Fig. 4.

Changes in the potential of mean force at increasing membrane fluidity. (A and B) The three graphs each show the free-energy profiles ${\mathcal{V}}_s\left(z_{cm}\right)$ (red) and ${\mathcal{V}}_{\beta }\left(z_{cm}\right)$ (blue) at increasing fluidities $k_{\text{B}}T/\epsilon =0.775,1.015$, and 1.135, while protein–membrane interactions are kept fixed at ${\epsilon }_{s\text{m}}=3.5\hspace{0.17em}{k}_{\text{B}}T$ and ${\epsilon }_{\beta \text{m}}=12\hspace{0.17em}{k}_{\text{B}}T$ (A), and at increasing protein–membrane affinities ${\epsilon }_{s\text{m}}=2.0,3.5$, and $5.5\hspace{0.17em}{k}_{\text{B}}T$, while the fluidity is kept fixed at $k_{\text{B}}T/\epsilon =1.135$ and ${\epsilon }_{\beta \text{m}}=12\hspace{0.17em}{k}_{\text{B}}T$ (B). The arrows indicate the free-energy cost for conformational conversion $\mathrm{\Delta }\mathcal{V}$, providing a proxy for the nucleation barrier. (C) Initial snapshot of umbrella simulations for both particle species. (D) Difference between potentials of mean force in the “$s$” and “$\beta$” conformation evaluated at the minimum of ${\mathcal{V}}_s\left(z\right)$ as a function of the membrane fluidity and the membrane–protein affinity ${\epsilon }_{s\text{m}}$.