Does A Darwinian Evolution Have The potential To Generate Average-Sized Functional Enzymes?

Does an unplanned evolution have the potential to generate a gene coding for the first member of a new family of average-sized enzymes?

          First of all, average-sized enzymes are composed of 300 to 400 amino acid residuals.¹ The probability of generating a gene coding for a specific enzyme of 101 amino acid residuals is 2 chances in 10⁶⁵ tries.2 The probability of generating a gene coding for a specific enzyme of 150 amino acid residuals is 1 chance in 10⁷⁷ tries.³

          So, how many tries does a Darwinian evolution provide? The number of tries is the total number of mutations provided by all organisms ever existent. Since such a number is unknown and unknowable, a generous estimate of this number will suffice.

          Nature has three domains: prokaryotes (bacteria), eukaryotes, and archaebacteria. Prokaryotes are in the majority.⁴ Prokaryotes produce about 1.7x10³⁰ cells per year.5 Since evolution began less than 4 billion years ago, there have been fewer than 6.8x10³⁹ prokaryotes. This number can be rounded up to fewer than 1040.

                Since prokaryotes are in the majority, eukaryotes and archaebacteria are in the minority; they both have had fewer than 1040 individuals. Therefore, the total number of organisms from the three domains is less then 3x1040.

                The mutation rates for these organisms is less than 1,000 (103) heritable mutations per organism per replication. Together, these organisms have had a total of fewer than 3x1040 x 103 mutations or 3x1043 mutations. Each mutation is one try at the generation of a gene coding for the first member of a new family of enzymes.

                As noted the probability of generating a gene coding for a specific enzyme of 101 amino acid residuals is 2 chances in 1065 tries. So, what is the overall potential of 3x1043 mutations or tries? Multiplying the probability times 3x1043 mutations or tries gives the answer:

       2 chances / 1065 tries x  <3x1043 tries =  <6 chances / 1022            

<6 chances / 1022  = <1 chance in 1.66x1021

                So, the overall probability of generating a gene coding for a specific enzyme of 101 amino acid residuals using all mutations since the onset of the evolutionary process is less than one chance in a billion trillion.

                What is the overall probability of generating a gene coding for a specific enzyme of 150 amino acid residuals with 3x1043 mutations or tries? The probability of generating a gene coding for a specific enzyme of 150 amino acid residuals is 1 chance in 1077 tries. Again, the probability is multiplied by  3x1043 mutations or tries:

1 chance /1077 tries x <3x1043 tries = <1 chance in 3.3x1033

                Here the overall probability of generating a gene coding for a specific enzyme of 150 amino acid residuals with fewer than 3x1043 mutations or tries is less than one chance in 3 billion trillion trillion.

                If a Darwinian evolution does not have the potential to generate genes coding for specific enzymes of 101 and 150 amino acid residuals, it does not have the potential to generate genes coding for specific average-sized functional enzymes.

                An unplanned Darwinian evolution is impotent in generating the genes coding for the specific average-sized enzymes associated with metabolism, reproduction, and the origin of species.

                                                                                                                                                Fredric P. Nelson, M.D.

Endnotes:

1. S. Carroll, The Making of the Fittest, New York: W.W. Norton & Co., 2006, 74.

2. H. P. Yockey, “A calculation of the probability of spontaneous biogenesis by information theory.”  J. Theor. Bio., 67 (1977), 387.

            &

J. Reidhaar-Olson and R. Sauer, “Functionally Acceptable Substitutions in Two α-Helical Regions of λ Repressor.” Proteins: Structure, Function, and Genetics, 7 (1990), 315.

3. D. Axe, “Estimating the Prevalence of Protein Sequences Adopting Functional Enzyme Folds,” Journal of Molecular Biology 2004 Aug 27; 341 (5): 1295-1315.

4. W. Whitman, D. Coleman, and W. Wiebe, “Prokaryotes: The unseen majority,” Proc. Nat. Acad. Sci., 95, June 1998.

5. Ibid, Table 7, 6581, and abstract, 6578.