Department of Biomedical Engineering, Boston University, Boston, Massachusetts 02215, USA.
Chaos. 2013 Mar;23(1):013132. doi: 10.1063/1.4793573.
The synthetic construction of intracellular circuits is frequently hindered by a poor knowledge of appropriate kinetics and precise rate parameters. Here, we use generalized modeling (GM) to study the dynamical behavior of topological models of a family of hybrid metabolic-genetic circuits known as "metabolators." Under mild assumptions on the kinetics, we use GM to analytically prove that all explicit kinetic models which are topologically analogous to one such circuit, the "core metabolator," cannot undergo Hopf bifurcations. Then, we examine more detailed models of the metabolator. Inspired by the experimental observation of a Hopf bifurcation in a synthetically constructed circuit related to the core metabolator, we apply GM to identify the critical components of the synthetically constructed metabolator which must be reintroduced in order to recover the Hopf bifurcation. Next, we study the dynamics of a re-wired version of the core metabolator, dubbed the "reverse" metabolator, and show that it exhibits a substantially richer set of dynamical behaviors, including both local and global oscillations. Prompted by the observation of relaxation oscillations in the reverse metabolator, we study the role that a separation of genetic and metabolic time scales may play in its dynamics, and find that widely separated time scales promote stability in the circuit. Our results illustrate a generic pipeline for vetting the potential success of a circuit design, simply by studying the dynamics of the corresponding generalized model.
细胞内电路的合成构建经常受到对适当动力学和精确速率参数的了解不足的阻碍。在这里，我们使用广义建模 (GM) 来研究一类称为“代谢物”的混合代谢遗传电路的拓扑模型的动态行为。在动力学的温和假设下，我们使用 GM 从理论上证明，所有拓扑上类似于一个这样的电路（“核心代谢物”）的显式动力学模型都不能发生 Hopf 分岔。然后，我们研究了代谢物的更详细模型。受在与核心代谢物相关的合成构建电路中观察到 Hopf 分岔的实验观察的启发，我们应用 GM 来确定为了恢复 Hopf 分岔必须重新引入的合成构建代谢物的关键组件。接下来，我们研究了核心代谢物的重新布线版本（称为“反向”代谢物）的动力学，并表明它表现出更丰富的动力学行为，包括局部和全局振荡。受反向代谢物中弛豫振荡的观察的启发，我们研究了遗传和代谢时间尺度分离可能在其动力学中起的作用，并发现广泛分离的时间尺度促进了电路的稳定性。我们的结果说明了一种通用的方法，用于通过研究相应的广义模型的动力学来验证电路设计的潜在成功。
