A thermodynamic perspective on enhanced enzyme diffusion

We are well into the 21st century and even the most fundamental aspects of protein biophysics continue to perplex us. For example, counter to any expectation, proteins are excellent conductors (1); globular proteins, the once hallowed paradigm of structural biology, are now believed to sample their unfolded ensemble multiple times over their lifetime due to their unexpectedly small folding equilibrium constants (2); and proteins, often naïvely depicted as solitary biological actors capable of forming static multimeric assemblies, are now thought to form large transient phase-separated condensates (3). Equally surprising is the observation, counter to any macroscopic hydrodynamic expectation, that catalytic proteins (enzymes) exhibit enhanced diffusion upon catalysis (4). The latter is the focus of “Master curve of boosted diffusion for 10 catalytic enzymes” by Jee et al. (4), where the effect of diffusion enhancement of 10 enzymes is probed by fluorescence correlation spectroscopy (FCS) (Fig. 1).

Fig. 1.

Diffusion coefficients are deduced by correlating photon arrivals. Fluorescently labeled proteins (shown as red dots, Left) are allowed to freely diffuse across an inhomogeneously illuminated confocal volume. Shown in blue (Left) is the overlap between the illuminated (excitation) region and the detected volume. Photon arrivals, $\{t_1,t_2,\cdots \}$, encode the number of molecules emitting photons, their distance from the center of the spot, their diffusion coefficients, photophysical artifacts, and other parameters (Middle). In principle, this information can be decoded directly from the photon arrivals (8, 9), though traditionally, in a process reminiscent of the Hanbury–Twiss experiments for deducing star sizes, large datasets are collected and photon arrivals are instead correlated in time, $\tau$ (Right). The correlation function, $G(\tau )$, itself is then fitted with an analytical function (red line, Right). Faster correlation function decays coincide with faster diffusion coefficients. It was this setup that has allowed Jee et al. (4) to deduce the diffusion coefficient of 10 different enzymes. Figure adapted from refs. 8 and 9.

Work on enhanced enzyme diffusion (5) was inspired by earlier work on diffusing nanoparticle catalysts (e.g., ref. 6). Despite over a decade of work, the mechanistic origin of enhanced enzyme diffusion has evaded simple explanation. Perhaps reminiscent of high-energy physics—and otherwise unusual for biophysics—the field of enhanced enzyme diffusion is sparse in experiments and littered with a constellation of theories, often casually borrowed from the field of active matter and catalyst propulsion, that remain unsatisfactory (7).

An initial attempt at a mechanistic description of enhanced enzyme diffusion was attributed to the heat (enthalpy) of reaction causing a sudden translational displacement in the center of mass of the enzyme upon catalysis (10). The restrictions imposed by the experimental method (FCS) limited the number of proteins, catalyzing exothermic reactions, that could be probed. Yet, despite these restrictions, a number of experimental controls could immediately be used to eliminate candidate models. The remaining, phenomenological, model described the enzyme as experiencing, immediately following catalysis, asymmetric internal stresses upon the release of catalytically evolved heat, thereby inducing a net translation of the enzyme's center of mass through fluid. Of concern, as highlighted in ref. 10, was the fluid model used and, in particular, the bulk viscosity that would have to be treated as a phenomenological parameter as the bulk viscosity was too high to support the types of enhancements observed in experiments.

One way to explain why the enzyme shows an apparent increase in diffusion is to assume that the temperature of bulk fluid, containing the enzyme and its substrate, rises due to the catalytic heat evolved. However, this explanation is eliminated by experimental controls (and by simple heat capacity calculations). Models later purporting this effect (11) erred in accidently assuming a much larger amount of substrate than otherwise experimentally available and using the thermal conductivity of air (as opposed to water) as pointed out in ref. 7.

More serious theoretical concerns were levied at the possibility that catalytically driven photophysical artifacts may be interpreted as the origin of enhanced diffusion (12). These concerns, in addition to others—for example, on the possibility of dissociation of mutimeric catalytic enzymes into monomers (13, 14) and basic issues of bulk fluid convection for enhanced enzyme and small molecule catalyst diffusion experiments performed in microfluidic devices (15)—ultimately drove the reconsideration or otherwise partial withdrawal of claims including those on the enhanced diffusion of alkaline phosphatase (16).

Despite this withdrawal, the effect remained in many enzymes as it did in small-molecule catalysts (17). Yet, the experimental plot thickened as 1) the diffusion enhancement effect was shown for aldolase (18) (an enzyme catalyzing an endothermic, as opposed to exothermic, reaction) and 2) imaging experiments (19) reported enzyme diffusion enhancements vastly exceeding those reported from FCS, raising further questions on the role of the matrix in which the enzymes were embedded for imaging purposes (7).

The theoretical plot followed suit—with a delightfully complex dumbbell enzyme model attributing diffusion effects to a reduction of the enzyme’s size and the suppression of hydrodynamically coupled conformational fluctuations in the dumbbell (20). This elaborate model was short-lived as Brownian dynamics simulations quickly cast irrecoverable doubt on its most basic assumptions (7, 21).

Despite a lack of theoretical explanation for the effect stretching beyond simple phenomenological fitting, if the effect purported by Jee et al. (4) holds to further scrutiny the consequences of enhanced enzyme diffusion are profound. For example, it may provide insight into how one may go about spatiotemporally organizing assemblies of enzymes (18, 22, 23) and power nanometer and micron-sized spherical- and tubular-shaped swimmers decorated with enzymes (24).

Along these lines, it has been proposed through microfluidic assays that enzymes (18) and enzyme-coated Janus particles (25) may chemotax toward their substrate, providing a possible mechanism by which protein condensates may assemble. This effect has been exploited as a candidate for targeted delivery (26, 27). However, consistent with the prediction that faster-moving, catalytically active enzymes diffuse away faster from their substrate (23), repulsive chemotaxis (22) was later shown for the case of urease and acetylcholinesterase.

This, in turn, brings us back to the need for more complete datasets as a way to explain the perplexing effect of enhanced enzyme diffusion. For this reason, the perspective brought to us by Jee et al. (4) comes a long way. Indeed, it reports a strong positive correlation between enhanced diffusion and the change in Gibbs free energy (as well as the Michaelis–Menten reaction rate) from FCS also supported by dynamic light scattering experiments. Such a correlation, whose robustness is further tested by tuning the reaction rate with both temperature and pH, may explain why the effect has been observed for enzymes catalyzing both endothermic as well as exothermic reactions and provides a path toward a satisfactory mechanistic framework, grounded in thermodynamics, of the origin of enhanced diffusion (4). It also unequivocally predicts where future enzymes are expected to fall on the master curve based on the intrinsic properties of the reactions they catalyze. The ability to find exceptions or further examples of enzymes falling on this curve should, in turn, motivate a family of future experiments and provide theorists with data from which to build a framework grounded in physical principles.