# Calculating the Probability of Abiogenesis

There is a misconception prevalent in society today: the Darwinian theory of evolution by way of natural selection acting on random variation explains the origin of life. Ignoring for the moment whether or not the theory accurately explains the origin of the species, the fact of the matter is that the Darwinian theory says nothing with respect to how life began. Thus, proponents of naturalism are forced into the position of conjoining Darwinism with the theory of abiogenesis—the view that organic molecules and subsequent simple life forms first originated from inorganic substances. Naturally (excuse the pun), naturalists must posit that this process was purely unguided; all of the inorganic components of the hypothetical first living cell (hereafter, FLC) arranged themselves by chance (i.e., without the help of a guiding intelligence). Many uncritically embrace this theory, all the while oblivious to the insurmountable mathematical improbability it faces. In this post I shall lay out this improbability and offer some comparative calculations to demonstrate its unreasonableness.

In his book Signature in the Cell1, Dr. Stephen Meyer explains how building a living cell not only requires specified information, it requires a vast amount of it—and the probability of this amount of specified information arising by chance is vanishingly small. But how small? What exactly is the probability that the information necessary to build the first living cell would arise by chance alone? During Darwin’s time, it was virtually impossible to quantify the answer to this question because biologists did not know exactly how much information was necessary to build and maintain the simplest living cell. But beginning in the 1990’s, scientists began to do “minimal complexity” experiments in which they tried to reduce cellular function to its simplest form. Thus, biologists have been able to make increasingly informed estimates of the minimum number of proteins and genes that a hypothetical FLC might have needed to survive.

Mycoplasma genitalium, a tiny bacterium that inhabits the human urinary tract, is the simplest extant cell. It requires 482 proteins to perform its necessary functions and 562,000 nucleotide bases of DNA (just under 1,200 base pairs per gene) to assemble those proteins. Based upon the most conservative minimal-complexity experiments, some scientists speculate (but have not yet demonstrated) that FLC might have been able to survive with as few as 250–400 genes. Of course, building a functional cell would require much more than just the genetic information responsible for directing protein synthesis; at the very least, it would also need a suite of preexisting proteins and RNA molecules—polymerases, tRNAs, ribosomal RNAs, mRNAs, synthetases, ribosomal proteins, etc.—to process and express the information stored in DNA. Therefore, any hypothetical FLC would have required not only genetic information, but a sizable preexisting suite of proteins for processing that information. (Building such a cell also would have required other preexisting components. But I will be generous to naturalism and grant them all for the sake of the argument.)

To calculate this probability, scientists typically use a slightly indirect method. First they calculate the probability of a single functional protein of average length arising by chance alone. Then they multiply that probability by the probability of each of the other necessary proteins arising by chance. The product of these probabilities determines the probability that all the proteins necessary to service a minimally complex cell would come together by chance. Further, since measures of probability and information are related (albeit, inversely), the probability that a particular gene would arise by chance is roughly the same as the probability that its corresponding gene product (the protein that the gene encodes) would do so. For that reason, the relevant probability calculation can be made either by analyzing the odds of arranging amino acids into a functional protein or by analyzing the odds of arranging nucleotide bases into a gene that encodes that protein.

Consider the way this combinatorial problem might play itself out in the case of proteins in a hypothetical prebiotic soup. To construct even one short protein molecule of 150 amino acids by chance within the prebiotic soup there are several combinatorial problems—probabilistic hurdles—to overcome. Lets assume that FLC needs only 250 genes to survive. Now lets assume that each of these 250 genes require only a mere 150 amino acids each. At each position on the gene, any one of the 20 amino acids could occur with equal probability. What’s more, these amino acids must form a peptide bond or else they won’t fold into a functional protein. The problem is that amino acids form peptide and non-peptide bonds with equal probability. Thus, with each amino acid addition the probability of forming a peptide bond is 1/2. Therefore, for a chain 150 amino acids long, the probability of forming all peptide bonds is (1/2)$^{149}$, or about 1 in 10$^{45}$.

Next, every amino acid found in proteins (except one) has a mirror image of itself—there is a left-handed version and a right-handed version. Functional proteins tolerate only left-handed versions. Yet, in abiotic amino acid production, right-handed isomers and left-handed isomers occur with roughly equal frequency. Therefore, the probability of attaining only L-form isomers in a chain of 150 amino acids is again (1/2)$^{149}$, or approximately 1 in 10$^{45}$. Therefore, the probability of randomly forming a chain of 150 amino acids where each is not only a peptide bond, but also a left-handed isomer, is approximately 1 in 10$^{90}$.

Finally, there is a third independent requirement. Most importantly, the amino acids—like alphabetical characters in a meaningful sentence—must be in functionally specified sequential arrangements. Because there are 20 biologically occuring amino acids, the chance of getting any one of them at a specific site is 1/20. Molecular biologists have found that in many cases the proteins can tolerate several of the 20 different amino acids along the chain without destroying function. Douglas Axe was able to experimentally demonstrate2 www.ncbi.nlm.nih.gov/pubmed/15321723 that the ratio of tolerance while still producing a functional protein 150 amino acids in length yields a probability of 1 in 10$^{74}$.

Therefore, the probability that a 150 amino acid compound assembled by random interactions in a prebiotic soup would form a functional protein is the product of each of the 3 individual probabilities:

• Probability of only peptide bonds = 1 in 10$^{45}$
• Probability of only L-form isomers = 1 in 10$^{45}$
• Probability of achieving correct amino acid sequencing = 1 in 10$^{74}$
• Total probability = 1 in 10$^{164}$

Therefore, if the FLC requires 250 proteins that, on average, are 150 amino acids in length, and each individual protein yields a probability of 1 in 10$^{164}$, then the probability of 250 necessary proteins forming in order to service a minimally complex cell is 1 in 10$^{41,000}$.

1 in 10$^{41,000}$! Here are a couple of ways to demonstrate just how astronomical this number is:

First, in order to win the Mega Millions Jackpot, you must correctly select 5 numbers from a pool of 56, while also selecting 1 additional number from a pool of 46. The probability of winning once? 1 in 175,711,536. One would need to win 5,408 consecutive drawings to actualize a probability almost identical to that of the first living cell forming by chance. In other words, you have a better chance of winning the jackpot in every consecutive drawing for the next 52 years!

Finally, all matter in the universe is composed of subatomic particles. These particles are virtually infinitesimal in size. For instance, the number of particles in a 16 ounce glass of water is much greater than the number of glasses that it would take to scoop all of the water out of all the oceans on the earth. In other words, there are lots of particles in even a small glass of water. These particles are scattered throughout our observable universe. How big is our observable universe? Light travels at a speed of 186,282 miles per second. Thus, it would take light approximately 93,000,000,000 years to go from one edge of the observable universe to the other. Moreover, in this astronomical volume of space, these infinitesimal sub-atomic particles are scattered throughout. How many particles are in the universe? 10$^{80}$. This number defies the imagination. But compared to 10$^{41,000}$, 10$^{80}$ is infinitesimal. What’s more, each of these particles can change its position 10$^{45}$ times per second. This is known as an “event”. If the universe were a 1,000,000,000 times older than the typical estimated age, the total number of seconds since the Big Bang would be 10$^{25}$. Therefore, the number of events—the product of the number of times every particle in the observable universe has changed it’s position since the Big Bang—that have occurred is 10$^{150}$. That is every event that has ever occurred, and then some.

Compare 10$^{150}$ to 10$^{41,000}$. If I told you that you had one chance to guess which specific 273 events that I’m thinking of that have ever occurred since the beginning of the universe, you would have a better chance of picking all 273 on your first guess than a living cell has of forming by chance! Remember, there have been 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 events. Anyone want to bet that they can pick all 273 in one guess?

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Posted in Biology.