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The phrase "active form of the cofactor" is correct and usable in written English.
It can be used in scientific or biochemical contexts when discussing the functional state of a cofactor in relation to enzymes or biochemical reactions.
Example: "The enzyme requires the active form of the cofactor to catalyze the reaction efficiently."
Alternatives: "functional form of the cofactor" or "bioactive form of the cofactor."
Exact(4)
Thiamine pyrophosphate (TPP), the active form of the cofactor, must be either salvaged or synthesised de novo.
As clearly shown in Figure 4, the ThiE reaction generates TMP, but TMP is not the active form of the cofactor and has to be further phosphorylated to TPP.
TPK is a thiamin salvage enzyme that transfers the diphosphate group of ATP to thiamin to form thiamin diphosphate, the active form of the cofactor.
In order to restore the reduced active form of the cofactor, cob II)alamin is reductively methylated by MSR using NADPH as electron source and SAM as methyl group donor [26,27].
Similar(56)
Molybdenum is added to MPT in subsequent steps to generate MPT-Mo, the active form of the molybdopterin cofactor.
However, pyridoxal 5-phosphate (PLP) is the only active form of the enzymatic cofactor which is mainly involved in decarboxylation and transamination reactions [ 15].
Pyridoxal 5′-phosphate, the active form of vitamin B6, optimizes the substrate flux in the KYN pathway by acting as cofactor for two key enzymes, KYN aminotransferase and kynureninase [ 10].
The active form of FA, 5-methyltetrahydrofolate restores the function of uncoupled eNOS by increasing the availability of its cofactor tetrahydrobiopterin (BH4)[ 27].
As the active form of thiamine, thiamine pyrophosphate (TPP) is an essential cofactor for particular metabolic processes such as BCAA biosynthesis.
The active form of coagulation factor V is involved as an essential non-enzymatic cofactor for the activated factor X catalysed conversion of prothrombin to thrombin.
As the main active form of intracellular thiamine (vitamin B1), thiamine pyrophosphate (TPP) is an essential cofactor in oxidative metabolism of the sugars, fatty acids and amino acids.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com