Modulation of Nanoparticle Diffusion by Surface Ligand Length and Charge: Analysis with Molecular Dynamics Simulations

Remarkable Insensitivity of Protein Diffusion to Protein Charge

Friction to translational diffusion of ionic particles in polar liquids should scale linearly with the squared ion charge, according to standard theories. Substantial slowing of translational diffusion is expected for proteins in water. In contrast, our simulations of charge mutants of green fluorescent proteins in water show remarkable insensitivity of the translational diffusion constant to protein's charge in the range of charges between -29 and +35. The friction coefficient is given as a product of the force variance and the memory function relaxation time. We find remarkably accurate equality between the variance of the electrostatic force and the negative cross-correlation of the electrostatic and van der Waals forces. The charge invariance of the diffusion constant is a combined effect of the force variance and relaxation time invariances with the protein charge. The temperature dependence of the protein diffusion constant is highly non-Arrhenius, with a fragile-to-strong crossover at the glass transition.

Do Electrostatics Control the Diffusive Dynamics of Solitary Water? NMR and MD Studies of Water Translation and Rotation in Dipolar and Ionic Solvents

NMR-based measurements of the diffusion coefficients and rotation times of solitary water and benzene at 300 K are reported in a diverse collection of 13 conventional organic solvents and 10 imidazolium ionic liquids. Proton chemical shifts of water are found to be correlated to water OH-stretching frequencies, confirming the importance of electrostatic interactions in these shifts. However, the influence of magnetic interactions in aromatic solvents renders chemical shifts a less reliable indicator of electrostatics. Diffusion coefficients (DB) and rotational correlation times (τB) of benzene in the solvents examined are accurately described as functions of viscosity (η) by DB ∝ η-0.81 and τB ∝ η0.64. Literature values of DB and τB in alkane and normal alcohols, which were not included among the solvents studied here, are systematically faster than predicted by these correlations, indicating that factors beyond solvent viscosity play a role in determining the friction on benzene. In contrast to benzene, water diffusion and rotation are poorly described in terms of viscosity alone, even in the dipolar and ionic solvents measured here. The present data and the substantial literature data already available on dilute water diffusion show a systematic dependence of DW on solvent polarity among isoviscous solvents. The aspect of solvent polarity most relevant to water dynamics is the ability of a solvent to accept hydrogen bonds from water, as conveniently quantified by the frequency of water's OH stretching band, ΔνOH. The friction on translation, ζtr = kBT/DW, and rotation, ζrot = kBTτW, are both well correlated by functions of the form ζ(η, ΔνOH) = a1ηa2 exp (a3ΔνOH), where the ai are adjustable parameters. Molecular dynamics simulations reveal a strong coupling between electrostatic and nonelectrostatic water-solvent interactions, which makes it impossible to dissect the friction on water into additive dielectric and hydrodynamic components. Simulations also provide a tentative explanation for the unusual form of the correlating function ζ(η, ΔνOH), at least in the case of ζrot.

War and Peace between Electrostatic and van der Walls Forces Regulate Translational and Rotational Diffusion

Diffusion of a Brownian particle or a molecule in a liquid solvent is caused, in the Stokes-Einstein picture, by unbalanced fluctuations of osmotic forces on different sides of the particle. When the particle carries a charge or a higher multipolar moment, this picture is amended by fluctuations of electrostatic forces producing dielectric friction. Dielectric friction slows both the translational and rotational diffusion down. While this picture is well established and is physically sound, standard theories grossly overestimate the magnitude of dielectric friction for small dipolar solutes and larger colloidal particles, such as proteins. Motivated by recent simulation studies, this perspective discusses the interplay between osmotic (van der Waals) and electrostatic forces in promoting molecular and colloidal diffusion. Much can be learned about microscopic friction mechanisms from statistical and dynamical correlations between osmotic and electrostatic forces.

Ionic mobility driven by correlated van der Waals and electrostatic forces

Classical theories of dielectric friction make two critical assumptions: (i) friction due to van der Waals (vdW) forces is described by hydrodynamic drag and is independent of the ionic charge and (ii) vdW and electrostatic forces are statistically independent. Both assumptions turn out to be incorrect when tested against simulations of anions and cations with varying charge magnitude dissolved in water. Both the vdW and electrostatic components of the force variance scale linearly with the ionic charge squared. The two components are strongly anticorrelated producing simple relations for the total force variance in terms of self-variances. The inverse diffusion constant scales linearly with the charge squared. Solvation asymmetry between cations and anions extends to linear transport coefficients.

Enhanced Molecular Diffusivity through Destructive Interference between Electrostatic and Osmotic Forces

Molecular charge asymmetrically distributed in a diffusing tagged particle causes a nonzero electrostatic force balanced by an opposing van der Waals (vdW) force. Fluctuations of electrostatic and vdW forces are highly correlated, and they destructively interfere in the force variance. This phenomenology is caused by the formation of a structurally frozen hydration layer for a particle diffusing in water and is responsible for a substantial speedup of translational diffusion compared to traditional theories of dielectric friction. Diffusion of proteins is insensitive to charge mutations, while smaller particles with asymmetric charge distribution can show a strong dependence of translational and rotational diffusion on molecular charge. Dielectric calculations of the electrostatic force require low values of ≃5 for the effective dielectric constant of interfacial water to be consistent with simulations.