Dissolve the yeast and sugar in the 1/4 cup of warm water. Let stand for 5 minutes. Combine the flours and salt in a mixing bowl. Make a well in the center of the flour mixture and add the egg, oil, yeast mixture and remaining 1-1/4 cups of water. Mix well. Knead the dough on a floured board, adding more whole wheat flour until the dough is smooth and elastic. Place in an oiled bowl. Cover with a damp towel and let rise until doubled, about 1 hour. Divide the dough into three parts. Roll each third into a strip about 15 inches long. Braid the strips together and place on a lightly-oiled baking sheet. Brush with the beaten egg. Sprinkle on the poppy seeds. Cover and let rise until doubled. Bake in a 375-degree oven for 40 to 45 minutes, or until golden brown.