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

Abstract

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.

Mind from Matter: The Chemical Connection

“…Indeed, a potentially infinite set of dynamic kinetic states for X,Y interconversion exist, as each individual state would depend on the X and Y interconversion rates, which are not pre‐determined, but are dependent on the rates of material and energy supply. The existence of such DKS stable chemical systems as a general class of stable kinetic systems was reported a little over a decade ago by van Esch, Eelkema, and colleagues [31] and has been intensively investigated following that early pioneering study [32–35] …”

“…The existence of such DKS stable chemical systems as a general class of stable kinetic systems was reported a little over a decade ago by van Esch, Eelkema, and colleagues [31] and has been intensively investigated following that early pioneering study. [32][33][34][35] But the importance of the DKS concept in the context of the life phenomenon is that it describes not just certain chemical systems, but the entire class of living things. [12,13] By definition, each and every living entity, as well as many of the chemical systems from which those entities are composed, are now understood to be in that DKS state.…”

Kinetic Asymmetry and Directionality of Nonequilibrium Molecular Systems

“…This independence of the cycle direction on the equilibrium constants can be lifted in the presence of spatial gradients. [53,86] The cycling through the states in a particular order can describe, among many other possibilities, rotation of a rotor or directional walking of a molecular walker of a track. The directionality is attained at the expense of consuming substrate, where the available energy per stoichimetric conversion of substrate to waste product is denoted Dm SP , or harvested from external perturbations, where the available energy per stoichimetric conversion of substrate to waste product is denoted 2de.…”

“…[61] In this Scientific Perspective I present a general approach to theoretical description of molecular machines based on trajectory thermodynamics [40,62] that provides a consistent framework for a theory of molecular motors, rotors, and pumps, as well as for other non-equilibrium chemical phenomena [63] such as driven self-assembly, [64,65] molecular adaptation, [66][67][68][69] and single enzyme chemotaxis. [53] Standard thermodynamic approaches focus on the states of a system, and their free energies. In contrast, trajectory thermodynamics focusses on forward and microscopic reverse trajectories between the states, and on the relations between the probabilities of these trajectories and the energy exchanged with the environment dictated by the principle of microscopic reversibility [70][71][72] (MR).…”

Artificial Molecular Ratchets: Tools Enabling Endergonic Processes

“…The role of information ratchets in regulating macroscopic scale spatial phenomena is starting to emerge, specifically in relation to chemotaxis. Chemotaxis is the directional movement in response to a gradient of chemical species, and several possibilities have been envisioned to explain this phenomenon, including kinetic asymmetry [86–88] …”