Pearce John A
J Biomech Eng. 2015 Dec;137(12):121006. doi: 10.1115/1.4031851.
The Arrhenius formulation for single-step irreversible unimolecular reactions has been used for many decades to describe the thermal damage and cell death processes. Arrhenius predictions are acceptably accurate for structural proteins, for some cell death assays, and for cell death at higher temperatures in most cell lines, above about 55 °C. However, in many cases--and particularly at hyperthermic temperatures, between about 43 and 55 °C--the particular intrinsic cell death or damage process under study exhibits a significant "shoulder" region that constant-rate Arrhenius models are unable to represent with acceptable accuracy. The primary limitation is that Arrhenius calculations always overestimate the cell death fraction, which leads to severely overoptimistic predictions of heating effectiveness in tumor treatment. Several more sophisticated mathematical model approaches have been suggested and show much-improved performance. But simpler models that have adequate accuracy would provide useful and practical alternatives to intricate biochemical analyses. Typical transient intrinsic cell death processes at hyperthermic temperatures consist of a slowly developing shoulder region followed by an essentially constant-rate region. The shoulder regions have been demonstrated to arise chiefly from complex functional protein signaling cascades that generate delays in the onset of the constant-rate region, but may involve heat shock protein activity as well. This paper shows that acceptably accurate and much-improved predictions in the simpler Arrhenius models can be obtained by adding a temperature-dependent time delay. Kinetic coefficients and the appropriate time delay are obtained from the constant-rate regions of the measured survival curves. The resulting predictions are seen to provide acceptably accurate results while not overestimating cell death. The method can be relatively easily incorporated into numerical models. Additionally, evidence is presented to support the application of compensation law behavior to the cell death processes--that is, the strong correlation between the kinetic coefficients, ln{A} and E(a), is confirmed.
几十年来，单步不可逆单分子反应的阿伦尼乌斯公式一直被用于描述热损伤和细胞死亡过程。对于结构蛋白、一些细胞死亡检测以及大多数细胞系在高于约55°C的较高温度下的细胞死亡，阿伦尼乌斯预测的准确性是可以接受的。然而，在许多情况下，特别是在热疗温度（约43至55°C）下，所研究的特定内在细胞死亡或损伤过程表现出显著的“肩部”区域，恒定速率的阿伦尼乌斯模型无法以可接受的准确性表示该区域。主要限制在于阿伦尼乌斯计算总是高估细胞死亡分数，这导致在肿瘤治疗中对加热效果的预测严重过于乐观。已经提出了几种更复杂的数学模型方法，并且表现出了显著改进。但是具有足够准确性的更简单模型将为复杂的生化分析提供有用且实用的替代方案。热疗温度下典型的瞬态内在细胞死亡过程包括一个缓慢发展的肩部区域，随后是一个基本恒定速率的区域。已证明肩部区域主要源于复杂的功能性蛋白质信号级联反应，这些反应在恒定速率区域的开始产生延迟，但也可能涉及热休克蛋白活性。本文表明，通过添加与温度相关的时间延迟，可以在更简单的阿伦尼乌斯模型中获得可接受的准确且显著改进的预测。动力学系数和适当的时间延迟从测量的存活曲线的恒定速率区域获得。结果表明，所得预测提供了可接受的准确结果，同时不会高估细胞死亡。该方法可以相对容易地纳入数值模型。此外，还提供了证据来支持补偿定律行为在细胞死亡过程中的应用——也就是说，证实了动力学系数ln{A}和E(a)之间的强相关性。
