Stanley H E, Buldyrev S V, Goldberger A L, Hausdorff J M, Havlin S, Mietus J, Sciortino F, Simons M
Center for Polymer Studies and Department of Physics, Boston University, MA 02215.
Physica A. 1992 Dec 15;191(1-4):1-12. doi: 10.1016/0378-4371(92)90497-e.
Here we discuss recent advances in applying ideas of fractals and disordered systems to two topics of biological interest, both topics having common the appearance of scale-free phenomena, i.e., correlations that have no characteristic length scale, typically exhibited by physical systems near a critical point and dynamical systems far from equilibrium. (i) DNA nucleotide sequences have traditionally been analyzed using models which incorporate the possibility of short-range nucleotide correlations. We found, instead, a remarkably long-range power law correlation. We found such long-range correlations in intron-containing genes and in non-transcribed regulatory DNA sequences as well as intragenomic DNA, but not in cDNA sequences or intron-less genes. We also found that the myosin heavy chain family gene evolution increases the fractal complexity of the DNA landscapes, consistent with the intron-late hypothesis of gene evolution. (ii) The healthy heartbeat is traditionally thought to be regulated according to the classical principle of homeostasis, whereby physiologic systems operate to reduce variability and achieve an equilibrium-like state. We found, however, that under normal conditions, beat-to-beat fluctuations in heart rate display long-range power law correlations.
在此，我们讨论将分形和无序系统的概念应用于两个生物学相关主题的最新进展，这两个主题都呈现出无标度现象，即不存在特征长度尺度的相关性，通常在临界点附近的物理系统和远离平衡的动力学系统中表现出来。（i）传统上，DNA核苷酸序列是使用纳入短程核苷酸相关性可能性的模型进行分析的。相反，我们发现了一种显著的长程幂律相关性。我们在含内含子的基因、非转录调控DNA序列以及基因组内DNA中发现了这种长程相关性，但在cDNA序列或无内含子基因中未发现。我们还发现肌球蛋白重链家族基因的进化增加了DNA景观的分形复杂性，这与基因进化的内含子后期假说一致。（ii）传统上认为健康的心跳是根据经典的稳态原理进行调节的，即生理系统通过运作来减少变异性并达到类似平衡的状态。然而，我们发现，在正常情况下，心率的逐搏波动呈现出长程幂律相关性。
