NOVELTY - Isolated oleaginous cell comprising a genetic modification that increases expression of: a xylose reductase gene product and a xylitol dehydrogenase gene product; and/or a xylose isomerase gene product, is new.    USE - The isolated oleaginous cell is useful for producing biofuel precursors such as a fatty acid or a triacylglycerol (claimed) and biofuel such as biodiesel.    ADVANTAGE - The isolated oleaginous cell: provides the biofuel precursors (fatty acid or triacylglycerol) with increased synthesis rate, yield or accumulation of at least 2-fold, preferably 10-fold, as compared to unmodified cells of the same cell type, in an economically-viable and industrially scalable manner by utilizing cheap, abundant and readily available carbon source; is capable of converting a carbon source to a fatty acid or a triacylglycerol at a conversion rate of 0.025-0.32 g/g (g triacylglycerol produced/g glucose consumed); and allows large carbon flux amplifications into fatty acid synthesis pathways without significant departures of the concentrations of intermediate metabolites from their homeostatic physiological levels, thus avoiding feedback inhibition of fatty acid synthesis.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are also included for:    (1) a culture comprising the oleaginous cell;    (2) producing biofuel precursor, comprising contacting a carbon source with the isolated oleaginous cell, and incubating the carbon source contacted with the cell under conditions suitable for at least partial conversion of the carbon source into a fatty acid or a triacylglycerol by the cell; and    (3) increasing productivity of production of fatty acid or triacylglycerol by the oleaginous cell, comprising culturing the oleaginous cell with at least two types of carbon sources, where the first type of carbon source contains or is xylose, and the second type of carbon source is a carbon source other than xylose, by which the productivity of production of fatty acid or triacylglycerol by an oleaginous cell is improved relative to culturing the cell or the culture without the second type of carbon source.