Size limits the sensitivity of kinetic schemes

Area of Science:

• Biophysics
• Molecular Biology
• Systems Biology

Background:

• Living organisms exhibit remarkable molecular sensitivity crucial for processes like DNA replication and chemical sensing.
• Cooperative binding, characterized by the Hill coefficient, is a key biophysical mechanism for sensitivity at thermodynamic equilibrium, with inherent limitations.
• Existing models often struggle to precisely bridge experimental observations with theoretical frameworks for biological sensitivity.

Purpose of the Study:

• To identify a universal biophysical principle limiting molecular sensitivity across diverse biological processes.
• To generalize the understanding of sensitivity beyond thermodynamic equilibrium.
• To explore novel mechanisms that can achieve maximal or enhanced molecular sensitivity.

Main Methods:

• Developed a generalized theoretical framework applicable to any kinetic scheme, both at and away from thermodynamic equilibrium.
• Introduced the concept of 'size of the support of a perturbation' as a fundamental structural quantity limiting sensitivity.
• Analyzed specific biological systems, including kinetic proofreading and a nonequilibrium Monod-Wyman-Changeux (MWC) model for the E. coli flagellar motor switch.

Main Results:

• Established that the size of the support of a perturbation universally bounds the effective Hill coefficient for any kinetic scheme.
• Demonstrated how this bound unifies and explains the sensitivity limits observed in various biological mechanisms.
• Identified a novel nonequilibrium binding mechanism, 'nested hysteresis,' exhibiting sensitivity exponential in the number of binding sites.

Conclusions:

• The size of the support provides a fundamental, simple structural constraint on biological molecular sensitivity.
• The findings offer a unified perspective on diverse sensitivity mechanisms and their limitations.
• Nested hysteresis represents a potential mechanism for achieving ultra-sensitive biological regulation and function, with implications for gene regulation and biomolecular condensates.