Two genera of bacteria, Nocardia and Mycobacterium are said to be acid-fast.
The cell envelope of acid-fast cells is different from that of gram-positive and
gram-negative cells in that the outermost layer is composed of a complex
polysaccharide, arbinogalactan, bonded to fatty-waxy compounds called
mycolic acids.  These cells have porins that penetrate the envelope like
gram-negatives and are very difficult to control using chemical means of