老化与复杂性的数学联系
Mathematical link of evolving aging and complexity
摘要：
衰老是生命系统的一个基本方面，随着年龄的增长，生理功能逐渐退化，对疾病和死亡的脆弱性增加。生命系统，被称为复杂系统，需要分子、细胞、器官和个体之间相互作用的复杂性或调节机制来执行各种生存活动。在此基础上，衰老可以理解为随着年龄的增长，复杂性逐渐丧失;这表明生命系统的复杂性会随着年龄的增长而进化。一般来说，老化动力学在数学上由生存函数描述，其随着年龄单调地从1变化到0。然后，找到一个适当的生存函数来联系衰老动力学和复杂性进化将是有用的。在这里，我们描述了一个灵活的生存函数，这是来自拉伸指数函数，通过采用年龄相关的指数。我们注意到，指数与演化的复杂性相关联，即，一个类似分形的累积死亡率比例。生存函数很好地描述了生存曲线的一般特征;健康人群显示出向矩形生存曲线进化的趋势，例如人类或实验室动物。这种趋势表明，老化和复杂性都将朝着生命系统中健康生存的方向发展。我们将衰老与复杂性联系起来的功能可能有助于更好地理解复杂性进化方面的生物衰老。
英文摘要：
Aging is a fundamental aspect of living systems that undergo a progressive deterioration of physiological function with age and an increase of vulnerability to disease and death. Living systems, known as complex systems, require complexity in interactions among molecules, cells, organs, and individuals or regulatory mechanisms to perform a variety of activities for survival. On this basis, aging can be understood in terms of a progressive loss of complexity with age; this suggests that complexity in living systems would evolve with age. In general, aging dynamics is mathematically depicted by a survival function, which monotonically changes from 1 to 0 with age. It would be then useful to find an adequate survival function to link aging dynamics and complexity evolution. Here we describe a flexible survival function, which is derived from the stretched exponential function by adopting an age-dependent exponent. We note that the exponent is associated with evolving complexity, i.e., a fractal-like scaling in cumulative mortality. The survival function well depicts a general feature in survival curves; healthy populations show a tendency to evolve towards rectangular-like survival curves, as examples in humans or laboratory animals. This tendency suggests that both aging and complexity would evolve towards healthy survival in living systems. Our function to link aging with complexity may contribute to better understanding of biological aging in terms of complexity evolution.
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