Chance, probability and the origin of life

Calculating the probability that a protein – a molecule essential to life – could have formed by chance.

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Peptide bond

بسم الله الرحمٰن الرحيم، وصلوات الله وسلامه على أشرف المرسلين

In the name of God, Most Gracious, Most Merciful.

I’m currently reading a book called Signature in the Cell: DNA and the Evidence for Intelligent Design by Stephen C. Meyer. The book makes lots of well-argued points as well as convincing rebuttals of Darwinist arguments. I plan on writing a detailed review of the book after finishing it, In Sha Allah (God willing). For now, I want to focus on one particular aspect of the book that I found quite intriguing: the probability of life arising out of chance.

How the Cell Works (sort of)

Before getting into the argument, I’ll give a quick overview of some of the necessary scientific knowledge. If you are familiar with how the biological cell works at a molecular level you can skip this section, otherwise keep reading. Keep in mind that I’m only covering an extremely tiny aspect of one of the many functions of the cell, so this is by no means a complete description. Also, my knowledge is quite sketchy – if I make a mistake please let me know and I’ll correct it.

DNA is where information in the cell is encoded, stored as a highly-specified series of nucleotide bases. The cell reads information from the DNA and constructs proteins by assembling amino acids. Each 3-nucleotide sequence corresponds to 1 amino acid (out of a possible 20). This is not a one-to-one function, as there are 43 = 64 possible bases and only 20 amino acids. See page 102 of the book for a handy table.

The problem is: DNA itself is formed by proteins. When DNA replicates, it is proteins – themselves formed by decoding DNA sequences – that do the job. So this creates a chicken-and-egg scenario: which came first, the DNA or the proteins?

There are various reasons to rule out DNA arising first, which will not be the subject of this post. If requested, I could deal with it in another post though. One reason is that the DNA molecule is full of information. Chance or purely materialistic processes do not produce information. Another reason is that DNA has no way to self-replicate without the help of proteins. Again, I don’t want to go into detail about that in this post. If you want to learn more, either read the book or ask me and I’ll write a blog post about that topic.

The Probability of a Materialistic Explanation

So that means we have to explain how protein arose via purely materialistic mechanisms. For simplicity’s sake, I’ll presume the existence of amino acids. A protein is a chain of amino acids.

According to biologists, the simplest protein must have at least 150 amino acids. We’ll use this as our number since we’re looking for the probability that the least complex protein could have arisen by chance. I will denote the probability of this event happening as “P.”

First of all, amino acids can form two kinds of bonds with each other – peptide bonds or non-peptide bonds. It has been observed in nature that these kinds of bonds occur with equal frequency, so probability of two amino acids forming a peptide bond with each other is 1/2. The problem is: proteins require that all bonds between amino acids are peptide bonds. A protein of length 150 (amino acids) has 149 bonds, so the probability of all of them being peptide bonds is 1 in 2149, or roughly 1 in 1045.

Next, every amino acid (with 1 exception) can either be “left-handed” or (a mirror image of itself) “right-handed.” But functional proteins require that all amino acids are left-handed. Left-handed and right-handed varieties of amino acids occur with equal probability in nature, so again we’re looking at a 1 in 2 chance for a single amino acid. For a string of 150, that reduces to 1 in 2150, or approximately 1 in 1045.

Third, we have to calculate what proportion of possible amino acid combinations produce proteins that can fold into the proper structure and perform a biological function. In other words, this is the ratio of “working” proteins to just chains of amino acids. The number of possible 150 amino acid combinations is pretty huge, since there are 20 amino acids. The number of proteins divided by the number of possible amino acid sequences equals 1 in 1074.

So we need the probability of all three of the above-described events happening (All bonds formed are peptide bonds) AND (all amino acids are left-handed) AND (the combination is a working protein).

Probability theory says that when you see the word “and” (i.e., all of those conditions are necessary), you have to multiply the probabilities. That yields:

P = (1/1045) * (1/1045) * (1/1074) = 1/1045+45+74 = 1/10164.

This number is unimaginably small. But before I give you an idea of how small it is, I want to address a popular but misguided counter-argument. Some people say that we witness extremely improbable things happen all the time. For example, if you flip a coin 1000 times you will get a particular sequence (we’ll call it S). Before you had started flipping, the probability of you getting S had been 1 in 21000 which is about 1 in 10301. This is many orders of magnitude smaller than P, but it still happens – all you have to do is flip a coin 1000 times, or have 10 people flip a coin 100 times each. So that means this “probability game” doesn’t really work, right?

Wrong. Repeat the experiment. Try to reproduce S by flipping a random coin 1000 times. You will never be able to. Why? Because now we have specified the sequence you’re looking for. We’re not just looking for some random string of heads and tails, we’re looking for a specific sequence. That’s what makes the protein-by-chance problem so hard: the patterns we’re looking for are highly specific.

How Small That Number Actually Is

Anyway, let’s get back to the subject. I was trying to demonstrate how mind-bogglingly small P is. There are 1080 particles in the entire observable universe. Imagine if I selected one of those particles at random and told you to pick a random one as well. The probability that yours matched mine would be minute. The actual number would be 1 * 1/1080, where the first number is 1 because I could have chosen any particle. But that’s still 84 orders of magnitude smaller than P. So the probability of making a functional protein via chance is a trillion, trillion, trillion, trillion, trillion, trillion, trillion times smaller than finding a specific small particle in the entire known universe.

If you’re still not convinced, I’ll try a simple thought experiment. I’ll give you the entire universe, the laws of physics, and space-time itself to try to come up with a functional protein by chance. Here’s how it works:

Let’s say that every particle in the universe got magically turned into an amino acid – 1080 in total. 1016 seconds have elapsed since the Big Bang, so we’ll wind back the clock to the beginning and give you those too. Let’s say that the particles were interacting once every “Planck time.”

A Planck time is equal to the time light takes to travel one Planck length. Light travels unimaginably fast, reaching from Earth to the moon in just over 1 second. But a Planck length is insanely tiny. Wikipedia says:

If a particle or dot about 0.1 mm in size (which is at or near the smallest the unaided human eye can see) were magnified in size to be as large as the observable universe, then inside that universe-sized “dot”, the Planck length would be roughly the size of an actual 0.1 mm dot. In other words, the universe is to a visible dot as a visible dot is to a Planck dot.

For the sake of generosity, we’ll say that every particle experiences a new chemical reaction once every Planck time, or 1043 times per second. That means that the total number of reactions is:

(1016 seconds since Big Bang) * (1043 reactions per second) * (1080 amino acids total) = 10139 reactions. P = 1/10164, so multiplying these numbers yields 10139/10164 = 1/1025.

In other words: If all the particles in the universe were amino acids, and they were continuously reacting with each other since the Big Bang at a rate of 1043 times per second, the probability of a functional protein of even minimum length arising by chance would still be just 1/1025. That’s less than 1 out of a trillion trillion.

My first thought upon encountering that number is: holy crap, that is a tiny probability! My second thought is: wait, do people actually believe this stuff? And then have the nerve to call themselves rationalists? Apparently, they do, and what’s worse is that it’s being taught at schools and colleges across America. For example, a popular Biochemistry textbook claims that “the first semblance of life appeared through the chance association of a number of abiotically formed macromolecular components” (Albert L. Lehninger, Biochemistry: The Molecular Basis of Cell Structure and Function, p. 782, my emphasis).

Anyway, I have a lot more to say about this book and this subject in general, so stay tuned.

Salaam,

~ Yousuf

24 December 2014

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