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Register a new userPhoresis and Enhanced Diffusion Compete in Enzyme Chemotaxis
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Added by
Jaime Agudo-Canalejo
Publication date
2021
fields
Physics
and research's language is
English
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Chemotaxis of enzymes in response to gradients in the concentration of their substrate has been widely reported in recent experiments, but a basic understanding of the process is still lacking. Here, we develop a microscopic theory for chemotaxis, valid for enzymes and other small molecules. Our theory includes both non-specific interactions between enzyme and substrate, as well as complex formation through specific binding between the enzyme and the substrate. We find that two distinct mechanisms contribute to enzyme chemotaxis: a diffusiophoretic mechanism due to the non-specific interactions, and a new type of mechanism due to binding-induced changes in the diffusion coefficient of the enzyme. The latter chemotactic mechanism points towards lower substrate concentration if the substrate enhances enzyme diffusion, and towards higher substrate concentration if the substrate inhibits enzyme diffusion. For a typical enzyme, attractive phoresis and binding-induced enhanced diffusion will compete against each other. We find that phoresis dominates above a critical substrate concentration, whereas binding-induced enhanced diffusion dominates for low substrate concentration. Our results resolve an apparent contradiction regarding the direction of urease chemotaxis observed in experiments, and in general clarify the relation between enhanced diffusion and chemotaxis of enzymes. Finally, we show that the competition between the two distinct chemotactic mechanisms may be used to engineer nanomachines that move towards or away from regions with a specific substrate concentration.
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Enzymes have been recently proposed to have mechanical activity associated with their chemical activity. In a number of recent studies, it has been reported that enzymes undergo enhanced diffusion in the presence of their corresponding substrate, when this substrate is uniformly distributed in solution. Moreover, if the concentration of the substrate is non-uniform, enzymes and other small molecules have been reported to show chemotaxis -- biased stochastic movement in the direction of the substrate gradient -- typically towards higher concentrations of this substrate, with a few exceptions. The underlying physical mechanisms responsible for enhanced diffusion and chemotaxis at the nanoscale, however, are still not well understood. Understanding these processes is important both for fundamental biological research, e.g. in the context of spatial organization of enzymes in metabolic pathways (metabolon formation), as well as for engineering applications, such as in the design of new vehicles for targeted drug delivery. In this Account, we will review the available experimental observations of both enhanced diffusion and chemotaxis, and we will discuss critically the different theories that have been proposed to explain the two. We first focus on enhanced diffusion, beginning with an overview of the experimental results. We then discuss the two main types of mechanisms that have been proposed, namely active mechanisms relying on the catalytic step of the enzymatic reaction, and equilibrium mechanisms which consider the reversible binding and unbinding of the substrate to the enzyme. We put particular emphasis on an equilibrium model recently introduced by us, which describes how the diffusion of dumbbell-like modular enzymes can be enhanced in the presence of substrate, thanks to a binding-induced reduction of the internal fluctuations of the enzyme. We then turn to chemotaxis, [...]
Enhanced diffusion and anti-chemotaxis of enzymes have been reported in several experiments in the last decade, opening up entirely new avenues of research in the bio-nanosciences both at the applied and fundamental level. Here, we introduce a novel theoretical framework, rooted in non-equilibrium effects characteristic of catalytic cycles, that explains all observations made so far in this field. In addition, our theory predicts entirely novel effects, such as dissipation-induced switch between anti-chemotactic and chemotactic behavior.
The concept that catalytic enzymes can act as molecular machines transducing chemical activity into motion has conceptual and experimental support, but much of the claimed support comes from experimental conditions where the substrate concentration is higher than biologically relevant and accordingly exceeds kM, the Michaelis-Menten constant. Moreover, many of the enzymes studied experimentally to date are oligomeric. Urease, a hexamer of subunits, has been considered to be the gold standard demonstrating enhanced diffusion. Here we show that urease and certain other oligomeric enzymes of high catalytic activity above kM dissociate into their smaller subunit fragments that diffuse more rapidly, thus providing a simple physical mechanism of enhanced diffusion in this regime of concentrations. Mindful that this conclusion may be controversial, our findings are sup-ported by four independent analytical techniques, static light scattering, dynamic light scattering (DLS), size-exclusion chroma-tography (SEC), and fluorescence correlation spectroscopy (FCS). Data for urease are presented in the main text and the con-clusion is validated for hexokinase and acetylcholinesterase with data presented in supplementary information. For substrate concentration regimes below kM at which these enzymes do not dissociate, our findings from both FCS and DLS validate that enzymatic catalysis does lead to the enhanced diffusion phenomenon. INTRODUCT
We show, using differential dynamic microscopy, that the diffusivity of non-motile cells in a three-dimensional (3D) population of motile E. coli is enhanced by an amount proportional to the active cell flux. While non-motile mutants without flagella and mutants with paralysed flagella have quite different thermal diffusivities and therefore hydrodynamic radii, their diffusivities are enhanced to the same extent by swimmers in the regime of cell densities explored here. Integrating the advective motion of non-swimmers caused by swimmers with finite persistence-length trajectories predicts our observations to within 2%, indicating that fluid entrainment is not relevant for diffusion enhancement in 3D.
A stochastic version of the Barkai-Leibler model of chemotaxis receptors in {it E. coli} is studied here to elucidate the effects of intrinsic network noise in their conformational dynamics. It was originally proposed to explain the robust and near-perfect adaptation of {it E. coli} observed across a wide range of spatially uniform attractant/repellent (ligand) concentrations. A receptor is either active or inactive and can stochastically switch between the two states. Enzyme CheR methylates inactive receptors while CheB demethylates active ones and the probability for it to be active depends on its level of methylation and ligandation. A simple version of the model with two methylation sites per receptor (M=2) shows zero-order ultrasensitivity (ZOU) akin to the classical 2-state model of covalent modification studied by Goldbeter and Koshland (GK). For extremely small and large ligand concentrations, the system reduces to two 2-state GK modules. A quantitative measure of the spontaneous fluctuations in activity (variance) estimated mathematically under linear noise approximation (LNA) is found to peak near the ZOU transition. The variance is a weak, non-monotonic and decreasing functions of ligand and receptor concentrations. Gillespie simulations for M=2 show excellent agreement with analytical results obtained under LNA. Numerical results for M=2, 3 and 4 show ZOU in mean activity; the variance is found to be smaller for larger M. The magnitude of receptor noise deduced from available experimental data is consistent with our predictions. A simple analysis of the downstream signaling pathway shows that this noise is large enough to have a beneficial effect on the motility of the organism. The response of mean receptor activity to small time-dependent changes in the external ligand concentration, computed within linear response theory, is found to have a bilobe form.
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