Page History

...

Algorithm

Frequencies  of fragment sizes d sizes  produced by a uniform random fragmentation process have demonstrated to fall along Weibull distributions , if the fragmentation thermodynamics depends on the molecule size:

f(d)= d/h (d/ h)^d-1 exp—(d/h)^d (2)

Scale parameter  Scale parameter h represents the intensity of fragmentation (i.e., breaks per unit length), and—as a determinant of the mean expected fragment size—is assumbed assumed to be constant across molecules of different lengths for fragmentation protocols where the number of produced fragments depends on the molecule length. Shape parameter d parameter  reflects the geometric relation in which random fragmentation is breaking a molecule (e.g., d=1   corresponds to uniform fragmentation on the linear chain of nucleotides, d=2   splits uniformly the surface, and d=3 and  the volume, etc.).

Employing empirical data from spike-in sequences, we evaluated the fitting obtained by weighted subsampling from Weibull distributions with varying shape parameters. Weights for the subsampling (Fig. 2B, solid line) were derived by separating the characteristics of the combined Weibull distributions before filtering (dashed line in Fig. 2B and 2C) from the observed insert size distribution (Fig. 2B, dashed-dotted line). The quality of fit was measured as the p-value computed by a Kolgomorov-Smirnov test, comparing the in silico produced insert size distribution (Fig.2A, dashed lines) for each of the spike-in sequences under investigation with its experimental couterpart (Fig.2A, solid lines) under the null hypothesis that both samples were drawn from the same distribution. By this, we empirically found that the observed differences can be qualitatively reproduced under a constant decay rate (h=200nt), when shape parameter d depends logarithmically on the molecule length (Supplementary Fig.4).

In our uniform random fragmentation model, we adopt The Flux Simulator employs a 3-step algorithm to tokenize a respective molecule; first, geometry d and the number n of fragments that are obtained from the molecule are determined. We found empirically that parameter d depends logarithmically on len, the length of the molecule that is fragmented d=log(len). The number of fragments produced from a specific RNA molecule is determined by n=len/E(d_max), where E(d_max) is the expectancy of the most abundant fragment size, computed from h and the gamma-function G of d:

...