Lost in Sequence Space

The Darwinian Mechanism's Problem of Ballooning Improbabilities

In April 1966, some leading mathematicians and biologists met in Philadelphia to debate the subject of evolutionary theory. The mathematicians were skeptical of the theory.

One of them, MIT professor Murray Eden, compared genetic information to computer software. When you randomly alter lines of computer code over and over, you don't get a flowering of new and better computer programs, he noted. You get a degraded or broken program. "No currently existing formal language can tolerate random changes in the symbol sequences which express its sentences," he said. "Meaning is almost invariably destroyed."¹ He suggested that the DNA software in our cells faces the same constraints. It's a matter of low probabilities. The problem is that there are vastly more ways to arrange genetic sequences into nonfunctional gibberish than into functional genetic text.

Two decades later the Australian geneticist Michael Denton made the same point in Chapter 13 of Evolution: A Theory in Crisis. He used the English language to illustrate his point. He noted that, with short words, say of three letters, you can randomly alter one letter at a time and quickly luck onto one three-letter word after another, and so end up with a very different but actual word. That's because the fraction of three-letter English words to all possible three-letter combinations isn't terribly small.

There are 26 x 26 x 26 (263) three-letter combinations—17,576. According to the Scrabble dictionary, there are just over a thousand three-letter words in English. So there is one meaningful three-letter combination for about every seventeen gibberish combinations. If genetic information is like three-letter English words in this regard, then random mutations might be able to luck upon new functional texts and evolve all manner of changes over time.

But now consider seven-letter English words. There are tens of thousands of those, but there are eight billion possible seven-letter combinations, so for every meaningful combination, there are some 80,000 gibberish combinations.

Notice what happened. In going from three-letter words to seven-letter words, we've gone from one chance in 17, to one chance in 80,000.

This is a general pattern. As the length of the letter sequence grows, the ratio of gibberish combinations to meaningful combinations rises geometrically. And if we're talking about an entire sentence rather than a single word, the ratio is unimaginably large.

We grasp this general pattern intuitively. If a kitten pawing at your keyboard happened to type a three-letter word, you'd be surprised but not blown away (unless it was the word cat!). But if the kitten typed out a lengthy English sentence, you'd probably freak out, because intuitively you get that the chances of lucking onto a sentence are far, far lower than lucking onto a three-letter word.

Denton suggested that genetic information is much more akin to sentences than to three-letter words. Why? The various kinds of proteins are biology's most basic toolkit for getting things done. Without a wide variety of highly distinct protein tools, each with a quite distinct sequence of amino acid "letters," nothing in biology gets done. Proteins are the smallest functional structural unit in biology, and each type is, on average, a few hundred amino acids long. So when the evolutionary process fiddles with proteins, it's fiddling with what amount to lengthy biological sentences. Given what we know about long English sentences, we can expect nonfunctional amino acid sequences to outstrip functional amino acid sequences by many orders of magnitude.

That is, if the analogy holds. If it does, then random processes, even aided by natural selection, will never be able to traverse an evolutionary pathway from one functioning protein tool to a fundamentally different one. This means that mindless evolution could not have created the many protein tools essential to life.

The Problem of Limits

Understand, neither the skeptical mathematicians nor Denton rejected the idea of random mutations generating minor evolutionary changes and natural selection preserving them. Such changes are widely observed and non-controversial.

Consider an illustration. An alcoholic descendent of Charles Darwin gets drunk on 40-proof eggnog at a holiday party. When his young son scolds him in front of the guests, the drunkard insists the boy's mother punish the boy by taking him to his room to type out a sentence a thousand times. The mother, hoping to prick her husband's conscience when he wakes the next morning, has the boy type out, "Daddy Darwin was trapped by the nog."

It's dull work and occasionally the boy makes a typo—a chance mutation if you will. Most of these simply spoil the sentence. "Daddy Darwin was grapped by the nog." Grapped? Doesn't mean anything. He deletes the sentence and continues on. But a few typos yield meaningful variations. "Daddy Darwin was trapped by the dog." He pictures a snarling bulldog cornering his drunken father. The boy likes that one and keeps it.

Other meaningful chance variations during his interminable stint at the keyboard include his father being trapped by a bog, a log, a cog, and a fog.

At one point in the typing marathon his father is "tapped" by the nog. The boy decides that typo has a delicious poetic flare, a distinct improvement over the original. He begins typing that variation out instead of the original, and eventually another typo produces "Daddy Darwin was rapped by the nog." Hilarious! He loves it. His father was rapped on the head by the 40-proof eggnog—exactly!

Later in the typing marathon his poor father is "raped by the nog." Unsettling, to be sure, but the boy, better than anyone, knows that alcohol does dreadful violence to his father. The metaphor is disturbing but accurate—another improvement,
he decides. This now becomes the sentence he copies.

And so it goes. By the end, the boy has had to erase scores of meaningless sentences, but he's kept a dozen or so variations, and via a series of random but meaningful variations, the sentence has evolved all the way to "Baddy Darwin was raped by the nog." Many other variations are possible in this 28-character sequence (a sequence that includes spaces and a period), but because the number of gibberish sequences for a text of this length is mind-blowingly larger than the number of possible meaningful sentences of that length, the sentence as it is cannot reach the vast majority of radically different sentences of this length. It's stuck on an island of reachable meaningful sequences, with no access to whole continents of other dramatically different sentences too far away in sequence space to be reached one small mutation at a time, with each step encoding a meaningful English sentence.

This story illustrates how the neo-Darwinian mechanism of natural selection acting on random variations could generate some measurable changes, but also why it might get stuck at the level of microevolution—at, say, altering the beak size of a bird species, or the color of a bear's fur, or the size of a horse. An organism's DNA plays a central role in coding for its form and function. Occasionally there is a "typo" in the genetic text, a random mutation. Most of these are neutral or unhelpful. The unhelpful ones have a good chance of being discarded, since a less fit plant or animal is less likely to survive, reproduce, and pass its genes down to the next generation. The muffed genetic sentence is eliminated from the gene pool. But if an offspring contains a genetic typo that confers an advantage in its ecological niche, that mutation has a decent chance of being passed down to other generations.

Later that variation may get augmented by another helpful typo. And then another. And another. How far can this process take the organism's descendants? The mathematicians at the Wistar gathering, and subsequently Michael Denton, suggested there were severe limits. The biologists at Wistar took the opposite view. They insisted the analogy to computer software must be misleading.

Evidential Support

What does the evidence suggest? In the 56 years since the Philadelphia gathering, two lines of evidence have emerged suggesting that Denton and the mathematicians were correct.

One involves laboratory research on proteins. At the University of Cambridge, Douglas Axe initiated research on enzyme proteins and, specifically, on the sequences of amino-acid letters that code for these proteins. He sought to discover how rare functional amino-acid sequences are compared to dysfunctional ones. It turns out that the ratio of functional to dysfunctional sequences is so small that even with the help of natural selection, a given protein type is stuck on an island of function surrounded by vast and unbridgeable seas of nonfunction. It can handle minor changes. It can, if you will, wander out into the shallows for a dip at the beach and survive, but it can't swim across the shark-infested Pacific. It would become dysfunctional and be discarded long before it could evolve into a fundamentally different functional protein.

A grain of sand contains more than a billion times a billion atoms. The Milky Way galaxy holds hundreds of billions of stars, along with all manner of comets, planets, and space dust. Now imagine you must pick, blindfolded, one special atom in the entire Milky Way. Your chances are unimaginably bad, and yet, according to Axe's research findings, they are better than the odds of a randomly mutating protein eventually lucking onto a fundamentally different functional protein.² That's bad news for the idea that all the life around us evolved from a common ancestor through mindless evolutionary processes.

Axe's experimental work on proteins is corroborated by other laboratory work. Stephen Meyer reports:

First, at least four other studies using different methods of estimating the rarity of functional proteins have confirmed Axe's multiyear experimental study. Moreover, recent work at the Weizmann Institute in Israel buttresses Axe's original conclusions. Protein scientist Dan Tawfik has shown that protein folds lose their structural and thermodynamic stability as more and more mutations accumulate. Experimentally, Tawfik found that he could completely destroy the stability of numerous different protein folds with between three and fifteen random mutational changes. Yet to turn one protein fold into another requires many more than just fifteen mutations.³

The second line of evidence comes from research on microbes such as the malaria parasite, the HIV virus, and E. coli. This research allows us to follow tens of thousands of generations of microbes, and population numbers in the billions of trillions. These microbes do experience mutations, and occasionally there's a micromutation that creates a niche advantage. But the microbes do not evolve into a fundamentally new microbe, and the rare helpful mutations overwhelmingly involve blunting or breaking something in the microbe.

Lehigh University biologist Michael Behe compares this to tossing out the backseat of your car to improve gas mileage, or to a backdoor lock rusting shut, making it harder for a thief to break in. Both changes involve improvements of a sort, but that's not how you build anything new. It's the same with these microbes. When researchers investigate the nature of the mutations that created the niche advantage (say, when a malaria strain shows improved resistance to an anti-malaria drug), it turns out to be this sort of thing—a devolutionary mutation. It's interesting, but nothing new was built, and the microbe isn't on the way to building anything fundamentally new.

If you want a new computer program, stage play, or novel, if you want a fundamentally new machine (say, the first bicycle or the first airplane), mindless processes won't cut it. What's required is foresight, planning, and knowhow—intelligent design. The latest evidence from research into protein folding and microbes suggests the same goes for new living forms. 

Notes
1. Murray Eden, "Inadequacies of Neo-Darwinian Evolution as a Scientific Theory," Mathematical Challenges to the Neo-Darwinian Interpretation of Evolution, edited by P. S. Moorhead and M. M. Kaplan, 5–19. Wister Institute Symposium Monograph No. 5 (Liss, 1967).
2. Douglas Axe, "Estimating the Prevalence of Protein Sequences Adopting Functional Enzyme Folds," Journal of Molecular Biology 341 (2004), 1295–1315.
3. Stephen C. Meyer, Return of the God Hypothesis: Three Scientific Discoveries That Reveal the Mind Behind the Universe (HarperOne, 2021), 319. The four studies Meyer cites as corroborating Axe's work on protein folds are: K. K. Durston et al., "Measuring the Functional Sequence Complexity of Proteins," Theoretical Biology and Medical Modelling 4 (2007), 47; John Reidhaar-Olson and Robert Sauer, "Functional Acceptable Solutions in Two Alpha-Helical Regions of Lambda Repressor," Proteins: Structure, Function, and Genetics 7 (1990), 306–316; Sean V. Taylor et al., "Search Sequence Space for Protein Catalysts," Proceedings of the National Academy of Sciences USA 98 (2001), 10596–10601; H. P. Yockey, "A Calculation of the Probability of Spontaneous Biogenesis by Information Theory," Journal of Theoretical Biology 67/3 (Aug. 7, 1977), 377–398. For Tawfik, Meyer provides two citations: Nobuhiko Tokuriki and Dan S. Tawfik, "Stability Effects of Mutations and Protein Evolvability," Current Opinion in Structural Biology 19/5 (2009), 596–604; and Nobuhiko Tokuriki and Dan S. Tawfik et al., "The Stability Effects of Protein Mutations Appear to Be Universally Distributed," Journal of Molecular Biology 369/5 (June 22, 2007), 1318–1332.