Stanley H E, Buldyrev S V, Goldberger A L, Goldberger Z D, Havlin S, Mantegna R N, Ossadnik S M, Peng C K, Simons M
Department of Physics, Boston University, MA 02215, USA.
Physica A. 1994 Apr 1;205(1-3):214-53. doi: 10.1016/0378-4371(94)90502-9.
The purpose of this opening talk is to describe examples of recent progress in applying statistical mechanics to biological systems. We first briefly review several biological systems, and then focus on the fractal features characterized by the long-range correlations found recently in DNA sequences containing non-coding material. We discuss the evidence supporting the finding that for sequences containing only coding regions, there are no long-range correlations. We also discuss the recent finding that the exponent alpha characterizing the long-range correlations increases with evolution, and we discuss two related models, the insertion model and the insertion-deletion model, that may account for the presence of long-range correlations. Finally, we summarize the analysis of long-term data on human heartbeats (up to 10(4) heart beats) that supports the possibility that the successive increments in the cardiac beat-to-beat intervals of healthy subjects display scale-invariant, long-range "anti-correlations" (a tendency to beat faster is balanced by a tendency to beat slower later on). In contrast, for a group of subjects with severe heart disease, long-range correlations vanish. This finding suggests that the classical theory of homeostasis, according to which stable physiological processes seek to maintain "constancy," should be extended to account for this type of dynamical, far from equilibrium, behavior.
本次开场演讲的目的是介绍将统计力学应用于生物系统的近期进展实例。我们首先简要回顾几个生物系统，然后重点关注最近在包含非编码物质的DNA序列中发现的以长程相关性为特征的分形特征。我们讨论支持以下发现的证据：对于仅包含编码区域的序列，不存在长程相关性。我们还讨论了最近的发现，即表征长程相关性的指数α随进化而增加，并且我们讨论了两个相关模型，即插入模型和插入 - 删除模型，它们可能解释长程相关性的存在。最后，我们总结了对人类心跳长期数据（长达10^4次心跳）的分析，该分析支持以下可能性：健康受试者心跳间期的连续增量显示出尺度不变的长程“反相关性”（稍后心跳加快的趋势会被心跳减慢的趋势所平衡）。相比之下，对于一组患有严重心脏病的受试者，长程相关性消失。这一发现表明，经典的稳态理论（根据该理论，稳定的生理过程试图维持“恒定”）应加以扩展，以解释这种远离平衡的动态行为。
