The present invention relates to the construction and engineering of cells, more particularly microorganisms for producing PUFAs with four or more double bonds from non-fatty acid substrates through heterologous expression of an oxygen requiring pathway.The invention especially involves improvement of the PUFA content in the host organism through fermentation optimization, e.g. decreasing the temperature and/or designing an optimal medium, or through improving the flux towards fatty acids by metabolic engineering, e.g. through over-expression of fatty acid synthases, over-expression of other enzymes involved in biosynthesis of the precursors for PUFAs, or codon optimization of the heterologous genes, or expression of heterologous enzymes involved in the biosynthesis of the precursor for PUFAs.