Bigan Erwan, Plateau Pierre
École Polytechnique.
Artif Life. 2017 Fall;23(4):453-480. doi: 10.1162/ARTL_a_00241. Epub 2017 Oct 6.
One proposed scenario for the emergence of biochemical oscillations is that they may have provided the basic mechanism behind cellular self-replication by growth and division. However, alternative scenarios not requiring any chemical oscillation have also been proposed. Each of the various protocell models proposed to support one or another scenario comes with its own set of specific assumptions, which makes it difficult to ascertain whether chemical oscillations are required or not for cellular self-replication. This article compares these two cases within a single whole-cell model framework. This model relies upon a membrane embedding a chemical reaction network (CRN) synthesizing all the cellular constituents, including the membrane, by feeding from an external nutrient. Assuming the osmolarity is kept constant, the system dynamics are governed by a set of nonlinear differential equations coupling the chemical concentrations and the surface-area-to-volume ratio. The resulting asymptotic trajectories are used to determine the cellular shape by minimizing the membrane bending energy (within an approximate predefined family of shapes). While the stationary case can be handled quite generally, the oscillatory one is investigated using a simple oscillating CRN example, which is used to identify features that are expected to hold for any network. It is found that cellular self-replication can be reached with or without chemical oscillations, and that a requirement common to both stationary and oscillatory cases is that a minimum spontaneous curvature of the membrane is required for the cell to divide once its area and volume are both doubled. The oscillatory case can result in a greater variety of cellular shape trajectories but raises additional constraints for cellular division and self-replication: (i) the ratio of doubling time to oscillation period should be an integer, and (ii) if the oscillation amplitude is sufficiently high, then the spontaneous curvature must be below a maximum value to avoid early division before the end of the cycle. Because of these additional stringent constraints, it is likely that early protocells did not rely upon chemical oscillations. Biochemical oscillations typical of modern evolved cells may have emerged later through evolution for other reasons (e.g., metabolic advantage) and must have required additional feedback mechanisms for such a self-replicating system to be robust against even slight environmental variations (e.g., temperature fluctuations).
关于生化振荡出现的一种假设情景是，它们可能为细胞通过生长和分裂进行自我复制提供了基本机制。然而，也有人提出了不需要任何化学振荡的替代情景。为支持一种或另一种情景而提出的各种原始细胞模型，每一个都有其自身的一套特定假设，这使得难以确定细胞自我复制是否需要化学振荡。本文在单个全细胞模型框架内比较这两种情况。该模型依赖于嵌入化学反应网络（CRN）的膜，该网络通过从外部营养物质获取养分来合成包括膜在内的所有细胞成分。假设渗透压保持恒定，系统动力学由一组耦合化学浓度和表面积与体积比的非线性微分方程控制。通过最小化膜弯曲能量（在一组近似预定义的形状族内），利用所得的渐近轨迹来确定细胞形状。虽然稳态情况可以相当普遍地处理，但对于振荡情况，使用一个简单的振荡CRN示例进行研究，该示例用于识别预期对任何网络都成立的特征。研究发现，无论有无化学振荡都能实现细胞自我复制，并且稳态和振荡情况的一个共同要求是，一旦细胞的面积和体积都翻倍，细胞分裂需要膜具有最小的自发曲率。振荡情况可能导致更多样化的细胞形状轨迹，但对细胞分裂和自我复制提出了额外的限制：（i）倍增时间与振荡周期的比值应为整数，（ii）如果振荡幅度足够高，那么自发曲率必须低于最大值，以避免在周期结束前过早分裂。由于这些额外的严格限制，早期的原始细胞很可能不依赖化学振荡。现代进化细胞典型的生化振荡可能是后来由于其他原因（例如代谢优势）通过进化出现的，并且对于这样一个自我复制系统来说，为了对即使是轻微的环境变化（例如温度波动）具有鲁棒性，必然需要额外的反馈机制。
