PORTLAND, Ore. — By the time her mother received the doctor’s email, Yuna Lee was already 2 years old, a child with a frightening medical mystery. Plagued with body-rattling seizures and inconsolable crying, she could not speak, walk or stand.

“Why is she suffering so much?” her mother, Soo-Kyung Lee, anguished. Brain scans, genetic tests and neurological exams yielded no answers. But when an email popped up suggesting that Yuna might have a mutation on a gene called FOXG1, Soo-Kyung froze.

“I knew,” she said, “what that gene was.”

Almost no one else in the world would have had any idea. But Soo-Kyung is a specialist in the genetics of the brain—“a star,” said Robert Riddle, a program director in neurogenetics at the National Institute of Neurological Disorders and Stroke. For years, Soo-Kyung, a developmental biologist at Oregon Health and Science University, had worked with the FOX family of genes.

“I knew how critical FOXG1 is for brain development,” she said.

She also knew harmful FOXG1 mutations are exceedingly rare and usually not inherited — the gene mutates spontaneously during pregnancy. Only about 300 people worldwide are known to have FOXG1 syndrome, a condition designated a separate disorder relatively recently. The odds her own daughter would have it were infinitesimal.

“It is an astounding story,” Dr. Riddle said. “A basic researcher working on something that might help humanity, and it turns out it directly affects her child.”

Suddenly, Soo-Kyung, 42, and her husband Jae Lee, 57, another genetics specialist at O.H.S.U., had to transform from dispassionate scientists into parents of a patient, desperate for answers.

They were plunged into a fast-moving ocean of newly identified gene mutations, newly named diagnoses, and answers that raise new questions.The newfound capacity to sequence genomes is spurring a genetic gold rush, linking mystifying diseases to specific mutations — often random mutations not passed down from parents.

New research shows that each year, about 400,000 babies born worldwide have neurological disorders caused by random mutations, said Matthew Hurles, head of human genetics at Wellcome Trust Sanger Institute. As sequencing becomes cheaper, more children will receive specific diagnoses like FOXG1 syndrome, doctors say.

This burst of discovery might eventually help doctors treat or prevent some brain damage. “We used to lump them all together under autism or another category,” said Dr. Joseph Gleeson, a neurogeneticist at University of California San Diego. “It’s really changing the way doctors are thinking about disease.”

Balancing the missions of science and motherhood, Soo-Kyung has begun doing what she is uniquely positioned to do: aiming her research squarely at her daughter’s disorder. With Jae’s help, she is studying how the FOXG1 gene works and why mutations like Yuna’s are so devastating.

“Our ultimate goal is to find a better treatment for FOXG1 syndrome patients,” she said. Her day-to-day goal is helping Yuna make slivers of developmental progress.

Yuna is now a sweet-natured 8-year-old still wearing a toddler’s onesie over a diaper. “Cognitively she’s about 18 months,” Jae, her father, said.

A major achievement would be getting Yuna to indicate when her diaper is wet. Or to stand when they prop her against a kitchen corner and remove their hands for a split second. “If Yuna doesn’t fall down right away,” Soo-Kyung said, “we consider that a success.”

“My daughter’s brain is so damaged,” Soo-Kyung said, eyes brimming with tears. “Can we rescue any of her skills?”

When their daughter was born in Houston in January 2010, southeast Texas experienced a rare snowfall. It inspired the Lees, then professors at Baylor College of Medicine, to name her “Yuna,” meaning “snow girl” in a Korean dialect, with the middle name “Heidi” for its allusion to snowy peaks.

“She was perfectly normal,” Jae said. “We were joking, ‘What will come later?’ Yuna’s mom is a very smart person, so we thought, ‘Well, she will make the world better.’”

But soon, things seemed off. Yuna often failed to respond to sounds. She struggled to swallow milk from breast or bottle. What she did swallow she vomited. “She looked like someone with malnutrition,” Soo-Kyung said.

A doctor said her head circumference was not growing enough. Then Yuna began having seizures , often sending the Lees to the emergency room. She cried so persistently that Soo-Kyung had to assure neighbors Yuna was not being abused.

“What did I do wrong?” Soo-Kyung grilled herself. Had she eaten something while pregnant that infected Yuna? “I was traveling a lot during the pregnancy to attend seminars — was I too stressed?”

Shortly after Yuna’s second birthday, Soo-Kyung traveled to Washington, D.C. to serve on a National Institutes of Health panel reviewing grant proposals from brain development researchers. At dinner, she found herself next to Dr. David Rowitch, a respected neonatologist and neuroscientist she knew only by reputation.

“She started to tell me what’s going on with her daughter,” recalled Dr. Rowitch, professor and head of pediatrics at the University of Cambridge who was then at the University of California San Francisco. He was stumped but offered to send Yuna’s brain scans to “the world’s expert” in neuroradiology: Dr. Jim Barkovich at U.C.S.F.

Dr. Barkovich said Yuna’s scans revealed “a very unusual pattern,” one he had not seen in decades of evaluating brain images sent to him from around the world. Yuna’s cerebral cortex had abnormal white matter, meaning “there were probably cells dying,” he said, and the corpus callosum, the corridor across which cells in the left and right hemispheres communicate, was “way too thin.”

Searching scientific literature, he said, “I found a gene that seemed to be expressed in that area and found that when it was mutated it caused a very similar pattern.” That gene was FOXG1.

FOXG1 is so crucial that its original name was “Brain Factor 1,” said Dr. William Dobyns, a professor of pediatrics and neurology at University of Washington, who published a 2011 study recommending a separate diagnosis: FOXG1 syndrome. “It’s one of the most important genes in brain development.”

FOXG1 provides blueprints for a protein that helps other genes switch on or off. It helps with three vital fetal brain stages: delineating the top and bottom regions, adjusting the number of nerve cells produced and “setting up the organization of the entire cortex,” Dr. Dobyns said.

So, when Dr. Barkovich’s email said he “would not be surprised if this is a FOXG1 mutation,” Soo-Kyung’s heart shuddered. “That’s unthinkable,” she despaired.

Yuna’s neurologist declined to authorize FOXG1 gene analysis, considering the possibility improbable — and irrelevant because it would not change Yuna’s treatment, Soo-Kyung said. So she decided to sequence the gene herself, preparing to seek university permission since her lab only worked with animals. Then, she became pregnant again. That provided justification for professional analysis of Yuna’s gene to determine if there was a heritable mutation the Lees could have also transmitted to their second child.

When results showed a FOXG1 mutation, Soo-Kyung requested the raw data, hoping the lab had messed up. But scanning the data, Soo-Kyung spotted the problem instantly: Yuna was missing one nucleotide, Number 256 in the 86th amino acid of one copy of FOXG1, which has 489 amino acids.

It was a random mutation, so she felt relief her second child was at little risk. But its location in the DNA sequence had given Yuna a smaller, incompletely functioning brain. A single mutation had disabled the entire gene.

Bridlemile Elementary School’s long hallway is both minefield and laboratory for Yuna. In a wheelchair or special walker, she is guided by a paraprofessional, Audrey Lungershausen, who tries to keep her from grabbing student artwork and coats, while encouraging her to identify balls and faces on a mural.

Soo-Kyung must also navigate a daunting hallway. In June 2016, overcome by stress, she collapsed. Diagnosed with vestibular neuritis, an infection involving nerves linking the ear and brain, she was bedridden for weeks and struggled to stand. She still experiences vertigo and nausea walking the hall to her lab, “like I’m on a ship that’s constantly moving.”

Her disability, glancingly parallel to her daughter’s, helps her understand that “the world that Yuna has to face with her limited ability to control her body — that must be really scary to her,” she said.

While Yuna’s condition gives Soo-Kyung’s work personal importance, her own condition makes it harder. She cannot look at her computer more than 25 minutes straight, reads with a yellow filter often used by children with autism, and does visual exercises using paper images taped to her office wall..

Like Yuna, Soo-Kyung needed physical, occupational and speech therapy. A psychiatrist prescribed an antidepressant. Instead of sleeping in Yuna’s room, Soo-Kyung began blocking out light and sound by sleeping on a mattress on the floor of the master bedroom closet. “They say I may not recover to a normal level.”

Long before Yuna was born, Soo-Kyung stumbled upon research she found fascinating, showing that mice missing both FOXG1 genes did not form brains. That would apply to humans, too. “There’s nobody who is missing two copies of the gene,” said Dr. Riddle of the National Institute of Neurological Disorders and Stroke. “They don’t survive.”

Soo-Kyung told Jae she wanted to someday study how FOXG1 drives brain development. “Then Yuna arrived,” Jae said.

Now, studying mouse brains, the Lees have identified genes that interact with FOXG1, helping explain why one crippled copy of FOXG1 damages the corpus callosum’s ability to transmit signals between hemispheres.

“We now understand how this gene works and why,” Soo-Kyung said.

Many mysteries remain. Individual FOXG1 mutations affect gene function differently, so one FOXG1 patient’s symptoms can vary from another’s. For example, Charles A. Nelson III, an expert in child development and neurodevelopmental disorders at Boston Children’s Hospital and Harvard Medical School, evaluated two 10-year-old patients with mutations in different locations and markedly distinct levels of impairment.

Since patients like Yuna, with one dysfunctional and one functional FOXG1 gene, produce half the necessary FOXG1 protein, Soo-Kyung wonders if gene therapy could restore some protein or boost protein activity in the good gene.

But because FOXG1 is crucial so early in development, Dr. Rowitch said, “I don’t think you can just go back when the baby’s born and build the brain back up.”

Still, Dr. Dobyns said, “are there parts of FOXG1 syndrome that we might be able to fix once we understand it better? Sure, parts of it.”

When Yuna was 6, Soo-Kyung, half-asleep in bed with her, noticed something extraordinary: Yuna was sitting up. “Am I dreaming?” Soo-Kyung wondered. For years, Yuna failed to learn this skill, usually mastered by six-month-old babies.

Physical therapists had stopped Yuna’s sessions, saying “ ‘What’s the point of doing it when she’s not making any progress?’” Soo-Kyung recalled. She began painstakingly urging Yuna to push up using her elbow, never sure Yuna understood. Then, “suddenly Yuna was sitting up and I didn’t know how it happened.” Probably a fluke, Soo-Kyung thought—but soon Yuna began sitting up regularly.

Experts say too little is understood about newly recognized neurological disorders to know children’s developmental limits. But the Lees believe the sitting-up success shows that if they persevere, Yuna can make incremental progress. Their next goal is for Yuna to communicate when she is hungry, uncomfortable or wants something.

Speech therapists could not get Yuna to intentionally press a button activating a recorded voice saying things like “more.” “I don’t know if she understands what I am telling her,” said Diana Deaibes, a speech-language pathologist at Shriners Hospital for Children.

But the Lees refused to let Shriners pause speech therapy, urging therapists to try teaching Yuna to stare at something she wants. “We insisted,” said Jae, optimistic even though they attempted visual communication before “and it was a complete mess — she wasn’t able to do it at all.”

Ms. Deaibes tried pictures and then computer eye-gaze programs that track Yuna’s eye movements. After months of Ms. Deaibes darkening the room to minimize distractions, buckling Yuna to control her jerky movements, Yuna can now stare for about three seconds, causing barn doors to open in computerized farmyards and other onscreen responses. The Lees hope to train Yuna to choose toys or books with her eyes.

At school, Yuna spends time in a regular second-grade classroom where social exposure helps her and enlightens other students, said Bridlemile’s principal, Brad Pearson. These days, she increasingly responds to her name with eye contact or sound and rarely puts school materials in her mouth anymore, said Jim Steranko, who teaches Yuna in Bridlemile’s learning resource center.

Ms. Lungershausen assists Yuna with everything, including feeding her and, with another aide’s help, changing her diapers. She recently made colorful shapes for Yuna to grab while the second-graders studied fractions. “We have our bad days,” Ms. Lungershausen said. But she said Yuna increasingly recognizes phrases like “Let’s find the library door,” recently “brought a Kleenex to her nose after being prompted” and “brought my hand to her mouth and ‘kissed’ it, deliberately, first time since I’ve known her.”

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At 41 pounds, Yuna weighs 10 pounds less than her little brother, Joon, 5, who has begun helping care for his older sister. One day, after Yuna’s state-funded caregiver, Anne Marie Nguyen, bathed her and propped her in a baby play center to dry her, Joon, announcing he had finished “going potty,” brushed Yuna’s hair. Seeing her rip the bathroom thermostat’s cover off, Joon pulled Yuna’s hands from the wall, saying, “Don’t touch that.”

When Soo-Kyung returned home after lab work involving gene manipulation in mouse and chicken brains, she crouched on the playroom carpet, watching Yuna commando crawl and elbow herself to a sitting position. She lifted Yuna into the special walker, called a gait trainer and, waving toys, coaxed her to propel the contraption with her feet.

Then came Yuna’s nightly FaceTime visit with her grandparents in South Korea, who sing and show pictures as Yuna intermittently eyes the screen. Later, Jae played guitar, while Soo-Kyung held Yuna, keeping her rangy arms from tearing into the instrument. Yuna smiled and bobbed.

Soo-Kyung rarely used to mention her daughter to fellow scientists, but recently began thanking Yuna during presentations. “I was afraid every day that she might not be with me the next day,” Soo-Kyung said, voice breaking. “But she’s done amazing things that we wouldn’t dare to dream. So, how can anyone say she will never be able to do this, she will never be able to do that?”

They carried Yuna upstairs to her giant crib, her body arching elastically. Carting her up and down is getting harder, so the Lees expect to move from the three-level, cliff-side house they bought to be closer, for Yuna’s sake, to the hospital and their labs. With breathtaking views of Mount St. Helens, it is an optimist’s house, where it is possible to see beyond the horizon.