where Nlife is how many stars with life there are in the Milky Way and it is assumed that a) once self-replicating molecule is evolved it produces life with 100% probability; b) there is an infinite supply of RNA monomers, and c) lifetime of RNA does not depend on its length. In addition:
Nstars—how many stars capable of supporting life there are (between 100 and 400 billion),
Fplanet—Number of planets and moons capable of supporting life per star—between 0.0006 (which is 0.2 of Earth-size planets per G2 star) and 20 (upper bound on planets, each having Enceladus/Europe-like moon)
Tplanet—mean age of a planet capable of sustaining life (5-10 Gy)
Splanet—typical surface area of a planet capable of sustaining life (can be obtained from radii of between 252 km for Enceladus and 2Rearth for Super Earths)
Fsurface—fraction of surface where life can originate (between tectonically-active area fraction of about 0.3, and total area 1.0)
D—typical depth of a layer above surface where life can originate (between 1m for surface-catalyzed RNA synthesis and 50 km for ocean depth on Enceladus or Europa)
TRNA—typical time required to synthesize RNA molecule of typical size for replication, between 1s (from replication rate of 1000 nucleotides per second for RNA polymerases) and 30 min, a replication rate of E.coli
VRNA—minimal volume where RNA synthesis can take place, between volume of a ribosome (20 nm in diameter) and size of eukaryotic cell (100 um in diameter)
Rvolume—dilution of RNA replicators—between 1 (for tightly packed replicating units) and 10 million (which is calculated from a typical cell density for Earth’ ocean of 5*10^4 cells/ml and a typical diameter of prokaryotic cell of 1.5 um)
Nbase—number of bases in genetic code, equals to 4
LRNA—minimal length of self-replicating RNA molecule.
You can combine everything except Nbase and LRNA into one factor Pabio, which would give you an approximation of “sampling power” of the galaxy: how many base pairs could have been sampled. If you take assumption that parameters are distributed log-normally with lower estimated range corresponding to mean minus 2 standard deviations and upper range to mean plus 2 standard deviations (and converting all to the same units), you will get the approximate sampling power of Milky Way of
log10Pabio∼Normal(55,4)
Using this approximation you can see how long an RNA molecule should be to be found if you take top 5% of Pabio distribution: 102 bases. Sequence of 122 bases could be found in at least one galaxy in the observable universe (with 5% probability).
In 2009 article https://www.science.org/doi/10.1126/science.1167856 the sequence of the RNA on the Fig. 1B contained 63 bases. Given the assumptions above, such an RNA molecule could have evolved 0.3 times − 300 trillion times per planet (for comparison, abiogenesis event on Earth’ could have occurred 6-17 times in Earth’s history, as calculated from the date of earliest evidence of life).
Small 16S ribosomal subunit of prokaryotes contains ~1500 nucleotides, there is no way such a complex machinery could have evolved in the observable universe by pure chance.
You can do something similar to the Drake equation:
Nlife=Nstars∗Fplanet∗Tplanet∗Splanet∗Fsurface∗DTRNA∗VRNA∗NLRNAbase
where Nlife is how many stars with life there are in the Milky Way and it is assumed that a) once self-replicating molecule is evolved it produces life with 100% probability; b) there is an infinite supply of RNA monomers, and c) lifetime of RNA does not depend on its length. In addition:
Nstars—how many stars capable of supporting life there are (between 100 and 400 billion),
Fplanet—Number of planets and moons capable of supporting life per star—between 0.0006 (which is 0.2 of Earth-size planets per G2 star) and 20 (upper bound on planets, each having Enceladus/Europe-like moon)
Tplanet—mean age of a planet capable of sustaining life (5-10 Gy)
Splanet—typical surface area of a planet capable of sustaining life (can be obtained from radii of between 252 km for Enceladus and 2Rearth for Super Earths)
Fsurface—fraction of surface where life can originate (between tectonically-active area fraction of about 0.3, and total area 1.0)
D—typical depth of a layer above surface where life can originate (between 1m for surface-catalyzed RNA synthesis and 50 km for ocean depth on Enceladus or Europa)
TRNA—typical time required to synthesize RNA molecule of typical size for replication, between 1s (from replication rate of 1000 nucleotides per second for RNA polymerases) and 30 min, a replication rate of E.coli
VRNA—minimal volume where RNA synthesis can take place, between volume of a ribosome (20 nm in diameter) and size of eukaryotic cell (100 um in diameter)
Rvolume—dilution of RNA replicators—between 1 (for tightly packed replicating units) and 10 million (which is calculated from a typical cell density for Earth’ ocean of 5*10^4 cells/ml and a typical diameter of prokaryotic cell of 1.5 um)
Nbase—number of bases in genetic code, equals to 4
LRNA—minimal length of self-replicating RNA molecule.
You can combine everything except Nbase and LRNA into one factor Pabio, which would give you an approximation of “sampling power” of the galaxy: how many base pairs could have been sampled. If you take assumption that parameters are distributed log-normally with lower estimated range corresponding to mean minus 2 standard deviations and upper range to mean plus 2 standard deviations (and converting all to the same units), you will get the approximate sampling power of Milky Way of
log10Pabio∼Normal(55,4)
Using this approximation you can see how long an RNA molecule should be to be found if you take top 5% of Pabio distribution: 102 bases. Sequence of 122 bases could be found in at least one galaxy in the observable universe (with 5% probability).
In 2009 article https://www.science.org/doi/10.1126/science.1167856 the sequence of the RNA on the Fig. 1B contained 63 bases. Given the assumptions above, such an RNA molecule could have evolved 0.3 times − 300 trillion times per planet (for comparison, abiogenesis event on Earth’ could have occurred 6-17 times in Earth’s history, as calculated from the date of earliest evidence of life).
Small 16S ribosomal subunit of prokaryotes contains ~1500 nucleotides, there is no way such a complex machinery could have evolved in the observable universe by pure chance.