A Mathematical Explanation of why the Origin of Life by Chance is not possible.

See companion Excell spreadsheet

In order for this to make sense, one needs to understand what proteins are made of and why that is important. Proteins themselves are important because they are responsible for thousands of chemical reactions that are important for life. Chemical reactions such as the production of energy from sugar, the transportation of chemicals from one point to another in the cell, the structure and integrity of the cell wall, and also the elimination of sodium from the cell. I won’t spend the time to explain all of these, but take it on faith that they are all important and without them, the organism cannot survive.

 

Proteins themselves are made up of a string of amino acids. There are 20 amino acids known that are used in life.  Here is the Wikipedia[1] description of Amino Acids: “Amino acids (  /əˈmiːnoʊ/, /əˈmaɪnoʊ/, or /ˈæmɪnoʊ/) are molecules containing an amine group, a carboxylic acid group, and a side-chain that is specific to each amino acid. The key elements of an amino acid are carbon, hydrogen, oxygen, and nitrogen. They are particularly important in biochemistry, where the term usually refers to alpha-amino acids.”

 To make a protein, amino acids are attached together with a Peptide bond[2].  Most proteins are quite large. There are literally thousands of proteins in our cells, each with a very specific important function.  For our purposes we will choose a fictional very small protein of 100 amino acids.

 

[3]

 Basically, it isn’t the sequence of the amino acids that make up the protein that is important, it is what happens once all the amino acids are in sequence. It is the shape of the protein once it folds up into its final position of least energy. The final shape is dependent on the sequence of amino acids. If the sequence or code is altered, the protein will not function properly.  It is the particular shape of the protein that determines its functionality.  In the case of hemoglobin, which is composed of two alpha and two beta globulin proteins and an Iron molecule held in a porphyrin ring, it has four sites that preferentially accept oxygen in the lungs and give it up in the cells. There are mutations of hemoglobin that do still function, although poorly, one such mutation is responsible for sickle cell anemia[4].

So, the question is: what are the odds of producing by accident a small, 100 amino acid,  protein. I am assuming there are abundant amounts of amino acids and a perfect environment for protein production, even though that will never be the case.

 First, we must take into account that amino acids are produced in equal amounts of left handed and right handed isomers[5].  In the wild, amino acids are racemic, or are produced in equal amounts.  In life, only left handed amino acids will do, with some few exceptions, see Cone snales[6].  So we start with making the odds that all the amino acids in our protein chain will be left handed. The odds that the first one will be left handed is 50%, or 1 out of 2 or 1 divided by 2 to the power of 1 (1/2¹) .  The odds that the next one will also be left handed is also 50%, but the odds that both of them will be left handed is 50% times 50% is 0.5x0.5 or 25%, or 1 out of 4 or (1/2²). Carrying that out for the full 100 amino acid sequence we can calculate that as 1/100 to the 100^th power which is 1/100¹⁰⁰ = 1/ 1,267,650,600,228,230,000,000,000,000,000, a very large number. To give this number perspective, the number of seconds in 15 billion years (the reported age of the universe) is only 473,040,000,000,000,000.  It would take 2,679,795,789,422 iterations every second since the universe reportedly began to equal the odds of making a 100 amino acid protein of any sequence that was all left handed.

But, that is not where the story ends.  In order to make just the right protein, that would fold up in just the right shape and be effective, the sequence of the amino acids must be perfect. It is like computer code, the letters in a literary piece, or notes in a musical score, it must be just so.

Since there are 20 different possible[7] choices for amino acids at each position and the odds of picking the right one at the start, or position 1, are 1 in 20 or 20¹. The odds of picking the correct one at position 1 & 2 are 20*20 or 400, or 20². So the odds of getting all 100 correct are 20¹⁰⁰, or 1.27E+130, or 1.27 * 10¹³⁰.

But, not to pile on, we can’t stop there. The final odds require we multiply the odds of each part together, the odds of all the amino acids being left handed multiplied times the odds that all 100 amino in correct sequence. That calculation is 1.27E+30 * 1.27E+130 = 1.6069E+160.

 Let’s try to put that number in perspective. Let’ say we marked a single dime with a red X as the one we were searching for and covered the State of Oregon to a depth of 1 mile in dimes? Would that represent the odds of producing a 100 amino acid protein that was all left handed and the correct sequence? We know that the volume of a dime is 340.106 mm^3[8] or .020754 in^3[9]. Divide 1 by the volume of a dime and we get 48.1834827 dimes per cubic inch. If we then multiply that by 12 inches per foot cubed we get the number of dimes per cubic foot = 48.1834827 * 12 * 12 * 12 = 83,261.05811 dimes per cubic foot. Multiply that by 5280 (ft per mile) cubed and we get 1.22559E+16 dimes per cubic mile.The area covered by the State of Oregon is 98,381square miles[10].  The volume of a stack of dimes over the entire State of Oregon a mile high would be 1.22559E+16 dimes per cubic mile multiplied by 98,381 square miles = 1.20574E+21 cubic miles. This is not even close to the volume represented by the odds we are faced with.

 So, let’s try to find just how big the volume of dimes it would take with only 1 being the right one. We know that there are1.22559E+16 dimes per cubic mile.  If we divide the odds for making our 100 amino acid protein by the number of dimes (each dime equals one iteration) per cubic mile, we will produce the volume of dimes represented by odds in cubic miles, 1.6069E+160 iterations / 1.22559E+16 dimes (iterations)/mile = 1.31E+144 cubic miles.  Just how big is that? Using the formula[11] (V = (4/3) × pi × r³), it equates to a diameter of sphere equaling 1.36E+48 miles[12]. That is much larger than our solar system. Converting  to light years we know  light year is 186,000 (miles per second) * 86400 (seconds per day ) * 365.25 days per year = 5.86971E+12 miles/light year. In light years, 1.36E+48 miles = ( 1.36E+48 / 5.86971E+12) = 2.31E+35 light years in diameter, which is much larger than the known universe reported at 15,000,000,000 light years. In this enormous sphere, one would be able to place 3.65E+75 known universes.

 It is actually worse than this because we haven’t included other variables such as the odds of making a peptide bond rather than other bonds, the odds of sufficient material being available and the odds of the right conditions being available.

 Casino’s make their money with just a slight edge in the odds. Does anyone think the incredible odds represented above make life by chance  possible? 

 

 

 

 

 

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