细胞中的最佳酶节律
Optimal enzyme rhythms in cells
摘要：
细胞可以使用周期性的酶活性来适应周期性的环境或现有的内部节奏，并建立代谢周期，及时安排生化过程。蛋白质预算在反应或途径之间的周期性变化分配可以增加总体代谢效率。为了研究这一假设，我量化了动力学模型中小幅度酶节律的可能益处。从酶优化的稳态开始，我对可能的酶节律对代谢目标的影响进行评分，并优化其振幅和相移。假设围绕最佳参考状态的小幅度节律，可以通过求解二次最优性问题来计算最佳相位和幅度。在没有振幅约束的模型中，一般的周期性酶谱可以通过傅立叶合成得到。最佳酶节律理论结合了代谢系统的动力学和经济学，并解释了网络结构、动力学、外部节律和代谢目标如何塑造最佳的小幅度酶谱。这些公式显示了协调的酶节律如何利用协同效应来改善代谢性能，并且最佳的酶谱不仅仅是适应现有的代谢节律，而是积极地塑造这些节律以提高其自身（和其他酶）的效率。由此产生的最佳酶谱“描绘”了酶在网络中的动态效应：例如，协同作用的酶可以周期性地共表达，并具有一些最佳相移。该理论产生代谢周期中酶节律的最优条件，静态酶适应作为特例，并预测细胞应如何结合转录和翻译后调节，以实现不同频率的酶节律。
英文摘要：
Cells can use periodic enzyme activities to adapt to periodic environments or existing internal rhythms and to establish metabolic cycles that schedule biochemical processes in time. A periodically changing allocation of the protein budget between reactions or pathways may increase the overall metabolic efficiency. To study this hypothesis, I quantify the possible benefits of small-amplitude enzyme rhythms in kinetic models. Starting from an enzyme-optimised steady state, I score the effects of possible enzyme rhythms on a metabolic objective and optimise their amplitudes and phase shifts. Assuming small-amplitude rhythms around an optimal reference state, optimal phases and amplitudes can be computed by solving a quadratic optimality problem. In models without amplitude constraints, general periodic enzyme profiles can be obtained by Fourier synthesis. The theory of optimal enzyme rhythms combines the dynamics and economics of metabolic systems and explains how optimal small-amplitude enzyme profiles are shaped by network structure, kinetics, external rhythms, and the metabolic objective. The formulae show how orchestrated enzyme rhythms can exploit synergy effects to improve metabolic performance and that optimal enzyme profiles are not simply adapted to existing metabolic rhythms, but that they actively shape these rhythms to improve their own (and other enzymes') efficiency. The resulting optimal enzyme profiles "portray" the enzymes' dynamic effects in the network: for example, enzymes that act synergistically may be coexpressed, periodically and with some optimal phase shifts. The theory yields optimality conditions for enzyme rhythms in metabolic cycles, with static enzyme adaptation as a special case, and predicts how cells should combine transcriptional and posttranslational regulation to realise enzyme rhythms at different frequencies.
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