“This takes us a lot further than we have been,” said Dr. Avindra Nath, a senior investigator for the National Institute of Neurological Disorders and Stroke, who was not involved in either study. “Coming from two entirely different laboratories with two entirely different techniques, we are now at the point where we can say we have a candidate virus to study.”

Enteroviruses have been suspected in A.F.M., partly because of its similarity to polio, a type of enterovirus now vanquished by vaccines in most countries, including the United States. Also, the recent every-other-year A.F.M. surges have occurred between August and October, when certain enteroviruses flourish.

The strongest suspect has been enterovirus D68 (EV-D68) because the Centers for Disease Control and Prevention has found that increased A.F.M. cases often coincided with greater prevalence of EV-D68. Also, EV-D68 can produce A.F.M.-like symptoms in mice. Another possible suspect is enterovirus A71 (EV-A71).

But finding evidence is difficult. A.F.M.’s paralysis and weakness usually occur days after common cold symptoms.

And while enteroviruses have been detected in stool and respiratory mucus of some A.F.M. patients, substantiating a role in neurological disease requires evidence involving cerebrospinal fluid, which circulates in the brain and spinal cord. But enteroviruses dissipate quickly from this fluid. The C.D.C. has found enteroviruses (EV-D68, EV-A71 or Coxsackievirus) in cerebrospinal fluid in only four of the 590 cases since 2014.

The Nature Medicine study involved nearly 500,000 DNA protein fragments from thousands of viruses that infect humans and other vertebrates or are carried by mosquitoes and ticks, said the senior author, Dr. Michael R. Wilson, a U.C.S.F. neurologist specializing in mysterious neurological illnesses.

Using a technique called phage display, each fragment was inserted into a bacteriophage, a type of virus that sticks to bacteria. Each bacteriophage displayed a specific fragment on its surface like a billboard. Then the researchers incubated a “soup” of bacteriophages with a patient’s spinal fluid sample, Dr. Wilson said.