Thermal fluctuations assist mechanical signal propagation in coiled-coil proteins

Recently, it has been shown that the long coiled-coil membrane tether protein early endosome antigen 1 (EEA1) switches from a rigid to a flexible conformation upon binding of a signaling protein to its free end. This flexibility switch represents a motorlike activity, allowing EEA1 to generate a force that moves vesicles closer to the membrane they will fuse with. It was hypothesized that the binding-induced signal could propagate along the coiled coil and lead to conformational changes through the localized domains of the protein chain that deviate from a perfect coiled-coil structure. To elucidate, if upon binding of a single protein the corresponding mechanical signal could propagate through the whole 200-nm-long chain, we propose a simplified description of the coiled coil as a one-dimensional Frenkel-Kontorova chain. Using numerical simulations, we find that an initial perturbation of the chain can propagate along its whole length in the presence of thermal fluctuations. This may enable the change of the configuration of the entire molecule and thereby affect its stiffness. Our work sheds light on intramolecular communication and force generation in long coiled-coil proteins.

Figure 1

Modeling hydrophobic interactions between strands in a canonical coiled-coil structure. (a) Sketch of the EEA1 structure. (b) Coiled-coil fold prediction for EEA1 in humans [16]. (c) Register shift between the $\alpha$-helices of the EEA1 after Rab5 binding at the N-terminus. (d) Sketch of the application of the Frenkel-Kontorova model to map the hydrophobic contacts stabilizing the two $\alpha$-helical strands forming a homodimeric canonical coiled-coil protein. (e) Frenkel-Kontorova model represented by a chain of beads connected by harmonic springs in the periodic potential. $E_B$ and $l_0$ are the strength and the period of the hydrophobic interaction potential, respectively, where $l_0$ is also the half turn separating two hydrophobic residues and the equilibrium length of the harmonic spring (with the spring constant $k$) connecting two beads.

Figure 2

Signal propagation analysis. (a) Evolution of the potential energy distribution profile along a Frenkel-Kontorova chain in the absence of thermal fluctuations with $E_B=1k_{B}T$ and $k=100k_{B}T{\mathrm{nm}}^{-2}$. The initial contraction relaxes and does not propagate. (b) Potential energy distribution profile averaged over 5000 trajectories for identical chains affected by thermal fluctuations, normalized by the average energy per bead in a chain without perturbations, $\langle U_{i,0}\rangle$. In this case, the compression is active and propagates diffusively. The averaged signal has been filtered by applying the Savitzky-Golay algorithm with a window size of 51 data points [27] (black). The fit curve (red) corresponds to the solution to the diffusion equation with a reflecting boundary at $x=0$ with the diffusion constant $D$ extracted from the fit. (c) Dynamics of the position of the potential energy front $x_{fr}$ for different $E_B$ and $k$ pairs, indicated in brackets. The front position $x_{\text{fr}}$ is the position where the filtered signal reaches the threshold. The units of $E_B$ and $k$ are $k_{B}T$ and $k_{B}T{\mathrm{nm}}^{-2}$, in all plots, respectively, where $T$ is the room temperature.

Figure 3

Diffusion coefficient of a kink generated in the center of a Frenkel-Kontorova chain for different chain stiffness $k$ and bond energy $E_B$, each extracted from the energy average of 2000 kink trajectories, normalized by the minimum diffusion constant required to transmit the signal, $D_0$, the maximum chain stiffness, $k_0=65k_{B}T{\mathrm{nm}}^{-2}$, and the maximum activation energy, $E_A=20k_{B}T$. The upper limit (magenta) corresponds to the limit where the activation energy cannot overcome the first potential barrier. The orange line limits the cases where the diffusion constant is $D_0$. Hydrophobic bond energy differences $E_B$ below $1k_{B}T$ ($E_B/E_A=0.05$) lead to unstable chains (white). Finally, the maximum energy released between a pair of hydrophobic residues $E_B$ is approximately $4k_{B}T$ ($E_B/E_A=0.2$) [35] (light green).

Figure 4

(a) Sketch of the discontinuity model. (b) Potential energy distribution profile at $t=1\mu \mathrm{s}$ averaged over 5000 trajectories for chains with $E_B=1k_{B}T$ and $k=100k_{B}T{\mathrm{nm}}^{-2}$ affected by thermal fluctuations, which include a discontinuity (light gray line) affecting the region highlighted in light red, normalized by the average energy per bead in a chain without perturbations, $\langle U_{i,0}\rangle$. This distribution is compared with that of a chain with the same $k,E_B$ properties which does not have a discontinuity (black line), discussed in Fig. 2. Both filtered signals have been obtained by applying the Savitzky-Golay algorithm with a window size of 51 data points [27] on the original signal averages. The fit curves (dashed lines, red and blue for the no-discontinuity and discontinuity cases, respectively) correspond to the solution to the diffusion equation with a reflecting boundary at $x=0$ with the indicated diffusion constant $D$ values extracted from the fit.