Ion-specific counterion condensation on charged peptides: Poisson–Boltzmann vs. atomistic simulations

Abstract

We investigate ion-specific effects in the counterion condensation on a charged polypeptide by explicit-water molecular dynamics (MD) computer simulations. The charged polypeptide is a 10mer of polyglutamic acid (PGA), E₁₀, and is simulated in a stretched, rod-like configuration which enables us to neatly compare to mean-field cell models for charged cylinders. The latter predict a fraction of condensed counterions of x_c = 53% for our system independent of cell size. Using the inflection point criterion on the MD simulation density profiles, we find larger values of 71%, 66%, and 60% for Na⁺, K⁺, and Cs⁺, respectively, due to ion-specific adsorption effects, while the threshold radius for condensation is roughly constant at 1.4 nm. However, the values of x_c decrease for larger cell radii R indicating that the specific effect is concentration-dependent and may reach the mean-field limit at infinite dilution. A simple scaling law indeed predicts that the nonelectrostatic adsorption decays ∝R⁻¹ within the condensation layer. We further demonstrate that the Poisson–Boltzmann (PB) model can still be a valid description for the distance-dependent fraction of counterions around the polypeptide if ion-specificity is introduced by an empirical, attractive potential in the PB equation. The modeling of ion-specific effects by inclusion of such potentials may be useful in coarse-grained (implicit-model) simulations of PGA chains. The PB performance worsens, however, with the inclusion of salt at physiological concentration. Finally, we show that the binding time distribution of the condensed ions shows anomalous diffusive behavior, with faster decay in the order Cs⁺ > K⁺ > Na⁺ in the nanosecond time regime.