DNA Localization and Stretching on Periodically Microstructured Lipid Membranes

We study the conformational behavior of DNA molecules adsorbed on cationic-lipid membranes that are supported on grooved, one-dimensionally periodic microstructured surfaces. We reveal a striking ability of these periodically structured membranes to stretch DNA coils. We elucidate this DNA stretching phenomenon in terms of surface curvature dependent potential energy attained by the adsorbed DNA molecules. Because of it, DNA molecules undergo a localization transition causing them to stretch by binding to highly curved sections of the supported membranes.

Figure 1

AFM images of small subsections of the periodic COC surface: (a) 3D view and (b) cross-sectional profile of two consecutive grooves. (c) To-scale AFM cross-sectional image of the surface profile $h(x)$ of a single groove, perpendicular to the grooves. We also give close views on the right-hand side, in terms of the local surface slope angle $\Theta (x)={tan}^{-1}(dh/dx)$, and $C=d\Theta /ds=(d^{2}h/d{x}^2)/[1+(dh/dx{)}^2{]}^{3/2}$, the local surface curvature (along $x$). Across the inward (IN) curved edge, $\Theta (x)$ increases rapidly by $\Delta \Theta \approx 1\mathrm{rad}$, yielding a very strong peak (with $C>0$) in the $C$ vs $x$ plot, corresponding to $1/C=R=w/\Delta \Theta =20–30\mathrm{nm}$ (or even smaller, as this size $\approx \mathrm{AFM}$ tip radius). In contrast, the outward (OUT) curved edge has a much smaller curvature, and its would-be peak in the $C$ vs $x$ plot is depressed by a background of curvature variations (of both signs) due to local surface roughness.

Figure 2

FM images of DNA on a periodically structured membrane with 5% of DOTAP: (a) from stage 1 ($t=48\min$ after exchanging the solvent with the salt solution, see the text) and (b) from stage 2 (two different surface sections, left at $t=264\min$, right at $t=369\min$; $\mathrm{\text{scale bar}}=10\mu \mathrm{m}$). The grooves (invisible) form a vertical grid with $1.2\mu \mathrm{m}$ period, seen in the to-scale scanning electron microscopy image of the COC surface [lower inset in (b)]. The average DNA projected length along the grooves $\approx 10.5\mu \mathrm{m}$, at $t\approx 5\mathrm{h}$. In the upper inset in (b), DNA on the planar 5% DOTAP membrane (here at $t=140\min$; qualitatively the same images are obtained at any $t>25\min$). In (c), DNA on the periodically structured membranes with 3% of DOTAP ($t=180\min$) and, in (d), with 7% of DOTAP ($t=185\min$).

Figure 3

Surface curvature dependent potential energy of DNA, Eq. (1), along the periodic surface, is a sequence of potential traps ($C>0$) and barriers ($C<0$). DNA may form crossings between two edge traps. On exiting the traps, the DNA makes small nearly circular bends, with estimated radius $R_b\approx (\pi /4(\pi -2){)}^{1/2}(l_{\sigma }{\xi }_{\mathrm{pers}}{)}^{1/2}\sim 30\mathrm{nm}$, ($l_{\sigma }\sim w\sim 20\mathrm{nm}$). Their bending elasticity contributes to the total crossing energy $\Delta F_{\mathrm{cross}}$ the amount $\approx k_{B}T(\pi (\pi -2){)}^{1/2}({\xi }_{\mathrm{pers}}/l_{\sigma }{)}^{1/2}\sim 3.5k_{B}T$ (from the two bends per each crossing). It is much smaller than the extraction tension contribution to the $\mathrm{\text{crossing energy}}=k_{B}T(L_{\mathrm{cross}}/l_{\sigma })\sim 50k_{B}T$ for the long crossings between grooves, with $L_{\mathrm{cross}}\approx 1\mu \mathrm{m}$.