Figure 5

Time evolution of the system and fission time dependency on elasticity. (a) The Debye-corrected conductance of the internal lumen (upper) is measured during constriction and fission of \(1.4\ \upmu m\)-long tubules coated by differently polymerized dynamins (\(H=20; 70; 200 \,\mathrm {nm}\), \(F_{\tau }=2.5\,\mathrm {pN}\)). Concurrently, the associated elastic energy change is shown (lower), evidencing the presence of an intrinsic energy barrier determining the closure of the lumen, i.e. null conductance. (b) Comparison of the time evolution of lumen conductance with experimentally available measurements^6,19. The effect of a single short dynamin (\(H=20\,\mathrm {nm}\)) is depicted by the long dashed red line for \(F_{\tau }=3.25\,\pm 0.75\,\mathrm {pN}\)²⁴, with the reddish area delineated by the uncertainty range of \(F_{\tau }\). The effect of multiple (five) short dynamins, with \(H=20\,\mathrm {nm}\), \(F_{\tau }=3.25\,\mathrm {pN}\), and set \(\sim 90\,\mathrm {nm}\) apart, is shown by the short dashed red line. The same elastic parameters characterize both the experiments and the numerical analysis, specifically \(k_b=16\, k_B T\) and \(\gamma =5 \times 10^{-4} \, \mathrm{Nm}^{-1}\), determining an initial tubule radius of \(\sim 8\,\mathrm {nm}\). (c) Snapshots of the deformed tubules with arrows depicting the local dynamin force (per unit of volume) in the different conditions analyzed in panels a and b; scale arrow is \(0.8\,\mathrm {pN}/\text{nm}^3\). From left to right, \(16\,\mathrm {nm}\)-radius tubule with a short dynamin, \(16\,\mathrm {nm}\)-radius tubule with a fairly long dynamin, and \(8\,\mathrm {nm}\)-radius tubule with five short dynamins, set \(\sim 90\,\mathrm {nm}\) apart (only two shown here). Arrow scale, show on the left, is \(0.8\,\mathrm {pN}\,\text{nm}^{-3}\). (d) Analytical prediction of the fission time, Eq. (2), compared with experimental results¹⁸ shown by the points with error bars. The solid, shaded lines represent the analytical predictions for the different values of \(k_b\) together with their uncertainties, provided by Ref.¹⁸. Here, dynamin characteristics are \(H=200\,\mathrm {nm}\) (experiments state \(H>150\,\mathrm {nm}\)) and \(N_{d}\times F_{\tau } \approx 15\times 4\,\mathrm {pN}\). The actual time scale of the simulations is determined by a direct comparison with osmotic pressure induced constriction experiments⁶, as further discussed in “Methods” section and Supplementary Information.