bud development might suppress overall plant growth, while a concentration that favors plant growth could inhibit the formation of lateral buds.

The leaf area and plant height with the concentration of 6-BA increase. At a concentration of 6-BA which was 80 mg/L, significant differences in leaf area and plant height are observed compared to the 20, 60 mg/L, and the control group.

GA₃ is a widely utilized plant growth regulator that exerts a profound influence on various aspects of plant development, including stem and leaf growth, seedling development, and the formation of lateral buds. As shown in Figs. 1C and 3, GA₃ significantly influences the formation of lateral buds. The highest number of lateral buds (1.92) was observed at a GA₃ concentration of 150 mg/L, with the new buds exhibiting a slender morphology (Fig. 1C). In contrast, at the lowest concentration of 50 mg/L only 1.25 lateral buds were noted. This trend indicates that increasing GA₃ concentration generally promotes lateral bud formation. However, it is important to recognize that excessively high concentrations of GA₃ (>150 mg/L) may inhibit lateral bud formation.

The leaf area and plant height with the concentration of GA₃ increases. When the GA₃ concentration was 200 mg/L, it significantly differed from other levels, while the line chart from 0 to 150 mg/L displayed only minor changes. Overall, while GA₃ promotes lateral bud formation, leaf area, and plant height up to a certain concentration, excessive levels may hinder these developments.

NAA is known to regulate plant elongation and promote cell division. As illustrated in Figs. 1D and 4, the highest number of lateral buds (2.2) was observed at an NAA concentration of 30 mg/L, while the lowest (1.33) was noted at 0 mg/L. This trend suggests that increasing NAA levels can effectively promote lateral bud germination. However, the germination of lateral buds was suppressed at concentrations higher than 30 mg/L.

Regarding leaf area, NAA did not show significant differences across the tested concentrations. The exhibit shows a relatively gentle trend in the line graph of plant height between the NAA concentrations of 10 and 40 mg/L, with no significant differences observed. This suggests that while NAA positively influences lateral bud formation within a certain concentration range, its impact on leaf area and plant height may be limited.

Y₁ = 2.34 − 0.4625A + 0.2588B − 0.1788C − 0.300AB + 0.2750AC − 0.0675BC − 0.0218A² − 0.1793B² + 0.3758C²

The number of lateral buds ranged from 1.67 to 3.6. The three independent variables had important effects on the response (number of lateral buds) (Table 3). The value of the coefficient of determination (R²) was 0.9776; the proficiency of the model is demonstrated if R² is equal to 0.75 or higher than this value [25]. The adjusted determination coefficient (adjusted R²) was found to be 0.9488. The regression equation model yielded a p value of less than 0.0001. Upon subjecting the equation to a lack of fit test, the results were F = 0.24 and p = 0.8621 > 0.05, indicating a non-significant lack of fit. This suggests that the regression equation aligns well with the actual experiment data, exhibiting minimal experimental errors, and can accurately describe the relationship between the various factors and response values. The quadratic coefficients of B² and C²; A, B, and C were statistically the most significant factors. The cross-coefficient AB and AC were also significant. However, the regression coefficients of BC and A² were not significant. The interaction between 6-BA and both GA₃ and NAA significantly affected the quantity of lateral buds. In contrast, the interaction between GA₃ and NAA did not significantly affect the quantity of lateral buds of the species.

The utilization of Design-Expert 13 software to generate contour plots and response surface plots (Fig. 6) provides a detailed analysis of the influence of various factors on the response values. The interaction among various factors and their impact on the number of lateral buds can be discerned through the morphology of the contour line and the curvature of the response surface. A steeper curvature of the response surface and a denser distribution of contour line indicate a more significant influence, while a shape that approaches an elliptical form suggests a stronger interaction between the two factors.

Fig. 6 shows a 2D contour plot and 3D response surface plots for the number of lateral buds. Fig. 6A and B demonstrates a significant interaction between 6-BA and GA₃. When the concentration NAA was fixed at 30 mg/L and GA₃ was maintained at a constant level, an increase in the concentration of 6-BA resulted in a corresponding increase in the number of lateral buds. At higher levels of GA₃, the number of lateral buds increases rapidly with rising concentrations of 6-BA. In contrast, when GA₃ was at lower levels, the number of lateral buds increased more gradually. Additionally, when lower concentrations of 6-BA were applied, the number of lateral bud increased slowly with rising concentrations of GA₃. Conversely, at higher concentrations of 6-BA, the number of lateral buds rose rapidly as GA₃ concentrations were increased.

As illustrated in Fig. 6C and D, the interaction between 6-BA and NAA was significant. When the concentration of GA₃ was held constant at 150 mg/L and NAA was maintained at a constant level, the number of lateral buds increased with the concentration of 6-BA. However, at a higher level of NAA, the number of lateral buds roses rapidly with increasing concentrations of 6-BA. Conversely, when NAA was at a lower level, the growth of lateral buds was slower, and even with a constant 6-BA concentration, the number of lateral buds still increased with the concentration of NAA.

From Fig. 6E and F, the response surface curves for GA₃ and NAA were relatively flat, suggesting that the interaction between GA₃ and NAA was not significant, and their effects on the number of lateral buds were not significant.

In summary, the concentration of 6-BA had the most significant impact on the germination of lateral buds, followed by GA₃, while NAA concentration had the least effect. Therefore, it can be inferred that the germination of lateral buds was relatively sensitive to variations in 6-BA concentration, with sensitivity levels ranked as 6-BA > GA₃ > NAA.

Y₂ = 1.858 − 0.1725A + 0.1763B + 0.4738C + 0.0375AB – 0.1375AC + 0.0500BC + 0.0785A² – 0.7140B² + 0.0560C²

The three independent variables significantly influenced the response variable (leaf area). As indicated in Table 4, the p value of the regression equation model was less than 0.0001, suggesting a highly significant model fit. A lack-of-fit test was conducted on the equation, and the results revealed that the lack-of-fit term was not significant (F = 3.34, p = 0.1371 > 0.05), indicating that the model adequately describes the experimental data. The coefficient of determination (R²) was 0.9862, and the adjusted determination coefficient (adjusted R²) was 0.9688, both of which imply that the regression equation closely aligns with the actual experiment data, exhibiting minimal experimental errors and accurately capturing the relationship between the various factors and response values. The quadratic coefficients of B², A, B, and C were statistically the most significant factors. Additionally, the cross-coefficient AC was also significant. Conversely, the following factors were statistically insignificant: the quadratic coefficient of (A², C²) and the cross-coefficient (AB, BC). The results demonstrated that the interaction between 6-BA and NAA significantly affected the growth rate of leaf area. However, the interactions between GA₃ and NAA, and between GA₃ and 6-BA, did not exert a significant effect on the growth rate of the leaf area in this species.

The results of the 2D contour plot and 3D response surface plots are presented in Fig. 7. Fig. 7A,C demonstrates that the response surface for 6-BA was relatively flat. When the concentration of 6-BA exceeded 60 mg/L, it had minimal effect on the increase in leaf area. In contrast, the response surface curve for GA₃ (Fig. 7A,E) was parabolic and steeper. When the NAA concentration was 30 mg/L and 6-BA concentration remained constant, with increasing GA₃ concentration leaf area first increased and then decreased. When GA₃ exceeds 175 mg/L, the curve flattens, and the leaf area decreases with increasing concentration. This pattern indicates that the leaf area dependent on a specific range of GA₃ concentration.

Fig. 7C and E highlights that the response curves for NAA were steep and linear, signifying a substantial influence on leaf area growth. In Fig. 7C and D, the interaction between 6-BA and NAA was pronounced, as evidenced by dense contour lines. When the GA₃ concentration was 150 mg/L and the 6-BA concentration remained constant, the increase in leaf area corresponded with the concentration of NAA. However, at high levels of 6-BA, the increase in leaf area was slow. Conversely, when 6-BA was at a low level, the leaf area increment rapidly increased with rising NAA concentrations.

In summary, the concentration of NAA had the largest effect impact on the increase in leaf area, followed by GA₃, while the influence of 6-BA concentration was the least. Therefore, it can be concluded that the leaf area growth was relatively sensitive to changes in NAA concentration, with sensitivity levels ranked as follows: NAA > GA₃ > 6-BA.

Y₃ = 2.98 + 0.1325A + 0.4338B − 0.0063C – 0.0400AB – 0.0200AC + 0.1875BC – 0.5225A² – 1.0128B² – 0.6528C²

The regression equation model (Table 5) had a p value of less than 0.0001, indicating significance and suggesting that the model was appropriate for this experiment. The lack-of-fit term test was used to analyze the equation, yielding F = 0.24, p = 0.8669 > 0.05, which indicates a non-significant lack-of-fit term, suggesting that the model fits the test well. Among them, the coefficient of determination (R²) was 0.9851, and the adjusted determination coefficient (adjusted R²) was found to be 0.9659. These values indicate that the regression closely aligns with the actual experiment data, exhibiting minimal experimental errors and accurately describing the relationship between the various factors and response values. The quadratic coefficients of A², B², and C² were also significant. The cross-coefficient BC, A, and B displayed statistically significant factors. While C, AB, and AC had non-significant regression coefficients. The results demonstrated that the interaction of GA₃ with NAA significantly affected the relative growth rate of plant height. However, the interaction between 6-BA and NAA, GA₃, did not significantly affect the relative growth rate of plant height in this species.

The response surface plots and contour maps, which depict interactions among various factors through fitting equations, typically display a hilly curvature, indicating the presence of a maximum within the selected ranges of each factor. As illustrated in Fig. 8A,C, and E, the response curve of GA₃ exhibits a parabolic trend and is relatively steep, while the response curves for 6-BA and NAA are comparatively flat. This indicates that the concentration of GA₃ significantly influences the plant height, followed by 6-BA and NAA. When the NAA concentration was 30 mg/L and 6-BA remained constant, as GA₃ concentration increased, plant height initially rose and then decreased (Fig. 8A). When GA₃ was at 150 mg/L, the increase in plant height was the greatest. While concentrations exceeding 175 mg/L lead to a flattening of the response curve and a reduction in height, indicating that excessively high concentrations inhibit growth.

As shown in Fig. 8A–D, it is clearly shown that the interactions between 6-BA and GA₃, and between 6-BA and NAA, were not significant. The projections of the contour maps predominantly appear circular or nearly circular, which aligns with the results of the variance analysis. In contrast, the projections in Fig. 8E and F exhibit an elliptical shape with a parabolic and steep response curve, indicating a significant interaction between GA₃ and NAA, consistent with the variance analysis findings.

In summary, the concentration of GA₃ had the most pronounced effect on plant height, followed by 6-BA and NAA. Therefore, it can be concluded that plant height growth is relatively sensitive to changes in GA₃ concentration, with the sensitivity levels ranked as follows: GA₃ > 6-BA > NAA.

The analysis conducted using Design-Expert 13 software determined that the optimal conditions for enhancing the number of lateral buds, leaf area growth, and plant height growth were as follows: 6-BA at 43.34 mg/L, GA₃ at 168.55 mg/L, and NAA at 35.68 mg/L. The predicted optimal value for lateral buds was 2.75 buds per plant, and the leaf area growth was 2.38 cm², while the plant height was 2.38 cm. For practical application, adjustments were made based on actual conditions, setting 6-BA to 43 mg/L, GA₃ to 169 mg/L, and NAA to 36 mg/L for three parallel experiments. The results yielded an average of 2.78 lateral buds, 2.87 cm² for leaf area growth, and 2.67 cm for plant height growth, which were generally consistent with the theoretical predictions. This indicates that the model is reliable and can be utilized for optimizing the growth of C. tortisepalum var. longibracteatum and its rapid propagation beyond tissue culture.