Transients generate memory and break hyperbolicity in stochastic enzymatic networks

Area of Science:

• Biochemistry
• Chemical Kinetics
• Systems Biology

Background:

• Enzyme kinetics traditionally follows the Michaelis-Menten equation, describing hyperbolic substrate concentration dependence.
• Molecular noise (stochasticity) causes deviations, leading to effects like molecular memory in enzyme systems.
• Previous analyses rationalized deterministic networks but struggled with stochastic effects.

Purpose of the Study:

• To identify the common source of molecular memory and non-hyperbolicity in enzyme kinetics.
• To analyze transient and steady-state behaviors in stochastic reaction networks.
• To develop methods for distinguishing these regimes and understanding the transition to classical kinetics.

Main Methods:

• Developed a novel analytical method for stochastic reaction networks.
• Investigated transient dynamics in multi-enzyme systems.
• Proposed new statistical measures based on turnover times.

Main Results:

• Identified a common source for memory and non-hyperbolicity in initial, long transients of multi-enzyme stochastic networks.
• Demonstrated that single-enzyme networks lack these transients.
• Showed that transients asymptotically resolve into a steady-state where memory and non-hyperbolicity disappear.
• Applied new measures to experimental data exhibiting molecular memory.

Conclusions:

• Catalysis involving multiple enzymes inherently includes a non-classical regime due to initial transients.
• The classical Michaelis-Menten limit is approached as these transients resolve into a steady state.
• The findings offer insights into stochastic effects in enzyme kinetics and the emergence of classical behavior.