Calculating potential of mean force between like-charged nanoparticles: A comprehensive study on salt effects

Abstract

Ions are critical to the structure and stability of polyelectrolytes such as nucleic acids. In this work, we systematically calculated the potentials of mean force between two like-charged nanoparticles in salt solutions by Monte Carlo simulations. The pseudo-spring method is employed to calculate the potential of mean force and compared systematically with the inversed-Boltzmann method. An effective attraction is predicted between two like-charged nanoparticles in divalent/trivalent salt solution and such attraction becomes weakened at very high salt concentration. Our analysis reveals that for the system, the configuration of ion-bridging nanoparticles is responsible for the attraction, and the invasion of anions into the internanoparticles region at high salt concentration would induce attraction weakening rather than the charge inversion effect. The present method would be useful for calculating effective interactions during nucleic acid folding.

Ligand-modulated interactions between charged monolayer-protected Au144(SR)60gold nanoparticles in physiological saline

“…The MPS − -MPS − pair has a PMF well located at 4.9 nm and the MPM + -MPM + pair at 4.6 nm. This attractive regime resembles the attraction between two like-charged colloids in electrolyte solution 20-30 mediated by the counter ions that are distributed with a higher density in the inter-AuNP space.…”

“…19 On the μm-scale, numerous studies performed on charged colloids interacting in electrolyte solutions have shown that they display attraction when equally charged. 20-30 …”

Multivalent ion-mediated nucleic acid helix-helix interactions: RNA versus DNA

“…The Na + and Co(NH 3 ) 6 3+ (Co-Hex) ions are added with Amber tleap Program ( 64 , 65 ). To get the desirable bulk ion concentrations, the simplified Monte Carlo simulations ( 50 , 66 ) are employed to estimate numbers of Co-Hex and Na + ions in the simulational cell before the all-atomistic MD simulations; see Supplementary Material for details. Afterward, the numbers of Co-Hex and Na + ions from the simplified Monte Carlo simulations are used in the all-atomistic simulations, and the realistic bulk Na + and Co-Hex concentrations from the all-atomistic MD simulations are close to the desirable values; see Supplementary Figure S1 in Supplementary Material for the cases of 100 mM Na + and 5 mM Co-Hex solutions.…”

“…In the work, we employ the pseudo-spring method ( 53 , 54 , 66 ) to calculate the PMF between two A-RNAs (or DNAs). In the method, a pseudo-spring with spring constant k is added to link the center of mass of two helices in MD simulations, as shown in Figure 1 .…”

“…After a series of F ( x ) at different separations x are obtained, the PMF Δ G ( x ) between the two A-RNA (or DNA) helices can be calculated through the integration ( 53 , 54 , 66 ) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}\begin{equation*} \Delta G(x) = G(x) - G(x_{{\rm ref}} ) = \int_x^{x_{{\rm ref}} } {F(x')} dx',\end{equation*}\end{document} where x ref is the outer reference separation. It has been shown previously that the pseudo-spring method is efficient and convenient in calculating PMF between two DNAs and two like-charged nanoparticles ( 53 , 54 , 66 ). In practice, the spring constant k is generally taken as 1000 kJ/(mol·nm 2 ) and x ref is taken as 40 Å.…”