Enhanced Diffusion of Enzymes that Catalyze Exothermic Reactions

Enzymes have been recently found to exhibit enhanced diffusion due to their catalytic activities. A recent experiment [C. Riedel et al., Nature (London) 517, 227 (2015)] has found evidence that suggests this phenomenon might be controlled by the degree of exothermicity of the catalytic reaction involved. Four mechanisms that can lead to this effect, namely, self-thermophoresis, boost in kinetic energy, stochastic swimming, and collective heating are critically discussed, and it is shown that only the last two can be strong enough to account for the observations. The resulting quantitative description is used to examine the biological significance of the effect.

Figure 1

Schematic illustration of the essence of Newton’s law of cooling. The heat generated in the bulk of a chamber (that is in contact with the environment that has a fixed ambient temperature $T_a$) and lost in the form of heat flux through the boundaries leads to the temperature profile $T_{\text{real}}$ (solid line), which is approximated by the average value over the distance $\sim \ell$, $T_{\text{app}}$ (dashed line). This approximation works best when there is a separation of length scales.

Figure 2

(a) The effective rate of catalytic reaction as a function of the reduced temperature $\theta$ for ${\theta }_d=0.1$, $g=50$, and $\epsilon =7$. The inset shows the fraction of catalytically active enzymes as a function of $\theta$ in each case. (b) The effective temperature of the catalytically active medium as a function of the coupling strength $\delta$. (c) The corresponding relative increase in diffusion coefficient. (d) The effective temperature for $\epsilon =30$ with the dashed region being unstable.