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The Berg-Purcell limit revisited.

Kazunari Kaizu1, Wiet de Ronde2, Joris Paijmans2

  • 1RIKEN Quantitative Biology Center (QBIC), RIKEN, 6-2-3 Furuedai, Suita, Osaka 565-0874, Japan.

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Summary

Biological systems face precision limits in measuring low chemical concentrations due to molecular randomness. This study derives an expression for measurement precision, confirming the fundamental physical limits for diffusing ligands binding to receptors.

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Area of Science:

  • Biophysics
  • Chemical Kinetics
  • Systems Biology

Background:

  • Biological systems require precise measurement of low chemical concentrations.
  • Molecular randomness in transport and binding reactions limits measurement precision.
  • Understanding the lower bound of noise in these measurements is crucial.

Purpose of the Study:

  • Derive an analytical expression for concentration estimation precision.
  • Investigate precision limits for diffusing ligands binding to receptors.
  • Compare theoretical predictions with simulation results.

Main Methods:

  • Utilized the theory of diffusion-influenced reactions.
  • Derived an analytical expression for the variance in concentration estimates.
  • Employed particle-based simulations for validation.

Main Results:

  • The variance in concentration estimates has two components: binding kinetics and ligand diffusion.
  • The diffusion term matches the Berg and Purcell fundamental limit.
  • Disagrees with a more recent expression by Bialek and Setayeshgar.

Conclusions:

  • The derived expression accurately predicts measurement precision.
  • Reaffirms the fundamental noise limit established by Berg and Purcell.
  • Provides a validated framework for understanding precision in molecular measurements.