Kinetic Asymmetry versus Dissipation in the Evolution of Chemical Systems as Exemplified by Single Enzyme Chemotaxis.

Single enzyme chemotaxis is a phenomenon by which a nonequilibrium spatial distribution of an enzyme is created and maintained by concentration gradients of the substrate and product of the catalyzed reaction. These gradients can arise either naturally through metabolism or experimentally, e.g., by flow of materials through microfluidic channels or by use of diffusion chambers with semipermeable membranes. Numerous hypotheses regarding the mechanism of this phenomenon have been proposed. Here, we discuss a mechanism based solely on diffusion and chemical reaction and show that kinetic asymmetry, a difference in the transition state energies for dissociation/association of substrate and product, and diffusion asymmetry, a difference in the diffusivities of the bound and free forms of the enzyme, are the determinates of the direction of chemotaxis and can result in either positive or negative chemotaxis, both of which have been demonstrated experimentally. Exploration of these fundamental symmetries that govern nonequilibrium behavior helps to distinguish between possible mechanisms for the evolution of a chemical system from initial to the steady state and whether the principle that determines the direction a system shifts when exposed to an external energy source is based on thermodynamics or on kinetics with the latter being supported by the results of the present paper. Our results show that, while dissipation ineluctably accompanies nonequilibrium phenomena, including chemotaxis, systems do not evolve to maximize or minimize dissipation but rather to attain greater kinetic stability and accumulate in regions where their effective diffusion coefficient is as small as possible. The chemotactic response to the chemical gradients formed by other enzymes participating in a catalytic cascade provides a mechanism for forming loose associations known as metabolons. Significantly, the direction of the effective force due to these gradients depends on the kinetic asymmetry of the enzyme and so can be nonreciprocal, where one enzyme is attracted to another enzyme, but the other enzyme is repelled by the one, in seeming contradiction to Newtons third law. This nonreciprocity is an important ingredient in the behavior of active matter.

Relative Diffusivities of Bound and Unbound Protein Can Control Chemotactic Directionality.

Enzyme-based systems have been shown to undergo chemotactic motion in response to their substrate gradient. This phenomenon has been exploited to direct the motion of enzymes and enzyme-attached particles to specific locations in space. Here, we propose a new kinetic model to analyze the directional movement of an ensemble of protein molecules in response to a gradient of the ligand. We also formulate a separate model to probe the motion of enzyme molecules in response to a gradient of the substrate under catalytic conditions. The only input for the new enzymatic model is the Michaelis-Menten constant which is the relevant measurable constant for enzymatic reactions. We show how our model differs from previously proposed models in a significant manner. For both binding and catalytic reactions, a net movement up the ligand/substrate gradient is predicted when the diffusivity of the ligand/substrate-bound protein is lower than that of the unbound protein (positive chemotaxis). Conversely, movement down the ligand/substrate gradient is expected when the diffusivity of the ligand/substrate-bound protein is higher than that of the unbound protein (negative chemotaxis). However, there is no net movement of protein/enzyme when the diffusivities of the bound and free species are equal. The work underscores the critical importance of measuring the diffusivity of the bound protein and comparing it with that of the free protein.

Enzyme Catalysis Causes Fluid Flow, Motility, and Directional Transport on Supported Lipid Bilayers.

The dynamic interplay between the composition of lipid membranes and the behavior of membrane-bound enzymes is critical to the understanding of cellular function and viability, and the design of membrane-based biosensing platforms. While there is a significant body of knowledge about how lipid composition and dynamics affect membrane-bound enzymes, little is known about how enzyme catalysis influences the motility and lateral transport on lipid membranes. Using enzyme-attached lipids in supported bilayers (SLBs), we provide direct evidence of catalysis-induced fluid flow that underlies the observed motility on SLBs. Additionally, by using active enzyme patches, we demonstrate the directional transport of tracer particles on SLBs. As expected, enhancing the membrane viscosity by incorporating cholesterol into the bilayer suppresses the overall movement. These are the first steps in understanding diffusion and transport on lipid membranes due to active, out-of-equilibrium processes that are the hallmark of living systems. In general, our study demonstrates how active enzymes can be used to control diffusion and transport in confined 2-D environments.