You need to do the analysis in terms of some molecule that can actually replicate itself. DNA requires a polymerase and a helicase to replicate, and it requires mRNA and tRNA for metabolism to grow a cell. There are RNA replicators: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3943892/ But the simplest self-replicator discovered in a poypeptide. http://www.nature.com/nature/journal/v382/n6591/abs/382525a0.html Of course replication is environment dependent. Brent On 5/7/2015 11:46 AM, Warren D Smith wrote:
If the simplest lifeform capable of independent existence had, say, 3000 base pair long DNA --actually I think the least the "minimal genome project" has been able to come up with is more like 100 times that -- then you might say "the chance of that is 4^(-3000) which is about 10^(-1806), which is so small that even if every atom in the observable universe were trying a new 3000-long DNA sequence every femtosecond, life almost certainly would still never have come into existence anywhere ever... therefore, life is a miracle and Earth is likely the only place in the universe that has any."
However, that calculation was wrong because more than one of those 4^3000 sequences probably works to produce a viable lifeform. In fact the number that work is probably also enormous. If the number were N then the viability probability is more like P=N/4^3000, and it is that chance P that really needs to be used to assess the miraculousness.
OK, that brings me to my point. We can do an experiment to approximately measure P. Start with some near-minimal bacterial genome which say has G base pairs in its genome. Randomly mutate K of its base pairs. There are binomial(G,K)*3^K possible mutated genomes obtainable in this way. We are taking a uniform random sample among them. When you do this, count how many of the resulting bacteria remain viable, versus how many are rendered unviable.
The result of such an experiment is a function F(K) estimating the chance that mutating K of the base pairs, still yields a viable lifeform. We will know, to good accuracy, the values of F(1), F(2), F(3), etc for some set of K's. We then want to EXTRAPOLATE this function to determine the value of F(G-1), which is, essentially, equal to P, the life-viability chance we were seeking.
To perform this extrapolation we need to obtain an empirical formula that fits the data F(1), F(2), F(3) etc that we have. I doubt this extrapolation will be very difficult. In fact I might a priori suspect that F(K) = K^Q * C^K for suitable fitting constants Q and C, will work decently.
Thinking some more, it might be possible to do an even better job than that. We can do a different kind of experiment to attempt to estimate F(K+J)/F(K), by starting with a viable K-mutant, and generating J-mutants of it. We might be able to reach very large K values this way and thus build a long chain of such ratio-estimates.
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