By Jorge Carballido-Landeira, Bruno Escribano
This ebook provides fresh examine effects in relation to functions of nonlinear dynamics, focusing particularly on 4 themes of large curiosity: center dynamics, DNA/RNA, mobilephone mobility, and proteins. The ebook derives from the 1st BCAM Workshop on Nonlinear Dynamics in organic structures, held in June 2014 on the Basque middle of utilized arithmetic (BCAM). At this overseas assembly, researchers from diversified yet complementary backgrounds, together with molecular dynamics, actual chemistry, bio-informatics and biophysics, provided their most up-to-date effects and mentioned the longer term path in their experiences utilizing theoretical, mathematical modeling and experimental techniques. Such used to be the extent of curiosity inspired that the choice was once taken to provide this ebook, with the organizers of the development performing as editors. the entire contributing authors are researchers engaged on different organic difficulties that may be approached utilizing nonlinear dynamics. The booklet will allure specifically to utilized mathematicians, biophysicists, and computational biologists.
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Extra resources for Nonlinear Dynamics in Biological Systems
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.