Single enzyme electroanalysis

Traditional studies of enzymatic activity rely on the combined kinetics of millions of enzyme molecules to produce a product, an experimental approach that may wash out heterogeneities that exist between individual enzymes. Evaluating these properties on an enzyme-by-enzyme basis represents an unambiguous means of elucidating heterogeneities; however, the quantification of enzymatic activity at the single-enzyme level is fundamentally limited by the maximum catalytic rate, k_cat, inherent to a given enzyme. For electrochemical methods measuring current, single enzymes must turn over greater than 10⁷ molecules per second to produce a measurable signal on the order of 10^-12 A. Enzymes with this capability are extremely rare in nature, with typical k_cat values for biologically relevant enzymes falling between 1 and 10 000 s^-1. Thus, clever amplification strategies are necessary to electrochemically detect the vast majority of enzymes. This review details the progress toward the electroanalytical detection and evaluation of single enzyme kinetics largely focused on the nanoimpact method, a chronoamperometric detection strategy that monitors the change in the current-time profile associated with stochastic collisions of freely diffusing entities (e.g., enzymes) onto a microelectrode or nanoelectrode surface. We discuss the experimental setups and methods developed in the last decade toward the quantification of single molecule enzymatic rates. Special emphasis is given to the limitations of measurement science in the observation of single enzyme activity and feasible methods of signal amplification with reasonable bandwidth.

Structural conditions on complex networks for the Michaelis-Menten input-output response

The Michaelis-Menten (MM) fundamental formula describes how the rate of enzyme catalysis depends on substrate concentration. The familiar hyperbolic relationship was derived by timescale separation for a network of three reactions. The same formula has subsequently been found to describe steady-state input-output responses in many biological contexts, including single-molecule enzyme kinetics, gene regulation, transcription, translation, and force generation. Previous attempts to explain its ubiquity have been limited to networks with regular structure or simplifying parametric assumptions. Here, we exploit the graph-based linear framework for timescale separation to derive general structural conditions under which the MM formula arises. The conditions require a partition of the graph into two parts, akin to a "coarse graining" into the original MM graph, and constraints on where and how the input variable occurs. Other features of the graph, including the numerical values of parameters, can remain arbitrary, thereby explaining the formula's ubiquity. For systems at thermodynamic equilibrium, we derive a necessary and sufficient condition. For systems away from thermodynamic equilibrium, especially those with irreversible reactions, distinct structural conditions arise and a general characterization remains open. Nevertheless, our results accommodate, in much greater generality, all examples known to us in the literature.

Enhanced photo-responsiveness in a photoswitchable system model: emergent hormetic catalysis

Michaelis Menten catalysis by a T-photochromic system has been analyzed numerically. Using an appropriate set of rate constants and quantum yields, we have evidenced an enhanced photo-responsiveness at a medium light intensity: the plot of the initial rate vs. light intensity is bell-shaped. This emergent phenomenon can be qualified as hormetic catalysis. The analysis of the chemical flows shows that a directional rotation occurs within the cyclic scheme. Non equilibrium conditions are provided by two independent sources: the chemical energy dissipation from the irreversible exergonic reaction and the steady transformation of light into heat by T-photochromism. A literature survey, showing that most of the required kinetic features are not so rare, let us anticipate its practical feasibility.