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Optimize Flue Gas Settings to Promote Microalgae Growth in Photobioreactors via Computer Simulations
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A deterministic mathematical model for bidirectional excluded flow with Langmuir kinetics.

Yoram Zarai1, Michael Margaliot2, Tamir Tuller3

  • 1Dept. of Biomedical Engineering, Tel-Aviv University, Tel-Aviv 69978, Israel.

Plos One
|August 24, 2017
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Summary

This study introduces a new mathematical model for particle transport along tracks, applicable to cellular processes like mRNA translation. The model predicts unique steady states and phase locking to external influences, aiding analysis of ribosome drop-off.

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Area of Science:

  • Biophysics
  • Mathematical Biology
  • Cellular Dynamics

Background:

  • Biological particles move along tracks in key cellular processes.
  • Particle motion can be modeled as 1D movement with exclusion and bidirectional dynamics.
  • Existing models may not fully capture attachment/detachment dynamics.

Purpose of the Study:

  • Develop a novel deterministic mathematical model for particle transport on tracks.
  • Analyze the model's steady-state behavior and convergence properties.
  • Investigate the model's response to periodic changes in transport rates.

Main Methods:

  • Derivation of a dynamic mean-field approximation.
  • Interpretation as an asymmetric simple exclusion process (ASEP) with Langmuir kinetics.
  • Application of monotone dynamical systems and contraction theory.

Main Results:

  • The model exhibits a unique steady-state.
  • All solutions demonstrably converge to this steady-state.
  • The model shows entrainment (phase locking) to periodic excitations in rates.

Conclusions:

  • The developed model offers a robust framework for analyzing complex particle transport phenomena.
  • It provides insights into ribosome drop-off during mRNA translation.
  • The model's convergence and entrainment properties are mathematically proven.