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This morning Dakota Johnson slept with Seth Rogen. The weird thing is, Rogen doesn’t even know it. The two were seated next to each other on a 6 a.m. flight to Los Angeles from Vancouver, where Johnson was shooting some non-naughty bits of Fifty Shades of Grey. Johnson is a big fan of Rogen, but he didn’t recognize her.

Her hair is dyed from her natural blond to dark brown for Fifty Shades, making her look even younger than 24. Not that Rogen would have known who she was anyway. She tells the story with a goofball smile, its DNA lifted straight from her mom, Melanie Griffith. “I didn’t want to be like, ‘Hey, wake up, I’m Dakota.’”

Johnson should cherish her relative anonymity — relative is the right term when your grandmother is Hitchcock muse Tippi Hedren and your parents are Griffith, dad Don Johnson, and stepfather Antonio Banderas — while she can. Fifty Shades of Grey unties itself in February 2015 with a built-in audience of 90 million mostly female readers, not to mention their panting male consorts, who will observe Johnson in various stages of love, bondage, and undress. Basically, Dakota Johnson is about to be revealed to Western civilization.

“I have no idea how it’s going to go,” says Johnson, widening her blue eyes. “I plan on handling it gracefully, to live my life as close as I can to how I do now.” She is exhausted from 14-hour workdays but musters a mischievous smirk. “I’m really a normal person.”

It’s true that Dakota Johnson has an appreciation from normal things, including a Red State love of skeet shootin’, and that her car of choice is sensible, “mom-style” Mercedes. But here’s the hitch: If Dakota Johnson aspires to be normal, she is soon going to be screwed — and not in an Anastasia Steele kind of way.

Johnson tries to deflect the issue, claiming the real sexpot of Fifty Shades is costar Jamie Dornan — who will be the one saying lines like, “You’ve really got a taste for this, haven’t you, Miss Steele? You’re becoming insatiable” — but she’s the one who’ll play proxy for those millions of breathless fans who fantasize about being taken by his Christian Grey. It’s Dakota Johnson who will be The Franchise. The film will rise or fall based on whether the audience has chemistry with the lip-chewing Ana.

Right now, the franchise is all but a blank slate. This month’s Need for Speed, a film about racing in which Johnson appears opposite Aaron Paul, will offer a taste. But if moviegoers have seen her at all before now, it’s been as Justin Timberlake’s Stanford one-night stand in The Social Network or as Jason Segel’s soon-to-be ex in The Five Year Engagement. In total, they account for less screen time than a music video.

To say Fifty Shades has been omnipresent in popular culture since its release in 2011 does a disservice to the word omnipresent. It was just over two years ago that an unknown writer named E.L. James, a British housewife and former television executive previously known for penning Twilight fan fiction under the name Snowqueens Icedragon — yes, really — published the story of a virginal college student, Anastasia Steel, who meets Christian Grey, a young Ayn Randian master of the universe with a predilection for helicopters, Audis, and sexual equipment borrowed from some combination of a Soviet torture chamber and Caligula’s basement. They fall into a sort of love that includes whips, chains, and nondisclosure agreements.

True Fifty Shades aficionados argue that all the S&M is just the backdrop for a retro love story in which Ana tries to melt Grey’s possibly sadistic heart. But let’s face it: How Ana and Grey talk about their feelings isn’t really the point. And it’s definitely not why the casting of Fifty Shades of Grey became the unofficial Hollywood parlor game of 2013.

No, that would be because the most sexually explicit mainstream film of the decade could easily make or destroy a young actress’s career. Sure, Universal Pictures chairman Donna Langley, one of the few women in Hollywood who can green-light a film, had optioned the trilogy’s rights in a rare deal that guaranteed James script, casting, and director approval. And Sam Taylor-Johnson (a photographer and member of the British art aristocracy whose only previous film is the indie John Lennon biopic Nowhere Boy), gave the project both a go-girl gloss and an unexpected shot at …tastefulness. Still, any actress taking the role risked a one-way ticket to Showgirls purgatory — a straight-to-DVD career (or worse). There was talk of Hollywood sweetheart Shailene Woodley. Emma Watson shot down rampant speculation by tweeting, “Who here actually thinks I would do Fifty Shades of Grey as a movie? Like really. For real. In real life.”

But if things broke right, the chosen actress might be the next Jennifer Lawrence, only sexier. Or, say, a Melanie Griffith.

Dakota Johnson says that whatever gets you through the night is all right with her.

“I think women should pursue whatever kind of relationship they want and makes them happy, and if that’s S&M, that’s great,” she says.

That’s good to hear, because even the audition process for Fifty Shades was NC-17. At the beginning, Johnson was just another face and body in the casting slush pile. But then she was asked to perform a monologue from Ingmar Berman’s Persona, a 1966 Swedish film, in which the character admits to cheating on her doctor fiancé in a ménage à quatre with another woman and two teenage boys on a beach, an incident that ended in an abortion. The passage includes such choice phrases as “sperm shooting inside me” and “I came over and over.” Persona is not a popcorn movie.

“I don’t have any problem doing anything,” Johnson says. “The secret is I have no shame.”

That attitude is what bumped Johnson ahead of name-brand actresses. While other starlets and their agents wrestled with whether Fifty Shades was classy enough for their resumes, she was exhibiting the chops and sexual honesty needed for the role. With those hurdles cleared, Johnson did a steamy screen test with Sons of Anarchy star Charlie Hunnam (who was originally cast to play Christian, before he withdrew and was replaced by Dornan). And then she waited.

“It was kind of brutal,” says Johnson. “I was calling every day, being like, ‘What the fuck is going on?’ Toward the end, it was like, ‘I either have this part or I’m an asshole.’”

She talks of Ana without trepidation or faux innocence, but as if she already inhabits the character. “I just thought Ana was a real girl,” says Johnson. “There’s nothing fake or phony about her, and I appreciate that. She’s goofy and she’s smart and she’s pretty normal.”

There’s that word again. But the more I talk with Johnson, the more it becomes evident that her idea of normal is hardly prosaic. This will happen when you’re the kind of Hollywood child who treats the Chateau Marmont like the neighborhood Sonic. When we meet there, she waves to the hostess, a longtime friend. With her dad’s cheekbones and her mom’s smoky eyes. Johnson looks the part of the next big thing, but she also possesses a this-is-my-town poise.

“Reading the book, I found myself more interested in the sex scenes,” says Johnson, gulping down black coffee and an omelet. (Her diet is relevant only because the tabloids have recently claimed she’s on an all-juice cleanse for Fifty Shades. This bit of gossip produces a spectacular eye roll from Johnson, who is, for the record, willowy without being scary skinny.) “I think there’s a part of a woman that wants to be the thing that breaks a man down.”

That part Johnson felt confident about from the get-go. Otherwise, she says, “I wasn’t very invested as first, just because I was a little scared of it. The material was intense, and I’ve never done anything like that before. But that just told me it was something I should do.”

She was hanging out at a friend’s house last summer in New York City, where she was shooting an adaptation of Shakespeare’s Cymbeline, when she finally got the call: She would be Ana. “I was just crying, and there were all these dogs in the house,” she remembers. “This one dog was below my feet sleeping, and I was like, ‘You fucker, wake up, this is really exciting’ — and then I had a glass of whiskey.”

For weeks after being cast, Johnson wasn’t allowed to tell anybody — not her father, not her mother, not her grandmother. And she kept the secret, because “sometimes your parents are the ones with the biggest mouths of all time.”

Being third-generation Hollywood provides her with a certain kind of armor that will soon some in handy. Hedren, best known for her starring role in Hitchcock’s The Birds, famously keeps a compound outside of Los Angeles filled with wild beasts; in some of the earliest public photos of Melanie, she has her head in the mouth of a lion. Griffith started dating Don Johnson when she was 14 and he was costarring in a movie with her mother. They married when she was 18, quickly divorced, and then remarried. Dakota was born in 1989. The couple divorced again in 1996, and Griffith married Banderas later that year.

Johnson downplays the fact that her dad and mom were the Brad and Jen (or maybe Liz and Dick?) of their era, but she realizes her childhood was at least different from that of the average high schooler. “My dad was doing Nash Bridges in San Francisco, so I was there, like, every day,” she says. “My mom was doing a bunch of stuff, still making movies, and Antontio was making movies. I was everywhere, all over the world. I loved it so much.”

But there’s a jagged side — or as Dakota puts it, “a mind fuck” — to refracted fame. “I feel like you learn how to do school in second grade through fifth grade. During those years I was never home.” After years of on-set tutoring and homeschooling, her parents sent her to a Catholic boarding high school in northern California. Dakota thought it was a great idea. Then she arrived. “I was just miserable there. It was a great school, but girls in that concentration are so horrific, just horrific.”

Eventually, she got her dad to set her free. When I ask her how she persuaded him to let her leave, she gives the biggest smile of the morning: “I’ve fucking got him on lock. I charmed him.” How, exactly? She draws a circle around her face with a finger and goes coy, then laughs. “I don’t know. This face?”

Next, it was off to the artsy New Roads School in Santa Monica, where Johnson whiled away high school sketching. “I would get so bored after a while. There’s only so many ways you can draw a naked woman or man. There are only so many penises I can see and draw.” The hardest part was dealing with the slings and arrows aimed at her family. Classmates would bring in clippings about her parents — some of them true, and a lot more not even close.

“I think people, especially the press, like to pick on children of famous people, and I think that’s fucking awful,” she says. “Things get made up. It’s so, so sad. And there’s absolutely nothing you can do about it as a 16-year-old. You’re like, ‘What the fuck? Why? What did I do?’”

Many of the stories about Johnson being cast in Fifty Shades mention that she spent 30 days in a Malibu rehab center for substance abuse as a teen. She swears it never happened.

“My parents has some problems of their own that put me in a position of having to deal with very grown-up stuff at a very young age,” says Johnson, obliquely hinting at both of her parents’ well-documented alcohol issues. “I needed some help with that, therapy-wise. And in turn, as a child, you trust someone and then they fuck you over.”

Given all that, why would she follow her parents into the family business? At the question, the fact of Hollywood’s next big vixen is consumed by a little-girl-lost look. “I think there’s a part of me that feels like there is nothing else I can do.”

Thing is, Dakota Johnson doesn’t just do it. She’s really good at it.

Convincing herself of that, however, took some time. She began to pursue acting in 2008, but a lack of experience and a cast of famous-daughter syndrome amounted to a self-sabotaging spree. “I was 18, and I would freak out,” Johnson says. “I think there was a part of me that really didn’t know if I was capable.”

Comedy saved her. In 2010, she found herself auditioning for Judd Apatow. “Dakota came in to read for Girls and was amazing, just naturally hilarious,” he told me. “We didn’t have a part for her, but she made a big impression.”

At the time, Apatow’s friend Nick Stoller was looking for someone to play Audrey, Jason Segel’s manic, way-too-young girlfriend in The Five Year Engagement. The possibly chemically imbalanced Audrey is sated only by constant sex or hosting a Zumba dance party in her bedroom at 4 a.m. The Apatow/Stoller world revolves around improv, something Johnson has never done in her life — but she was a natural. “She built that whole character. I thought to myself, She’s going to be a movie star,” says Stoller, who kept adding scenes for her. “I’ve had that feeling with Chris Pratt and Mila Kunis, and I had it with Dakota.” As for Fifty Shades, “If they hired someone not funny, it could be cheesy,” he says, “but it will have a sense of humor with her, and that’s key. And she’s really pretty! To find that in one actress is rare. It’s like Meg Ryan.”

The Five Year Engagement followed The Social Network, where Johnson — as a Stanford undergrad — perfected looking great in boy-short undies while holding her own with megastar Justin Timberlake. While Fifty Shades casting process plodded along, Johnson auditioned for Ben and Kate, a 2012 FOX comedy about a brother and sister raising a daughter together.

At the time, the show’s executive producer, Jake Kasdan, another Apatow accomplice, thought they were going to have to push the show back because they couldn’t find the right Kate. Then Johnson came in. “It was a no-brainer, and there was total consensus,” says Kasdan. “She has an inner natural feeling and an incredibly truthful look. Her wheelhouse for comedy is rooted in her being an uncomfortable, awkward person when we know she’s graceful.”

The show lasted only 13 episodes, but Johnson proved she could handle fastballs and change-ups; everything from tender moments with her on-screen daughter to humping a plant for laughs. As cancellation loomed, Kasdan says he told the network execs, “You’re going to be hearing from her and think, Oh, we had her on our TV show.” He laughs. “I just didn’t know it would happen instantly.”

The son of legendary writer-director Lawrence Kasdan (Body Heat, The Big Chill), Kasdan has a useful perspective on Johnson’s upbringing: “There is a familiarity with the machinery of it all. Most people have to figure that all out while trying to establish a career. She has a great advantage of knowing how that all already works.”

After the Chateau, Johnson and I ride to her ELLE cover shoot on the other side of Los Angeles. When she hangs up a phone call with her boyfriend, Jordan Masterson, an actor on the CBS series Last Man Standing, she is giddy. Earlier that morning, Masterson had given her a Christmas present, and she’s still high. “He gave me double sinks!” she exclaims. “He did it himself. I think double sinks are the key to any relationship.”

Just as I begin to consider that maybe she really is just another normal girl making her way through a crazy world, talk turns to the growing expectations in her life, and Johnson switches into the mode of a gimlet-eyed 35-year-old. “Look, I know just from watching and not being an idiot that it’s all up and down. One minute people think you’re the fucking shit, and the next minute they don’t even … That doesn’t matter to me.”

Besides, her parents have her back. After they got over the initial shock — “They were both like, Holy shit!” — they’ve been fully on board the Fifty Shades Express. When the Twittersphere criticized Johnson’s casting, Melanie Griffith went all mama bear. “She called someone a bitch,” says Dakota gleefully. “My mom is just the most loving person.”

When we arrive at the shoot, Johnson disappears for two hours. I still have some doubts about this smart-aleck kid pulling off an erotic role. But then she emerges in a tight green dress, blue eyes shining behind her make-up, grinning.

“I clean up good, don’t I?”

The cameras begin to flash. Johnson gazes into the lens with a vaguely hunted look, her hands pushing stockings downward. Then the shooting stops, and Dakota strolls over to a monitor for a look. She can’t suppress a giggle.

“There are a lot of good shots of my ass. You can’t go wrong with some good ass shots.”

Then she walks back to her dressing room, high heels in hand, a girlish bounce in her step.

She’s going to be fine.