Theory for Transitions Between Exponential and Stationary Phases: Universal Laws for Lag Time
Theory for Transitions Between Exponential and Stationary Phases: Universal Laws for Lag Time
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DOI：
10.1103/physrevx.7.021049
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发表时间：
2017-06-27
影响因子：
12.5
通讯作者：
Kaneko, Kunihiko
中科院分区：
文献类型：
--
作者：
Himeoka, Yusuke;Kaneko, Kunihiko
自从Monod的开创性研究以来，细菌生长的定量表征引起了人们的极大关注。理论和实验工作已经揭示了描述指数生长阶段的几个定律，在该阶段中细胞的数量呈指数增长。然而，微生物生长在饥饿条件下也表现出滞后期、静止期和死亡期，在饥饿条件下细胞生长受到高度抑制，对此定量规律或理论明显不发达。事实上，通常采用的指数阶段模型，包括自催化化学成分，包括核糖体，只能显示人口的指数增长或衰减;因此，停止增长的阶段是不可能实现的。在这里，我们提出了一个简单的，粗粒度的细胞模型，其中包括一个额外的类的大分子成分，除了促进细胞生长的自催化活性成分。这些额外的组分与活性组分形成复合物以抑制催化过程。根据营养条件，该模型表现出典型的滞后，指数，平稳和死亡阶段之间的过渡。此外，饥饿后生长恢复所需的滞后时间遵循饥饿时间的平方根，并与最大生长速率呈负相关。这与实验观察一致，其中细胞饥饿的时间长度在分子的缓慢积累中被记忆。此外，在单元之间分布的滞后时间是偏斜的，具有长的时间尾部。当饥饿时间较长时，出现指数尾，这也与实验数据一致。我们的理论进一步预测了滞后时间对底物耗尽速度的强烈依赖性，这可以通过实验进行测试。本模型和理论分析提供了超越指数期的普遍生长规律，提供了细胞如何停止生长而不进入死亡期的见解。
The quantitative characterization of bacterial growth has attracted substantial attention since Monod's pioneering study. Theoretical and experimental works have uncovered several laws for describing the exponential growth phase, in which the number of cells grows exponentially. However, microorganism growth also exhibits lag, stationary, and death phases under starvation conditions, in which cell growth is highly suppressed, for which quantitative laws or theories are markedly underdeveloped. In fact, the models commonly adopted for the exponential phase that consist of autocatalytic chemical components, including ribosomes, can only show exponential growth or decay in a population; thus, phases that halt growth are not realized. Here, we propose a simple, coarse-grained cell model that includes an extra class of macromolecular components in addition to the autocatalytic active components that facilitate cellular growth. These extra components form a complex with the active components to inhibit the catalytic process. Depending on the nutrient condition, the model exhibits typical transitions among the lag, exponential, stationary, and death phases. Furthermore, the lag time needed for growth recovery after starvation follows the square root of the starvation time and is inversely related to the maximal growth rate. This is in agreement with experimental observations, in which the length of time of cell starvation is memorized in the slow accumulation of molecules. Moreover, the lag time distributed among cells is skewed with a long time tail. If the starvation time is longer, an exponential tail appears, which is also consistent with experimental data. Our theory further predicts a strong dependence of lag time on the speed of substrate depletion, which can be tested experimentally. The present model and theoretical analysis provide universal growth laws beyond the exponential phase, offering insight into how cells halt growth without entering the death phase.