Fig. 3: Membrane deformations and fluctuations change during indentation.

a Series of fluorescent images (scale bars: \(3\,\mu {{{{{\rm{m}}}}}}\)) with circles indicating the bead (white) and the torus (red). Four stages are identified: I. Before contact at \(d \, < \,0\), II. Membrane deformation and wrapping for \(d \, < \,{d}_{{up}}\), III. Uptake and membrane tube formation at \(d\ge {d}_{{up}}\), and IV. Membrane tube elongation at constant force. b Deformation force F(d) (left axis, green) and deformation energy G(d) (right axis, orange) profiles versus indentation distance during induced uptake of a tense (left column) and flaccid (right column) DOPC vesicle. The force fluctuation during the uptake corresponds to the bright data points and the mean value of the force smoothed over \(\Delta t=100\,{{{{{{\rm{ms}}}}}}}\) corresponds to the dark curves. \({F}_{{up}}\) and \({G}_{{up}}\) indicate the uptake force and uptake energy, respectively, occurring at the distance \({d}_{{up}}\). After uptake, a membrane tube is elongated by a force \({F}_{t}\). c Particle position fluctuation changes expressed by the stiffness \({{\kappa }_{{tot}}=\kappa }_{{opt}}+{\kappa }_{{mem}}(d)\) (right axis, red) and the friction coefficient \({\gamma }_{{tot}}={\gamma }_{{bd}}+{\gamma }_{m{em}}(d)\) (left axis, light blue). The fluctuations in \({\kappa }_{{tot}}\) and \({\gamma }_{{tot}}\) during the uptake correspond to the bright lines and their corresponding mean values smoothed over Δt = 100 ms are represented by the dark solid curves. \({\kappa }_{{up}}\) and \({\gamma }_{{up}}\) are the uptake values for the stiffness and friction coefficient at \({d}_{{up}}\)._. d Distance-dependent increase in autocorrelation time \({\tau }_{c}\left(d\right)\) for tense and flaccid vesicle. The fluctuations in autocorrelation time \({\tau }_{c}\) during uptake are shown in bright blue, their mean values smoothed over Δt = 100 ms in dark blue with \({\tau }_{{up}}={\tau }_{c}({d}_{{up}})\). e Calculated increase in friction and stiffness by subsequent suppression of lower modes with distance d. f Tube profiles (left): lateral fluorescence mean intensity \(I(x)\) measured from images at stage IV at different positions across the tube (gray open circles). Error bars correspond to the standard deviation of the mean. A Gaussian fit (black solid line) is used to obtain the tether radius \({R}_{t}\). Tether formation (right): a close-up of the transition stage III with a sudden decay (tense GUV) and a smooth decay (flaccid GUV) of the force from \({F}_{{up}}\) to F_t described by the transition time τ.