Quantifying the flux as the driving force for nonequilibrium dynamics and thermodynamics in non-Michaelis–Menten enzyme kinetics

Abstract

The driving force for active physical and biological systems is determined by both the underlying landscape and nonequilibrium curl flux. While landscape can be experimentally quantified from the histograms of the collected real-time trajectories of the observables, quantifying the experimental flux remains challenging. In this work, we studied the single-molecule enzyme dynamics of horseradish peroxidase with dihydrorhodamine 123 and hydrogen peroxide (H2O2) as substrates. Surprisingly, significant deviations in the kinetics from the conventional Michaelis–Menten reaction rate were observed. Instead of a linear relationship between the inverse of the enzyme kinetic rate and the inverse of substrate concentration, a nonlinear relationship between the two emerged. We identified nonequilibrium flux as the origin of such non-Michaelis–Menten enzyme rate behavior. Furthermore, we quantified the nonequilibrium flux from experimentally obtained fluorescence correlation spectroscopy data and showed this flux to led to the deviations from the Michaelis–Menten kinetics. We also identified and quantified the nonequilibrium thermodynamic driving forces as the chemical potential and entropy production for such non-Michaelis–Menten kinetics. Moreover, through isothermal titration calorimetry measurements, we identified and quantified the origin of both nonequilibrium dynamic and thermodynamic driving forces as the heat absorbed (energy input) into the enzyme reaction system. Furthermore, we showed that the nonequilibrium driving forces led to time irreversibility through the difference between the forward and backward directions in time and high-order correlations were associated with the deviations from Michaelis–Menten kinetics. This study provided a general framework for experimentally quantifying the dynamic and thermodynamic driving forces for nonequilibrium systems.

Dissection of enzymatic kinetics and elucidation of detailed parameters based on the Michaelis‐Menten model. Kinetic and thermodynamic connections

“…As shown in classic double reciprocal plots ( Figure 6C and inset), the behavior was nonlinear. Recent studies 44 also showed nonlinear behavior on Lineweaver-Burk plot for horseradish peroxidase. Such results were attributed to enzyme conformational changes associated to change in the apparent rate constants.…”

Improved bounds on entropy production in living systems

“…1); an underlying Markovian description of the complete set of slow degrees of freedom remains appropriate. Within this framework, stochastic thermodynamics was introduced (24,35,57) and is now well validated experimentally (62)(63)(64)(65). Recent efforts have thus turned to the problem of thermodynamic inference: deducing thermodynamic quantities, such as the entropy production rate, from partial observations (19,27).…”

Physical bioenergetics: Energy fluxes, budgets, and constraints in cells

“…Applying thermodynamic principles to metabolic networks has resulted in the discovery of energetic constraints on metabolic fluxes (4,(121)(122)(123). New experimental and theoretical approaches have been developed to identify nonequilibrium dynamics in biological systems by quantifying the breaking of detailed balance (124)(125)(126) and irreversibility (127,128). The violation of the fluctuation-dissipation relation has also been used to quantify energy dissipation at the singlemolecular level (5).…”