It takes a while for someone to ask the vacationing literary professor Leda the obvious question.

“Are you angry? You seem angry.”

Leda may be on a long vacation on a seemingly idyllic Italian isle. But she always seems on the edge of something — a testy rebuff, a huff, maybe tears or at the very least an inappropriate sexual double entendre.

As played by Oscar-winner Olivia Colman in Maggie Gyllenhaal’s film, “The Lost Daughter,” Leda is a kindred spirit to a lot of Gyllenhaal characters over the years — a woman capable of things. Leda is smart and sexual, aloof and tetchy, not the sort to take kindly to an imposition or thoughtless request from the mob of Italian and New York Italian-American boors who noisily bowl onto “her” beach, her walk or her night at the cinema.

In Gyllenhaal’s directing debut, adapting Elena Ferrante’s novel, we fear Leda and fear for her. Because she has a hard edge — very hard. And these interlopers? They’re “bad people.” They don’t flinch at her furious professorial dismissals or profane working-class Leeds bark.

That’s not what “The Lost Daughter” is about, but it’s the subtext, a general unease that this subtle and unsettling film’s story unfolds against.

Proust’s narrator in “Remembrance of Thing’s Past” is triggered by a Madeleine cake. For Leda, it’s the sight of a beautiful, distracted and overwhelmed young mother from Queens (Dakota Johnson) whose needy, clingy toddler wanders off, throwing her entire Jersey-Shore-ready entourage into a panic.

Leda finds the child, and the wincing reveries that seeing Nina frantic or bickering profanely with her sinister lout of a husband (Oliver Jackson-Cohen) take her back to a time she lost her own daughter at the beach.

In flashbacks, we see young Leda (Jessie Buckley of “Wild Rose” and “I’m Thinking of Ending Things”), struggling to make time for herself, master Italian and write, with two young daughters who will not give her a moment’s peace. Leda didn’t handle that gracefully, and we wonder how this not-exactly-“instinctual” mother made out with them and what might have happened.

When present day Leda finds the little girl and returns her to her mother, we piece together more of her state of mind. She’s already noted “Children are a crushing responsibility” to a pregnant Queens queen (Dagmara Dominczyk). Now when Nina tells her she’s grappling with “something I just can’t handle,” Leda’s pithy response speaks volumes, two words of harsh judgment and naked confession.

“I know.“

Nina doesn’t see Leda make off with her little girl’s prized doll. That brittle exterior doesn’t so much hide the cruel streak we suspect lies beneath as make us anticipate it.

Gyllenhaal skillfully tracks Leda through this world, keeping her “I’d like to get back to my dinner now” distance from the friendly old caretaker of her rental house (Ed Harris), cozying up to beach cabana employee Will (Paul Mescal) to obtain a little adult literary conversation, with the odd sexual innuendo, from a college boy.

Colman gives an edge to almost every moment she’s on screen. Something about the nature of her chats with Will suggests this is standard operating procedure for our Boston professor.

We can’t know what her intentions are for that doll, but taking it doesn’t seem “normal” in any way, even as simple revenge for these cretins ruining her tranquility.

Johnson and especially Dominiczyk (TV’s “Succession”) have an element of danger about them that makes them seem at home in their rough extended family. Their questions of Leda have an interrogatory quality — part mother (or prospective mother) to mother bonding, part “What kind of mother are you?” judgement, with a hint of implied threat.

And as the flashbacks progress, Buckley skillfully gives us more and more of the young mother who became this often mean middle-aged woman.

Events play out in ways that can seem random, the “puzzle” of the picture is that cryptic.

“The Lost Daughter” isn’t melodramatic. But it uses the threat of melodrama — a touch of menace, glimpses of past callousness and cruelty, a flirtation in the present day, an affair (Gyllenhaal’s husband Peter Sarsgaard plays a bearded, vivacious fellow professor) — to keep us on our heels, on tenterhooks as we fret over all the bad things that might happen or terrible things that must have happened.

Colman’s performance is the film’s marvel. But Gyllenhaal’s brilliant, subtle manipulations make hers one of the most auspicious directing debuts in years, a veteran, intimidating cinematic “bad girl” who turns her withering gaze on us and strings us along, wondering what became of “The Lost Daughter.”

Rating:  R for sexual content/nudity and language

Cast: Olivia Colman, Dakota Johnson, Jessie Buckley, Dagmara Dominczyk, Oliver Jackson-Cohen, Ed Harris and Peter Sarsgaard

Credits: Scripted and directed by Maggie Gyllenhaal, based on a novel by Elena Ferrante. A Netflix (Dec. 31) release.

Running time: 2:01