An epoxide is a functional group derived from the ether group. In fact, it is a cyclic ether, forming a ring with 3 members (2 carbons and 1 oxygen). The cyclic structure is an equilateral triangle and presents a high rigidity and structural tension.
In biochemistry, epoxides are important molecules in many metabolic processes, such as, for example, in the synthesis of cholesterol.
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The thioester group, as its name indicates, is characterized by being derived from an ester group, in which the oxygen that is connected by a single bond to the carbon is replaced by a sulfur atom. Its chemical formula is COSR. Thioesters are obtained when a carboxylic acid reacts with a thiol.
Thioesters are very important in biochemistry, mostly as a consequence of the fact that the molecule coenzyme A (CoA) has a free thiol group which reacts with carboxylic groups to form thioesters. The best known example is the molecule of acetyl-CoA.
It is thought that thioesters may have been precursors of life, as advocated by de Duve in "Thioester World": It is revealing that thioesters are obligatory intermediates in several key processes in which ATP is either used or regenerated. Thioesters are involved in the synthesis of all esters, including those found in complex lipids. They also participate in the synthesis of a number of other cellular components, including peptides, fatty acids, sterols, terpenes, porphyrins, and others. In addition, thioesters are formed as key intermediates in several particularly ancient processes that result in the assembly of ATP. In both these instances, the thioester is closer than ATP to the process that uses or yields energy. In other words, thioesters could have actually played the role of ATP in a "thioester world" initially devoid of ATP. Eventually, [these] thioesters could have served to usher in ATP through its ability to support the formation of bonds between phosphate groups.
By the way, as a curiosity, if the oxygen from the ester group that is replaced by sulfur is the one of the double bond, the resulting functional group is called thionoester.
"A cell of a higher organism contains a thousand different substances, arranged in a complex system. This great organized system was not discovered by chemical or physical methods; they are inadequate to its refinement and delicacy and complexity." — Herbert Spencer Jennings