Division of Biology, IISER Pune, Dr. Homi Bhabha Road, Pashan, Pune 411008, India.
Phys Rev E. 2020 Jan;101(1-1):012417. doi: 10.1103/PhysRevE.101.012417.
Oscillatory gene circuits are ubiquitous to biology and are involved in fundamental processes of cell cycle, circadian rhythms, and developmental systems. The synthesis of small, non-natural oscillatory genetic circuits has been increasingly used to test the fundamental principles of genetic network dynamics. While the "repressilator" was used to first demonstrate the proof of principle, a more recently developed dual-feedback, fast, tunable genetic oscillator has demonstrated a greater degree of robustness and control over oscillatory behavior by combining positive- and negative-feedback loops. This oscillator, combining lacI (negative-) and araC (positive-) feedback loops, was, however, modeled using multiple layers of differential equations to capture the molecular complexity of regulation, in order to explain the experimentally measured oscillations. In the search for design principles of such minimal oscillatory circuits, we have developed a reduced model of this dual-feedback loop oscillator consisting of just six differential equations, two of which are delay differential equations. The delay term is optimized, as the only free parameter, to fit the experimental dynamics of the oscillator period and amplitude tunability by the two inducers isopropyl β-D-1-thiogalactopyranoside (IPTG) and arabinose. We proceed to use our reduced and experimentally validated model to redesign the network by comparing the effect of asymmetry in gene expression at the level of (a) DNA copy numbers and the rates of (b) mRNA translation and (c) degradation, since experimental and theoretical work had predicted a need for an asymmetry in the copy numbers of activator (araC) and repressor (lacI) genes encoded on plasmids. We confirm that the minimal period of the oscillator is sensitive to DNA copy number asymmetry, and can demonstrate that while the asymmetry in the translation rate has an identical effect as the plasmid copy numbers, modulating the asymmetry in mRNA degradation can improve the tunability of the period and amplitude of the oscillator. Thus, our model predicts control at the level of translation can be used to redesign such networks, for improved tunability, while at the same time making the network robust to replication "noise" and the effects of the host cell cycle. Thus, our model predicts experimentally testable principles to redesign a potentially more robust oscillatory genetic network.
振荡基因电路在生物学中无处不在，涉及细胞周期、昼夜节律和发育系统的基本过程。合成小型非天然振荡遗传电路已越来越多地用于测试遗传网络动力学的基本原理。虽然“阻遏子”首先被用来证明原理，但最近开发的双反馈、快速、可调谐的遗传振荡器通过结合正反馈和负反馈回路，展示了对振荡行为更大程度的鲁棒性和控制。这个振荡器，结合 lacI（负）和 araC（正）反馈回路，然而，为了捕捉调节的分子复杂性，使用了多层微分方程进行建模，以解释实验测量的振荡。在寻找这种最小振荡电路的设计原则的过程中，我们开发了一个由六个微分方程组成的双反馈环振荡器的简化模型，其中两个是时滞微分方程。时滞项是作为唯一的自由参数进行优化的，以拟合振荡器周期的实验动力学和两个诱导物异丙基-β-D-1-硫代半乳糖吡喃糖苷（IPTG）和阿拉伯糖对振幅可调性的影响。我们通过比较（a）DNA 拷贝数和（b）mRNA 翻译和（c）降解的基因表达水平上的不对称性对网络进行重新设计，继续使用我们简化的、经过实验验证的模型，因为实验和理论工作预测了在质粒上编码的激活剂（araC）和抑制剂（lacI）基因的拷贝数需要不对称。我们证实，振荡器的最小周期对 DNA 拷贝数的不对称性很敏感，并且可以证明，尽管翻译率的不对称性与质粒拷贝数具有相同的效果，但调节 mRNA 降解的不对称性可以提高振荡器的周期和振幅的可调性。因此，我们的模型预测，在翻译水平上的控制可以用于重新设计这种网络，以提高可调性，同时使网络对复制“噪声”和宿主细胞周期的影响具有鲁棒性。因此，我们的模型预测了可用于重新设计潜在更稳健的振荡遗传网络的可实验测试的原理。
