一个扩展的前生物同手性演化模型：一种自下而上的生命起源方法
An Extended Model for the Evolution of Prebiotic Homochirality: A Bottom-Up Approach to the Origin of Life
摘要：
本文详细研究了手性聚合的广义自催化模型。除了对映体交叉抑制，该模型允许自生（非催化）形成的左，右手单体从基板与反应速率$ε_L$和$ε_R$，分别。研究了具有几个最大聚合物长度N值的模型的净手性不对称性的时空演化。当N=2时，我们研究了文献中经常引用的绝热近似的有效性。我们表明，近似得到正确的平衡值的净手征，但未能重现短时间的行为。我们还表明，在完整的N=2模型中的自生项的行为作为一个控制参数的手性对称性破缺相变，导致从外消旋的初始条件完全同手性。我们研究了N ->无穷大对称（$ε_L = ε_R$）自生模型的动力学，发现它只对$ε< ε_c$实现了同手性，其中$ε_c$是N依赖的临界值.对于$ε\leq ε_c$，我们研究了具有几个N值的模型的行为，表明净手性不对称性随着tanh（N）而增长。我们发现，对于一个给定的对称自生反应速率，在模型中的最大聚合物长度的净手性和手性纯聚合物的浓度增加。我们简要地讨论了我们的研究结果的后果，为发展的同手性在前生物地球和可能的实验验证我们的研究结果。
英文摘要：
A generalized autocatalytic model for chiral polymerization is investigated in detail. Apart from enantiomeric cross-inhibition, the model allows for the autogenic (non-catalytic) formation of left and right-handed monomers from a substrate with reaction rates $ε_L$ and $ε_R$, respectively. The spatiotemporal evolution of the net chiral asymmetry is studied for models with several values of the maximum polymer length, N. For N=2, we study the validity of the adiabatic approximation often cited in the literature. We show that the approximation obtains the correct equilibrium values of the net chirality, but fails to reproduce the short time behavior. We show also that the autogenic term in the full N=2 model behaves as a control parameter in a chiral symmetry- breaking phase transition leading to full homochirality from racemic initial conditions. We study the dynamics of the N -> infinity model with symmetric ($ε_L = ε_R$) autogenic formation, showing that it only achieves homochirality for $ε< ε_c$, where $ε_c$ is an N-dependent critical value. For $ε\leq ε_c$ we investigate the behavior of models with several values of N, showing that the net chiral asymmetry grows as tanh(N). We show that for a given symmetric autogenic reaction rate, the net chirality and the concentrations of chirally pure polymers increase with the maximum polymer length in the model. We briefly discuss the consequences of our results for the development of homochirality in prebiotic Earth and possible experimental verification of our findings.
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