We study a very simple linear evolutionary model based on distribution of protocells by total enantiomeric excess and without any mutual inhibition and show that such model can produce two species with values of total enantiomeric excess in each of the species approaching \(\pm 1\) when there is a global \(L\leftrightarrow D\) symmetry. We then consider a scenario when there is a small external global asymmetry factor, like weak interaction, and show that only one of the species remains in such a case, and that is the one, which is more efficient in replication. We perform an estimate of the time necessary to reach homochirality in such a model and show that reasonable assumptions lead to an estimate of around 300 thousand years plus or minus a couple of orders of magnitude. Despite this seemingly large time to reach homochirality, the model is immune to racemization because amino acids in the model follow the lifespan of the protocells rather than the time needed to reach homochirality. We show that not needing mutual inhibition in such evolutionary model is due to the difference in the topology of the spaces in which considered model and many known models of biological homochirality operate. Bifurcation-based models operate in disconnected zero-dimensional space (the space is just two points with enantiomeric excess equal \(-1\) and \(1\)), whereas considered evolutionary model (in its continuous representation) operates in one-dimensional connected space, that is the whole interval between \(-1\) and \(1\) of total enantiomeric excess. We then proceed with the analysis of the replication process in non-homochiral environment and show that replication errors (the probability to attach an amino acid of wrong chirality) result in a smooth decrease of replication time when total enantiomeric excess of the replicated structure moves away from zero. We show that this decrease in replication time is sufficient for considered model to work.

我们研究了一个非常简单的线性进化模型，该模型基于原始细胞按总对映体过量分布且没有任何相互抑制，并表明该模型可以产生两个物种，每个物种的总对映体过量值接近\(\pm 1\)当存在全局\(L\leftrightarrow D\)对称性时。然后，我们考虑一种情况，当存在一个小的外部全局不对称因素（例如弱相互作用）时，并表明在这种情况下只有一个物种仍然存在，那就是复制效率更高的物种。我们对在这样的模型中达到同手性所需的时间进行了估计，并表明合理的假设导致估计大约 30 万年加上或减去几个数量级。尽管达到纯手性的时间看似很长，但该模型不受外消旋化的影响，因为模型中的氨基酸遵循原始细胞的寿命，而不是达到纯手性所需的时间。我们表明，在这种进化模型中不需要相互抑制是由于所考虑的模型和许多已知的生物同手性模型运行的空间拓扑的差异。基于分叉的模型在不连续的零维空间中运行（该空间只是对映体过量等于\(-1\)和\(1\)的两个点），而所考虑的进化模型（以其连续表示形式）在一维空间中运行维连通空间，即总对映体过量的\(-1\)和\(1\)之间的整个区间。然后，我们继续分析非同手性环境中的复制过程，并表明当复制结构的总对映体过量移走时，复制错误（连接错误手性氨基酸的概率）会导致复制时间平稳减少从零开始。我们表明，复制时间的减少足以使所考虑的模型发挥作用。