Motor-like Properties of Nonmotor Enzymes

Kinetic Asymmetry and Directionality of Nonequilibrium Molecular Systems

Scientists have long been fascinated by the biomolecular machines in living systems that process energy and information to sustain life. The first synthetic molecular rotor capable of performing repeated 360° rotations due to a combination of photo- and thermally activated processes was reported in 1999. The progress in designing different molecular machines in the intervening years has been remarkable, with several outstanding examples appearing in the last few years. Despite the synthetic accomplishments, there remains confusion regarding the fundamental design principles by which the motions of molecules can be controlled, with significant intellectual tension between mechanical and chemical ways of thinking about and describing molecular machines. A thermodynamically consistent analysis of the kinetics of several molecular rotors and pumps shows that while light driven rotors operate by a power-stroke mechanism, kinetic asymmetry-the relative heights of energy barriers-is the sole determinant of the directionality of catalysis driven machines. Power-strokes-the relative depths of energy wells-play no role whatsoever in determining the sign of the directionality. These results, elaborated using trajectory thermodynamics and the nonequilibrium pump equality, show that kinetic asymmetry governs the response of many non-equilibrium chemical phenomena.

Life's Mechanism

The multifarious internal workings of organisms are difficult to reconcile with a single feature defining a state of 'being alive'. Indeed, definitions of life rely on emergent properties (growth, capacity to evolve, agency) only symptomatic of intrinsic functioning. Empirical studies demonstrate that biomolecules including ratcheting or rotating enzymes and ribozymes undergo repetitive conformation state changes driven either directly or indirectly by thermodynamic gradients. They exhibit disparate structures, but govern processes relying on directional physical motion (DNA transcription, translation, cytoskeleton transport) and share the principle of repetitive uniplanar conformation changes driven by thermodynamic gradients, producing dependable unidirectional motion: 'heat engines' exploiting thermodynamic disequilibria to perform work. Recognition that disparate biological molecules demonstrate conformation state changes involving directional motion, working in self-regulating networks, allows a mechanistic definition: life is a self-regulating process whereby matter undergoes cyclic, uniplanar conformation state changes that convert thermodynamic disequilibria into directed motion, performing work that locally reduces entropy. 'Living things' are structures including an autonomous network of units exploiting thermodynamic gradients to drive uniplanar conformation state changes that perform work. These principles are independent of any specific chemical environment, and can be applied to other biospheres.

Perspective: a stirring role for metabolism in cells

Based on recent findings indicating that metabolism might be governed by a limit on the rate at which cells can dissipate Gibbs energy, in this Perspective, we propose a new mechanism of how metabolic activity could globally regulate biomolecular processes in a cell. Specifically, we postulate that Gibbs energy released in metabolic reactions is used to perform work, allowing enzymes to self‐propel or to break free from supramolecular structures. This catalysis‐induced enzyme movement will result in increased intracellular motion, which in turn can compromise biomolecular functions. Once the increased intracellular motion has a detrimental effect on regulatory mechanisms, this will establish a feedback mechanism on metabolic activity, and result in the observed thermodynamic limit. While this proposed explanation for the identified upper rate limit on cellular Gibbs energy dissipation rate awaits experimental validation, it offers an intriguing perspective of how metabolic activity can globally affect biomolecular functions and will hopefully spark new research.

Mechanistic analysis of light-driven overcrowded alkene-based molecular motors by multiscale molecular simulations

We analyze light-driven overcrowded alkene-based molecular motors, an intriguing class of small molecules that have the potential to generate MHz-scale rotation rates. The full rotation process is simulated at multiple scales by combining quantum surface-hopping molecular dynamics (MD) simulations for the photoisomerization step with classical MD simulations for the thermal helix inversion step. A Markov state analysis resolves conformational substates, their interconversion kinetics, and their roles in the motor's rotation process. Furthermore, motor performance metrics, including rotation rate and maximal power output, are computed to validate computations against experimental measurements and to inform future designs. Lastly, we find that to correctly model these motors, the force field must be optimized by fitting selected parameters to reference quantum mechanical energy surfaces. Overall, our simulations yield encouraging agreement with experimental observables such as rotation rates, and provide mechanistic insights that may help future designs.

Enhanced Diffusion and Chemotaxis of Enzymes

Many enzymes appear to diffuse faster in the presence of substrate and to drift either up or down a concentration gradient of their substrate. Observations of these phenomena, termed enhanced enzyme diffusion (EED) and enzyme chemotaxis, respectively, lead to a novel view of enzymes as active matter. Enzyme chemotaxis and EED may be important in biology and could have practical applications in biotechnology and nanotechnology. They are also of considerable biophysical interest; indeed, their physical mechanisms are still quite uncertain. This review provides an analytic summary of experimental studies of these phenomena and of the mechanisms that have been proposed to explain them and offers a perspective on future directions for the field.

On the beneficent thickness of water

In the 1930s, Lars Onsager published his famous 'reciprocal relations' describing free energy conversion processes. Importantly, these relations were derived on the assumption that the fluxes of the processes involved in the conversion were proportional to the forces (free energy gradients) driving them. For chemical reactions, however, this condition holds only for systems operating close to equilibrium-indeed very close; nominally requiring driving forces to be smaller than k B T. Fairly soon thereafter, however, it was quite inexplicably observed that in at least some biological conversions both the reciprocal relations and linear flux-force dependency appeared to be obeyed no matter how far from equilibrium the system was being driven. No successful explanation of how this 'paradoxical' behaviour could occur has emerged and it has remained a mystery. We here argue, however, that this anomalous behaviour is simply a gift of water, of its viscosity in particular; a gift, moreover, without which life almost certainly could not have emerged. And a gift whose appreciation we primarily owe to recent work by Prof. R. Dean Astumian who, as providence has kindly seen to it, was led to the relevant insights by the later work of Onsager himself.

Kinetic asymmetry allows macromolecular catalysts to drive an information ratchet

Molecular machines carry out their function by equilibrium mechanical motions in environments that are far from thermodynamic equilibrium. The mechanically equilibrated character of the trajectories of the macromolecule has allowed development of a powerful theoretical description, reminiscent of Onsager’s trajectory thermodynamics, that is based on the principle of microscopic reversibility. Unlike the situation at thermodynamic equilibrium, kinetic parameters play a dominant role in determining steady-state concentrations away from thermodynamic equilibrium, and kinetic asymmetry provides a mechanism by which chemical free-energy released by catalysis can drive directed motion, molecular adaptation, and self-assembly. Several examples drawn from the recent literature, including a catenane-based chemically driven molecular rotor and a synthetic molecular assembler or pump, are discussed.

The mechanism by which macromolecular catalysts use energy from exergonic reactions to move, adapt, and assemble has been unclear. In this Perspective article, R. Dean Astumian shows that in addition to disequilibrium of the catalyzed reaction, kinetic asymmetry is the essential feature required to drive non-equilibrium response by an information ratchet mechanism.

Theory of Nonequilibrium Free Energy Transduction by Molecular Machines

Biomolecular machines are protein complexes that convert between different forms of free energy. They are utilized in nature to accomplish many cellular tasks. As isothermal nonequilibrium stochastic objects at low Reynolds number, they face a distinct set of challenges compared with more familiar human-engineered macroscopic machines. Here we review central questions in their performance as free energy transducers, outline theoretical and modeling approaches to understand these questions, identify both physical limits on their operational characteristics and design principles for improving performance, and discuss emerging areas of research.

Tracking the rotation of single CdS nanorods during photocatalysis with surface plasmon resonance microscopy

Rotational dynamics of anisotropic nanomaterials reveals and regulates their behaviors and functions in diverse fields ranging from nanomotors, biomechanics, and enzymatic catalysis to microrheology. An optical imaging technique that is suitable for all kinds of anisotropic nanoobjects, regardless of its inherent optical property, is thus highly desirable and it is yet to be demonstrated. In the present work, by taking a nonfluorescent and nonplasmonic CdS nanorod as an example, we demonstrate the capability of a recently developed surface plasmon resonance microscopy for determining the orientation of single anisotropic nanomaterials with arbitrary chemical composition and morphology.

While rotational dynamics of anisotropic nanoobjects has often been limited in plasmonic and fluorescent nanomaterials, here we demonstrate the capability of a surface plasmon resonance microscopy (SPRM) to determine the orientation of all kinds of anisotropic nanomaterials. By taking CdS nanorods as an example, it was found that two-dimensional Fourier transform of the asymmetrical wave-like SPRM image resulted in a peak in its angular spectrum in k space. Consistency between the peak angle and the geometrical orientation of the nanorod was validated by both in situ scanning electron microscope characterizations and theoretical calculations. Real-time monitoring of the rotational dynamics of single CdS nanorods further revealed the accelerated rotation under appropriate reaction conditions for photocatalyzed hydrogen generation. The driving force was attributed to the asymmetric production of hydrogen molecules as a result of inhomogeneous distribution of reactive sites within the nanorod. The present work not only builds the experimental and theoretical connections between the orientation of anisotropic nanomaterials and its SPRM images; the general suitability of SPRM also sheds light on broad types of nonfluorescent and nonplasmonic anisotropic nanoobjects from semiconductors to bacteria and viruses.

An upper limit on Gibbs energy dissipation governs cellular metabolism

The principles governing cellular metabolic operation are poorly understood. Because diverse organisms show similar metabolic flux patterns, we hypothesized that a fundamental thermodynamic constraint might shape cellular metabolism. Here, we develop a constraint-based model for Saccharomyces cerevisiae with a comprehensive description of biochemical thermodynamics including a Gibbs energy balance. Non-linear regression analyses of quantitative metabolome and physiology data reveal the existence of an upper rate limit for cellular Gibbs energy dissipation. By applying this limit in flux balance analyses with growth maximization as the objective function, our model correctly predicts the physiology and intracellular metabolic fluxes for different glucose uptake rates as well as the maximal growth rate. We find that cells arrange their intracellular metabolic fluxes in such a way that, with increasing glucose uptake rates, they can accomplish optimal growth rates but stay below the critical rate limit on Gibbs energy dissipation. Once all possibilities for intracellular flux redistribution are exhausted, cells reach their maximal growth rate. This principle also holds for Escherichia coli and different carbon sources. Our work proposes that metabolic reaction stoichiometry, a limit on the cellular Gibbs energy dissipation rate, and the objective of growth maximization shape metabolism across organisms and conditions.

Trajectory and Cycle-Based Thermodynamics and Kinetics of Molecular Machines: The Importance of Microscopic Reversibility

A molecular machine is a nanoscale device that provides a mechanism for coupling energy from two (or more) processes that in the absence of the machine would be independent of one another. Examples include walking of a protein in one direction along a polymeric track (process 1, driving "force" X₁ = - F⃗· l⃗) and hydrolyzing ATP (process 2, driving "force" X₂ = Δμ_ATP); or synthesis of ATP (process 1, X₁ = -Δμ_ATP) and transport of protons from the periplasm to the cytoplasm across a membrane (process 2, X₂ = Δμ_H⁺); or rotation of a flagellum (process 1, X₁ = -torque) and transport of protons across a membrane (process 2, X₂ = Δμ_H⁺). In some ways, the function of a molecular machine is similar to that of a macroscopic machine such as a car that couples combustion of gasoline to translational motion. However, the low Reynolds number regime in which molecular machines operate is very different from that relevant for macroscopic machines. Inertia is negligible in comparison to viscous drag, and omnipresent thermal noise causes the machine to undergo continual transition among many states even at thermodynamic equilibrium. Cyclic trajectories among the states of the machine that result in a change in the environment can be broken into two classes: those in which process 1 in either the forward or backward direction ([Formula: see text]) occurs and which thereby exchange work [Formula: see text] with the environment; and those in which process 2 in either the forward or backward direction ([Formula: see text]) occurs and which thereby exchange work [Formula: see text] with the evironment. These two types of trajectories, [Formula: see text] and [Formula: see text], overlap, i.e., there are some trajectories in which both process 1 and process 2 occur, and for which the work exchanged is [Formula: see text]. The four subclasses of overlap trajectories [(+1,+2), (+1,-2), (-1,+2), (-1,-2)] are the coupled processes. The net probabilities for process 1 and process 2 are designated π₊₂ - π_-2 and π₊₁ - π_-1, respectively. The probabilities [Formula: see text] for any single trajectory [Formula: see text] and [Formula: see text] for its microscopic reverse [Formula: see text] are related by microscopic reversibility (MR), [Formula: see text], an equality that holds arbitrarily far from thermodynamic equilibrium, i.e., irrespective of the magnitudes of X₁ and X₂, and where [Formula: see text]. Using this formalism, we arrive at a remarkably simple and general expression for the rates of the processes, [Formula: see text], i = 1, 2, where the angle brackets indicate an average over the ensemble of all microscopic reverse trajectories. Stochastic description of coupling is doubtless less familiar than typical mechanical depictions of chemical coupling in terms of ATP induced violent kicks, judo throws, force generation and power-strokes. While the mechanical description of molecular machines is comforting in its familiarity, conclusions based on such a phenomenological perspective are often wrong. Specifically, a "power-stroke" model (i.e., a model based on energy driven "promotion" of a molecular machine to a high energy state followed by directional relaxation to a lower energy state) that has been the focus of mechanistic discussions of biomolecular machines for over a half century is, for catalysis driven molecular machines, incorrect. Instead, the key principle by which catalysis driven motors work is kinetic gating by a mechanism known as an information ratchet. Amazingly, this same principle is that by which catalytic molecular systems undergo adaptation to new steady states while facilitating an exergonic chemical reaction.