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Chin. Phys. B, 2020, Vol. 29(10): 108702    DOI: 10.1088/1674-1056/abb225
Special Issue: SPECIAL TOPIC — Modeling and simulations for the structures and functions of proteins and nucleic acids
Topical Review—Modeling and simulations for the structures and functions of proteins and nucleic acids Prev   Next  

Quantitative modeling of bacterial quorum sensing dynamics in time and space

Xiang Li(李翔)1,2, Hong Qi(祁宏)3, Xiao-Cui Zhang(张晓翠)1, Fei Xu(徐飞)1, Zhi-Yong Yin(尹智勇)1, Shi-Yang Huang(黄世阳)4, Zhao-Shou Wang(王兆守)4,†, and Jian-Wei Shuai(帅建伟)1,2,5,
1 Department of Physics, College of Physical Science and Technology, Xiamen University, Xiamen 361005, China
2 State Key Laboratory of Cellular Stress Biology, Innovation Center for Cell Signaling Network, Xiamen University, Xiamen 361102, China
3 Complex Systems Research Center, Shanxi University, Taiyuan 030006, China
4 Institute of Biochemical Engineering, Department of Chemical and Biochemical Engineering, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
5 National Institute for Data Science in Health and Medicine, Xiamen University, Xiamen 361102, China

Quorum sensing (QS) refers to the cell communication through signaling molecules that regulate many important biological functions of bacteria by monitoring their population density. Although a wide spectrum of studies on the QS system mechanisms have been carried out in experiments, mathematical modeling to explore the QS system has become a powerful approach as well. In this paper, we review the research progress of network modeling in bacterial QS to capture the system’s underlying mechanisms. There are four types of QS system models for bacteria: the Gram-negative QS system model, the Gram-positive QS system model, the model for both Gram-negative and Gram-positive QS system, and the synthetic QS system model. These QS system models are mostly described by the ordinary differential equations (ODE) or partial differential equations (PDE) to study the changes of signaling molecule dynamics in time and space and the cell population density variations. Besides the deterministic simulations, the stochastic modeling approaches have also been introduced to discuss the noise effects on kinetics in QS systems. Taken together, these current modeling efforts advance our understanding of the QS system by providing systematic and quantitative dynamics description, which can hardly be obtained in experiments.

Keywords:  bacterial quorum sensing      signaling molecules      mathematical modeling      dynamic analysis  
Received:  20 June 2020      Revised:  14 August 2020      Published:  05 October 2020
PACS:  87.17.Aa (Modeling, computer simulation of cell processes)  
  87.18.Vf (Systems biology) (Protein-protein interactions)  
Corresponding Authors:  Corresponding author. E-mail:第一通讯作者 Corresponding author. E-mail:   
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‡Corresponding author. E-mail:
* Project supported by the National Natural Science Foundation of China (Grant Nos. 11704318, 11675134, and 11874310) and the China Postdoctoral ScienceFoundation (Grant No. 2016M602071).

Cite this article: 

Xiang Li(李翔), Hong Qi(祁宏), Xiao-Cui Zhang(张晓翠), Fei Xu(徐飞), Zhi-Yong Yin(尹智勇), Shi-Yang Huang(黄世阳), Zhao-Shou Wang(王兆守)†, and Jian-Wei Shuai(帅建伟)‡ Quantitative modeling of bacterial quorum sensing dynamics in time and space 2020 Chin. Phys. B 29 108702

Fig. 1.  

An overview of the QS systems in bacterial cell. (a) At low cell density, the concentration of autoinducer is low. (b) At high cell density, the autoinducer concentration reaches a threshold to induce corresponding gene expression to trigger QS. (c) Schematic of the QS system in Gram-negative bacteria. AHL is the autoinducer in the system. (d) Schematic of the QS system in Gram-positive bacteria. AIP is the autoinducer. (e) Schematic of the synthetic QS system in E. coli. The synthetic strategies mainly include regulator modification, promoter modification, and circuitry addition.

Year Author Method Major conclusion
QS systems in Gram-negative bacteria
2000 James et al. ODE & bifurcation analysis lux genes can induce luminesce under the shortage of extracellular signal molecule
2001 Dockery et al. ODE & PDE The high and low states of auto-inducer are highly controlled by the size and local density of cells
2004 Chen et al. ODE Providing an important basis for the precise determination of the rhl QS system
2010 Melke et al. ODE & bifurcation analysis The cell density-dependent behavior of LuxR-AHL QS system depends on local cell-clustering and the geometry of the evolution space
2013 Mcintosh et al. ODE A negative feedback is required for state changing of the QS system in Sinorhizobium meliloti
2016 Barbarossa et al. DDE & bifurcation analysis The delay QS system is sufficient to explain the biological observations
2016 Marenda et al. ODE Demonstrating how tube height overtakes the role of producer density in triggering sensor activation
QS systems in Gram-positive bacteria
2004 Gustafsson et al. ODE Altering agr activity hardly affects RNAIII levels but changes the cells sensitivity to AIP
2005 Koerber et al. ODE & Monte-Carlo The first stochastic model for bacterial QS system
2007 Karlsson et al. ODE & bifurcation analysis A putative ComX-dependent repressor which inhibits the expression of comCDE and comX is determined
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2014 Hunter et al. ODE Qrr in Vibrio cholerae is more abundant and more sensitive to the changes in LuxO than Vibrio harveyi
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2001 Nilsson et al. ODE This study quantitatively explored the implications of the components for AHL regulation under different situations
2002 Lee et al. ODE The first molecular mechanism-based model in a recombinant E. coli system
2004 You et al. ODE A cell density control circuit that incorporates cell death was designed.
2005 Chen et al. ODE & bifurcation analysis Noises are essential for inducing the system cooperative behaviors
2006 Li et al. ODE & stochastic simulations Biological steps were determined to be exist in the synthesis of AI-2
2013 Saeidi et al. ODE The model can be used to predict the production of GFP
Table 1.  

Representative models of different QS systems in bacteria.

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