Diffusion and steady state distributions of flexible chemotactic enzymes

Abstract

Many experiments in recent years have reported that, when exposed to their corresponding substrate, catalytic enzymes undergo enhanced diffusion as well as chemotaxis (biased motion in the direction of a substrate gradient). Among other possible mechanisms, in a number of recent works we have explored several passive mechanisms for enhanced diffusion and chemotaxis, in the sense that they require only binding and unbinding of the enzyme to the substrate rather than the catalytic reaction itself. These mechanisms rely on conformational changes of the enzyme due to binding, as well as on phoresis due to non-contact interactions between enzyme and substrate. Here, after reviewing and generalizing our previous findings, we extend them in two different ways. In the case of enhanced diffusion, we show that an exact result for the long-time diffusion coefficient of the enzyme can be obtained using generalized Taylor dispersion theory, which results in much simpler and transparent analytical expressions for the diffusion enhancement. In the case of chemotaxis, we show that the competition between phoresis and binding-induced changes in diffusion results in non-trivial steady state distributions for the enzyme, which can either accumulate in or be depleted from regions with a specific substrate concentration.

Cooperatively enhanced reactivity and “stabilitaxis” of dissociating oligomeric proteins

“…Note that, in general, the bulkier dimer will diffuse more slowly than the monomer, so that D2 < D1. In fact, we have shown in previous work that, for two subunits that are linked into a dimer, the diffusion coefficient of the dimer goes as D2 = D1/2 − δD fluc , where δD fluc > 0 corresponds to a fluctuation-induced hydrodynamic correction (43)(44)(45). We therefore generically expect the even stronger condition D2 < D1/2.…”

Dependence of diffusion in Escherichia coli cytoplasm on protein size, environmental conditions and cell growth

“…The obtained overall dependence of diffusion coefficients on the molecular mass of the fusion protein showed the exponent β = 0.56, steeper than predicted by the Stokes-Einstein relation, with β = 0.33 for fully compact proteins or β = 0.4 for the more realistic case where proteins are assumed to be not entirely compact (Enright and Leitner 2005; Smilgies and Folta-Stogniew 2015). Nevertheless, at least for smaller constructs, the observed dependence of the diffusion coefficient on the molecular mass could be well reproduced when the specific shape of fusion constructs, where two roughly globular proteins are fused by a short linker, was taken into account along with their imperfect globularity (Agudo-Canalejo and Golestanian 2020). In contrast, the diffusion of larger proteins was still slower than calculated by this model.…”

Non-equilibrium phase separation in mixtures of catalytically active particles: size dispersity and screening effects

“…Synthetic colloids can be engineered to be chemotactic, for instance using phoretic effects [27,28]. Meanwhile, many enzymes have been reported to chemotax in gradients of their substrate [3][4][5][6][7], with a variety of mechanisms having been proposed to explain the phenomenon [1,[7][8][9][10][11].…”

“…One possible theoretical explanation for this process is based on the ability of enzymes to chemotax in the presence of gradients of their substrate, which has been experimentally observed in recent years for a variety of enzymes [3][4][5][6][7]. The mechanisms underlying enzyme chemotaxis, however, are as of yet still unclear, with diffusiophoresis and substrate-induced changes in enzyme diffusion being possible candidates [7][8][9][10][11]. In a recent publication [12], it was shown that the interplay between catalytic activity and chemotaxis can lead to effective non-reciprocal interactions [13][14][15] between enzyme-like particles, resulting in an active mechanism for the phase separation of such particles.…”