Differential Equations Models to Study Quorum Sensing. 2018

Judith Pérez-Velázquez, and Burkhard A Hense
Mathematical Modeling of Biological Systems, Centre for Mathematical Science, Technical University of Munich, Garching, Germany. perez-velazquez@helmholtz-muenchen.de.

Mathematical models to study quorum sensing (QS) have become an important tool to explore all aspects of this type of bacterial communication. A wide spectrum of mathematical tools and methods such as dynamical systems, stochastics, and spatial models can be employed. In this chapter, we focus on giving an overview of models consisting of differential equations (DE), which can be used to describe changing quantities, for example, the dynamics of one or more signaling molecule in time and space, often in conjunction with bacterial growth dynamics. The chapter is divided into two sections: ordinary differential equations (ODE) and partial differential equations (PDE) models of QS. Rates of change are represented mathematically by derivatives, i.e., in terms of DE. ODE models allow describing changes in one independent variable, for example, time. PDE models can be used to follow changes in more than one independent variable, for example, time and space. Both types of models often consist of systems (i.e., more than one equation) of equations, such as equations for bacterial growth and autoinducer concentration dynamics. Almost from the onset, mathematical modeling of QS using differential equations has been an interdisciplinary endeavor and many of the works we revised here will be placed into their biological context.

UI MeSH Term Description Entries
D007700 Kinetics The rate dynamics in chemical or physical systems.
D008954 Models, Biological Theoretical representations that simulate the behavior or activity of biological processes or diseases. For disease models in living animals, DISEASE MODELS, ANIMAL is available. Biological models include the use of mathematical equations, computers, and other electronic equipment. Biological Model,Biological Models,Model, Biological,Models, Biologic,Biologic Model,Biologic Models,Model, Biologic
D008962 Models, Theoretical Theoretical representations that simulate the behavior or activity of systems, processes, or phenomena. They include the use of mathematical equations, computers, and other electronic equipment. Experimental Model,Experimental Models,Mathematical Model,Model, Experimental,Models (Theoretical),Models, Experimental,Models, Theoretic,Theoretical Study,Mathematical Models,Model (Theoretical),Model, Mathematical,Model, Theoretical,Models, Mathematical,Studies, Theoretical,Study, Theoretical,Theoretical Model,Theoretical Models,Theoretical Studies
D009716 Numerical Analysis, Computer-Assisted Computer-assisted study of methods for obtaining useful quantitative solutions to problems that have been expressed mathematically. Analysis, Computer-Assisted Numerical,Computer-Assisted Numerical Analysis,Analyses, Computer-Assisted Numerical,Analysis, Computer Assisted Numerical,Computer Assisted Numerical Analysis,Computer-Assisted Numerical Analyses,Numerical Analyses, Computer-Assisted,Numerical Analysis, Computer Assisted
D003198 Computer Simulation Computer-based representation of physical systems and phenomena such as chemical processes. Computational Modeling,Computational Modelling,Computer Models,In silico Modeling,In silico Models,In silico Simulation,Models, Computer,Computerized Models,Computer Model,Computer Simulations,Computerized Model,In silico Model,Model, Computer,Model, Computerized,Model, In silico,Modeling, Computational,Modeling, In silico,Modelling, Computational,Simulation, Computer,Simulation, In silico,Simulations, Computer
D013997 Time Factors Elements of limited time intervals, contributing to particular results or situations. Time Series,Factor, Time,Time Factor
D014733 Vibrio A genus of VIBRIONACEAE, made up of short, slightly curved, motile, gram-negative rods. Various species produce cholera and other gastrointestinal disorders as well as abortion in sheep and cattle. Beneckea
D016958 Pseudomonas putida A species of gram-negative, aerobic bacteria isolated from soil and water as well as clinical specimens. Occasionally it is an opportunistic pathogen.
D053038 Quorum Sensing A phenomenon where microorganisms communicate and coordinate their behavior by the accumulation of signaling molecules. A reaction occurs when a substance accumulates to a sufficient concentration. This is most commonly seen in bacteria. Quorum Quenching,Quenching, Quorum,Quenchings, Quorum,Quorum Quenchings,Sensing, Quorum

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