Amino acids can be interconverted by transamination. In order for this to occur, the organism must produce the corresponding alpha-ketoacids. This is the case for 11 of the 20 amino acids.
Tyrosine can be produced from phenylalanine by modification of the side chain (hydroxylation of the phenyl residue).
The other 8 amino acids must be obtained through the diet. With histidine, this is only the case for infants.
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The degree to which an organism is supplied with essential amino acids depends on the "deficiency component". A graphical depiction of this concept is found in "Liebig's Barrel" (analogous to the determination of the mineral supply in plants).