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Threshold effects in assembling a cell on a young planet

Molecules in the young Earth's oceans underwent a finite number of collisions before life emerged. This sets an upper limit on the size of the genetic molecule that could be assembled for the first cell.
15 July 2011, SPIE Newsroom. DOI: 10.1117/2.1201106.003783

With at least 1200 planets now known to orbit around stars other than the sun,1 it is timely to ask how likely it is that life arises on a planet. On Earth, life emerged shortly after conditions became favorable: once the heavy bombardment by impacting bodies stopped, single-cell life emerged within about 200 million years. Here, we use conditions on the young Earth to determine a threshold for assembling the genetic molecule of a cell on a planet.

In discussing life's origins,2 a basic question regards whether proteins (chains of amino acids, AAs, that operate as catalysts and structural molecules) or nucleic acids (chains of nucleotides, NTs, that operate as information containers) formed first. For years, the synthesis of nucleic acids from pre-biotic (non-living) material was thought to be so complex that the idea that proteins appeared first seemed preferable. But in 2009, the successful pre-biotic synthesis3 of two (cytosine and uracil) of the 4 NTs (adenine, cytosine, guanine and uracil) that are ‘strung together’ to form ribonucleic acid (RNA), re-opened the possibility that life began in an ‘RNA world.’

During the time tL≤200 million years that life took to emerge on Earth, pre-biotic molecules in our planet's water experienced a finite number of collisions, Nc. Assuming a supply of NTs available, some collisions led to the formation of nucleic acids, with an RNA chain having no more than a limiting number, Nb, of NTs. Typically, this argument is used to exclude the emergence of a cell with a targeted Nb (such as that of a modern cell). But here we invert the argument: given that a number Nc of collisions did in fact occur during tL, what is the upper limit on Nb? Given this limit, we may also ask what size of cell could have had its RNA assembled during time tL.

In the RNA world, a genetic code developed,2 perhaps by means of collective non-Darwinian mechanisms that were present in early cell communities.4 The code translates a chain of Nb NTs (in RNA) into a chain of Na AAs (in protein), where Na=Nb/T, with T being the ‘codon size’. (In the modern world T=3, that is, to plug in a particular amino acid into a protein, the cell has to ‘read off’ a triplet of bases in the RNA that is specific to that amino acid.) Therefore, for proteins consisting of Nr AAs each, the RNA chain encodes for Ng=Na/Nr genes (assuming one gene corresponds to one protein). Regarding how many genes are needed for a cell to be viable, Simpson5 lists 5 or 6 functions for a minimal cell, with each regulated by an appropriate gene. Hence, we estimate that Ng≈10–12 could be viable. Therefore, we need to ensure that Nb/(TNr)≥10–12.

The key question that we consider here is: how are Nb and Nc related? If we demand that the Nb nucleotides are to be assembled in a particular order, then Nc must not be small compared to the RNA phase space, which has a size φ=4Nb (where 4 is the number of distinct NTs in RNA). However, a vast reduction in phase space (factor Q) occurs because multiple chains of AAs can perform the task of any one protein.2 If Q is so large (equal to a threshold Qr) that φ/Qr≈Nc, then RNA phase space can be sampled well during tL. Whether Q can in fact equal the limit Qr is another question. The maximum value of Q that allows for stable life requires that each of the Ng proteins in the cell must perform a non-overlapping function. This minimum ‘specificity’ sets an upper limit Qmax. We find that for T=3, Ng is too small to lead to a minimal cell. But if T=2, we find Ng≈15, that is, such a cell could be viable.

Threshold behavior occurs because Nc, which determines Nb, must exceed a minimum to ensure that a minimal cell can arise, that is, to ensure that Nb≥ (10–12)T Nr. If the molar concentration of NTs was as large as 10−7 in the young Earth's oceans, and if T was allowed to take the value T=2 in the young Earth, we find that Nc exceeds the minimum if the total mass of the NTs is a few tons.

In conclusion, genetic material (RNA) that encodes for a minimal cell (10–12 genes) could be assembled in non-living aqueous conditions in a time-scale less or equal to 200 million years provided a few tons of NTs were available. There is a need to determine if a viable cell can in fact exist with as few as 10–12 genes, and if the NT supply can be provided (does it come from the young Earth itself or were NTs introduced from an external source?). These issues represent the focus of our future work.

Dermott J. Mullan
University of Delaware
Newark, DE

Dermott J. Mullan is a professor of physics and astronomy. His research interests center on the effects of magnetic fields in stars, and his teaching interests include astrobiology and solar physics. His textbook ‘Physics of the Sun, A First Course’ was published in 2009.

2. M. Yarus, Life from an RNA World, Harvard Univ. Press, 2010.
3. M. W. Powner, B. Gerland, J. D. Sutherland, Synthesis of activated pyrimidine ribonucleotides in prebiotically plausible conditions, Nature 459, pp. 239, 2009.
4. K. Vetsigian, C. Woese, N. Goldenfeld, Collective evolution and the genetic code, Proc. Nat. Acad. Sci. 103, pp. 10696, 2006.
5. G. G. Simpson, The non-prevalence of humanoids, Science 143, pp. 769, 1964.