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Relationship between Decimal Hill Coefficient, Intermediate Processes, and Mesoscopic Fluctuations in Gene

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This study explains why gene expression often shows a noninteger Hill coefficient. Intermediate binding processes and concentration fluctuations at transcription factor sites lead to this observed decimal Hill coefficient.

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Area of Science:

  • Molecular Biology
  • Biophysics
  • Systems Biology

Background:

  • The Hill function models ligand-receptor binding, crucial for gene regulatory networks.
  • It's frequently used to fit gene expression data, often yielding noninteger Hill coefficients.
  • Existing models often simplify transcription factor binding, overlooking intermediate steps.

Purpose of the Study:

  • To investigate the origins of noninteger Hill coefficients in gene expression.
  • To explicitly model intermediate processes and concentration fluctuations in transcription factor binding.
  • To establish a mechanistic link between these processes and the observed decimal Hill coefficient.

Main Methods:

  • Developed a model incorporating intermediate states of transcription factor binding.
  • Included mesoscopic concentration fluctuations in the binding site analysis.
  • Derived relationships between dissociation constants and the Hill coefficient under fluctuating conditions.

Main Results:

  • Demonstrated that intermediate binding processes and concentration fluctuations directly cause noninteger Hill coefficients.
  • Established a quantitative relationship between underlying molecular mechanisms and the decimal Hill coefficient.
  • Showed that the effective Hill coefficient can be predicted from fundamental parameters.

Conclusions:

  • Provides a mechanistic explanation for the prevalence of noninteger Hill coefficients in gene expression.
  • Offers a method to predict the effective Hill coefficient from molecular details.
  • Simplifies the description of complex gene expression mechanisms through a mechanistic understanding.