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The phrase "achieve their functions through" is correct and usable in written English.
It can be used when discussing how entities or systems accomplish their roles or purposes by means of specific methods or processes.
Example: "The organs in the human body achieve their functions through a complex interplay of biological systems."
Alternatives: "fulfill their roles via" or "perform their functions by means of".
Exact(1)
These pieces of structure-efficacy information imply that artemisinins may not achieve their functions through binding specifically to a protein-target site and consequently inhibiting its function.
Similar(59)
Despite their inability to form a unique stable tertiary structure in isolation, many IDRs adopt a defined conformation upon binding and achieve their function through their interactions with other biomolecules.
Further analysis revealed that Htr2c is upstream of the sympathetic center of the brain while Htr1a and Htr2b achieve their functions on appetite through modulation of melanocortin signaling.
Many proteins require bound metals to achieve their function.
Three NOS isoforms, iNOS, eNOS and nNOS (inducible, endothelial, and neuronal NOS), achieve their biological functions by tight control of interdomain electron transfer (IET) process through interdomain interactions.
Proteins are produced to achieve their biological functions.
Often, different genes cooperate to achieve their biological functions.
Whether managers achieve their incentivized goals is a function of their subordinates' effort toward those goals.
The group functions as a forum to help these Ph.D. and postdoctoral programs achieve their goal of educating successful researchers through, although not limited to, a Web site, a listserv, and an annual meeting.
There is a significant need for research that clarifies the different functions of PROMs feedback and delineates more clearly the processes through which they are expected to achieve their intended outcomes.
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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