Collective behaviours: from biochemical kinetics to electronic circuits

Area of Science:

• Biophysics
• Statistical Mechanics
• Cybernetics

Background:

• Chemical kinetics describes reaction behaviors, while cybernetics models control systems.
• Mean-field statistical mechanics provides a framework for analyzing cooperative phenomena.
• Existing models for biochemical kinetics (Michaelis-Menten, Hill, Adair) lack a unified theoretical basis.

Purpose of the Study:

• To establish a direct analogy between cooperative behaviors in chemical kinetics and cybernetics.
• To demonstrate the utility of mean-field statistical mechanics as a common descriptive language.
• To bridge the gap between biochemical kinetics and cybernetic principles.

Main Methods:

• Performing a one-to-one mapping between chemical kinetic behaviors and statistical mechanics models.
• Applying mean-field statistical mechanics to unify descriptions of non-cooperative, cooperative, ultra-sensitive, and anti-cooperative kinetics.
• Interpreting the mapping from a cybernetic perspective, relating kinetics to electronic components.

Main Results:

• A unified theory encompassing various kinetic scenarios was developed using statistical mechanics.
• Established Michaelis-Menten, Hill, and Adair equations within the statistical mechanics framework.
• Demonstrated strong agreement between the theoretical model and experimental biological data.
• Identified structural analogies between biochemical kinetics and fundamental electronic circuits (operational amplifiers, flip-flops).

Conclusions:

• Mean-field statistical mechanics offers a powerful, unified approach to understanding chemical kinetics and its cybernetic parallels.
• The established framework successfully integrates diverse kinetic models and validates against biological data.
• This work provides a novel cybernetic perspective on biochemical kinetics, linking it to electronic systems.