arXiv subjects

J. S. Mattick

Publications and source records attributed to J. S. Mattick.

4 recordsLinked to original sources

arXiv2005

Accelerating, hyper-accelerating, and decelerating probabilistic networks

Many growing networks possess accelerating statistics where the number of links added with each new node is an increasing function of network size so the total number of links increases faster than linearly with network size. In particular, biological networks can display a quadratic growth in regulator number with genome size even while remaining sparsely connected. These features are mutually incompatible in standard treatments of network theory which typically require that every new network node possesses at least one connection. To model sparsely connected networks, we generalize existing approaches and add each new node with a probabilistic number of links to generate either accelerating, hyper-accelerating, or even decelerating network statistics in different regimes. Under preferential attachment for example, slowly accelerating networks display stationary scale-free statistics relatively independent of network size while more rapidly accelerating networks display a transition from scale-free to exponential statistics with network growth. Such transitions explain, for instance, the evolutionary record of single-celled organisms which display strict size and complexity limits.

q-bio.MN↗

arXiv2004

Increasing biological complexity is positively correlated with the relative genome-wide expansion of non-protein-coding DNA sequences

Background: Prior to the current genomic era it was suggested that the number of protein-coding genes that an organism made use of was a valid measure of its complexity. It is now clear, however, that major incongruities exist and that there is only a weak relationship between biological complexity and the number of protein coding genes. For example, using the protein-coding gene number as a basis for evaluating biological complexity would make urochordates and insects less complex than nematodes, and humans less complex than rice. Results: We analyzed the ratio of noncoding to total genomic DNA (ncDNA/tgDNA) for 85 sequenced species and found that this ratio correlates well with increasing biological complexity. The ncDNA/tgDNA ratio is generally contained within the bandwidth of 0.05-0.24 for prokaryotes, but rises to 0.26-0.52 in unicellular eukaryotes, and to 0.62-0.985 for developmentally complex multicellular organisms. Significantly, prokaryotic species display a non-uniform species distribution approaching the mean of 0.1177 ncDNA/tgDNA (p=1.58 x 10^-13), and a nonlinear ncDNA/tgDNA relationship to genome size (r=0.15). Importantly, the ncDNA/tgDNA ratio corrects for ploidy, and is not substantially affected by variable loads of repetitive sequences. Conclusions: We suggest that the observed noncoding DNA increases and compositional patterns are primarily a function of increased information content. It is therefore possible that introns, intergenic sequences, repeat elements, and genomic DNA previously regarded as genetically inert may be far more important to the evolution and functional repertoire of complex organisms than has been previously appreciated.

q-bio.GN↗

arXiv2004

Inherent size constraints on prokaryote gene networks due to "accelerating" growth

Networks exhibiting "accelerating" growth have total link numbers growing faster than linearly with network size and can exhibit transitions from stationary to nonstationary statistics and from random to scale-free to regular statistics at particular critical network sizes. However, if for any reason the network cannot tolerate such gross structural changes then accelerating networks are constrained to have sizes below some critical value. This is of interest as the regulatory gene networks of single celled prokaryotes are characterized by an accelerating quadratic growth and are size constrained to be less than about 10,000 genes encoded in DNA sequence of less than about 10 megabases. This paper presents a probabilistic accelerating network model for prokaryotic gene regulation which closely matches observed statistics by employing two classes of network nodes (regulatory and non-regulatory) and directed links whose inbound heads are exponentially distributed over all nodes and whose outbound tails are preferentially attached to regulatory nodes and described by a scale free distribution. This model explains the observed quadratic growth in regulator number with gene number and predicts an upper prokaryote size limit closely approximating the observed value.

q-bio.MN↗

arXiv2004

Failed "nonaccelerating" models of prokaryote gene regulatory networks

Much current network analysis is predicated on the assumption that important biological networks will either possess scale free or exponential statistics which are independent of network size allowing unconstrained network growth over time. In this paper, we demonstrate that such network growth models are unable to explain recent comparative genomics results on the growth of prokaryote regulatory gene networks as a function of gene number. This failure largely results as prokaryote regulatory gene networks are "accelerating" and have total link numbers growing faster than linearly with network size and so can exhibit transitions from stationary to nonstationary statistics and from random to scale-free to regular statistics at particular critical network sizes. In the limit, these networks can undergo transitions so marked as to constrain network sizes to be below some critical value. This is of interest as the regulatory gene networks of single celled prokaryotes are indeed characterized by an accelerating quadratic growth with gene count and are size constrained to be less than about 10,000 genes encoded in DNA sequence of less than about 10 megabases. We develop two "nonaccelerating" network models of prokaryote regulatory gene networks in an endeavor to match observation and demonstrate that these approaches fail to reproduce observed statistics.

q-bio.MN↗