Discreteness-induced concentration inversion in mesoscopic chemical systems

Area of Science:

• Biochemistry
• Chemical Kinetics
• Systems Biology

Background:

• Molecular discreteness is significant in small-volume systems like biological cells.
• This discreteness leads to stochastic kinetics, deviating from deterministic rate equations.
• Previous models often overlook discreteness effects in steady-state analysis.

Purpose of the Study:

• To develop a theoretical framework for understanding discreteness effects on the steady state of chemical reaction networks.
• To investigate how molecular discreteness influences average steady-state concentrations in systems of varying volumes.
• To identify conditions leading to concentration inversion and the impact of noise.

Main Methods:

• Theoretical modeling of chemical reaction networks considering molecular discreteness.
• Analysis of independent system realizations across different compartment volumes.
• Exact stochastic simulations to verify theoretical predictions.
• Investigation of extrinsic noise effects on critical volumes.

Main Results:

• Predicted that average steady-state concentrations vary with system volume due to molecular discreteness.
• Identified a critical volume below which concentration inversion occurs.
• Demonstrated that extrinsic noise increases the critical volume.
• Validated that standard rate equations are qualitatively incorrect in sub-critical volumes.

Conclusions:

• Molecular discreteness fundamentally alters the steady state of chemical systems in small volumes.
• Concentration inversion is a key consequence of discreteness, challenging predictions from rate equations.
• Stochastic simulations confirm the limitations of deterministic models at small scales.
• The framework provides insights into stochastic effects in cellular biochemistry.