Gagen M J, Mattick J S
ARC Special Research Centre for Functional and Applied Genomics Institute for Molecular Bioscience, University of Queensland, 4072, Brisbane, Qld, Australia,
Theory Biosci. 2005 Apr;123(4):381-411. doi: 10.1016/j.thbio.2005.02.002.
Networks exhibiting "accelerating" growth have total link numbers growing faster than linearly with network size and either reach a limit or exhibit graduated transitions from nonstationary-to-stationary statistics and from random to scale-free to regular statistics as the network size grows. 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.
呈现“加速”增长的网络，其总链接数的增长速度快于与网络规模的线性关系，并且要么达到一个极限，要么随着网络规模的增长，呈现出从非平稳统计到平稳统计、从随机统计到无标度统计再到规则统计的渐变过渡。然而，如果由于任何原因网络无法容忍这种总体结构变化，那么加速网络的规模就会受到限制，低于某个临界值。这一点很有意思，因为单细胞原核生物的调控基因网络具有加速的二次增长特征，并且规模受限，其编码的基因数量少于约10000个，对应的DNA序列长度少于约10兆碱基。本文提出了一种用于原核基因调控的概率加速网络模型，该模型通过采用两类网络节点（调控节点和非调控节点）以及有向链接来紧密匹配观测到的统计数据，这些有向链接的入头在所有节点上呈指数分布，而出尾则优先连接到调控节点，并由无标度分布描述。该模型解释了观测到的调控因子数量随基因数量的二次增长，并预测了原核生物的大小上限，与观测值非常接近。
