I've noticed when reaching my upper limits on squat, I start to get some impingement around the ankle and upper foot area. I've learned that this can be caused from weakness of the ankle and foot muscles. I try to keep these areas flexed throughout the movement.
I've read that barefoot running is a great way to improve foot and ankle musculature. I'm wondering if there is any evidence of carryover to squats.
Would barefoot running (or running with barefoot shoes) help keep my squat form from breaking down in the ankle and foot region during max effort lifts?
I should mention I'm using olympic lifting shoes and am not a beginner: I am 6'2", 195 lbs, and am maxing in the low 300lbs range with full range olympic-style back squat. As I mentioned in the comments, I feel that "clutching" the ground with my foot provides the most stable base when squatting, and would like to strengthen that musculature.