The comments by Another O-chemist and Yggdrasil on the last post were excellent, and just the type I’d hoped to get, but before responding I’d like to throw this post into the mix.
Why RNA? Because that’s what the earliest forms of life were made of according to the best current speculations. What is the mass of the average RNA nucleotide? (base + sugar + phosphate). Phosphate has a mass of 96 Daltons, ribose a mass of 115 Daltons, and the ‘average base has a mass of (112 + 115 + 134 + 150)/4 = 128. So the average mass of an RNA nucleotide is 96 + 115 + 128 = 339 or very nearly 3 nucleotides per kiloDalton.
As before, according to Halliday’s Physics 6 Edition the mass of the earth is 6 * 10^27 grams. Assume the earth is entirely made of C, H, O, N and P in just the proportions we need. By the calculations in the previous post, a kilodalton has a mass of 10^-21 grams. Each position in the polyribonucleotide can be one of the 4 bases.
Now it’s time to calculate the number of distinct possibilities for a polyribonucleotide of length n. Pretty simple — it’s just 4^n. Order is crucial, just as united has a different meaning from untied, GACU is different from AGCU (the nucleotides of RNA are abbreviated A, G, C, U).
So for a polyribonucleotide length of n = 21 there are 4,398,046,511,104 distinct orderings of the nucleotides, Each ordering has a mass of 21/3 = 7 kiloDaltons. That’s 4 trillion of them. We’re up to a mass for all orderings of 10^-9 of a gram (a nanoGram) without breathing hard.
Length 42 gets us to 18,446,744,073,709,551,616 — about 2 * 10^19 possibilities,m each with a mass of 42/3 = 14 kiloDaltons. We’re within two orders of magnitude of 1 gram.
Given the current ratio of the genetic code of 3 nucleotides/amino acid, that’s only enough for a 14 amino acid peptide. Now the 64 possible 3 nucleotide codons only code for 20 amino acids + 1 stop codon, so there is some coding overkill in these numbers.
Not so fast. Consider progeria, a terrible (but fortunately rare) disease — only 50 kids with it worldwide. [ Nature vol. 440 pp. 32 – 34 ’06 ]. Unfortunates with progeria age rapidly and die of old age diseases (heart attack and stroke) in their teens. [ Nature vol. 423 pp. 293 – 298, 298 – 301 ’03 ] The defective gene has been found and is Lamin A (a component of the nucleus which helps to shape it). 18/20 cases showed a de novo mutation at the same place in the gene (1825 C –> T) — in codon #608. This doesn’t change the amino acid (which is glycine) but results in a cryptic splice site within exon 11 resulting in the production of a protein with 50 amino acids missing near the carboxy terminus (but the carboxy terminal end of the protein is still there and can be farnesylated). The truncated mutant is called progerin.
So even two distinct codons mapping to the same amino acid can have profoundly different effects. Further examples include the exonic splicing enhancers and inhibitors. For details see my post of 20 Jan ’09 “The Death of the Synonymous Codon” under Chemiotics in the blog of “The Skeptical Chymist”. It’s too long to go into here but pretty interesting
Onward and upward. 4^60 is 1,329,227,995,784,915,872,903,807,060,280,344,580 or about 10^36 polynucleotides 60 bases long each with a mass of 20 kiloDaltons. The mass of all 10^36 of them is then 2 x 10^37 kiloDaltons. Recall that a kiloDalton is 10^-21 grams, so this group has an aggregate mass of 10^16 grams. It’s pretty clear that by the time we get to a polynucleotide of 90 units we’ll have exhausted the mass of the earth.
4^90 = 1532495540865888858358347027150309180000000000000000000
The ribosome is thought to be a molecular fossil of the RNA world. Although there are some 50 proteins to be found on its surface, its catalytic center is pure RNA. How large are the RNAs of the ribosome? Here’s what Molecular Biology of the Cell 4th edition says (p. 343). The eukaryotic ribosome has a molecular mass of 4.2 megaDaltons and is an 80S particle (S stands for Svedberg unit). It is comprised of a 60S subunit of mass 2.4 megaDaltons and a 40S subunit of mass 1.4 megaDaltons. The 60S subunit has 3 ribosomal RNAs of 5S (120 nucleotides), 28S (4700 nucleotides) and 5.8S (160 nucleotides). The 40S subunit has a single 18S rRNA of 1900 nucleotides.
I leave it to the readers to propose a mechanism to achieve this combinatorial feat. I’m satisfied that the above argument shows that randomly trying out all possibilities and coming up with the RNAs of the ribosome is physically impossible. In some way the nucleotides of the ribosomal RNAs must be linked together consistently. RNA dependent polymerases are known which can do it (but they are proteins). Assume that there exists an RNA which can act as the enzyme to link RNA nucleotides together (the way the ribosome links amino acid together) — a big assumption, but one which current speculation seems to require. Such an enzyme made out of RNA (a ribozyme) must have a pre-existing template of ribosomal RNA to do so. Where did the template come from? How did it arise?
And so grubby old chemistry, the province of nerds and other lower forms of animal life, puts us in direct contact with profound questions of existence. Perhaps it will supply an answer as well.