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The phrase 'the role of which' is correct and usable in written English.
It is used to introduce a clause that provides information about a noun or phrase that has been mentioned previously in the sentence. For example: The policy was widely criticized, the role of which was to limit the number of immigrants.
Exact(47)
It was richly done, and was probably the role of which I am most proud.
Thence they are ingested into the cell, where they disable another protein, SNAP-25, the role of which is to help release a chemical messenger called acetylcholine.
In this review, extrathyroidal expression of the thyrotropin receptor is described, the role of which is still poorly defined.
Finally, the impact of density is also unaffected by the inclusion of the other labor market institutions, the role of which is not commented upon here.
The organisation structure of work is a network, the role of which is to link different communities together and enable sharing of resources (Networked work).
A portion of this regulatory switching involves the mobile domain of cTnI (cTnI-MD), the role of which in muscle contractility is still elusive.
Similar(12)
The two enigmatic domains NOD and NODP, the roles of which are still unknown, seem to be an innovation of Eumetazoa.
Additional proteins of interest include a di-heme cytochrome c peroxidase and a partner protein, the roles of which remain a mystery.
A shortcoming in their analysis is that they do not switch the roles of which datasets are used for training and testing.
These fibres probably maintain the stiffness of the notochord, the main role of which is keeping the body from shortening when the animal swims.
The role of Rwanda — which borders the provinces and which denied the accusations in the United Nations report over the weekend — is of prime importance.
More suggestions(15)
the order of which
the body of which
the functionality of which
the authority of which
the operation of which
the dimension of which
the importance of which
the position of which
the basis of which
the mission of which
the element of which
the engagement of which
the play of which
the airline of which
the argument of which
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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