Direct measurement of single soft lipid nanotubes: Nanoscale information extracted in a noninvasive manner

We investigated the dynamics of single soft nanotubes of phospholipids to extract nanoscale information such as the size of the tube, which were several tens to hundreds of nanometers thick. The dynamic properties of the tubes obtained from direct observation by fluorescent microscopy, such as their persistence length, enable us to access the nanoscale characteristics through a simple elastic model of the membrane. The present methodology should be applicable to the nanosized membrane structure in living cells.

Figure 1

(a) Typical images of a single phospholipid tube in an aqueous solution. The images were taken at intervals of 5.0 s. The scale bar is 5 $\mu \mathrm{m}$. (b) A schematic illustration of a nanotube. (c) The measured values obtained from image analysis. The radius of gyration $R_g$ is calculated from the spatial distribution of fluorescent intensity; the rotational relaxation time ${\tau }_r$ represents the decay of the correlation of a unit end-to-end vector $\mathit{p}\left(t\right)$; the persistence length $l_p$ is defined as the decaying slope of a scalar product of two unit tangent vectors $\mathit{u}\left(s\right)$ and $\mathit{u}(s+▵s)$. (d) Frame representation of part of a tube. An eel-like tube is assumed to be composed of several sections of tori with various values of $R$ and homogeneous $r$. Notations used in the calculations are represented as above.

Figure 2

(a) Log-log plot of measurements of MSD of the center of mass. In the short time region to 10 s, each MSD is proportional to $▵t$. (b) Log-log plot of MSD of the end points.

Figure 3

Relations between (a) the lateral diffusion constant $D_G$ and the radius of gyration $R_g$, (b) the rotational relaxation time ${\tau }_r$ and $R_g$, and (c) ${\tau }_r$ and $D_G$ as determined experimentally. Fitting lines are $D_G\propto R_g^{\alpha }$ ($\alpha =-1.3$), ${\tau }_r\propto R_g^{\beta }$ ($\beta =2.9$), and ${\tau }_r\propto D_G^{\gamma }$ ($\gamma =-3.1$), respectively. Superimposed lines show the scaling law from the theory of polymer dynamics; $\alpha =-2$, $\beta =4$, and $\gamma =-2$ are indices of the Rouse model, and $\alpha =-1$, $\beta =3$, and $\gamma =-3$ are those of the Zimm model.

Figure 4

Typical examples of the correlations of scalar product $\langle \mathit{u}\left(s\right)·\mathit{u}(s+▵s)\rangle$. The persistence length $l_p$ is determined from the exponential decay in a short region. The correlation at long range and in the vicinity of 0 tends to deviate from exponential fitting.

Figure 5

Distribution of the radii of tubes with $\kappa =20k_{\mathrm{B}}T$.