Role of dissolved salts in thermophoresis of DNA: Lattice-Boltzmann-based simulations

We use a lattice Boltzmann based Brownian dynamics simulation to investigate the dependence of DNA thermophoresis on its interaction with dissolved salts. We find the thermal diffusion coefficient $D_T$ depends on the molecule size, in contrast with previous simulations without electrostatics. The measured $S_T$ also depends on the Debye length. This suggests thermophoresis of DNA is influenced by the electrostatic interactions between the polymer beads and the salt ions. However, when electrostatic forces are weak, DNA thermophoresis is not found, suggesting that other repulsive forces such as the excluded volume force prevent thermal migration.

Figure 1

Log of the concentration of DNA beads in the steady state plotted versus position in the channel. The thermal diffusion coefficient is determined from the slope of the linear fit. Here $D_T=0.53\hspace{0.5em}\mu {\text{m}}^2/$(s K). Data shown are the average of five independent simulations with ten $\lambda$-DNA chains, 220 salt molecules, and $\Delta T=2$ K between $y=0$ or $y=Y_{\max }$ ($10\hspace{0.5em}\mu \text{m}$) and $y=Y_{\max }/2$ ($5\hspace{0.5em}\mu \text{m}$).

Figure 2

Dependence of $S_T$ on $[\text{salt}]{}^{-1/2}$ or Debye length (${\lambda }_D\propto [\text{salt}]{}^{-1/2}$). The line represents a linear fit to the data. The calculation is done with $\lambda$-DNA, $k=0.0003$ is held constant, and $\Delta T=2$ K.

Figure 3

Dependence of $S_T$ on electrostatic force. The line represents the linear fit to the data. The calculation is done with $\lambda$-DNA, 220 salt ions, and $\Delta T=2$ K.

Figure 4

Density profile of DNA beads (•) and salt molecules ($\square$) averaged over $t=0$ s to $t=30$ s (top) and $t=270$ s to $t=300$ s (bottom). The best fit line is shown for each plot to show the development of the concentration gradient.

Figure 5

Net charge in units of $q$, the charge of a single DNA bead, in a $2\Delta x\times 1\Delta x\times 20\Delta x$ ($1\hspace{0.5em}\mu \text{m}\times 0.5\hspace{0.5em}\mu \text{m}\times 10\hspace{0.5em}\mu \text{m}$) slice. For this simulation, 10 DNA molecules with 330 salt molecules are simulated with a 2 K temperature difference. The net charge in a region is calculated by summing the charge of all species in a region. Shown is the average over the final 200 time steps.