Nonequilibrium Dynamic Mechanism for Allosteric Effect

Allosteric regulation is often viewed as thermodynamic in nature. However, protein internal motions during an enzymatic reaction cycle can slow the hoping processes over numerous potential barriers. We propose that regulating molecules may function by modifying the nonequilibrium protein dynamics. The theory predicts that an enzyme under the new mechanism has a different temperature dependence, waiting time distribution of the turnover cycle, and dynamic fluctuation patterns with and without an effector. Experimental tests of the theory are proposed.

Figure 1

A minimal model for the catalytic site (a) The free energy curves represent three distinct catalytic site binding states ($E$, $S$, $P$) projected onto the conformational coordinate $x$. The inset illustrates that the smooth potentials are actually coarse-grained over rugged potential surfaces. Effector binding at a distant site may modify the roughness of the potentials. (b) Two classes of reaction pathways along a multidimensional surface. Path 1 is along the long but low barrier minimum energy path. Path 2 is a short high barrier corner-cutting path.

Figure 2

Theoretical predictions. (a) Enzyme turnover rate as a function of the effective internal diffusion constant $D$. (b) Temperature dependence of the enzyme turnover rate. $D=D_0\exp [-(ϵ/k_{B}T{)}^2]$, where $ϵ$ is the roughness parameter, and $D_0={10}^3$. Solid line: $ϵ=0$. dashed line: $ϵ=4k_{B}T$, the dotted line gives the exponential dependence if the Arrhenius rate equation is assumed. The temperature dependence of $D_0$ is neglected in this calculation. (c) Turnover waiting time distribution with $D=1$ (solid line) and $D=0.001$ (dashed line).