By R. Mazo
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Additional resources for Brownian Motion - Fluctuations, Dynamics and Applns
All 378 fictitious sequences whose abundances were between 227 and 592 copies have been removed. We still have a number of unique sequences that appear a few times, most of them just once or twice, but the number has been reduced to 3878. In total, we now have 1,007,650 molecules, instead of the original 1,002,520 (again, slightly higher than the actual starting number of molecules, but only around a 0:5 % increase). Taken together, (1) we have recovered decent copy numbers for the seven real, original sequences, (2) all the erroneous unique sequences with relatively large abundances are gone, and (3) the number of the erroneous unique sequences that still remain appear only a few times.
Similarly, the probability of finding any of the 16 possible nucleotide dimers within the pool of synthesized sequences should be 1=16. , should be 1=64, 1=256, 1=1024, 1=4096, and 1=16384, respectively. Once again, our investigations contradict the assumption of randomness (data not shown). The fact that the synthesis process is not completely random should not be too surprising. Bearing the synthesis process in mind, the degree of randomness will depend on the relative concentrations of the nucleotides in solution.
The models considered are the seven first knucleotide models The x-axis represents the abundance of each sequence in the pool; the y-axis describes the fraction of sequences in the pool that are present at a given abundance. In the figure, the sequence probability distribution corresponding to the random model is only a single point. Obviously, if the correct synthesis model is the random one, then all sequences must have the same probability of appearing in the pool; that is, the number of copies of each unique sequence will be (approximately) the same.