Static conformation and dynamics of single DNA molecules confined in nanoslits

Nearly thirty years ago, Daoud and de Gennes derived the scaling predictions for the linear polymer chains trapped in a slit with dimension close to the Kuhn length; however, these predictions have yet to be compared with experiments. We have fabricated nanoslits with vertical dimension similar to the Kuhn length of ds-DNA $\left(110\mathrm{nm}\right)$ using standard photolithography techniques. Fluorescently labeled single DNA molecules with contour lengths $L$ ranging from $4\text{to}75\mu \mathrm{m}$ were successfully injected into the slits and the chain molecules undergoing Brownian motions were imaged by fluorescence microscopy. The distributions of the chain radius of gyration and the two-dimensional asphericity were measured. It is found that the DNA molecules exhibit highly anisotropic shape and the mean asphericity is chain length independence. The shape anisotropy of DNA in our measurements is between two and three dimensions (2D and 3D). The static scaling law of the chain extension and the radius of gyration $⟨R_{\parallel }⟩,⟨R_g⟩\sim L^{\nu }$ were observed with ${\nu }_{R\Vert }=0.65\pm 0.02$ and ${\nu }_{\mathrm{Rg}}=0.68\pm 0.05$. These results are close to the average value between two $({\nu }_{R\Vert ,\mathrm{Rg}}=0.75)$ and three $({\nu }_{R\Vert ,\mathrm{Rg}}=0.6)$ -dimensional theoretical value. The scaling of the extensional and rotational relaxation time are between Rouse model in nanoslits and Zimm model in the bulk solution, respectively. We show that the conformation and chain relaxation of DNA confined in a slit close to Kuhn length exhibit the quasi-two-dimensional behavior.

Figure 1

(Color online) (a) Cross-sectional scanning electron image of the $110\text{−}\mathrm{nm}$ slit. (b) The fluorescence image of T4-DNA, $\lambda \text{−}\mathrm{DNA}$, F1-DNA, and F2-DNA, confined in the $110\text{−}\mathrm{nm}$ slit. (c) The mean-squared displacements of center of mass vs time in double-logarithmic plot. (d) The $\lambda \text{−}\mathrm{DNA}$ image can be represented by an ellipse using the radius of gyration tensor, where $R_1$ is the major radius gyration component, $R_2$ is the minor radius gyration component, and $R_{\Vert }$ is the extension of this DNA image.

Figure 2

(Color online) (a) The probability distributions of $R_1^2$ and $R_2^2$ for $\lambda \text{−}\mathrm{DNA}$; the mean values of the major and minor eigenvalues are $⟨R_1^2⟩=0.62\pm 0.33\mu {\mathrm{m}}^2$ and $⟨R_2^2⟩=0.12\pm 0.05\mu {\mathrm{m}}^2$, respectively. (b) The probability distribution of experimental measurements for the asphericity $A_2$. The exposure time of F2–F1 and $\lambda –\mathrm{T}4$ are 0.01 and $0.033\mathrm{s}$, respectively. (c) The probability distribution of the simulation results for $A_2$ with chain length $n=32$ (solid: before convolution; dashed: after convolution) and $n=256$ (dotted: before convolution; dash-dotted: after convolution). (d) The mean asphericity $⟨A_2⟩$ with different chain lengths with different $t_{\text{exposure}}$ for experiment (F2–T4) and simulation ($n=32$, 256, and 512). The error bars represent the standard deviation calculated from the distribution of measured single molecule mean asphericity.

Figure 3

(Color online) Static and dynamical scaling analysis of DNA confined in the $110\text{−}\mathrm{nm}$ slit. All statistical quantities were calculated from 20–75 individual DNA molecules with exposure time $\left(0.033\mathrm{s}\right)$. Linear fit to the data leads to the scaling exponent. (a) The radius of gyration $\left(⟨R_{\mathrm{g}}⟩\right)$ and mean extensions $\left(⟨R_{\Vert }⟩\right)$ vs the number of base pairs $\left(N\right)$ for experimental results of the nanoslit. The dashed line and the dotted line are scaling theory predictions of the self-avoiding chain in two dimensions (0.75) and in three dimensions (0.6), respectively. The error bars represent the standard deviation of the distribution of $R_{\Vert }$. The slopes of linear fitting for $R_{\mathrm{g}}$ (solid line) and $R_{\Vert }$ (dash-dotted line) are $0.68\pm 0.05$ and $0.65\pm 0.02$, respectively. (b) Diffusivity $\left(D_{\mathrm{CM}}\right)$ vs number of base pairs $\left(N\right)$ for experimental results of the nanoslit. The $D_{\mathrm{CM}}$ was determined by averaging the trajectories of ten DNA molecules over $10–50\mathrm{s}$. The scaling exponent of $D_{\mathrm{CM}}$ is $-1.05\pm 0.05$. The dashed line and the dotted line are the scaling predictions of the Rouse model in two dimensions and the Zimm model in three dimensions, respectively.

Figure 4

(Color online) Extensional and rotational relaxation analysis of DNA molecules. (a) The autocorrelation function $C_{\delta R\Vert }$ of extension fluctuation $\delta R$. (b) The time correlation function of $u\left(t\right)$. The $C_{\delta R\Vert }$ and $C_u\left(t\right)$ show the single exponential decays and the insets in (a) and (b) show the linear plot of the autocorrelation function. (c) The data of ${\tau }_{\Vert }$ and ${\tau }_r$ around the solid line $(\text{slope}=2.2)$. The dashed line and dotted line show the theory scaling prediction of the Rouse model in nanoslits and the Zimm model in the bulk solution, respectively.