OPTIMIZATION OF MEDIUM FOR GRAPEVINE PLANT DEVELOPMENT BY APPLYING A MATHEMATICAL DESIGN OF EXPERIMENT
Two methods were developed, one to assess experimental results by reducing a number of developmental parameters to the overall quality, leading to the overall quality criterion, and the other to optimize processes affected by numerous interacting factors, <i>in-vitro </i>plant development in this case, by applying a mathematical design of experiment. Single-bud cuttings with one leaf of two <i>Vitis vinifera </i>L.<i> </i>genotypes were excised from the central part of two-month-old <i>in-vitro</i> grown plants and used as explants. The explants were established on bridges of filtering paper in liquid media and on solid media. Eighteen modifications of these media contained five macro-elements, each at three concentrations, and the distribution of these macro-element concentrations followed the law of random numbers (Experiment I). Parameters characterizing arm, leaf and root development of two-month-old plants of each study genotype established on each liquid or solid medium were reduced to the overall quality of plant development. Since the study genotypes differed in the ability to grow on liquid and solid media with different macro-element concentrations and also in the ability to utilize these macro-elements, the dependence of <i>in-vitro </i>plant development on macro-element concentrations was described by different regression equations. That is why the regression equation describing the average outcome of plant development in the two genotypes on liquid and solid media was not as significant and the description of the process was not as adequate (determined) as regression equations calculated for each process. The regression equation which describes the dependence of the average outcome of plant development on macro-element concentrations in Experiment I is as follows: y<sub>5 </sub>= 0.027 + 0.116x<sub>2</sub><sup>2 </sup>+ 0.109x<sub>2</sub>x<sub>4 </sub>+ 0.106x<sub>2</sub>x<sub>3 </sub>+ 0.114x<sub>4</sub>. Stepwise calculation of macro-element concentrations to optimize <i>in-vitro</i> plant development was done based on macro-element concentrations of the initial medium of Experiment I as starting points since that medium was best efficient for this purpose by using regression equation (y<sub>5</sub>) and algorithms of multiple curvilinear stepwise regression according to the Box-Wilson method of steepest ascent. Experiment II was undertaken where macro-element concentrations ('steps') were calculated in a stepwise manner to optimize <i>in-vitro</i> plant development of the two <i>V. vinifera </i>genotypes and the rootstock 'Kober 5BB'. This led to a liquid medium and a solid one which enabled a better plant development in the three<i> </i>genotypes relative to the use of controls: media with Ѕ MS macro-elements and the initial medium whose macro-element concentrations entered as starting points to calculate 'steps' for optimization of <i>in-vitro</i> plant development. The optimized medium contained macro-elements: 318 mg l<sup>-1</sup> NH<sub>4</sub>NO<sub>3 </sub>(x<sub>1</sub>), 1188 mg l<sup>-1</sup> KNO<sub>3</sub> (x<sub>2</sub>), 370 mg l<sup>-1</sup> MgSO<sub>4</sub> 7H<sub>2</sub>0 (x<sub>3</sub>) (MS), 370 mg l<sup>-1</sup> KH<sub>2</sub>PO<sub>4</sub> (x<sub>4</sub>), 331 mg l<sup>-1</sup> CaCl<sub>2 </sub>(x<sub>5</sub>) (MS), and other substances at optimum concentrations adjusted earlier: ј MS Fe-EDTA, ј MS micro-elements, 20 mg l<sup>-1</sup> myo-inositol, 0.1 mg l<sup>-1</sup> thiamine (MS), 0.5 mg l<sup>-1</sup> nicotinic acid (MS), 0.2 mg l<sup>-1 </sup>pyridoxine, 2 mg l<sup>-1 </sup>glycine (MS), 0.1 mg l<sup>-1</sup> indole-3-acetic acid, 10 g l<sup>-1</sup> sucrose and, only for solid media, 7 g l<sup>-1</sup> Difco agar. The optimized medium may be used for propagation of virus-free plants, valuable clones and grapevine genotypes created by gene engineering. The mathematical design of experiment reported in this paper which enables stepwise optimization of <i>in-vitro</i> plant development