Time hierarchy, equilibrium and non-equilibrium in metabolic systems

Area of Science:

• Biochemistry
• Systems Biology
• Chemical Kinetics

Background:

• Metabolic systems comprise interconnected biochemical reactions governed by metabolite concentrations.
• Reaction velocities depend non-linearly on metabolite concentrations via the law of mass action.
• A characteristic metabolic time governs system-wide events, distinct from individual reaction times.

Purpose of the Study:

• To define and analyze the concept of characteristic times in metabolic systems.
• To investigate the relationship between individual reaction times, metabolic times, and deviations from equilibrium.
• To elucidate the emergence of a time hierarchy and its impact on metabolic regulation.

Main Methods:

• Modeling metabolic systems using differential equations.
• Analyzing reaction velocities based on the law of mass action.
• Applying scaling and linear transformation to reveal system dynamics.
• Characterizing fast and slow reaction phases and their equilibria.

Main Results:

• A time hierarchy emerges from reactions with differing characteristic times.
• Fast reactions (e.g., dehydrogenases, phosphotransferases) rapidly approach equilibrium.
• Metabolic pools and carrier occupancy emerge as key variables at the metabolic time scale.
• Stoichiometric linkage via fast cofactor equilibration transmits changes across metabolic pathways (distance effects).

Conclusions:

• The ratio of individual reaction time to metabolic time dictates a reaction's behavior (fast, slow, essential).
• Near-equilibria of fast reactions create stoichiometric linkages, forming metabolic pools.
• Carrier pools and their occupancy are critical for metabolic regulation and signal propagation.