PHYSIOLOGY

Regulating plant tissue growth by mineral nutrition

Randall P. Niedz & Terrence J. Evens

Received: 30 December 2006 /Accepted: 20 June 2007 / Published online: 20 July 2007 / Editor: T. J. Jones# The Society for In Vitro Biology 2007

Abstract The objective of this study was to determine ifthe growth of sweet orange (Citrus sinensis (L.) Osbeck cv.‘Valencia’) nonembryogenic callus could be regulated andcontrolled via the mineral nutrient components of themedium. The 14 salts comprising Murashige and Skoog(MS) basal medium were subdivided into five componentgroups. These five groups constituted the independentfactors in the design. A five-dimensional hypervolumeconstituted the experimental design space. Design pointswere selected algorithmically by D-optimality criteria tosample of the design space. Growth of the callus at eachdesign point was measured as % increase of fresh weight at14 d. An analysis of variance was conducted and a responsesurface polynomial model generated. Model validation wasconducted by mining the polynomial for design points totwo regions—“MS-like” growth and MS+25% growth andcomparing callus growth to predicted growth. Five of theeight selected MS-like points and three of the six MS+25%growth points validated, indicating regions within thedesign space where growth was equivalent to MS, but thesalt combinations were substantially different from MS, anda smaller region where growth exceeded MS by greaterthan 25%. NH4NO3 and Fe were identified as importantfactors affecting callus growth. A second experiment wasconducted where NH4NO3 and Fe were varied, thuscreating a two-dimensional slice through the region ofgreatest callus growth and provided increased resolution ofthe response.

Keywords Callus . Sweet orange . Citrus . Salts .

Response surface

Introduction

The basic components of plant tissue culture media are themineral nutrients. How rapidly a tissue grows and theextent and quality of morphogenetic responses are stronglyinfluenced by the type and concentration of nutrientssupplied. Early research by Gautheret (1939), Heller(1953), White (1942), Hildebrandt et al. (1946), and Nitschand Nitsch (1956) culminated in the development ofMurashige and Skoog (MS) medium by Murashige andSkoog (1962). The potential benefits of optimizing thenutrient component of culture media for a particular re-sponse are well documented across a wide range of speciesand applications. For example, the concentration of NH4

+

and NO3− affects numerous in vitro responses including the

development of somatic embryos (Reinert et al. 1967;Halperin and Wetherell 1965; Meijer and Brown 1987;Leljak-Levanic’ et al. 2004; Elkonin and Pakhomova 2000;Poddar et al. 1997), the plating efficiency of protoplasts(Attree et al. 1989), the efficiency of plant recovery afterovule culture (McCoy and Smith 1986), shoot regeneration(Leblay et al. 1991), regulation of growth and biomass ofbioreactor-grown plantlets (Sivakumar et al. 2005), andcontrolling the rate of root initiation on shoot cultures(Hyndman et al. 1982). The effects of some other mineralnutrients include the induction or suppression of shoot-tipnecrosis by varying Ca2+ levels (Sha et al. 1985);reduction of vitrification by Ca(NO3)2·4H2O or by reduc-ing the level of NH4NO3 (McLaughlin and Karnosky1989); increasing shoot regeneration by varying theNa2SO4 level (Chandramu et al. 2003); AgNO3 acted

In Vitro Cell.Dev.Biol.—Plant (2007) 43:370–381DOI 10.1007/s11627-007-9062-5

R. P. Niedz (*) : T. J. EvensAgricultural Research Service,US Horticultural Research Laboratory,2001 South Rock Road,Ft. Pierce, FL 34945-3030, USAe-mail: rniedz@ushrl.ars.usda.gov

synergistically with 6-benzylaminopurine to increase shootregeneration in thin cell layer explants (Carvalho et al.2000); and increased levels of sodium molybdate increasedthe percentage of responding cultures and the number ofshoot buds from cultured embryos (Chauhan and Kothari2004). The interaction of the mineral nutrients and plantgrowth regulators (PGR) is a particularly intriguing rela-tionship. Preece (1995) argued that PGR partially compen-sate for nutrient imbalances and that, by correcting theimbalance, PGR can be reduced or eliminated, as Gomezand Segura (1994) and Kothari et al. (2004) observed forNAA for shoot regeneration of Juniperus and finger millet,respectively. For additional information, see the review byRamage and Williams (2002) on the effects of mineralnutrition on morphogenesis.

Because there are 13 mineral elements essential for plantgrowth (Epstein and Bloom 2005), the experimentaldetermination of optimal nutrient levels is complex. Thiscomplexity illustrates why the “revised medium” developedby Murashige and Skoog (1962) was an important devel-opment; although MS medium is not optimal for manytissues, many tissues will grow on it to some degree; hence,MS medium represents a starting point to begin the processof improving a response. A medium where there is noresponse cannot be optimized as the direction of improve-ment is unknown. This is why many media developed forspecific applications are derivatives of MS.

A number of approaches for estimating the correct balanceof mineral nutrients have been developed. Hildebrandt et al.(1946) tested various salt combinations and their effect ontobacco and sunflower callus growth in a set of elegantexperiments using his “triangulation method” and six 3-saltcombinations. Callus growth was increased 63 and 162%for tobacco and sunflower by reformulating the salt levelsin White’s (1942) basal medium. Murashige and Skoog(1962) increased callus growth fourfold over White’s basalmedium by varying the level of each nutrient over severallevels of the other nutrients. De Fossard et al. (1974)introduced the “broad spectrum” approach as a “universal”approach to defining the type of media formulation for “anynew or unresolved tissue culture situation.” The broadspectrum experiment is a 43 factorial with 81 treatmentcombinations; the four factors are broad groupings of mediacomponents—mineral, auxin, cytokinin, and organicgrowth factors (e.g., amino acids and vitamins) includingsucrose. The original intent of the broad spectrum exper-iment was to include sucrose as a component separate fromthe organic growth factors, but the resulting 53 factorialwould have required an impractical 243 treatment combi-nations. Margara (1977 and 1978) devised a set of eightmedia for identifying the approximate mineral nutrientformulation suitable for particular situation; the mediavaried in total N,NHþ

4 , NO�3 , Cl

−, K+, and Ca2+. Spaargaren

(1996) proposed that the ideal nutrient media for biologicalgrowth would have the same elemental composition as thecell, tissue, or organism being grown. Monteiro et al. (2000),Nas and Read (2004), Bouman (2001), and Staikidou et al.(2006) tested a variation of Spaargaren’s concept bysuccessfully improving in vitro growth by devising culturemedia where the mineral nutrient levels and/or proportionsmatched the those of the cultured organism.

The objective of this study was to efficiently characterizethe mineral nutrient requirements to accurately predict andregulate the growth of plant tissue in vitro.

Materials and Methods

Experimental approach. The basic strategy was to (1)create a n-dimensional experimental design space whereeach dimension was defined by a specific MS salt or group ofMS salts; (2) grow the tissue on a set of treatment combinationsrepresented as points contained within or on the surface of then-dimensional design space; (3) generate a prediction equationthat describes tissue growth through the n-dimensional designspace; (4) test the prediction equation by growing callus atpoints not included in the original design but contained withinthe n-dimensional design space and comparing the actualgrowth to the predicted growth; and (5) explore a lowerdimensional region of the n-dimensional design space usingfactors identified by the analysis of variance (ANOVA) asimportant. The specific steps were as follows:

1. The 14 salts comprising MS basal medium weresubdivided into five component groups (Table 1). Thesefive groups constituted the independent factors in thedesign and the five dimensions that would be studied.

Table 1. The five factors used to construct the five-dimensionaldesign space, their component MS salts, and concentration rangeexpressed as × MS levels

Factors MS Salts Range

Group 1 NH4NO3 0.5–1.5×Group 2 KNO3 0.5–1.5×Group 3 (mesos) CaCl2·2H2O 0.5–1.5×

KH2PO4

MgSO4

MnSO4·H2OZnSO4·7H2O

Group 4 (micros) CuSO4·5H2O 0.5–4×KICoCl2·6H2OH3BO3

Na2MoO4·2H2OGroup 5 (Fe) FeSO4·7H2O 0.5–4×

Na2EDTA

MINERAL NUTRITION 371

Selection of five factors was considered appropriate asthis allowed us to both test the suitability of usingn-dimensional design spaces for understanding a basic invitro growth response and, two, the number of treatmentcombinations were small enough to be manageable.

2. A range, defined as a minimum and maximum multipleof those salts in MS medium, was selected for each ofthe five factors (Table 1).

3. Design points were selected to adequately sample thefive-dimensional design space.

Table 2. Five-factor design including 23 model points, 10 lack-of-fit points, and 11 replicated points, including MS (points 44–46) for pure errorestimation

Treatment design pointsa Factor 1 NH4NO3 Factor 2 KNO3 Factor 3 mesos Factor 4 micros Factor 5 Fe % Fresh wgt. Increase

1 0.50 1.50 1.50 0.50 2.36 8552 1.36 0.50 0.67 0.50 4.00 2063 0.50 1.50 0.88 2.11 0.50 4884 1.44 1.50 0.52 4.00 3.79 4345 1.50 1.50 1.50 4.00 4.00 4596 0.50 0.50 0.62 3.57 3.57 6557 0.62 0.60 1.50 0.50 3.94 3108 0.97 1.03 0.50 4.00 0.50 4479 1.50 0.50 1.50 4.00 0.50 20410 1.50 0.50 0.50 0.50 0.50 31911 0.50 1.50 0.88 2.11 0.50 45012 1.50 0.50 0.50 0.50 0.50 34913 0.62 0.62 1.38 3.57 0.50 41514 1.50 0.50 1.50 4.00 0.50 19815 1.50 1.50 1.50 4.00 4.00 65116 0.50 1.43 1.50 1.80 4.00 78617 0.50 1.50 0.50 4.00 4.00 64118 1.50 1.50 0.50 0.50 2.34 59219 0.95 0.80 0.84 1.24 2.07 70520 0.50 0.50 1.50 0.50 0.50 34721 1.50 1.04 1.05 4.00 0.50 24222 1.50 0.50 0.50 4.00 4.00 63523 1.50 1.04 1.05 4.00 0.50 25724 0.50 0.50 0.50 4.00 0.50 45825 1.06 1.50 1.50 2.45 0.50 32226 1.38 0.62 1.50 4.00 3.57 61227 1.50 0.50 1.50 0.50 4.00 38928 1.50 1.50 0.50 0.50 2.34 60029 0.50 1.50 0.50 4.00 4.00 64130 1.01 1.50 0.95 0.50 4.00 47831 0.50 1.50 1.50 4.00 0.50 23732 1.50 1.50 1.50 0.50 0.50 7133 0.50 0.50 1.50 4.00 4.00 83034 1.01 1.50 0.95 0.50 4.00 51535 1.50 1.19 0.50 1.67 4.00 51836 0.50 1.50 1.50 4.00 0.50 35437 0.90 1.11 1.05 3.79 2.84 80338 0.50 0.50 0.50 0.50 4.00 28039 1.50 0.50 0.52 3.25 1.24 49640 1.38 0.62 1.50 0.93 0.93 35041 0.50 1.24 0.50 0.50 0.50 52542 1.50 1.50 0.50 4.00 0.50 22743 1.50 1.19 0.50 1.67 4.00 59444 1.00 1.00 1.00 1.00 1.00 58845 1.00 1.00 1.00 1.00 1.00 64846 1.00 1.00 1.00 1.00 1.00 634

a Design points 1–43 were randomly assigned to blocks as follows: Block 1 (points 1–15); Block 2 (points 16–29); Block 3 (points 30–43).Additionally, one MS point was run with each block (points 44–46).

372 NIEDZ AND EVENS

4. Sweet orange callus was grown on the salt combinationspecified at each design point.

5. Fresh weight growth, the primary response variable inthis report, was collected after 14 d of growth. Dryweights were also recorded.

6. ANOVA7. A polynomial equation was generated from the

ANOVA model terms describing growth through thefive-dimensional design space.

8. Additional design points were selected in the designspace not included in the original design. Callus wasgrown on the salt formulations specified at these newpoints. The resulting fresh weight growth was thencompared to the growth predicted to occur from theequation calculated in step #7.

9. A two-factor experiment based on the validated pointsidentified in step #8 was conducted to further character-ize growth in a region of the original five-dimensionaldesign space.

Plant material and tissue. A 4-yr-old nonembryogenic cellline (Val01) was developed from epicotyl explants of in

vitro grown seedlings of Citrus sinensis (L.) Osbeck cv.‘Valencia.’ Seed were germinated in MS basal mediumwithout PGR and supplemented with 3% (w/v) sucrose.One-centimeter epicotyl explants were excised from 15- to21-d-old seedlings and placed onto MT medium (Murashigeand Tucker 1962) supplemented with 2.5-μM 2,4-dichlor-ophenoxyacetic acid (2,4-D), 1-μM 6-benzylaminopurine(BA), and 100 mg l−1 casein hydrolysate. The cultures weregrown in a growth cabinet under low light (15–20 μmolm−2 s−1), provided by cool-white fluorescent lamps,constant 27°C, and a 4-h photoperiod. After 6 mo. ofselection, a rapidly growing callus designated Val01 wasobtained. For maintenance, the 2,4-D concentration wasreduced to 1 μM.

Experiments were initiated by first subculturing approx-imately 1 g of callus onto each treatment formulation (i.e.,design point), using 100×20 mm polystyrene culturedishes, for acclimation to the formulation. Preliminaryexperiments (data not shown) indicated that a singlesubculture cycle substantially reduced carry-over effects.After an acclimation cycle on each treatment formulation,approximately 1 g from the acclimated cultures wassubcultured again onto each treatment formulation. Freshweight was determined on day 14. Six duplicate plates (i.e.,pseudoreplicates) were used per treatment in the five-factorexperiment and eight in the two-factor experiment. Percentincrease in fresh weight was calculated from the initialsubcultured weight of the callus.

Experimental design. The objective was to regulate thebiomass accumulation by varying the basal salt composi-tion. The initial five-factor experimental design was a 23-model-point D-optimal response surface sufficient formodeling a quadratic polynomial. The design was aug-

Table 3. Two-factor design including ten model points and fiveadditional lack-of-fit points and ten replicated points

Treatmentdesign points

Factor 1NH4NO3

Factor 2Fe

% Fresh wgt.increase

1 0.42 3.21 5052 0.25 2.14 9063 0.25 1.07 6834 0.38 2.67 7815 0.42 1.07 8066 0.58 3.21 4197 0.63 2.67 6668 0.58 1.07 8459 0.38 2.67 64610 0.38 1.61 1,12911 0.75 3.21 34212 0.50 2.14 68613 0.75 2.14 75814 0.58 1.07 85015 0.63 1.61 79916 0.25 3.21 74717 0.75 1.07 84818 0.25 3.21 61219 0.75 3.21 61820 0.75 2.14 63821 0.38 1.61 90322 0.25 2.14 87223 0.25 1.07 80324 0.75 1.07 83225 0.58 3.21 575

Table 4. ANOVA of % fresh weight increase of sweet orange callusin the five-factor experiment

Term % Fresh wgt. increasea

Overall model—F value (p value)* 26.45 (<0.0001)Lack-of-fit—F value (p value)** 0.96 (0.5432)R2 0.9544Adjusted R2 0.9183Predicted R2 0.7856Adequate precision*** 18.691

*The F value for the overall model and the probability of obtaining alarger F value. The overall model is a reduced cubic and includes 25terms (Table 5).**A p>0.05 indicates no additional variation that might be accountedfor using a better model.***Design-Expert recommends a value greater than four to ensureadequate predictions.a The measured response variable.

MINERAL NUTRITION 373

mented to include ten additional points for lack-of-fitanalysis for detecting additional signal (i.e., curvature)possibly not captured in the design. Eleven points werereplicated for pure error estimation; this included one point,replicated twice, for MS medium, as it was a coordinatewithin the five-dimensional design space. The number ofreplicates was chosen based on the minimum requireddegrees of freedom for a statistically valid, pure error

estimation for the chosen experimental design. The designpoints selected in both experiments, including replicatepoints, were selected to achieve a statistical power >90%.The statistical power of this design provided a >99%chance of detecting an effect of two standard deviations forthe main effects and two-way interactions and >94% for thequadratic terms. Thus, the complete design included 46treatment points (Table 2). The experiment contained three

Figure 1. Five-factor model ad-equacy plots—(a) Box–Coxplot; (b) normal plot of resid-uals; (c) residuals vs. predictedplot; (d) outlier t value plot; (e)Cook’s distance plot; (f) pre-dicted vs. actual plot.

374 NIEDZ AND EVENS

blocks based on the number of treatments that could bemanaged at one time; this removed any variation introducedfrom running the blocked treatments at different times.

The second design included two factors and was a ten-model-point D-optimal response surface sufficient formodeling a cubic polynomial. The purpose was to explorein additional detail the region of greatest growth in the five-dimensional design space. The design was augmented toinclude five additional points for lack-of-fit analysis. Eightpoints were replicated for pure error estimation. Thecomplete design included 25 treatment points (Table 3).

Data analysis. The ANOVA data were the means of the sixor eight duplicate plates (i.e., pseudoreplicates) that wereaveraged together to arrive at the specific response for eachtreatment design point. Thus, the eleven replicated points inthe first experiment were composed of 66 plates (i.e., 6pseudoreplicates×11 replicates), and the eight replicatedpoints of the second experiment were composed of 64plates (i.e., 8 duplicates×8 replicates). For each experiment,the highest order polynomial model where additional modelterms were significant at the 0.05 level was analyzed byANOVA. Model adequacy tests as described by Andersonand Whitcomb (2005) and calculated by Design Expert® 7(Stat-Ease, Minneapolis, MN) were as follows:

1. Box–Cox plot—used to determine if the data require apower law transformation. A transformation is recom-mended, based on the best lambda value, which isfound at the minimum point of the curve generated bythe natural log of the sum of squares of the residuals(Box and Cox 1964; Myers and Montgomery 2002;Anderson and Whitcomb 2005).

2. Normality assumption—a normal probability plot of theinternally studentized residuals was examined; the assump-tion is satisfied if the residuals plot closely along a line.

3. Constant variance assumption—a plot of the internallystudentized residuals vs. predicted response value wasexamined; the assumption is satisfied if the points fallwithin the interval of −3 to +3 standard deviations (i.e.,sigma), exhibit random scatter, and do not show a“megaphone” (<) pattern where the residuals increasewith the predicted response.

4. Outlier t values—a statistic calculated for each point; apoint outside + 3.5 standard deviations is defined as anoutlier and indicates either a problem with that point orwith the chosen model.

5. Lack-of-fit test—additional design points were includ-ed in every experiment for this test. A significant lack-of-fit indicates the model may not be capturing theentire signal in the observations.

6. Predicted vs. actual values plot—points that are ran-domly scattered along and around a 45° line (i.e.,perfect correlation) indicate the model appears to beunbiased when predicting new observations.

7. Cook’s distance—a statistic to identify points withunusually high influence on the fitted model (i.e. highleverage points), thus resulting in a model fitted moreto the high leverage points than to the majority ofpoints in the data set (Anderson and Whitcomb 2005).Myers and Montgomery (2002) suggest using a cutoffvalue of 1 to identify high leverage points.

Table 5. Significant terms with F value and p value in the ANOVA of% fresh weight increase of sweet orange callus in the five-factorexperiment

Significant ANOVA terms F value p value (Prob>F)

NH4NO3 62.71 <0.0001NH4NO3×KNO3 13.91 0.0010NH4NO3×Mesos 9.72 0.0047NH4NO3×Fe 5.68 0.0254KNO3×micros 30.26 <0.0001KNO3×Fe 13.23 0.0013Mesos×Fe 40.01 <0.0001Micros×Fe 27.00 <0.0001Mesos2 11.09 0.0028Fe2 48.42 <0.0001(NH4NO3)

2×Fe 20.61 0.0001

Table 6. Reduced cubic polynomial generated from the ANOVA ofthe % fresh weight increase of sweet orange callus in the five-factorexperiment

% Fresh weight increase =

+705.68−77.44 ×NH4NO3

+11.43 ×KNO3

−2.61 ×Mesos−2.14 ×Micros−16.30 ×Fe−41.47 ×NH4NO3×KNO3

−35.98 ×NH4NO3×mesos+25.38 ×NH4NO3×Fe−63.68 ×KNO3×micros+45.26 ×KNO3*Fe+66.57 ×*Mesos×Fe+60.62 ×Micros×Fe+34.91 ×(NH4NO3)

2

−103.54 ×Mesos2

−1.99 ×Micros2

−205.76 ×Fe2

+181.94 ×(NH4NO3)2×Fe

−38.24 ×(KNO3)2×Fe

+38.14 ×Mesos3

Equation is reported in terms of coded factors. Coding normalizes thefactor ranges by placing their low and high range value between −1and +1.

MINERAL NUTRITION 375

8. R2, adjusted-R2, and predicted-R2—calculated as fol-lows: R2=1−SSresiduals/(SSmodel+SSresiduals) and is thefraction of overall variation explained by the model;adjusted-R2 is R2 adjusted for the number of terms inthe model relative to the number of points in thedesign; predicted R2=1− (PRESS/SSTotal) wherePRESS is the “predicted residual sum of squares”.When selecting the best model, we maximized pre-dicted-R2 (or minimized PRESS).

9. Adequate precision—a measure of signal to noise in thedata; it compares the predicted values at the designpoints to the average prediction error. Ratios greaterthan 4 are preferred (Anderson and Whitcomb 2005).

The software application Design-Expert (2005)® 7 (Stat-Ease) was used for experimental design construction, modelevaluation, and all analyses.

Validation points. Points in the design space not included inthe five-factor experiment were selected, callus was grownon these points, growth recorded, and the growth at thesepoints was compared to the predicted growth. The two-factordesign was constructed using information from thesevalidated points. The purpose of validation points is toempirically assess the usefulness of the predictivecapabilities of a proposed model.

Results

Analysis of five-factor. The growth response of the sweetorange callus as measured by % fresh weight increaseranged from 71–855% (Table 2); this wide range suggested

that in vitro tissue growth could be regulated by alterationsin the mineral nutrition. A summary of the ANOVA, lack-of-fit test, three R2 statistics, and adequate precision statisticfor % fresh weight increase is presented in Table 4. Thebest fitting model was a reduced cubic response surfaceobtained by stepwise regression. The data did not requiretransformation per the Box–Cox analysis (Fig. 1a), and theremaining diagnostics were all within acceptable limitsincluding the normality assumption (Fig. 1b), the constantvariance assumption (Fig. 1c), no outlier t points (Fig. 1d),no points that exceeded a Cook’s distance of one (Fig. 1e),and the predicted vs. actual value plot (Fig. 1f ). Additionally,the lack-of-fit test was not significant (p=0.5432) indicatingthat additional variation in the residuals could not beremoved with a better model, the three R2 statistics wereclustered with a difference less than 0.2, and the adequateprecision statistic of 18.691 was greater than 4. The overallmodel was highly significant (p<0.0001), thus indicatingsignificant factor effects on growth and was considered ofsufficient quality to navigate the experimental design spaceand, therefore, useful for predicting new observations. TheANOVA revealed 11 significant terms; five of the terms hada p value<0.0001 (Table 5). The 19-term reduced cubicpolynomial model is presented in Table 6. As the equation isreported in coded terms, the coefficients are directlycomparable and provide information on how each termcontributes to the shape of the callus growth response.

To test the model’s predictive capabilities, we utilized thesoftware’s numerical optimization routine that uses thedesirability function of Derringer and Suich (1980). Twospecific region(s) were selected for optimization in the five-dimensional design space; (1) the region where callus

Table 7. Predicted design points for MS-like and MS(+25%) growth

Solution # NH4NO3 KNO3 Mesos Minors Fe Predicted growth Observed growth

MS-2 0.59 0.51 0.61 3.56 3.57 475–758 526MS-3 0.53 1.47 0.91 2.03 0.78 461–718 596MS-5 0.5 1.5 1.49 0.54 1.05 495–760 812MS-8 1.49 0.55 0.53 3.98 3.62 544–809 349MS-10 0.51 1.48 0.52 3.96 3.97 514–775 600MS-21 1.38 0.64 1.45 3.99 3.42 533–792 602MS-24 1.27 0.52 0.52 3.94 1.57 551–812 445MS-26 1 1 1 1 1 519–768 690MS (+25%)-1 0.5 1.5 1.15 1.19 2.77 790–1,070 806MS (+25%)-8 0.5 1.24 1.21 4 2.99 757–1,033 691MS (+25%)-16 0.53 0.8 1.19 4 2.84 738–1,007 768MS (+25%)-18 0.5 1.5 0.98 0.5 2.49 753–1,052 690MS (+25%)-21 0.5 0.5 0.89 4 3.24 702–982 449MS (+25%)-22 0.5 1.5 0.71 1.04 2.14 704–980 928

Rows colored italicized validated since the observed growth fell within the 95% predicted growth confidence interval.

376 NIEDZ AND EVENS

growth was equivalent to MS and (2) the region wherecallus growth exceeded MS by a minimum of 25%. Weselected eight design points from the “MS” optimizationsolution set (including the actual MS formulation) and sixdesign points from the “MS (+25%)” optimization solutionset for validation. The points were selected by taking theminimum and maximum of each factor. These points andthe resulting % fresh weight increase are listed in Table 7.Five of the eight observed “MS” points fell within the 95%prediction interval; three of the six “MS (+25%)” points fell

within the 95% prediction interval. MS(+25%) % freshweight increase was 928%, the largest observed growthresponse. A two-dimensional slice through the NHþ

4 NO�3 and

Fe dimensions while holding the remaining three factorsfixed at point #22 levels is shown in the contour plot(Fig. 2a); the response surface for this region is shown inFig. 2b to more clearly visualize the shape of the response.MS-equivalent growth is delineated by the MS-623contour lines illustrating where MS-equivalent growthoccurs. The point #22 coordinate on the contour is 0.5×

Figure 2. (a) Five-factor response surface contour plot including thetwo predicted MS-equivalent growth contours. (b) Five-factor re-sponse surface plot. X and Y scales on both plots are × MS levels. Figure 3. Callus grown on MS salt formulation vs. callus grown on

predicted point #22 salt formulation.

MINERAL NUTRITION 377

NHþ4 NO

�3 and 2.14× Fe. From this information, we con-

cluded the following:

1. MS-equivalent growth is probably a larger region ofthe design space than the region of greatest growth. Alarge (or larger) region would explain the largersolution set and the greater number of validated points.A smaller region for the greatest growth would explainthe smaller solution set (112 with six unique extremepoints vs. 133 with eight unique extreme points).

2. A region exists within the five-dimensional designspace where callus growth is significantly greater thanMS. Validated point #22 had the largest increase ingrowth of the six validation points, exceeding MSgrowth by 44% and was visually distinct from MS(Fig. 3).

3. Iron has a large interactive effect on callus growth.Four of the six model terms where the p<0.0001included Fe (Table 6).

4. Additional experimentation is required to better definethis region. A single validating point provides littleinformation on the size and characteristics of the regionof greatest growth; additional exploration of the designspace is required.

Analysis of two-factor. The strategy to further explore theregion of greatest % fresh weight increase was to; (1)initiate the exploration around a previously validated MS(+25%) point and (2) explore a two-dimensional slicethrough the original five-dimensional design space. Con-structing a two-dimensional design space required selectingtwo factors to vary and fixing the remaining three factors.NHþ

4 NO�3 and Fe (Factor groups 1 and 5) were selected as

the two factors to vary, as NHþ4 NO

�3 had the single largest

F value, and the MS (+25%) predicted point set NHþ4 NO

�3

at or near its lowest level of 0.5× MS. This indicated that anincrease in growth might be observed if the lower range ofNHþ

4 NO�3 was extended downward. Reducing the lower

limit of the range for NHþ4 NO

�3 was also consistent with the

data obtained in the five-factor design—the NHþ4 NO

�3 level

was set at its lowest level of 0.5× for two of the three pointswhere growth exceeded 800%—points #1 and #33. Fe wasselected, as it was involved in six of the significant higherorder terms (Table 6). Additionally, Fe was greater than 2×for each of the three points (#1, #33, and #37) wheregrowth exceeded 800%. To determine the levels to fix theremaining three factors (Factor groups 2, 3, and 4), point#22 was selected as the location to build the two-dimensional design space. Treatment point selection isshown in Fig. 4a.

The growth response of the callus in the two-factorexperiment ranged from 342–1,129% (Table 3). A summa-ry of the ANOVA, lack-of-fit test, three R2 statistics, andadequate precision statistic for % fresh weight increase ispresented in Table 8. The best fitting model was a reducedquadratic response surface obtained by backward elimina-tion. The data did not require transformation per the Box–Cox analysis, and the residual and model diagnostics wereall within acceptable limits, including the normalityassumption, the constant variance assumption, no outlier tpoints, and the predicted vs. actual value plot. Additionally,the lack-of-fit test was not significant (p=0.5535), indicat-

Figure 4. (a) Two-factor re-sponse surface contour plot of% fresh weight increase withtreatment point locations anddemarcation 800% contour ofregion of greatest growth. Bluepoints were replicated to obtainan estimate of pure error. (b)Two-factor response surface plotof % fresh weight increase. (c)Two-factor response surface plotof dry weight increase.

Table 8. ANOVA of the response variable % fresh weight increase ofsweet orange callus in the two-factor experiment

Term % Fresh wgt. increasea

Overall model—F value (p value) 11.35<0.0001Lack-of-fit—F value (p value) 0.92 (0.5535)R2 0.6941Adjusted R2 0.6330Predicted R2 0.5105Adequate precision 9.551

*The F value for the overall model and the probability of obtaining alarger F value. The overall model is a reduced cubic and includes 25terms (Table 5).**A p>0.05 indicates no additional variation that might be accountedfor using a better model.***Design-Expert recommends a value greater than four to ensureadequate predictions.a The measured response variable.

378 NIEDZ AND EVENS

ing that additional variation in the residuals could not beremoved with a better model, the three R2 statistics wereclustered (difference less than 0.2), and the adequateprecision statistic of 9.551 was greater than 4. The modelwas highly significant (p<0.0001), thus indicating signifi-cant factor effects on growth. The ANOVA revealed threesignificant terms with the Fe linear term having the largesteffect on % fresh weigh increase (Table 9). The reducedquadratic polynomial model is presented in Table 10. Theregion of greatest fresh weight increase is a band runningthrough the design plane defined by the 800% contour lines(Fig. 4a). The corresponding response surface visualizes theshape of the response and shows that fresh weightprogressively declines as Fe levels increase; the declineincreases as NH4NO3 levels increase (Fig. 4a and b).

Discussion

A simple in vitro system was chosen to initiate this studyfor two reasons: one, our interest in better understandingthe role of mineral nutrition in regulating and controlling invitro growth and development, and two, a simple systemseemed appropriate in characterizing the usefulness of anefficient experimental approach we thought would be usefulin quantifying the inherent multivariate nature of in vitrosystems. For example, a five-factor factorial where eachfactor is set at a low, medium, and high level would require243 treatment combinations. The experimental design weused only required 33 treatment combinations (the remain-ing 10 were replicates for estimating pure error) to samplethe same design space. The additional dissection of thefive-dimensional design space required an additional 15treatment combinations and was particularly helpful infurther characterizing the response. This process of sub-dividing the larger design space into smaller and easilyvisualized components can continue until the precise regionof interest is fully explored. We could have selected othertwo or three factor slices (e.g., KNO3×Minors) through thefive-dimensional design space.

The growth of citrus nonembryogenic callus tissue canbe empirically studied, the effect of the mineral nutrients ongrowth measured, the mineral nutrient relationships ongrowth determined, and the resultant information then used

to regulate future growth to predictable levels. Reducing anin vitro response to an accurate predictive equation isdirectly useful for calculating the specific media formula-tions to achieve predefined levels of growth, but moreimportantly, it emphasizes the conceptual relativity ofoptimality. For example, given a growth response such asis depicted in Figs. 2 or 4, where does the callus grow“best”? This question in and of itself has no meaning, butrequires a specific application to provide the appropriatecontext. “Best” is defined by the specifications required bythe application. Thus, if the application is a maintenanceformulation Point #22, where the callus grows 40% fasterthan MS, is probably not a good choice, as it would requiremore frequent subcultures.

An aspect of this approach that we consider essential isthe use of “validation points.” These are points generatedfrom the prediction equation that are then empirically testedor validated. Validation becomes particularly important asthe dimensionality of the design space increases. Given thecomplexity of working in a five-dimensional design spacewith a biological system, Point #22 would have beenvirtually impossible to find using a one-factor-at-a-timeapproach. By generating an estimate of the response throughthe five-dimensional design space, it became possible tolocate Point #22. Of course, if the level of response is alreadycontained among the design treatment points, then predict-ing other regions of the design space may not be required.For example, there were several treatments in the five-dimensional design space that exceeded MS by varyingdegrees.

Mapping a response in a predefined region of interest notonly provides information that is directly useable in anapplied sense about how to control and optimize theresponse, but also contributes to the basic understandingof how the selected factors relate to the response or, asstated by George Box, “what does what to what” (Box et al.2005). For example, the importance of iron and itsinteractions with the other factors in affecting callus growthis clear from these experiments.

One problem of our experimental design is that we usedsalts as factors. The five factors included both single (Factors

Table 10. Reduced quadratic polynomial generated from the ANOVAof the % fresh weight increase of sweet orange callus in the two-factorexperiment

% fresh weight increase =

+804.98−56.98 ×NH4NO3

−141.59 ×Fe−60.76 ×NH4NO3×Fe−120.88 ×Fe2

Equation is reported in terms of coded factors.

Table 9. Significant terms with F value and p value in the ANOVA of% fresh weight increase of sweet orange callus in the two-factorexperiment

Significant ANOVA terms F value p value (Prob>F)

NH4NO3 4.36 0.0497Fe 29.63 <0.0001Fe2 6.61 0.0182

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1, 2, and 5) and multiple salts (Factors 3 and 4). Thisintroduces tremendous complexity into the design, asspecific ion effects are confounded. Ion confounding is aninherent problem when experiments are designed using saltsas factors. For example, factor 2 in the five-factor experi-ment was KNO3. Varying KNO3 actually varies both the K+

and NO�3 ions simultaneously; hence, effects associated

with KNO3 cannot be attributed to K+ or NO�3 , as the ion-

specific effects are confounded. To understand the effects ofthe mineral nutrients on particular in vitro responses, it isessential to treat the ions, and not the salts, as the factors.Niedz and Evens (2006) have recently reported a solution(and software) to the problem of ion confounding thatallows ions rather than salts to be used as the independentfactors. We are not aware of any studies, including this one,in plant mineral nutrition that do not exhibit ion confound-ing. Although our experimental design exhibited substantialion confounding, the factor effects on callus growth arereal; we are just unable to conclude anything about ion-specific effects from these experiments.

Acknowledgements We thank Mr. Eldridge Wynn for initiating andmaintaining the cell line used in this study and his excellent work insetting up all the treatment combinations and careful data collection.We thank the folks at Stat-Ease for the extremely informativediscussions on the various statistical aspects of this research.

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