The Hill function is the universal Hopfield barrier for sharpness of input-output responses
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View abstract on PubMed
Summary
This summary is machine-generated.Hill functions are now biophysically justified as universal Hopfield barriers for response sharpness in biological systems. This finding provides a fundamental thermodynamic limit for molecular signaling pathways.
Area Of Science
- Biophysics
- Systems Biology
- Biochemistry
Background
- Hill functions are widely used in biology to model input-output responses but lack theoretical justification.
- Previous applications relied on empirical data fitting, limiting fundamental understanding.
Approach
- Utilized a graph-theoretic linear framework and coarse-graining methods.
- Analyzed Markov process models at thermodynamic equilibrium with arbitrary molecular complexity.
- Investigated sharpness measures for input-output responses within a bounded region.
Key Points
- Demonstrated Hill functions represent universal limits for response sharpness in equilibrium systems.
- Introduced 'Hopfield barriers' as fundamental thermodynamic limits for molecular signaling.
- Showcased that deviations from thermodynamic equilibrium can exceed these barriers.
Conclusions
- Provided a biophysical justification for the widespread use of Hill functions.
- Established Hopfield barriers as a key concept for understanding cellular information processing.
- Highlighted the mathematical interest of a newly introduced object, <math></math>.
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