Second messengers, c-di-GMP and (p)ppGpp, are vital regulatory molecules in bacteria, influencing cellular processes such as biofilm formation, transcription, virulence, quorum sensing, and proliferation. While c-di-GMP and (p)ppGpp are both synthesized from GTP molecules, they play antagonistic roles in regulating the cell cycle. In C. crescentus, c-di-GMP works as a major regulator of pole morphogenesis and cell development. It inhibits cell motility and promotes S-phase entry by inhibiting the activity of the master regulator, CtrA. Intracellular (p)ppGpp accumulates under starvation, which helps bacteria to survive under stressful conditions through regulating nucleotide levels and halting proliferation. (p)ppGpp responds to nitrogen levels through RelA-SpoT homolog enzymes, detecting glutamine concentration using a nitrogen phosphotransferase system (PTS Ntr). This work relates the guanine nucleotide-based second messenger regulatory network with the bacterial PTS Ntr system and investigates how bacteria respond to nutrient availability. We propose a mathematical model for the dynamics of c-di-GMP and (p)ppGpp in C. crescentus and analyze how the guanine nucleotide-based second messenger system responds to certain environmental changes communicated through the PTS Ntr system. Our mathematical model consists of seven ODEs describing the dynamics of nucleotides and PTS Ntr enzymes. Our simulations are consistent with experimental observations and suggest, among other predictions, that SpoT can effectively decrease c-di-GMP levels in response to nitrogen starvation just as well as it increases (p)ppGpp levels. Thus, the activity of SpoT (or its homologues in other bacterial species) can likely influence the cell cycle by influencing both c-di-GMP and (p)ppGpp. In this work, we integrate current knowledge and experimental observations from the literature to formulate a novel mathematical model. We analyze the model and demonstrate how the PTS Ntr system influences (p)ppGpp, c-di-GMP, GMP and GTP concentrations. While this model does not consider all aspects of PTS Ntr signaling, such as cross-talk with the carbon PTS system, here we present our first effort to develop a model of nutrient signaling in C. crescentus.

中文翻译：

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新月形棒状杆菌中第二信使的细胞周期控制和环境响应

第二信使c-di-GMP和（p）ppGpp是细菌中至关重要的调节分子，影响细胞过程，例如生物膜形成，转录，毒力，群体感应和增殖。虽然c-di-GMP和（p）ppGpp都是从GTP分子合成的，但它们在调节细胞周期中起着拮抗作用。在C.crescentus中，c-di-GMP充当杆形态发生和细胞发育的主要调节剂。它通过抑制主调节剂CtrA的活性来抑制细胞运动并促进S期进入。细胞内（p）ppGpp在饥饿状态下积聚，通过调节核苷酸水平和阻止增殖，帮助细菌在压力条件下生存。（p）ppGpp通过RelA-SpoT同源酶响应氮水平，使用氮磷酸转移酶系统（PTS Ntr）检测谷氨酰胺浓度。这项工作将基于鸟嘌呤核苷酸的第二信使调节网络与细菌PTS Ntr系统联系起来，并研究细菌如何对营养物的利用作出反应。我们提出了一个数学模型，用于C.di-GMP和新月形梭菌中的（p）ppGpp动力学，并分析了基于鸟嘌呤核苷酸的第二信使系统如何响应通过PTS Ntr系统传达的某些环境变化。我们的数学模型由七个描述核苷酸和PTS Ntr酶动力学的ODE组成。我们的模拟与实验观察结果一致，并且除其他预测外，还表明SpoT可以有效地响应氮饥饿而降低c-di-GMP水平，也可以提高（p）ppGpp水平。从而，SpoT的活性（或其他细菌物种的同系物）可能通过影响c-di-GMP和（p）ppGpp来影响细胞周期。在这项工作中，我们结合了当前的知识和来自文献的实验观察，以建立一个新颖的数学模型。我们分析该模型并证明PTS Ntr系统如何影响（p）ppGpp，c-di-GMP，GMP和GTP浓度。虽然此模型并未考虑PTS Ntr信号传导的所有方面，例如与碳PTS系统的串扰，但在此我们展示了我们在开发C.crescentus中营养信号传导模型的第一项努力。我们结合文献中的最新知识和实验观察结果，建立了新颖的数学模型。我们分析该模型并证明PTS Ntr系统如何影响（p）ppGpp，c-di-GMP，GMP和GTP浓度。虽然此模型并未考虑PTS Ntr信号传导的所有方面，例如与碳PTS系统的串扰，但在此我们展示了我们在开发C.crescentus中营养信号传导模型的第一项努力。我们结合文献中的最新知识和实验观察结果，建立了新颖的数学模型。我们分析该模型并证明PTS Ntr系统如何影响（p）ppGpp，c-di-GMP，GMP和GTP浓度。尽管此模型并未考虑PTS Ntr信号传导的所有方面，例如与碳PTS系统的串扰，但在此我们展示了我们在开发C.crescentus中营养信号传导模型的第一项努力。