Transients generate memory and break hyperbolicity in stochastic enzymatic networks
arXiv:2010.00758 · doi:10.1063/5.0031368
Abstract
The hyperbolic dependence of catalytic rate on substrate concentration is a classical result in enzyme kinetics, quantified by the celebrated Michaelis-Menten equation. The ubiquity of this relation in diverse chemical and biological contexts has recently been rationalized by a graph-theoretic analysis of deterministic reaction networks. Experiments, however, have revealed that "molecular noise" - intrinsic stochasticity at the molecular scale - leads to significant deviations from classical results and to unexpected effects like "molecular memory", i.e., the breakdown of statistical independence between turnover events. Here we show, through a new method of analysis, that memory and non-hyperbolicity have a common source in an initial, and observably long, transient peculiar to stochastic reaction networks of multiple enzymes. Networks of single enzymes do not admit such transients. The transient yields, asymptotically, to a steady-state in which memory vanishes and hyperbolicity is recovered. We propose new statistical measures, defined in terms of turnover times, to distinguish between the transient and steady states and apply these to experimental data from a landmark experiment that first observed molecular memory in a single enzyme with multiple binding sites. Our study shows that catalysis at the molecular level with more than one enzyme always contains a non-classical regime and provides insight on how the classical limit is attained.
arXiv comment17 pages, 8 figures
References in corpus (12)
- Stochastic mechano-chemical kinetics of molecular motors: a multidisciplinary enterprise from a physicist's perspective
- Optical detection of single electron transport dynamics
- Detection of interactions via generalized factorial cumulants in systems in and out of equilibrium
- Full counting statistics and shot noise of cotunneling in quantum dots and single-molecule transistors
- First-passage times in renewal and nonrenewal systems
- Short-time counting statistics of charge transfer in Coulomb-blockade systems
- Non-renewal statistics in the catalytic activity of enzyme molecules at mesoscopic concentrations
- Counting quantum jumps: a summary and comparison of fixed-time and fluctuating-time statistics in electron transport
- Revealing attractive electron-electron interaction in a quantum dot by full counting statistics
- Non-renewal statistics in quantum transport through the eyes of first-passage and waiting time distributions
- Emergence of Dynamic Cooperativity in the Stochastic Kinetics of Fluctuating Enzymes
- Enzyme kinetics at the molecular level