by Sam Kean
Even worse, radioactivity can delete chunks of DNA. Higher creatures have to pack their many coils of DNA into tiny nuclei; in humans, six linear feet cram into a space less than a thousandth of an inch wide. This intense scrunching often leaves DNA looking like a gnarly telephone cord, with the strand crossing itself or folding back over itself many times. If gamma rays happen to streak through and snip the DNA near one of these crossing points, there will be multiple loose ends in close proximity. Cells don’t “know” how the original strands lined up (they don’t have memories), and in their haste to fix this catastrophe, they sometimes solder together what should be separate strands. This cuts out and effectively deletes the DNA in between.
So what happens after these mutations? Cells overwhelmed with DNA damage can sense trouble and will kill themselves rather than live with malfunctions. This self-sacrifice can spare the body trouble in small doses, but if too many cells die at once, whole organ systems might shut down. Combined with intense burns, these shutdowns led to many deaths in Japan, and some of the victims who didn’t die immediately probably wished they had. Survivors remember seeing people’s fingernails fall off whole, dropping from their fists like dried shell pasta. They remember human-sized “dolls of charcoal” slumped in alleys. Someone recalled a man struggling along on two stumps, holding a charred baby upside down. Another recalled a shirtless woman whose breasts had burst “like pomegranates.”
During his torment in the air-raid shelter in Nagasaki, Yamaguchi—bald, boily, feverish, half deaf—nearly joined this list of casualties. Only dedicated nursing by his family pulled him through. Some of his wounds still required bandages and would for years. But overall he traded Job’s life for something like Samson’s: his sores mostly healed, his strength returned, his hair grew back. He began working again, first at Mitsubishi, later as a teacher.
Far from escaping unscathed, however, Yamaguchi now faced a more insidious, more patient threat, because if radioactivity doesn’t kill cells outright, it can induce mutations that lead to cancer. That link might seem counterintuitive, since mutations generally harm cells, and tumor cells are thriving if anything, growing and dividing at alarming rates. In truth all healthy cells have genes that act like governors on engines, slowing down their rpm’s and keeping their metabolisms in check. If a mutation happens to disable a governor, the cell might not sense enough damage to kill itself, but eventually—especially if other genes, like those that control how often a cell divides, also sustain damage—it can start gobbling up resources and choking off neighbors.
Many survivors of Hiroshima and Nagasaki absorbed doses of radiation a hundred times higher—and in one gulp—than the background radiation a normal person absorbs in a year. And the closer survivors got caught to the epicenter, the more deletions and mutations appeared in their DNA. Predictably, cells that divide rapidly spread their DNA damage more quickly, and Japan saw an immediate spike in leukemia, a cancer of prolific white blood cells. The leukemia epidemic started to fade within a decade, but other cancers gained momentum in the meantime—stomach, colon, ovary, lung, bladder, thyroid, breast.
As bad as things were for adults, fetuses proved more vulnerable: any mutation or deletion in utero multiplied over and over in their cells. Many fetuses younger than four weeks spontaneously aborted, and among those that lived, a rash of birth defects, including tiny heads and malformed brains, appeared in late 1945 and early 1946. (The highest measured IQ among the handicapped ones was 68.) And on top of everything else, by the late 1940s, many of the quarter-million hibakusha in Japan began to have new children and pass on their exposed DNA.
Experts on radiation could offer little advice on the wisdom of hibakusha having children. Despite the high rates of liver or breast or blood cancer, none of the parents’ cancerous DNA would get passed to their children, since children inherit only the DNA in sperm and eggs. Sperm or egg DNA could still mutate, of course, perhaps hideously. But no one had actually measured the damage of Hiroshima-like radiation on humans. So scientists had to work on assumptions. Iconoclastic physicist Edward Teller, father of the H-bomb (and RNA Tie Club member), went around suggesting that small pulses of radiation might even benefit humanity—that for all we knew, mutations goosed our genomes. Even among less reckless scientists, not everyone predicted fairy-tale monstrosities and babes with two heads. Hermann Muller had prophesied in the New York Times about future generations of Japanese misfortune, but his ideological opposition to Teller and others may have colored his commentary. (In 2011 a toxicologist, after perusing some now-declassified letters between Muller and another colleague, accused them both of lying to the government about the threat that low doses of radioactivity posed for DNA, then manipulating data and later research to cover themselves. Other historians dispute this interpretation.) Even with high doses of radioactivity, Muller ended up backing away from and qualifying his dire early predictions. Most mutations, he reasoned, however harmful, would prove recessive. And the odds of both parents having flaws in the same gene were remote. So at least among the children of survivors, Mom’s healthy genes would probably mask any flaws lurking in Dad’s, and vice versa.
But again, no one knew anything for certain, and a sword hung over every birth in Hiroshima and Nagasaki for decades, compounding all the normal anxieties of being a parent. This must have been doubly true for Yamaguchi and his wife, Hisako. Both had regained enough vigor by the early 1950s to want more children, no matter the long-term prognosis. And the birth of their first daughter, Naoko, initially supported Muller’s reasoning, as she had no visible defects or deformities. Another daughter followed, Toshiko, and she too proved healthy. However bouncing they were at birth, though, both Yamaguchi daughters endured sickly adolescences and adulthoods. They suspect they inherited a genetically compromised immune system from their twice-bombed father and once-bombed mother.
And yet in Japan generally, the long-feared epidemic of cancers and birth defects among children of hibakusha never materialized. In fact no large-scale studies have ever found significant evidence that these children had higher rates of any disease, or even higher rates of mutations. Naoko and Toshiko may well have inherited genetic flaws; it’s impossible to rule out, and it sure sounds true, intuitively and emotionally. But at least in the vast majority of cases, genetic fallout didn’t settle onto the succeeding generation.*
Even many of the people directly exposed to atomic radiation proved more resilient than scientists expected. Yamaguchi’s young son Katsutoshi survived for fifty-plus years after Nagasaki before dying of cancer at fifty-eight. Hisako lasted even longer, dying in 2008 of liver and kidney cancer at eighty-eight. The Nagasaki plutonium bomb probably caused both cancers, yes; but at those ages, it’s conceivable that either one would have gotten cancer anyway, for unrelated reasons. As for Yamaguchi himself, despite his double exposure at Hiroshima and Nagasaki in 1945, he lived all the way until 2010, sixty-five extra years, finally dying of stomach cancer at ninety-three.
No one can say definitively what set Yamaguchi apart—why he lived so long after being exposed, twice, while others died from a comparative sprinkling of radioactivity. Yamaguchi never underwent genetic testing (at least not extensive testing), and even if he had, medical science might not have known enough to decide. Still, we can hazard educated guesses. First, his cells clearly did a hell of a job repairing DNA, both single-strand breaks and deadly doubles. It’s possible he even had slightly superior repair proteins that worked faster or more efficiently, or certain combinations of repair genes that worked especially well together. We can also surmise that although he could hardly have avoided some mutations, they didn’t disable key circuits in his cells. Perhaps the mutations fell along stretches of DNA that don’t code for proteins. Or perhaps his were mostly “silent” mutations, where the DNA triplet changes but the amino acid, because of redundancy, doesn’t. (If that’s the case, the kludgy DNA/RNA code that frustrated the Tie Club actually saved him.) Finally, Yamaguchi apparently avo
ided until late in life any serious damage to the genetic governors in DNA that keep would-be tumors in check. Any or perhaps all of these factors could have spared him.
Or perhaps—and this seems equally likely—he wasn’t all that special biologically. Perhaps many others would have survived just as long. And there is, dare I say it, some small hope in that. Even the most deadly weapons ever deployed, weapons that killed tens of thousands at once, that attacked and scrambled people’s biological essences, their DNA, didn’t wipe out a nation. Nor did they poison the next generation: thousands of children of A-bomb survivors remain alive today, alive and healthy. After more than three billion years of being exposed to cosmic rays and solar radiation and enduring DNA damage in various forms, nature has its safeguards, its methods of mending and preserving the integrity of DNA. And not just the dogmatic DNA whose messages get transcribed into RNA and translated into proteins—but all DNA, including DNA whose subtler linguistic and mathematical patterns scientists are just beginning to explore.*
4
The Musical Score of DNA
What Kinds of Information Does DNA Store?
Although inadvertent, a certain pun in Alice’s Adventures in Wonderland has, in recent years, developed a curious resonance with DNA. In real life, Alice’s author, Lewis Carroll, taught mathematics at Oxford University as Charles Lutwidge Dodgson, and one famous line in Alice (famous among geeks, at least) has the Mock Turtle moaning about “different branches of arithmetic—ambition, distraction, uglification, and derision.” Just before that eye roller, though, the Mock Turtle says something peculiar. He maintains that during his school days, he studied not reading and writing but “reeling and writhing.” It’s probably just another groaner, but that last term, writhing, has piqued the interest of some mathematically savvy DNA scientists.
Lewis Carroll’s Mock Turtle cried over memories of studying “reeling and writhing” in school, a complaint that resonates with modern DNA research into knots and tangles. (John Tenniel)
Scientists have known for decades that DNA, a long and active molecule, can tangle itself into some horrific snarls. What scientists didn’t grasp was why these snarls don’t choke our cells. In recent years, biologists have turned to an obscure twig of mathematics called knot theory for answers. Sailors and seamstresses mastered the practical side of knots many millennia ago, and religious traditions as distant as Celtic and Buddhist hold certain knots sacred, but the systematic study of knots began only in the later nineteenth century, in Carroll/Dodgson’s Victorian Britain. At that time the polymath William Thomson, Lord Kelvin, proposed that the elements on the periodic table were really microscopic knots of different shapes. For precision’s sake, Kelvin defined his atomic knots as closed loops. (Knots with loose ends, somewhat like shoelaces, are “tangles.”) And he defined a “unique” knot as a unique pattern of strands crossing over and under each other. So if you can slide the loops around on one knot and jimmy its over-under crossings to make it look like another, they’re really the same knot. Kelvin suggested that the unique shape of each knot gave rise to the unique properties of each chemical element. Atomic physicists soon proved this clever theory false, but Kelvin did inspire Scottish physicist P. G. Tait to make a chart of unique knots, and knot theory developed independently from there.
Much of early knot theory involved playing cat’s cradle and tallying the results. Somewhat pedantically, knot theorists defined the most trivial knot—O, what laymen call a circle—as the “unknot.” They classified other unique knots by the number of over-under crossings and by July 2003 could identify 6,217,553,258 distinct knots with up to twenty-two over-under do-si-dos—roughly one knot per person on earth. Meanwhile other knot theorists had moved beyond taking simple censuses, and devised ways to transform one knot into another. This usually involved snipping the string at an under-over crossing, passing the top strand below, and fusing the snipped ends—which sometimes made knots more complicated but often simplified them. Although studied by legitimate mathematicians, knot theory retained a sense of play throughout. And America’s Cup aspirants aside, no one dreamed of applications for knot theory until scientists discovered knotted DNA in 1976.
Knots and tangles form in DNA for a few reasons: its length, its constant activity, and its confinement. Scientists have effectively run simulations of DNA inside a busy nucleus by putting a long, thin rope in a box and jostling it. The rope ends proved quite adept at snaking their way through the rope’s coils, and surprisingly complicated knots, with up to eleven crossings, formed in just seconds. (You probably could have guessed this if you’ve ever dropped earphones into a bag and tried to pull them out later.) Snarls like this can be lethal because the cellular machinery that copies and transcribes DNA needs a smooth track to run on; knots derail it. Unfortunately, the very processes of copying and transcribing DNA can create deadly knots and tangles. Copying DNA requires separating its two strands, but two interlaced helix strands cannot simply be pulled apart, any more than plaits of tightly braided hair can. What’s more, when cells do start copying DNA, the long, sticky strings dangling behind sometimes get tangled together. If the strings won’t disentangle after a good tug, cells commit suicide—it’s that devastating.
Beyond knots per se, DNA can find itself in all sorts of other topological predicaments. Strands can get welded around each other like interlocking links in a chain. They can get twisted excruciatingly tight, like someone wringing out a rag or giving a snake burn on the forearm. They can get wound up into coils tenser than any rattlesnake. And it’s this last configuration, the coils, that loops back to Lewis Carroll and his Mock Turtle. Rather imaginatively, knot theorists refer to such coils as “writhes” and refer to the act of coiling as “writhing,” as if ropes or DNA were bunched that way in agony. So could the Mock Turtle, per a few recent rumors, have slyly been referring to knot theory with his “reeling and writhing”?
On the one hand, Carroll was working at a prestigious university when Kelvin and Tait began studying knot theory. He might easily have come across their work, and this sort of play math would have appealed to him. Plus, Carroll did write another book called A Tangled Tale in which each section—called not chapters but “knots”—consisted of a puzzle to solve. So he certainly incorporated knotty themes into his writing. Still, to be a party pooper, there’s good reason to think the Mock Turtle knew nothing about knot theory. Carroll published Alice in 1865, some two years before Kelvin broached the idea of knots on the periodic table, at least publicly. What’s more, while the term writhing might well have been used informally in knot theory before, it first appeared as a technical term in the 1970s. So it seems likely the Mock Turtle didn’t progress much past ambition, distraction, uglification, and derision after all.
Nevertheless, even if the punniness of the line postdates Carroll, that doesn’t mean we can’t enjoy it today. Great literature remains great when it says new things to new generations, and the loops of a knot quite nicely parallel the contours and convolutions of Carroll’s plot anyway. What’s more, he probably would have delighted at how this whimsical branch of math invaded the real world and became crucial to understanding our biology.
Different combinations of twists and writhes and knots ensure that DNA can form an almost unlimited number of snarls, and what saves our DNA from this torture are mathematically savvy proteins called topoisomerases. Each of these proteins grasps one or two theorems of knot theory and uses them to relieve tension in DNA. Some topoisomerases unlink DNA chains. Other types nick one strand of DNA and rotate it around the other to eliminate twists and writhes. Still others snip DNA wherever it crosses itself, pass the upper strand beneath the lower, and re-fuse them, undoing a knot. Each topoisomerase saves our DNA from a Torquemada-style doom countless time each year, and we couldn’t survive without these math nerds. If knot theory sprang from Lord Kelvin’s twisted atoms and then went off on its own, it has now circled back to its billions-of-years-old molecular roots in DNA.
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nbsp; Knot theory hasn’t been the only unexpected math to pop up during DNA research. Scientists have used Venn diagrams to study DNA, and the Heisenberg uncertainty principle. The architecture of DNA shows traces of the “golden ratio” of length to width found in classical edifices like the Parthenon. Geometry enthusiasts have twisted DNA into Möbius strips and constructed the five Platonic solids. Cell biologists now realize that, to even fit inside the nucleus, long, stringy DNA must fold and refold itself into a fractal pattern of loops within loops within loops, a pattern where it becomes nearly impossible to tell what scale—nano-, micro-, or millimeter—you’re looking at. Perhaps most unlikely, in 2011 Japanese scientists used a Tie Club–like code to assign combinations of A, C, G, and T to numbers and letters, then inserted the code for “E = mc2 1905!” in the DNA of common soil bacteria.
DNA has especially intimate ties to an oddball piece of math called Zipf’s law, a phenomenon first discovered by a linguist. George Kingsley Zipf came from solid German stock—his family had run breweries in Germany—and he eventually became a professor of German at Harvard University. Despite his love of language, Zipf didn’t believe in owning books, and unlike his colleagues, he lived outside Boston on a seven-acre farm with a vineyard and pigs and chickens, where he chopped down the Zipf family Christmas tree each December. Temperamentally, though, Zipf did not make much of a farmer; he slept through most dawns because he stayed awake most nights studying (from library books) the statistical properties of languages.