Modeling pollen tube growth of apple
Raw data Sixty flowering shoots of around 0.40 m length were collected from 60 trees that were randomly selected from two commercial orchards of ‘Fuji’ and ‘Gala’ apples in Prosser, Washington (USA). The king flowers were hand pollinated with ‘Red Delicious’ commercial pollen. Pollinated flowers were placed in growth chambers at eight constant temperatures of 4.5, 7, 11.5, 14.5, 21.5, 22.6, 28 and 30°C. At 12, 24, 48, 72 and 96 hours after pollination for lower temperatures, i.e., 4.5, 7, 11.5 and 14.5°C and at 4, 8, 12, 24 and 48 hours after pollination for the warmer temperatures, i.e., 21.5, 22.6, 28 and 30°C; pistils of tree flowers were detached and stored for one night in FAA (5% formalin, 5% acetic acid, 45% ethanol, 45% water: by vol.). The pistils were then washed and boiled for 30 minutes in a solution of sodium sulfite (50 g l-1) and then refrigerated. For evaluation the styles were detached from the ovary, rinsed with distilled water and placed in a water-soluble fluorescent solution of 0.1% Aniline Blue stain and 3.5 g l-1 of tribasic potassium phosphate for three days. Styles were then squashed between two microscope slides with a drop of fluorescent solution. The pollen tube length was measured as the distance between the pollen tube tip and the upper cell layer of the stigma, this process was carried out using a stage micrometer of 10 mm by 0.1 mm, 20X magnification and a fluorescence microscope. Response surface data Pollen tube lengths for each evaluated temperature were adjusted to logarithmic and logistic curves depending of the type of response as a function of the hours after pollination and the derivatives of the curves were calculated to determine the hourly growth rate of the pollen tube and the percentage of penetration of the pollen tube in the style (%) was calculated by dividing the adjusted pollen tube length from logarithmic and logistic curves by the average style length of the sampled flowers, 14.3 mm for ‘Fuji’ and 14 mm for ‘Gala.’ This data was used to fit a segmented nonlinear response surface for each cultivar to estimate the HGR as a function of temperature and style penetration.