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Quorum sensing is a mechanism of bacterial communication that enables coordinated gene expression in response to changes in population density. This facilitates collective behaviors that enhance survival, resource acquisition, and ecological adaptation. This process relies on small signaling molecules called autoinducers that accumulate as bacterial populations grow. When a critical threshold concentration of autoinducers is reached, bacterial cells collectively modify gene expression,...
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Bacterial signaling can occur within bacteria (intracellular) or between bacteria (intercellular). At times, a group of bacteria behaves like a community. To achieve this, they engage in quorum sensing, the perception of higher cell density that causes changes in gene expression. Quorum sensing involves both extracellular and intracellular signaling. The signaling cascade starts with a molecule called an autoinducer (AI). Individual bacteria produce AIs that move out of the bacterial cell...
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Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
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Global regulatory systems in bacteria enable rapid and coordinated responses to environmental changes by integrating sensory inputs with gene expression, ensuring efficient adaptation to fluctuating conditions. Key global regulatory mechanisms include regulons, two-component systems, sigma factors, and secondary messengers.Regulons and Global RegulatorsA regulon is a collection of genes and operons controlled by a common global regulator. These regulators enable bacteria to prioritize resource...
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Yeasts are single-celled organisms, but unlike bacteria, they are eukaryotes (cells with a nucleus). Cell signaling in yeast is similar to signaling in other eukaryotic cells. A ligand, such as a protein or a small molecule released from a yeast cell, attaches to a receptor on the cell surface. The binding stimulates second-messenger kinases to activate or inactivate transcription factors that further regulate gene expression. Many of the yeast intracellular signaling cascades have similar...
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Differential Equations Models to Study Quorum Sensing.

Judith Pérez-Velázquez1,2, Burkhard A Hense3

  • 1Mathematical Modeling of Biological Systems, Centre for Mathematical Science, Technical University of Munich, Garching, Germany. perez-velazquez@helmholtz-muenchen.de.

Methods in Molecular Biology (Clifton, N.J.)
|November 14, 2017
PubMed
Summary
This summary is machine-generated.

Mathematical models using differential equations (DE) are crucial for understanding bacterial communication (quorum sensing, QS). This chapter reviews ordinary differential equations (ODE) and partial differential equations (PDE) models of QS dynamics.

Keywords:
DerivativesDifferential equationsMathematical modelsOrdinary differential equationsPartial differential equationsQuorum sensing

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Area of Science:

  • Mathematical Biology
  • Computational Biology
  • Microbiology

Background:

  • Quorum sensing (QS) is a type of bacterial communication vital for microbial communities.
  • Mathematical modeling provides a powerful framework to study complex biological processes like QS.
  • Differential equations (DE) are essential tools for describing dynamic systems in biology.

Purpose of the Study:

  • To provide an overview of mathematical models based on differential equations for studying quorum sensing.
  • To categorize and explain the application of ordinary differential equations (ODE) and partial differential equations (PDE) in QS research.
  • To highlight the interdisciplinary nature of QS modeling, integrating mathematical approaches with biological context.

Main Methods:

  • Focus on differential equation (DE) models, including ordinary differential equations (ODE) and partial differential equations (PDE).
  • Explanation of how DEs represent rates of change for quantities like signaling molecules and bacterial growth.
  • Discussion of system dynamics, involving multiple coupled equations for various QS components.

Main Results:

  • ODE models are suitable for changes over a single independent variable (e.g., time).
  • PDE models are used for changes across multiple independent variables (e.g., time and space).
  • Both ODE and PDE models are frequently employed as systems of equations to capture complex QS dynamics.

Conclusions:

  • Differential equation-based models are indispensable for analyzing quorum sensing mechanisms.
  • The choice between ODE and PDE depends on whether spatial dynamics need to be considered.
  • Mathematical modeling of QS is an inherently interdisciplinary field, bridging mathematics and biology.