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

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.