Minimal Replicator Theory I: Parabolic Versus Exponential Growth
Minimal Replicator Theory I: Parabolic Versus Exponential Growth
复制标题
最小复制理论 I：抛物线增长与指数增长
DOI：
10.1007/978-3-642-78110-0_4
复制
发表时间：
1993
期刊：
影响因子：
--
通讯作者：
G. Kiedrowski
中科院分区：
文献类型：
--
作者：
G. Kiedrowski
本文描述了人工自复制系统的一种解析处理方法。今天已知的所有人工自我复制系统都是最小复制子，从这个意义上说，它们的动力学行为可以通过导言中概述的常见的最小反应模型来合理化。在第二部分中，介绍了经验速率方程，这些方程被证明对实验浓度-时间分布的评估是有用的。第三部分首先讨论了前面描述的解释自复制模板分子的自催化合成的反应模型。然后对最小反应模型进行了分析处理：A+B+C⇌ABC→C2；⇌2C，其中C是自互补模板分子，A和B是其前体分子，ABC是三分子络合物，C2是模板双链体。假设ABC不可逆地生成C2是反应的限速步骤，且模板总浓度小于其前体。推导出的解析表达式允许我们从基本速率和平衡常数估计合成自复制系统的速率和自催化反应级数。最小自复制系统的三个极限增长定律--称为抛物线、弱指数和强指数--可以区分开来。下一节讨论温度的影响。预计在低温下会出现强劲的指数增长，而在高温下应该会出现微弱的指数增长。预计平均气温将呈抛物线增长。根据不可逆步骤的活化能以及ABC和C2的生成热，自催化速率的最大值要么出现在从强指数增长到抛物线增长的转变温度，要么出现在从抛物线增长到弱指数增长的转变温度，或者出现在平均温度。然后将处理上述最小反应模型的分析结果与更接近实际的模型的结果进行比较。特别是，A和B形成的络合物AB使得很难观察到在低温下可能出现的强劲的指数增长。
The paper describes an analytical treatment of artificial self-replicating systems. All artificial self-replicating systems known today are minimal replicators in the sense that their kinetic behavior can be rationalized by a common, minimal reaction model which is outlined in the introduction. In the second section, empirical rate equations are introduced which have proven useful for the evaluation of experimental concentration-time profiles. The third section begins with an discussion of reaction models which have been described earlier to explain the autocatalytic synthesis of self-replicating template molecules. It is followed by an analytical treatment of the minimal reaction model: A + B + C⇌ABC→ C 2;⇌ 2C, where C is a self-complementary template molecule, A and B its precursor molecules, ABC a termolecular complex, and C 2 a template duplex. It is assumed that the irreversible formation of C 2 from ABC is the rate limiting step and that the total template concentration is small as compared to its precursors. The analytical expressions derived allow us to estimate the rate and autocatalytic reaction order for synthetic self-replicating systems from the elementary rate and equilibria constants involved. Three limit growth laws for minimal self-replicating systems—termed as parabolic, weak exponential, and strong exponential—can be distinguished. The following section deals with the influence of temperature. Strong exponential growth is to be expected for low temperatures, whereas weak exponential growth should occur at high temperatures. Parabolic growth is expected for average temperatures. Depending on the activation energy of the irreversible step as well as on the enthalpies of the formation of ABC and C 2, the maximum of the autocatalytic rate occurs either at the temperature of the transition from strong exponential to parabolic growth, or, at the temperature of transition from parabolic to weak exponential growth, or, at an average temperature. The analytical results from the treatment of the above minimal reaction model are then compared to results from more realistic models. In particular, it is shown that the formation of a complex AB from A and B makes it difficult to observe strong exponential growth which otherwise might be found at low temperatures.
DOI：
10.1073/pnas.83.11.3746
发表时间：
1986-06-01
影响因子：
11.1
作者：
BRESLAUER, KJ;FRANK, R;MARKY, LA
通讯作者：
MARKY, LA