Phase behavior of crowded like-charged mixed polyelectrolytes in a cell-sized sphere

We studied the phase behavior of a mixture of two semiflexible negatively charged polyelectrolytes, giant DNA and alginate, under crowded condition in a cell-sized sphere (5–40 $\mu$m in diameter), where the persistence length of giant DNA is 50 nm and that of alginate is 5 nm. Through microscopic observation, we found that the polymer mixture exhibits a unique phase behavior, which depends on the size of the sphere, whereas the mixture remains homogeneous and isotropic in bulk solution. When the sphere is small, DNA is completely depleted on the surface. When the sphere is medium sized, a portion of the DNA is depleted on the surface, and the remainder stays within the sphere. By introducing a curvature-dependent term for the interaction between DNA and the surface into the Flory-Huggins model, we interpret the observed characteristics of the phase behavior in terms of the relative importance of the surface-to-volume effect.

Figure 1

(A) Phase diagram of a DNA and alginate mixture in the bulk phase. The labels a, b, and c correspond to in (a), (b), (c) in Fig. 1b. (B) Change in the conformation of a DNA molecule where 0.34 mg/mL DNA is mixed with alginate. The average long-axis length of single-DNA molecules $\xi$${}_{\mathit{DNA}}$ is indicated together with the standard deviation. Insets (a) and (b) show representative fluorescence images of coil or metastable coil DNA molecules with 1.0 and 5.5 mg/mL alginate, respectively. The scale bars are 5 $\mu$m. Inset (c) shows a fluorescence microscopic image of DNA domains with 10.0 mg/mL alginate. The scale bar is 50 $\mu$m.

Figure 2

DNA localization in PMSs observed within 10 min after PMS preparation. Bottom images show the schematic DNA distribution. (a)–(c) Fluorescence microscopic images of DNA localization in PMSs for regions (i)–(iii) and fluorescence intensity profiles along the yellow dotted lines in the fluorescence images. RFI and Dist. are relative fluorescence intensity and distance, respectively. Scale bars are 10 $\mu$m.

Figure 3

Phase diagram of the DNA distribution in PMSs in a pseudoequilibrium state, where 0.34 mg/mL DNA with alginate is confined in a PMS. Schematic illustrations of the DNA distribution are in the rectangle with a dotted line. After preparation, PMSs were allowed to stand at 20${}^{°}$C for 60 min. (a)–(d) Representative fluorescence microscopic images of DNA localization in the PMSs, and their relative fluorescence intensity profiles at the yellow dotted lines in the fluorescence images. The labels a–d are the same as those in the phase diagram. RFI and Dist. are relative fluorescence intensity and distance, respectively. Scale bars are 10 $\mu$m.

Figure 4

The long-axis length of single DNA molecules $\xi$${}_{\mathit{DNA}}$ with 5.5 mg/mL alginate on PMS surfaces and within PMSs in region IV in Fig. 3. The insets show representative microscopic images of a single-DNA molecule (a) on a surface and (b) within a PMS. The scale bars are 3 $\mu$m. The labels a and b in the plot correspond to (a) and (b) for the single-DNA microscopic images in the insets.

Figure 5

Numerical representation of the free energy profile for the localization of DNA depending on the size of the sphere. (a) Schematic illustration of the surface region (SR) and the volume region (VR) of a PMS. (b) Profiles of the total free energy difference function of $\eta$ for various values of $r$. The vertical axis shows the free energy per DNA chain. The parameters are $\chi$($T$) $=$ 1.1, $N$/$\Omega$${}_{\mathit{VR}}$ $=$ 0.3, $r$${}_c$ $=$ 100, and $a$ $=$ 50. The degree of occupation is described by $\eta :\eta =0$ and corresponds to the state where all of the DNA molecules are located near the surface inside the volume part; $\eta$ $=$ 1 corresponds to the state where all of the DNA molecules are inside the sphere.