Martin's Axiom and separated mad families

Two families A,B of subsets of ω are said to be separated if there is a subset of ω which mod finite contains every member of A and is almost disjoint from every member of B. If A and B are countable disjoint subsets of an almost disjoint family, then they are separated. Luzin gaps are well-known examples of ω₁-sized subfamilies of an almost disjoint family which can not be separated. An almost disjoint family will be said to be ω₁-separated if any disjoint pair of ≤ω₁-sized subsets are separated. It is known that the proper forcing axiom (PFA) implies that no maximal almost disjoint family is ≤ω₁-separated. We prove that this does not follow from Martin's Axiom.