My previous blog, DNA Points to Design, was about some fascinating information about DNA. Scientists have also determined another factor in how incredibly fine-tuned even a cell is.

Stephen Meyer, in chapter 9 of his book Signature in the Cell: DNA and the Evidence for Intelligent Design, entitled Odds and Ends, talks about the odds of a minimally complex cell coming into existence. As I have said elsewhere on this site, I’m a math guy, so when I read numbers, it really puts it in perspective for me. (I should note that Dr. Meyer’s book is actually very easy to read for the layperson (i.e. generally speaking, you and me), and covers the entire history of the scientific discovery of DNA and the cell, as well as his own inquiries and research into it.)

On pg 205, he talks about how even a relatively short protein, of which cells are made of, in the range of “say, 150 amino acids”, that there are approximately 10^195 possible combinations. I’ve previously explained the scientific method of writing numbers here, but to quote myself:

Let’s start with something small. The generally accepted age of the universe is around 13.8 billion years. When you translate that into seconds, the number of seconds that have passed in the entire history of the universe is 10^17, also known as 10 to the power of 17. This is 1 followed by 17 zeroes. Or 100,000,000,000,000,000. When you start dealing with incredibly large numbers, it’s easier to write 10^17. This is called the scientific notation.

So the number of seconds that have passed in the universe is 10^17. Or 1 followed by 17 zeroes.

The number of estimated cells in the human body is 10^14. Or 1 followed by 14 zeroes.

The number of sub-atomic particles in the known universe is 10^80. Or 1 followed by 80 zeroes.

Just like in that blog, these numbers will help put the rest of this blog in perspective.

Back to Dr. Meyer’s book and the Odds and Ends chapter. He discusses how “the probability of building a chain of 150 amino acids in which all linkages are peptide linkages” (or the linkages that bond together the amino acids of DNA) is roughly 1 chance in 10^45. (pg 206)

He also explains that

…in nature every amino acid found in proteins…has a distinct mirror image of itself; there is one left-handed version, or L-form, and one right-handed version, or D-form…The probability of attaining, at random, only L-amino acids in a hypothetical peptide chain 150 amino acids long is…again roughly 1 chance in 10^45.

(Pg 206-207)

On page 209, he begins to tell the story of Douglas Axe, who earned his Ph. D. at Caltech and was at Cambridge University researching the question of “How rare, or common, are the amino acid sequences that produce the stable folds that make it possible for proteins to perform their biological functions?”

The results of a paper he published in 2004 were particularly telling. Axe performed a mutagenesis experiment using his refined method on a functionally significant 150-amino-acid section of a protein called betalactamase, an enzyme that confers antibiotic resistance uopn bacteria. On the basis of his experiments, Axe was able to make a careful estimate of the ratio of (a) the number of 150-amino-acid-sequences that can perform that particular function to (b) the whole set of possible amino-acid sequences of this length. Axe estimated this ratio to be a 1 to 10^77. 

(Pg 210, Emphasis mine)

The next 2 paragraphs explain that Axe further determined that regarding the odds of finding any functional protein whatsoever within a space of combinational possibilities, the odds go down to 1 to 10^74.

Since proteins can’t perform functions unless they first fold into stable structures, Axe’s measure of the frequency of folded sequences also provided a measure of the frequency of functional proteins – any functional proteins – within that space of possibilities (or “sequence space”). Indeed, by taking what he knew about protein folding into account, Axe estimated the ratio of (a) the number of 150-amino-acid sequences that produce any functional protein whatsoever to (b) the whole set of possible amino-acid sequences of that length. Axe’s estimated ratio of 1 to 10^74 implied that the probability of producing any properly sequenced 150-amino-acid protein at random is also about 1 to 10^74.  In other words, a random process producing amin-acid chains of this length would stumble onto a functional protein only about once in every 10^74 attempts.

(Pg 210-211, emphasis his).

The next couple of paragraphs discuss how Axe research built on the works of others before him.

…the odds are prohibitively stacked against a random process producing functional proteins. Functional proteins are exceedingly rare among all the possible combinations of amino acids.

Axe’s improved estimate of how rare functional proteins are within “sequence space” has now made it possible to calculate the probability that a 150-amino-acide compound assembled by random interactions in a prebiotic soup would be a functional protein. This calculation can be made by multiplying the three independent probabilities by one another: the probability of incorporating only peptide bonds (1 in 10^45), the probability of incorporating only left-handed amino acids (1 in 10^45), and the probability of achieving correct amino-acid sequencing (using Axe’s 1 in 10^74 estimate). Making that calculation (multiplying the separate probabilities by adding their exponents: 10^45+45+74) gives a dramatic answer. The odds of getting even one functional protein of modest length (150 amino acids) by chance from a prebiotic soup is no better than 1 chance in 10^164.

(Pg 211-212, emphasis mine)

This number is more than the number of subatomic particles (protons, electrons, and neutrons) in the known universe SQUARED! Meyer then puts it in perspective:

It is impossible to convery what this number represents, but let me try. We have a colloquial expression in English, “That’s like looking for a needle in a haystack.” We understand from this expression that finding a needle will be difficult because the needle – the thing we want – is mixed in with a great number of other things we don’t want. to have a realistic chance of finding the needle, we will need to search for a long, long time. Now consider that there are only 10^80 protons, neutrons, and electrons in the observable univserse. Thus, if the odds of finding a functional protein by chance on the first attempt had been 1 in 10^80, we could have said that’s like finding a marked particle – proton, neutron, or electron (a much smaller needle) – among all the particles in the universe (a much larger haystack). Unfortunately, the problem is much worse than that. With the odds standing at 1 chance in 10^164 of finding a functional protein among the possible 150-amino-acid compounds, the probability is 84 orders of magnitude (or powers of ten) smaller than the probability of finding the marked particle in the whole universe. Another way to say that is the probability of finding a functional protein by chance alone is a trillion, trillion, trillion, trillion, trillion, trillion, trillion times smaller than the odds of finding a single specified particle among all the particles in the universe.

(pg 212, emphasis of the last sentence is mine)

Hopefully, you are starting to see how much of a problem this is. But just as Vizzini had only just begun in his battle of wits against the dread pirate Roberts, Meyer has only just begun to put this in perspective.

And the problem is even worse than this for at least two reasons. First, Axe’s experiments calculated the odds of finding a relatively short protein by chance alone. More typical proteins have hundreds of amino acids, and in many cases their function requires close association with other protein chains. For example, the typical RNA polymerase – the large molecular machine the cell uses to copy genetic information during transcription… – has over 3,000 functionally specified amino acids. The probability of producing such a protein and many other necessary proteins by chance would be far smaller than the odds of producing a 150-amino-acid protein.

Second, as discussed, a minimally complex cell would require many more proteins than just one. Taking this into account only causes the improbability of generating the necessary proteins by chance – or the genetic information to produce them – to balloon beyond comprehension. In 1983 distinguished British cosmologist Sir Fred Hoyle calculated the odds of producing the proteins necessary to service a simple one-celled organism by chance at 1 in 10^40,000. At that time, scientists could have questioned his figure. Scientists knew how long proteins were and roughly how many protein types there were in simple cells. But since the amount of functionally specified information in each protein had not yet been measured, probability calculations like Hoyle’s required some guesswork.

I’ve already written about Hoyle in my blog Infinite Time Plus Chance. In that blog, I quoted Paul E. Little’s Know Why You Believe:

Hoyle then explains that it would be equally as difficult for the accidental formation of only one of the many chains of amino acids in a living cell in which there are about 200,000 such amino acids. Now if you would compute the time required to get all 200,00 amino acids for one human cell to come together by chance, it would be about 293.5 times the estimated age of the earth (set at the standard 4.6 billion years). The odds against this happening would be far greater than a blindfolded person trying to solve the Rubik’s Cube!

In another analogy Hoyle bolsters his argument. He likens this to a “junkyard mentality” and asks, “What are the chances that a tornado might blow through a junkyard containing all the parts of a 747, accidentally assembling them into a plane, and leave it ready for takeoff?” Hoyle answers, “The possibilities are so small as to be negligible even if a tornado were to blow through enough junkyards to fill the whole universe!”

Back to Meyer’s book, he now delivers the punchline:

If we assume that a minimally complex cell needs at least 250 proteins of, on average, 150 amino acids and that the probability of producing just one such protein is 1 in 10^164 as calculated above, then the probability of producing all the necessary proteins needed to service a minimally complex cell is 1 in 10^164 multiplied by itself 250 times, or 1 in 10^41,000.

(pg 213, Emphasis mine).

Did you catch that? The odds of a minimally complex cell forming randomly by chance is 1 in 10^41,000!

Dr. Meyer finishes this with:

This kind of number allows a great amount of quibbling about the accuracy of various estimates without altering the conclusion. The probability of producing the proteins necessary to build a minimally complex cell – or the genetic information necessary to produce those proteins – by chance is unimaginably small.

(pg 213)