Universal bound on the Fano factor in enzyme kinetics

Area of Science:

• Biophysics
• Enzyme kinetics
• Chemical thermodynamics

Background:

• The Fano factor quantifies product generation fluctuations in single enzymes.
• A lower bound on the Fano factor, dependent on thermodynamic affinity, limits enzymatic cycle intermediate states.
• This bound was previously established only for unicyclic reaction networks.

Purpose of the Study:

• To extend the Fano factor lower bound to multicyclic enzymatic networks.
• To investigate the relationship between Fano factor and effective cycle length in complex enzymatic systems.

Main Methods:

• Theoretical analysis of enzymatic reaction networks.
• Mathematical derivation of bounds for the Fano factor.
• Extension of existing theoretical frameworks to multicyclic systems.

Main Results:

• The lower bound on the Fano factor is successfully extended to arbitrary multicyclic networks.
• The Fano factor is shown to constrain the maximum effective length across all cycles in a network.
• Effective length is defined as the ratio of states to products within a cycle.

Conclusions:

• The Fano factor serves as a universal constraint on enzymatic cycle complexity, regardless of network topology.
• This work provides a more generalized understanding of enzyme fluctuation-affinity relationships.
• The findings have implications for characterizing complex enzymatic pathways and their efficiency.