Single-Molecule Kinetics of an Enzyme in the Presence of Multiple Substrates

Theoretical Tools to Quantify Stochastic Fluctuations in Single-Molecule Catalysis by Enzymes and Nanoparticles

Single-molecule microscopic techniques allow the counting of successive turnover events and the study of the time-dependent fluctuations of the catalytic activities of individual enzymes and different sites on a single heterogeneous nanocatalyst. It is important to establish theoretical methods to obtain the statistical measurements of such stochastic fluctuations that provide insight into the catalytic mechanism. In this review, we discuss a few theoretical frameworks for evaluating the first passage time distribution functions using a self-consistent pathway approach and chemical master equations, to establish a connection with experimental observables. The measurable probability distribution functions and their moments depend on the molecular details of the reaction and provide a way to quantify the molecular mechanisms of the reaction process. The statistical measurements of these fluctuations should provide insight into the enzymatic mechanism.

Dissecting the Protein Dynamics Coupled Ligand Binding with Kinetic Models and Single-Molecule FRET

Protein-ligand interactions are crucial to many biological processes. Ligand binding and dissociation are the basic steps that allow proteins to function. Protein conformational dynamics have been shown to play important roles in ligand binding and dissociation. However, it is challenging to determine the ligand binding kinetics of dynamic proteins. Here, we undertook comprehensive single-molecule FRET (smFRET) measurements and kinetic model analysis to characterize the conformational dynamics coupled ligand binding of glutamine-binding protein (GlnBP). We showed that hinge and T118A mutations of GlnBP affect its conformational dynamics as well as the ligand binding affinity. Based on smFRET measurements, the kinetic model of ligand-GlnBP interactions was constructed. Using experimentally measured parameters, we solved the rate equations of the model and obtained the undetectable parameters of the model which allowed us to understand the ligand binding kinetics fully. Our results demonstrate that modulation of the conformational dynamics of GlnBP affects the ligand binding and dissociation rates. This study provides insights into the binding kinetics of ligands, which are related to the protein function itself.

Stochastic time-dependent enzyme kinetics: Closed-form solution and transient bimodality

We derive an approximate closed-form solution to the chemical master equation describing the Michaelis-Menten reaction mechanism of enzyme action. In particular, assuming that the probability of a complex dissociating into an enzyme and substrate is significantly larger than the probability of a product formation event, we obtain expressions for the time-dependent marginal probability distributions of the number of substrate and enzyme molecules. For delta function initial conditions, we show that the substrate distribution is either unimodal at all times or else becomes bimodal at intermediate times. This transient bimodality, which has no deterministic counterpart, manifests when the initial number of substrate molecules is much larger than the total number of enzyme molecules and if the frequency of enzyme-substrate binding events is large enough. Furthermore, we show that our closed-form solution is different from the solution of the chemical master equation reduced by means of the widely used discrete stochastic Michaelis-Menten approximation, where the propensity for substrate decay has a hyperbolic dependence on the number of substrate molecules. The differences arise because the latter does not take into account enzyme number fluctuations, while our approach includes them. We confirm by means of a stochastic simulation of all the elementary reaction steps in the Michaelis-Menten mechanism that our closed-form solution is accurate over a larger region of parameter space than that obtained using the discrete stochastic Michaelis-Menten approximation.

Order Through Disorder: The Characteristic Variability of Systems

Randomness characterizes many processes in nature, and therefore its importance cannot be overstated. In the present study, we investigate examples of randomness found in various fields, to underlie its fundamental processes. The fields we address include physics, chemistry, biology (biological systems from genes to whole organs), medicine, and environmental science. Through the chosen examples, we explore the seemingly paradoxical nature of life and demonstrate that randomness is preferred under specific conditions. Furthermore, under certain conditions, promoting or making use of variability-associated parameters may be necessary for improving the function of processes and systems.

Catalytic, Computational, and Evolutionary Analysis of the d-Lactate Dehydrogenases Responsible for d-Lactic Acid Production in Lactic Acid Bacteria

d-Lactate dehydrogenase (d-LDH) catalyzes the reversible reaction pyruvate + NADH + H⁺ ↔ lactate + NAD⁺, which is a principal step in the production of d-lactate in lactic acid bacteria. In this study, we identified and characterized the major d-LDH (d-LDH1) from three d-LDHs in Leuconostoc mesenteroides, which has been extensively used in food processing. A molecular simulation study of d-LDH1 showed that the conformation changes during substrate binding. During catalysis, Tyr101 and Arg235 bind the substrates by hydrogen bonds and His296 acts as a general acid/base for proton transfer. These residues are also highly conserved and have coevolved. Point mutations proved that the substrate binding sites and catalytic site are crucial for enzyme activity. Network and phylogenetic analyses indicated that d-LDH1 and the homologues are widely distributed but are most abundant in bacteria and fungi. This study expands the understanding of the functions, catalytic mechanism, and evolution of d-LDH.

Dissecting the Conformational Dynamics-Modulated Enzyme Catalysis with Single-Molecule FRET

Conformational changes of enzyme proteins are often coupled with a catalytic reaction and modulate the enzyme activity. Single-molecule technology is a powerful tool to study the mechanism of enzyme catalysis in these complicated cases. However, the chemical reaction cycles and conformational changes could not be monitored simultaneously in a single-molecule detection experiment, resulting in some unresolved key kinetic parameters. Here, we describe a method to extract all of the kinetic parameters from comprehensive single-molecule FRET (smFRET) measurements and model analysis. On the basis of the smFRET, we calculated the undetectable parameters by solving the rate equations of the kinetic model with the input of the smFRET-measured conformational state populations and state-transition rate constants. A case study of MalK₂ ATPase demonstrates that this method could reveal the quantitative mechanism of the catalytic reaction of the enzyme as well as its coupled conformational dynamics. The strategy employed in this study could be widely applied to investigate the conformational fluctuation-coupled catalysis of other enzymes.