If you search for each term individually, you will find hundreds of references dating to the nineteenth century. They were both common scientific phrases, but it took time for them to be combined.
If you search for the two phrases combined, the earliest link is to a book review from 1920, but skimming the document, I could not find either phrase.
The next reference comes from a 1950 paper, "THE SIGNIFICANCE OF THE "ONE-MINUTE" (PROMPT DIRECT REACTING) BILIRUBIN IN SERUM'," although they use each fragment in different sentences:
"The mechanisms underlying the renal excretion of bilirubin are still obscure." (I like that twist, I'm going to steal it.)
"The factors governing the speed of diazotization of bilirubin in serum are not fully understood."It was not until 1962 that the full power of the phrase was unlocked almost simultaneously by two papers, "Physiology of acclimation to low temperature in poikilotherms:"
The degree of compensa- tion is different in different groups of animals (2, 3) and the mechanisms underlying this compensation are not fully understood.and "The inflammatory response to a foreign body within transplantable tumors."
This response seemingly lies in the stroma and, although mechanisms underlying the inflammatory reaction in normal tissues are not fully understood...The science world would never be the same.