Calculating Protein Probability Using
BIG SCARY NUMBER THEORY
There are 20 amino acids common in organic systems.[1]
The simplest protein currently known , TRP-Cage, has only 20 amino acids. [2]
So the odds of that protein being generated is 20^20 or 1 in 1.048576e+26 ‘tries’.
Now lets say that this protein is being generated in a very simple primitive bacteria in the ocean.
In a drop of sea water there are 1 million bacteria.[3]
In 1 cc, that is 20 drops, that is 20 million bacteria per cc or 20 billion bacteria per litre.
Now the estimated number of litres of water in the ocean is 1.335 e+21 litres. [4]
So the oceans contain 20e+9 * 1.335e+21 = 2.67e+31 bacteria which is more than there are stars in the known universe which there are estimated to be 2.0e+23 stars.[5]
So at any given time we will have 2.67e+31 / 1.048576e+26 = 254631 or over a quarter million copies of that simple protein generated by random assembly.
Now lets assume that this process has been going on since the first cell was known from about 3.5 billion years ago[6] and that the aggregation of these amino acids happens every 20 seconds since the average time of amino acid building is 20 units per second [7], 3.5e+9365246060 = 1.10376e+17 seconds.
This means that since the beginning of life on Earth that simple protein has been generated 1.10376e+17 * 254631=2.8105151e+22 times.
[7] https://www.quora.com/How-long-does-it-take-a-cell-to... Mike Adams
, PhD Molecular Genetics & Biochemistry, Duke University (1975)
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