Facilitated diffusion moves impermeable compounds from one side of the membrane to the other by exploiting a concentration gradient. Molecules are transported across until their concentration is the same on both sides of the membrane. This mechanism can only eliminate a difference in concentration; it cannot create one. As cells typically grow in relatively nutrient-poor environments, they generally cannot rely on this passive transport mechanism to take in nutrients. Glycerol is one of the few nutrients known to enter E. coli cells this way.
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