The Chemical Evolution of Cytochrome C Under Ideal Conditions

Did an unplanned chemical evolution, under ideal conditions, have the potential to generate the genome and the enzymes for the first functional cells?

Checking Out First Cells

          What did the first functional cells look like? One proposal is for an experimental minimal genome coding for 151 genes and made up of 113,000 base pairs,1 which averages out to 249 codons per gene and each gene coding for a structural protein or an enzyme averaging 249 amino acid residuals.2

          Another possibility is a minimal bacterium that might grow in pure culture. Such a bacterium is estimated to contain 387 essential protein-coding genes plus 43 structural RNA genes.3

          The first functional cell probably contained somewhere between 151 and 387 genes coding for structural proteins or enzymes averaging 249 amino acid residuals. These numbers will be used in the following thought experiment.

A Thought Experiment

          This thought experiment takes place during an unplanned chemical evolution. The term chemical evolution incorporates all biochemical events that occurred prior to the generation of the first functional cells.

          The goal is to calculate the maximum overall probability of generating at least one representative enzyme from available resources.

          The maximum potential within an unplanned chemical evolution equals the maximum number of unique proteins that the resources from nature can generate. The greater the number of unique proteins generated, the greater the potential.

          This statement bares repeating: The maximum potential within an unplanned chemical evolution equals the maximum number of unique proteins that the resources from nature can generate.

          The data used to calculate the number of unique proteins comes from nature. It is limited by the amount of time and material nature had to offer. The data is obtained through bench science and is not speculative.  When multiple unique proteins are generated the odds are improved that one of them will have the specific enzymatic function.

          Every experiment begins with a question.

                   What is the maximum overall probability of generating one                               representative enzyme for the first functional cells during an                                      unplanned chemical evolution?

          The search is for one number─the maximum overall probability.

          Once this number is obtained, an interpretation of the data can be used to answer a second question:

          Does an unplanned chemical evolution have the potential to self-generate 151 to 387 protein-coding genes for the first functional cells?

A Representative Enzyme

          The probability of generating a new gene coding for an enzyme is identical to the probability of generating the enzyme. This thought experiment will begin by looking at the probability of generating one enzyme from available resources. The reason for generating the enzyme is that, for the same amount of material, more enzymes than genes would be generated. This improves the odds of generating a functional enzyme.

          Cytochrome c is selected as the representative enzyme. This enzyme requires a gene less than one-half the length of an average-sized gene within an “experimental minimal genome”. The probability of its generation under ideal conditions is known.

          Since the potential within an unplanned chemical evolution equals the maximum number of unique proteins that the resources from nature can generate, the number of unique proteins needs to be calculated.

          Chemical evolution was not observed and proximate conditions are unknown. Therefore, it is impossible to approximate the number of unique proteins that may have been generated. However, a calculation can be made of the maximum number of unique proteins that could have been generated under ideal conditions. Ideal conditions are not infinite conditions. Ideal conditions are the best conditions that nature could provide. Logically, if an event does not occur within ideal conditions, it would not occur within actual conditions.

          Once the number of unique proteins is calculated, the overall probability of generation–the goal of the thought experiment─can be calculated by multiplying the number of unique proteins or tries by the probability of generating a representative enzyme, cytochrome c, per try.

Required Resources

          To calculate a maximum number of unique proteins, the following is required:

                   A maximum amount of time,

                   A maximum amount of the right material,

                   A maximum rate of assembly, and

                   A minimum time to turnover

Time

          Chemical evolution followed by a biological evolution has occurred on earth for approximately 3.9 billion years. The first cells on earth were functional within the first hundreds of millions of those years. For this thought experiment, the maximum amount of time available for the generation of one enzyme, cytochrome c, for the first functional cells is set at three billion years, which is slightly less than 10¹⁷ seconds.

Material And Assembly

          Biological life is written in carbon; carbon is the material of choice. The maximum amount of carbon available for the generation of the first functional cells is set as the amount of carbon present within the top ten kilometers (six miles) of Earth's surface. To mimic ideal conditions, every carbon atom in the top ten kilometers is used in the instantaneous assembly of a random collection of the twenty L-isomer biological amino acids. The twenty types of biological amino acids would be equally represented and randomly distributed.

          These biological amino acids are, in turn, randomly and instantaneously assembled into proteins that are 101 amino acid residuals in length. This gives the maximum number of protein structures at any one time.

Turnover

          To maximize the number of unique proteins assembled over a period of three billion years, once every second every protein instantly disassembles back into amino acid residuals, which randomly shuffle and instantly reassemble into a new protein structure that is composed of 101 amino acid residuals. A completely new set of proteins would be assembled once every second for three billion years.

The Available Potential

          Multiplying the number of proteins in each set by the number of seconds in three billion years provides the number of unique proteins assembled over three billion years. This number equals the available potential under ideal conditions.

The Required Potential

          Lastly, the probability of aligning 101 biological amino acid residuals into a protein with the function of a cytochrome c enzyme is two chances in 10⁶⁵ tries.4

          The maximum overall probability of a chemical evolution is obtained by multiplying the available potential by the required potential.

The Experiment Begins

          The top ten kilometers of earth's surface contain fewer than 2x10⁴⁵ carbon atoms.5 Since every amino acid has at least two carbon atoms, fewer than 2x10⁴⁵ carbon atoms could be assembled into fewer than 10⁴⁵ biological amino acids.6 Fewer that 10⁴⁵ biological amino acids could be assembled into fewer than 10⁴³ proteins, each containing 101 amino acid residuals.

          The probability that any one of the fewer than 10⁴³ proteins, each containing 101 amino acid residuals, would have the function of a cytochrome c is less than 2 chances in 10²² or 2 chances in 10 billion trillion.7

          Once per second for three billion years, all proteins disassemble into amino acid residuals, and all amino acid residuals reshuffle and instantly reassemble into new proteins. Over three billion years, fewer than 10⁶⁰ unique proteins would be assembled.8

The Results

          The overall probability that any one of these fewer than 10⁶⁰ unique proteins would have the enzymatic function of a cytochrome c is less than one chance in 50,000.9

          An unplanned chemical evolution, using all the available carbon for three billion years, and under ideal conditions, has less than one chance in 50,000 of generating a cytochrome c enzyme. This probability, one chance in 50,000, is the overall probability and is the conclusion to the experimental question.

Less Than Ideal

          The overall probability of generating a cytochrome c enzyme outside of ideal conditions plummets toward zero. The vast amount of carbon would not assemble into L-isomer biological amino acids, and the vast majority of L-isomer biological amino acids would not assemble into proteins containing more than 100 amino acid residuals.

          Nature produces about eighty types of non-biological amino acids, which are chemically produced on earth by lightning or are transported to earth by meteorites.10 All D-isomers and all non-biological amino acids needed to be separated from growing peptides, proteins, and enzymes. Also, these growing molecules had to be separated from reducing substances including the sugar, ribose, the sugar present in ribonucleic acid (RNA) and deoxyribonucleic acid (DNA). How these separations were accomplished during an unplanned chemical evolution is not known.

          Replicators, RNA molecules that promote protein assembly, do not circumvent the improbability of enzyme generation. Replicators impede evolution as they assemble identical proteins or proteins with minor variants, producing uniformity rather than generating unique proteins to produce diversity.

Representing Others

          The enzyme, cytochrome c, is a representative of the 151 to  387 structural proteins and enzymes needed by the first functional cell. It is less than half the length of an average-sized enzyme from the “experimental minimal genome”. As noted, if an event does not occur under ideal conditions, it could not occur under actual conditions. In the thought experiment, a cytochrome c enzyme was not generated under ideal conditions. Therefore, it would not be generated under actual conditions. Since cytochrome c is a representative enzyme, many if not most, genes and enzymes required by the first functional cells also could not be generated within an unplanned chemical evolution.

          The interpretation of the data answers a second question:

                   Does an unplanned chemical evolution have the potential to self-                              generate 151 to 387 protein-coding genes for the first functional cells?

          The conclusion is negative. An unplanned chemical evolution does not have the potential to generate the genes and the enzymes required by the first functional cells. An unplanned chemical evolution has a vast deficit, by many orders of magnitude, of unique protein chains to search sequence space.

          Each of the 10⁶⁰ unique proteins represents the results of “random accumulation”. Random accumulation provides no benefit towards the generation of the first member of a new family of proteins or enzymes. Nature does not plan ahead and is not prescient. Therefore, the “beneficial accumulation” of Richard Dawkins occurs only if a gene codes for a beneficial structural protein or a beneficial enzyme. A beneficial structural protein or enzyme comes first, then accumulation can follow.

          Since nature used all available carbon for three billion years under absolutely ideal conditions and came up empty-handed, a planner and a plan were required. The planner and the plan existed prior to the onset of chemical evolution, and a chemical evolution could not generate the planner.

Endnotes For: The Chemical Evolution of the Enzyme Cytochrome c

1. A. Forster & G. Church, “Towards synthesis of a minimal cell,” Molecular Systems Biology, (2006), 3. doi:10.1038/msb4100090.

2. 113,000 base pairs/3 = 37,666 codons.

    37,666 codons/151 genes = 249 codons/gene = an enzyme   with 249 amino acid residuals.

3. J. Glass, et. al., “Essential genes of a minimal bacterium,” Proceedings of the National Academy of Sciences, 103, no. 2, (January 10, 2006), 429.

            See also:

A. Mushegian and E. Koonin, “A minimal gene set for cellular life derived by comparison of complete bacterial genomes,” Proceedings of the National Academy of Sciences, 93 (1996): 10268-10273

4.  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.

            &

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

5. The surface area of Earth is 5.101x10¹⁴ m²

      10 km = 10⁴ m

      Volume = 5.101x10¹⁴ m²  x 10⁴ m = 5.101x10¹⁸ m³ = 5.101x10¹⁸ m³ x 10⁶ cm³/m³   = 5.101x10²⁴ cm³                  

      Density of crust <2.9 gm/cm³

      Mass of top 10 km of Earth’s surface =  5.101x10²⁴ cm³ x <2.9 gm/cm³ = <1.479x10²⁵ grams  

      Abundance of carbon in Earth’s crust is 0.18%

      Mass of carbon in top 10 km of Earth’s surface = 0.0018 x <1.479x10²⁵ grams = <2.66x10²² grams of carbon

            This mass in carbon atoms = <2.66x10²² grams of carbon x 6.02214x10²³/12 =

            <1.335x10⁴⁵ carbon atoms .

6. Each amino acid contributes 2 carbon atoms to the linked chain of a protein. Side chains may contribute more carbon atoms.

7.   2 chances/10⁶⁵ tries x <10⁴³ tries = <2 chances in 10²²

8. <10⁴³ proteins/sec. x <10¹⁷ sec. = <10⁶⁰ unique proteins

9. Overall probability = 2 chances/10⁶⁵ tries x <10⁶⁰ tries = <2 chances in 10⁵ = <1 chance in 50,000.

10. Murchison meteorite as found at http://en.wikipedia.org/wiki/murchison meteorite.

                                                                                                            Fredric P. Nelson, MD   ©   2019