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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.
We report the first study of a network of connected enzyme-catalyzed reactions, with added chemical and enzymatic processes that incorporate the recently developed biochemical filtering steps into the functioning of this biocatalytic cascade. New the
During the last decade, network approaches became a powerful tool to describe protein structure and dynamics. Here, we describe first the protein structure networks of molecular chaperones, then characterize chaperone containing sub-networks of inter
We introduce a minimal model for the evolution of functional protein-interaction networks using a sequence-based mutational algorithm, and apply the model to study neutral drift in networks that yield oscillatory dynamics. Starting with a functional
Information transmission in biological signaling circuits has often been described using the metaphor of a noise filter. Cellular systems need accurate, real-time data about their environmental conditions, but the biochemical reaction networks that p
Are turn-on and turn-off functions in protein-protein interaction networks exact opposites of each other? To answer this question, we implement a minimal model for the evolution of functional protein-interaction networks using a sequence-based mutati