Sorry. As I chose not to restrict my diet for other reasons, I have not investigated the biology.
I am reporting what I have heard/read from people I know with Type 1 who have tried low carb and decided against it because they saw a significant increase in their insulin to carb ratio required for their bolus insulin aswell as a need for more basal insulin (which aims to keep BG stable in the absence of food, exercise, stress, etc.).
Edited to add : Insulin sensitivity (need for less insulin) returned after eating more carbs.