The US equivalents were abolished in 1776. The United States is a republic (small “r”, and proud of it).
The only title of address is for a male is “Mister” (even “Mister President”). Attempts to have something more Brit-like fizzled out by the 1790’s (exception: calling judges “Your Honor”, calling elected officials “the honorable”, and lawyers using “esq” after their names).