Using Catalysis to Drive Chemistry Away from Equilibrium: Relating Kinetic Asymmetry, Power Strokes, and the Curtin–Hammett Principle in Brownian Ratchets

Abstract

Chemically fueled autonomous molecular machines are catalysis-driven systems governed by Brownian information ratchet mechanisms. One fundamental principle behind their operation is kinetic asymmetry, which quantifies the directionality of molecular motors. However, it is difficult for synthetic chemists to apply this concept to molecular design because kinetic asymmetry is usually introduced in abstract mathematical terms involving experimentally inaccessible parameters. Furthermore, two seemingly contradictory mechanisms have been proposed for chemically driven autonomous molecular machines: Brownian ratchet and power stroke mechanisms. This Perspective addresses both these issues, providing accessible and experimentally useful design principles for catalysis-driven molecular machinery. We relate kinetic asymmetry to the Curtin−Hammett principle using a synthetic rotary motor and a kinesin walker as illustrative examples. Our approach describes these molecular motors in terms of the Brownian ratchet mechanism but pinpoints both chemical gating and power strokes as tunable design elements that can affect kinetic asymmetry. We explain why this approach to kinetic asymmetry is consistent with previous ones and outline conditions where power strokes can be useful design elements. Finally, we discuss the role of information, a concept used with different meanings in the literature. We hope that this Perspective will be accessible to a broad range of chemists, clarifying the parameters that can be usefully controlled in the design and synthesis of molecular machines and related systems. It may also aid a more comprehensive and interdisciplinary understanding of biomolecular machinery.

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

“…For the enzymatic reaction in , the rates of transition between the bound and the free states are each sum of two terms: Microscopic reversibility requires that the ratio between each pair of forward and reverse rate constants be the exponential of the energy exchanged with the environment Using eqs and , the local ratio of bound to free enzyme, λ­( x ), defined in eq is where (Figure ) is the ratio of “off” rate constants for S and P, which can also be written as the exponential of the difference in activation barrier heights for dissociation of S vs P. is the equilibrium constant of the reaction S ⇌ P. We have written the expression for λ­( x ) in two ways in eq to emphasize the connection between the general nonequilibrium pumping equality (eq ) that involves the exponential of the path dependent energy exchanged in the transition between two states averaged over an arbitrary number of pathways between the two states, , and the kinetic asymmetry factor, , that simplifies this result for systems with only two paths connecting the two states as is the case with an enzyme. , …”

Kinetic Barrier Diagrams to Visualize and Engineer Molecular Nonequilibrium Systems

“…a) Reaction network and molecular structure of light‐driven rotary motor (Table S2, Supporting Information for parameters). [ 48 ] b) Associated kinetic barrier diagram. The effect of increasing the photon flux is indicated using dashed arrows.…”

“…Insights remain fully coherent with related theoretical results, e.g., varying only the equilibrium constant for Steps 2 and 4 does not influence the directionality of the system (Δ), which confirms being a purely kinetic phenomenon. [12,37,38,48] To illustrate the insight offered by this approach in different contexts, we have constructed the kinetic barrier diagrams for three significant systems reported in the literature: a chemically driven motor, a light-driven motor, and the driven self-assembly of dimers. [33,37,49] Moreover, to help the reader familiarize with kinetic barrier diagrams, we provide an interactive tutorial in form of a Jupyter Notebook as supplementary material, which can be used to explore the features of kinetic barrier diagrams.…”

“…As [F] increases, the system evolves into nonequilibrium steady states, with kinetic asymmetry visually S2, Supporting Information for parameters). [48] b) Associated kinetic barrier diagram. The effect of increasing the photon flux is indicated using dashed arrows.…”

“…Insights on a light-driven rotary motor. a) Reaction network and molecular structure of light-driven rotary motor (TableS2, Supporting Information for parameters) [48]. b) Associated kinetic barrier diagram.…”