In Vitro Cell.Dev.Biol.—Plant DOI 10.1007/s11627-010-9309-4
PLANT TISSUE CULTURE
Use of response surface methodology for optimization of a shoot regeneration protocol in Basilicum polystachyon Dipjyoti Chakraborty & Abhijit Bandyopadhyay & Souvik Bandopadhyay & Kajal Gupta & Aditya Chatterjee
Received: 8 February 2009 / Accepted: 30 August 2010 / Editor: N. J. Taylor # The Society for In Vitro Biology 2010
Abstract Response surface methodology (RSM) is a collection of techniques useful for analyzing and optimizing problems where several explanatory covariates influence a response. Although this technique is extensively used in various mixture experiments, its application in standardization of micropropagation protocols is limited. The theoretical developments of RSM are usually concerned with continuous data; hence, linear model theory becomes relevant. In plant tissue culture, in which the response variables are mostly numerical data, the development of RSM in a generalized linear model (GLM) setup is of interest from both a theoretical as well as an application perspective. In the present paper, RSM, as applicable for count data, has been used for modeling, analyzing, and optimizing in vitro regeneration of multiple shoots of Basilicum polystachyon, an important medicinal plant. The specific issues addressed herein are the determination of the optimum concentration of plant growth regulators (i.e., the range of variation in dosages of each covariate) at which the regeneration potential of shoot tip explants is expected to increase, selection of the appropriate D. Chakraborty Department of Bioscience and Biotechnology, Banasthali Vidyapith, Banasthali, Rajasthan 304022, India A. Bandyopadhyay (*) : K. Gupta Department of Botany, The University of Burdwan, Bardhaman, West Bengal 713104, India e-mail:
[email protected] S. Bandopadhyay Indian Institute of Public Health, Hyderabad, India A. Chatterjee Department of Statistics, University of Calcutta, Kolkata, West Bengal 700019, India
growth function (response function) of shoot tip, and determination of the optimum levels of the explanatory variables (i.e., the different combination of dosages of various control factors) for experimentation. According to the present analysis, the optimum level combinations of growth regulators for regeneration of multiple shoots from shoot tip explants of B. polystachyon is 8.19 μM benzyladenine and 2.36 μM naphthalene acetic acid, with a response of approximately 12 regenerated shoots. Keywords Count data . Dispersion matrix . Generalized linear model (GLM) . Link function . Micropropagation . Optimum design . Quasi-Poisson family . Response function . Simultaneous confidence region
Introduction In vitro plant culture is an important aspect of plant science. The potential for commercial production of medicinal and aromatic plants through in vitro culture has gained considerable importance (Debnath et al. 2006; Sarasan et al. 2006), particularly with the increasing use of novel plant-based drugs (Itokawa et al. 2008). In vitro culture is also central to most current transformation protocols, as the protocols often involve a tissue culture stage used to recover transgenic plants (Wolf and Koch 2008). Response surface methodology (RSM) can be used to statistically design experiments and to model, analyze, and improve criteria of response variables that are influenced by several explanatory variables or covariates (Cornell 2002). In basic RSM models, the response variables are continuous and the errors in the observations are assumed to be uncorrelated and homoscedastic. Consequently, first- or second-order linear models are adequate for analysis (Khuri
CHAKRABORTY ET. AL
and Cornell 1996; Cornell 2002; Myers and Montgomery 2002). Extensions of RSM are possible where the error structures are correlated, or heteroscedastic, through the notion of slope rotatability, which requires evaluation of variance of a predicted response at a point that remains constant with all points equidistant from the design center. In the plant sciences, RSM has been used for the optimization of production of secondary metabolites or enzymatic reactions (Gorret et al. 2004; Can et al. 2006). The technique is also utilized for the optimization of plant growth medium (Omar et al. 2004; Niedz and Evens 2007) and as an alternate statistical method for in vitro analysis (Ibanez et al. 2003). Basilicum polystachyon (L) Moench is a traditionally important medicinal plant belonging to the Lamiaceae family (Anonymous 1950) that has a high phenolic content with antimicrobial activity (Chakraborty et al. 2007). Studies with the plant indicate the presence of high seed dormancy (Chakraborty et al. 2003), which accounts for its sparse distribution in the wild, despite large seed production. In vitro propagation is therefore an attractive alternative for this species. In the present study, we have analyzed the regeneration potential, expressed as the number of regenerated microshoots (the dependant variable), of B. polystachyon with the application of various concentrations of the growth regulators naphthaleneacetic acid (NAA) and benzyladenine (BA) (the explanatory factors). The primary aim is to find the concentrations of BA and NAA at which the maximum number of regenerated shoots are obtained. Since the response is count data, extension of RSM and the formulation of an optimization problem under the GLM setup are the focus of the present work. As we have a relatively good idea about the nature of response (represented and well approximated by a concave function in the multi-dimensional space), it is preferable to consider the second-order model without exploring the first-order model (Sen and Swaminathan 1997). Moreover, a first-order model based on the same data may be inadequate on the basis of model validation criterion (Akaike’s information criterion (AIC) in a Poisson or residual deviance in a quasi-Poisson setup). RSM requires a sequence of experiments that follow a central composite design or another optimal design relevant to the study (Khuri and Cornell 1996), which in this case takes 4–6 wk to obtain results. Thus, in terms of in vitro culture, we are looking for a growth regulator combination leading to an optimum response and, in terms of statistical methodology, we are looking for an efficient approach for count response leading to a good estimation of the optimal dosage in a small number of steps. The literature on theoretical developments of RSM in discrete data setup is scanty. Khuri and Mukhopadhyay (2006) considered quantile dispersion graphs of the meansquared error of prediction in GLM setup under the
framework of response surface design. Atkinson (2006) advocated the use of GLM in response surface perspective where the underlying model is guided by mean–variance relationship and also demonstrated the use of various transformations, including Box–Cox transformation (Box and Cox 1964). The special problem of design for nonlinear response functions has been resolved through the use of a structured parameter. Lin and Peterson (2006) recommended the use of reliable inference procedure with nonstandard regression model like rank-based regression or nonparametric regression in the context of response surface optima. However, all these authors have not referred to response surface optima in the context of GLM through actual model fitting and derivation of the optimum of response function by efficient choice of covariate levels. In this paper, we report a protocol for in vitro regeneration of B. polystachyon and optimization of the required concentration of the growth regulators BA and NAA by applying RSM in count data setup.
Materials and Methods Explant source. Mature seeds of B. polystachyon were collected in the month of December and sun-dried. To obtain axenic seedlings, the seeds were washed with NaOCl (1% available chlorine) for 2 min and thoroughly washed and imbibed in 288.7 μM gibberellic acid3 (GA3) for 12 h. The seeds were then placed aseptically in 250-ml conical flasks containing 50 ml of half-strength Murashige and Skoog (1962) medium without vitamins or sucrose and gelled with 0.8% agar (AMO11, SRL Pvt. Ltd., Mumbai, India). Seeds grew into plants for production of the experimental explants. Culture conditions. MS basal culture medium containing 3% w/v sucrose was used in the present study. The pH of the medium was adjusted to 5.8 prior to adding 0.8% agar and autoclaved at 1 kg cm−2 for 15 min. After cooling to about 60°C, media was poured into culture tubes (25× 150 mm at 10 ml per tube) aseptically under laminar air flow. The cultures were incubated in a growth chamber (NK Biotron, Nippon Medical and Chemical Instruments Co., Tokyo, Japan) maintained at 25 ± 1°C and 70% humidity under a 16-h photoperiod, illuminated with cool white fluorescent lamps (Phillips, Jalandhar, India) at a light intensity of 25 μmol s−1 m−2. Regeneration potential of explants. The growth regulators NAA and BA, either singly or in all possible combinations of different concentrations (0.0, 0.5, 2.5, 5.0, 10.0, and 12.5 μM), were added to the culture medium prior to autoclaving. Shoot tips about 3 mm in length were excised
APPLICATION OF RSM IN COUNT DATA SETUP
aseptically from 4-wk-old, in vitro grown seedlings and transferred to the culture tubes. Each treatment had six replicates, with each experiment performed three times. This is designated as the original experiment. In a subsequent experiment, concentrations of growth regulators and the number of replicates were calculated for the central composite design by following Cochran and Cox (1992). The concentrations of BA and NAA used in combination were 2.34 and 2.5, 4 and 1.4, 4 and 3.5, 8 and 1.08, 8 and 2.5, 8 and 3.91, 12 and 1.5, 12 and 3.5, and 13.65 and 2.5 μM, respectively. All experimental sets were replicated nine times, except for the combination of 8 μM BA and 2.5 μM NAA, which had 45 replicates. Culture conditions were identical to the previous experiment.
(Myers and Montgomery 2002). Under the count data setup, we model the summary measure μ = E(Y) through the response surface function given by suitable polynomial ’(·) and the “log” link function as logðmu Þ ¼ ϕðxu Þ; xu ¼ ðx1u ; x2u ; :::; xku Þ; u ¼ 1; 2; :::; N
ð1Þ
All the level combinations together give the design matrix X. In the presence of curvature in the system, we assume the response function ’(·) to be a second-order polynomial as follows, logðmu Þ ¼ b0 þ
k X
bi xiu þ
k X
i¼1
Scanning electron microscopy. Scanning electron micrographs of the in vitro regenerating calli of B. polystachyon were obtained. The samples were fixed in 2% glutaraldehyde in potassium phosphate buffer (pH 6.8), dehydrated in a graded alcohol and amyl acetate series, critical-point-dried with CO2, and sputter-coated with gold. Scanning electron micrographs were obtained using an SEM (Hitachi S-530, 15 kV) at USCI, Burdwan University. Response variable. The number of regenerated microshoots per shoot tip explant (Y) is the response variable. The regeneration potential depends on two explanatory factors (design variables or covariates): NAA and BA, denoted as Σ1 and Σ2, respectively. Here, we have assumed S(Y) (a summary measure of Y) as a function of two explanatory factors, (Σ1) and (Σ2) only. The true function is unknown, but it is approximated by a suitable polynomial. Response surface function. In RSM, the response variable Y is assumed to be random from a distribution in the natural exponential family with independent uth realization being yu. We have N such observations or data points. The bestknown GLM for count data assumes a Poisson distribution for response variables (Agresti 2002). However, in view of over-dispersion in the data owing to presence of sparsely located “0s” resulting from dose-level heterogeneity, we have taken the quasi-Poisson family as our model. Generally, it is assumed that the response for Y depends on k quantitative factors ξ1, ξ2, ... ξk that are known as explanatory or design variables. Therefore, Y or the corresponding summary measure S(Y) is a function of ξ1, ξ2, ... ξk. Let us write S(Y) = f (ξ1, ξ2, ... ξk), where f(·) denotes the true function, which is unknown. RSM assumes that f(·) can be approximated by a polynomial of appropriate order ’(·), which is known except the parameters involved in the function. We transform the original explanatory factors (ξ1, ξ2, ... ξk) by a set of new variables (x1, x2, ... xk) to reduce the operational region of each explanatory factor in (−1 to 1)
þ
k X
bii x2iu
i¼1
bij xiu xju ; u
ij¼1
¼ 1; 2; :::; N
ð2Þ
In matrix, notation 2 may be written as log (μ) = Xβ, which is linear in β, and hence GLM theory may be invoked. Here, logðmÞ ¼ ðlogðm1 Þ; logðm2 Þ; :::; logðmN ÞÞ is the vector of link function on the study variable Y for N data points and b ¼ ðb0 ; b1 ; b2 ; :::; bk ; b11 ; b22 ; :::; bkk ; b12 ; b13 ; :::; bk1k Þ is the vector of regression coefficients while the design matrix X constitutes the linear and quadratic terms involving ðxiu Þ; i ¼ 1; 2; :::; k and u ¼ 1; 2; :::; N . In the present problem, there are two factors, i.e., k=2 viz. BA (ξ1) and NAA (ξ2) and b ¼ ðb0 ; b1 ; b2 ; b11 ; b22 ; b12 Þ. Since our objective is to derive a precise estimate of the optimum BA/NAA combinations so as to maximize the response function, we consider RSM in the reduced region given by BA (4, 12 μM) and NAA (1.5, 3.5 μM) as obtained from the contour plot of the original experiment (Fig. 1). In the context of the codification of the variables in the specified operating region and following Khuri and Cornell (1996) or Cornell (2002), we take four design points at the axial settings (x1, x2)=(± √2, 0) and (x1, x2)= (0, ± √2). These four design settings along with four points at the factorial settings (x1, x2)=(±1, ±1) and the center point (x1, x2)=(0, 0) comprise a central composite rotatable design. Following Cochran and Cox (1992), we have considered nine replicates for each of the design and factorial settings and have taken five times more replication at the center point. This is especially important to estimate the curvature of the response function in all directions. The corresponding original level combinations of BA and NAA in terms of ξ1 and ξ2 are noted and a new experiment is conducted in those design points which have been termed as optimal experiment. The estimates of the regression coefficients both for original and optimal experiments are obtained through
CHAKRABORTY ET. AL
Figure 1. In vitro responses of shoot tip explants of B. polystachyon in different concentrations of NAA and BA after 1 mo in culture (bar 1 cm). (a) Regenerating shoots in 2.5 μM BA; (b) necrotic (arrow) callus in
2.5 μM NAA/0.5 μM BA; (c) regenerating shoots in 0.5 μM NAA/ 5.0 μM BA; (d) callogenesis and leaf regeneration (arrow) in 2.5 μM NAA/10 μM BA; e regenerated shoots in 0.5 μM NAA/2.5 μM BA.
GLM codes in R. In the computation of p values of the regression parameters, it has been assumed that the estimates are asymptotically following normal distribution (McCullagh and Nelder 1989). The estimates of optimum level combinations might be assumed to be fixed. As such, the estimated optimum expected response becomes a linear combination of the estimates of the regression parameters with coefficients determined through the optimum level combinations. The estimated dispersion matrix of the estimates of the parameters given by Disp b b is obtained using the command “summary (glm(.∼…))$cov.unscaled” in R. It is well known that the linear combination of such normal variables is normal with appropriate mean and variance. Disp b b is reported in Table 1 and is exploited to yield the 95% and 99% confidence intervals of the true value of optimum expected response. Because of the structural dissimilarity of the GLM setup with the corresponding linear model (LM) setup, neither the Box and Hunter (1954) approach nor its extensions by Peterson et al. (2002) and Cahya et al. (2004) [methods to construct simultaneous confidence region on the location of the stationary point (optimum dose level) in terms of design variables or covariates] may be directly applicable here. The directional derivatives of the second-order response surface function involving two factors with respect to the coded
design variables of interest, i.e., x1 and x2 and evaluated at the point t = (t1, t2), are given by dðtÞ ¼ ðd1 ðtÞ; d2 ðtÞÞ where d1 ðtÞ ¼ b1 þ 2b11 t1 þ b12 t2 and d2 ðtÞ ¼ b2 þ 2b22 t2 þ b12 t1 . As the directional derivatives are linear combinations of βs, they may be assumed to have a bivariate normal distribution in an asymptotic sense, where t = (t1, t2); the coordinates of the true stationary point is considered to be fixed but unknown. The mean vector of the joint distribution of d(t) may be crudely approximated by (0, 0); since t = (t1, t2) corresponds to stationary point solution. The estimate of the dispersion matrix of such joint distribution given by Disp(d(t)) may be evaluated by observing the linearity of the expressions of d1(t) and d2(t) with respect to βs. It is now possible to invoke the Box and Hunter (1954) approach in an asymptotic sense and suggest the simultaneous confidence intervals for the stationary point t as d 0 ðtÞ½DispðdðtÞÞ1 dðtÞ 2Fa ; 2 ;N 6 where Fa ; 2 ; N 6 is the upper αth percentile point of central F distribution with two and N−6 degrees of freedom.
Results and Discussion In vitro regeneration. B. polystachyon seeds treated with 288.7 μM GA3 for 12 h germinated within 72 h in vitro. The plantlets grew to 2–4 cm in size after about 4 wk. The
APPLICATION OF RSM IN COUNT DATA SETUP Table 1. Estimated dispersion matrix of the parameter estimates corresponding to the optimal experiment (the square roots of the diagonal elements give the standard errors as reported in last part of Table 3)
Intercept BA NAA BA2 NAA2 BA × NAA
Intercept
BA
NAA
BA2
NAA2
BA × NAA
0.084744 − 0.008678 − 0.039219 0.000177 0.004004 0.002169
− 0.008678 0.001679 0.001629 − 0.000059 0.000105 − 0.000267
− 0.039219 0.001629 0.027211 0.000032 − 0.003908 − 0.000882
0.000177 − 0.000059 0.000032 0.000004 − 0.000003 − 0.000002
0.004004 0.000105 − 0.003908 − 0.000003 0.000833 − 0.000021
− − − −
number of regenerated multiple shoots obtained on various combinations of NAA and BA under in vitro conditions is represented in Table 2. Photographic images of in vitro regeneration are provided in Fig. 1 while scanning electron micrographs are provided in Fig. 2. Multiple shoots were obtained within 2 wk in cultures treated with BA at 0.5–10 μM concentration. When BA and NAA were added to the medium in combination, green compact callus was obtained after 2 wk. At high concentrations of NAA (>5 μM), both singly and in combination with BA, the margin of the callus turned necrotic and brown in color, with inhibition of regeneration. High levels of NAA were not used in subsequent experiments. Some workers have reported the use of NAA to obtain compact callus (Johri et al. 1996) and eliminate the secretion of phenolic substances (Perez-Tornero et al. 2000), but the NAA and BA combination at high concentrations often led to browning of calli (Koroch et al. 2003). Shoot tip explants cultured on medium supplemented with an NAA and BA ratio of 1: 1 showed callogenesis within 2 wk and gave rise to multiple shoots per original explant, the maximum being 5.28±0.89 shoots from the treatment of 2.5 μM NAA/2.5 μM BA (Table 2). A high auxin–cytokinin ratio, i.e., NAA and BA concentrations of 2.5:0.5, 5:0.5, or 5/2.5 μM, was not favorable for multipleshoot generation, although green compact callus was formed. This callus readily formed roots if kept for more than 4 wk in the same media without sub-culturing and then subsequently turned brown and necrotic. A low auxin– cytokinin ratio, on the other hand, resulted in profuse multiple-shoot regeneration from callus at the concentrations of 0.5:2.5, 2.5:5, 2.5:7.5, 2.5:10, and 2.5:12.5 μM NAA/BA, respectively. Regenerated multiple shoots were taken for rooting and transferred to the experimental field with a 96% survival rate, as optimized earlier (Chakraborty et al. 2006). Preliminary analysis. The contour plot from the data of the original experiment with B. polystachyon clearly indicates that the response surface is concave starting from a low value, attaining a peak and then gradually decreasing with the increasing levels of NAA and BA
0.002169 0.000267 0.000882 0.000002 0.000021 0.000121
(Fig. 3). From the contour plot, it can be determined that the optimum response for shoot regeneration occurs in the region NAA (1.5, 3.5 μM) and BA (4, 12 μM). The maximum number of regenerated shoots was eight. Table 2. Number of regenerated multiple shoots from shoot tip explants of B. polystachyon on various combinations of NAA and BA under in vitro conditions in the original experiment Growth regulator (μM) NAA 0
0.5
2.5
5.0
Number of regenerated shoot tips per explant
BA 0 0.5
0.29±0.47 2.26±0.73
2.5 5.0 7.5 10.0 12.5 0 0.5 2.5 5.0 7.5 10.0 12.5 0 0.5 2.5 5.0 7.5 10.0
4.06±0.80 2.67±0.97 0.44±0.51 0.94±0.64 0.61±0.70 0.41±0.50 4.37±1.38 9.22±1.77 7.17±1.04 3.78±0.88 3.67±1.14 2.06±0.80 0.24±0.44 0.16±0.37 5.28±0.89 6.50±1.04 6.44±1.20 14.39±3.07
12.5 0 0.5 2.5 5.0 7.5 10.0 12.5
9.00±0.77 0.24±0.44 0.14±0.34 0.17±0.38 3.61±0.85 3.06±0.73 3.83±0.99 1.50±0.37
Data are mean ± SD. Each growth regulator level combination has six replicates and each experiment is repeated thrice (n=18)
CHAKRABORTY ET. AL
Response surface function. We have reported here the analysis done in R (R Development Core Team 2008) of the original experimental data using both the first-order and second-order model. Since we have to assume quasiPoisson family with “log” link function to model the data in the presence of possible over-dispersion, the model adequacy criterion of AIC could not be implemented. As an alternative, we have used residual deviance per degrees of freedom to test the model adequacy. It was observed from the first-order model, which corresponds to the original experiment, that high concentrations of NAA had a marginal inhibitory effect on shoot regeneration (Table 3). At the same time, all the coefficients of the related second-order model were significant. The residual deviance per degree of freedom decreased from 3.37 in the first-order model to 1.51 in the second-order model, while the null deviances per degree of freedom were approximately the same at 3.63. The extent of overdispersion decreased from 3.263 for the first-order model to 1.439 in the second-order model. This motivated the preference of the second-order model over the first-order model for subsequent discussion. With the second-order response function, the approximate optimum mean number of regenerated shoots comes out to be ten from a combination of BA at 8.37 μm and NAA at 2.54 μM. Figure 2. Scanning electron micrographs of regeneration calli of B. polystachyon. (a) Callus with meristematic zones (arrow) in 2.5 μM NAA/10 μM BA; (b) calli showing nodular structures in 0.5 μM NAA/2.5 μM BA; (c) emerging leaf from regenerating callus at 2.5 μM NAA/10 μM BA showing peltate gland (arrow).
Thus, if the level combinations of BA and NAA in the stipulated region were chosen, the number of regenerated shoots was expected to be at least eight. To find the actual concentration of NAA and BA for maximum response, we adopted the response surface methodology.
Figure 3. Contour plot of response corresponding to the original experiment of the shoot tip explants of B. polystachyon to various combinations of NAA and BA under in vitro conditions as in Table 2.
Interpretation. The summary of the responses corresponding to the in vitro optimized experiment is shown in Table 4. The corresponding contour plot is depicted in Fig. 4. The analysis is done in R for the second-order model involving interaction term under GLM setup with log link function, assuming the family to be “quasi-Poisson” to accommodate possible overdispersion. The results are presented in Table 3. It is to be noted that estimates of BA and BA2, as well as those of NAA and NAA2, have significant p values. The quadratic parts of BA and NAA have negative impact on shoot regeneration. However, the Hessian matrix computed by taking second-order partial derivatives of response function involving the present estimates of parameters becomes negative, resulting in maximum response function and hence shoot generation. In combination with BA, NAA is moderately significant (as revealed from BA × NAA interaction). The over-dispersion parameters with regard to first- and second-order models are estimated to be more than unity, in the case of the original experiment (Table 3). But, for the optimum experiment, we observed under-dispersion in the data as revealed from the over-dispersion parameter being estimated as less than unity with regard to the second-order model. In the optimum experimental setup, the variation among observations is reduced to a large extent, leading to under-dispersion in the data. However, quasi-Poisson family might still be invoked to model such situations.
APPLICATION OF RSM IN COUNT DATA SETUP Table 3. Model adequacy with original and optimal experimental data Model specification
Original experiment First order
Second order
Optimal experiment Second order
Parameters
Estimates
Standard error
Intercept BA NAA Intercept BA NAA
0.9176 0.0626 −0.0297 0.5648 0.3013 0.4854
0.0886 0.0097 0.0224 0.0886 0.0269 0.0583
