Hmmm, what shudda I done?

I'd treat MP's flop bet as a check and bet around pot... I would never expect a flop 3bet like this where villain holds A4, 44 or AA unless he's a braindead aggro idiot. This is one of those spots where I feel comfortable about getting it in with TPTK on the flop. You're either chopping, crushing worse Aces, or ahead of any frisky flush draws.

Even with those rare nut hands on the flop, you're still making out well.

Text results appended to pokerstove.txt
18,810 games 0.005 secs 3,762,000 games/sec

Board: 4h 4c Ac
Dead:

equity win tie pots won pots tied
Hand 0: 45.917% 45.45% 00.46% 8550 87.00 { AsKh }
Hand 1: 54.083% 53.62% 00.46% 10086 87.00 { AA, 44, A4s, KcQc, KcJc, KcTc, Kc9c, QcJc, QcTc, Qc9c, JcTc, Jc9c, Tc9c, 9c8c, 8c7c, 7c6c, A4o }