Origin: Probability of a Single Protein Forming by Chance

When applied to the origin of life and the random formation of large biomolecules, probability theory clarifies the limitations of chance as a creative agent on the primordial earth. For example, what are the odds a single protein could form exclusively through the blind interactions of chemistry? Our target is one smaller-than-average molecule made from a hundred and fifty amino acids, each aligned to ensure a folded chain. Researchers have calculated that on the ancient earth, the probability of success was one chance in 10164, that’s one correctly sequenced protein chain for every 100 million trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion failed attempts. Despite these enormous odds some theorists argue that given enough time, anything is possible. Let’s test the validity of this opinion.

We’ll begin by establishing an ideal environment for chemical evolution – an imaginary world that will provide chance with every opportunity to succeed. First, we stock the oceans to capacity with amino acids. That means all the atoms on earth including its entire supply of carbon, nitrogen, oxygen, hydrogen and sulfur are available to form 1041 complete sets of the 20 types of amino acids used to build proteins. Then we’ll alter the laws of nature to protect these building blocks from the destructive rays of ultraviolet light and chemical contamination in the primordial soup. Now let’s turn the chemistry loose and see what happens. The amino acids start bonding furiously. In our experiment, an entire chain of 150 units self-assembles in only one second. Since all 20 types of amino acids are available, at the majority of sites, there is a 5% or one in 20 chance the correct molecule will align in the chain. If the sequencing is incorrect, the chain is immediately destroyed and a new assembly begins. Throughout the planet 6,000 million billion trillion trillion attempts will take place every minute. That means in 4.6 billion years, the oldest estimated age of the earth, the number of chains that don’t fold will exceed 1058. It’s a staggering total but nowhere near 10164 trials necessary on average to build a protein of 150 amino acids by chance. 

If undirected chemistry can’t produce our coveted molecule during the entire history of the earth, then how much time would have been needed? To find out, let’s take a road trip. We’ll start by erecting a bridge that spans the diameter of the observable universe, a distance of more than 90 billion light years. Then we’ll place an amoeba on one end of the bridge. This single-celled organism will travel at the breakneck speed of one foot per year. It’s off. While we wait for one protein to form by chance, the amoeba slides along for more than five billion billion billion years to cross the entire universe and then return but this race is just getting started. The amoeba takes off again, successfully reaches the far side of the cosmos, then heads back home. Yet not even one functional protein is anywhere in sight. For the next trip, we’ll add a payload, a single atom. After inching its way another 500 billion trillion miles, the amoeba drops off its cargo and returns for more. Will it get back before our lucky protein forms? Absolutely. In fact, it will complete another ten round trips, then twenty, a hundred, a thousand, and there’s still no sign of a usable molecule. The amoeba continues making round trips until it has hauled off every atom on earth, then all of the atoms in our solar system, then every planet and star in the Milky Way galaxy, one atom at a time. In fact, as we wait for one protein to self-assemble, the amoeba has so much time that moving at just one foot a year and carrying one atom round trip, it will transport the entire universe more than 56 million times. That’s how long it would take for chance to build one functional protein. 

Suppose against all odds, chemical evolution produced our single functional protein, would we have life? No, we’d have one protein, just a lifeless arrangement of amino acids. The simplest living cell we know has more than 300 different proteins. But proteins are only part of the story when you consider any actual cell. Remember you’re going to have carbohydrates, complex sugars, nucleic acids, DNA and RNA, lipids, a whole variety of different chemicals ,which jointly constitute the living state. Those bits and pieces all have to be brought into the same micro environment at the same moment in time. Each chemical building plot must then be assembled and organized into the network of molecular machines that will control every facet of life. 

If we can appreciate exactly how hard it is to produce one molecular machine using nothing except atoms and energy, we can see that there’s a profound problem because once you have one molecular machine, you don’t have a living thing. These molecular machines need other molecular machines. Even if nature was capable of producing all the molecular machines necessary, that still wouldn’t be enough. They’d have to all be together all in this tiny little membrane bound space that we call a cell. 

From my understanding of what it takes to make a cell, it has to happen all at once. You can’t do it one bit at a time because everything works together in a causal loop. The higher level of organization transcends the pieces. The spatial organization in the cell requires that molecules end up in the right place at the right time. The DNA is copied into RNA. The polymerase that does the copying has to find the right spot in the DNA to start copying. The RNA has to somehow hook up with ribosomes, which have to be in a particular place and the proteins then that are made have to be going to a particular place. That’s an awful lot to account for by random chance. 

The probability that you would get them in the same space at the same time becomes beyond unimaginable and the probability that you would get them within a membrane inclusion like a cell is the next best thing to impossible.