How the excluded volume architecture influences ion-mediated forces between proteins

Energy variational analysis of ions in water and channels: Field theory for primitive models of complex ionic fluids

Ionic solutions are mixtures of interacting anions and cations. They hardly resemble dilute gases of uncharged noninteracting point particles described in elementary textbooks. Biological and electrochemical solutions have many components that interact strongly as they flow in concentrated environments near electrodes, ion channels, or active sites of enzymes. Interactions in concentrated environments help determine the characteristic properties of electrodes, enzymes, and ion channels. Flows are driven by a combination of electrical and chemical potentials that depend on the charges, concentrations, and sizes of all ions, not just the same type of ion. We use a variational method EnVarA (energy variational analysis) that combines Hamilton's least action and Rayleigh's dissipation principles to create a variational field theory that includes flow, friction, and complex structure with physical boundary conditions. EnVarA optimizes both the action integral functional of classical mechanics and the dissipation functional. These functionals can include entropy and dissipation as well as potential energy. The stationary point of the action is determined with respect to the trajectory of particles. The stationary point of the dissipation is determined with respect to rate functions (such as velocity). Both variations are written in one Eulerian (laboratory) framework. In variational analysis, an "extra layer" of mathematics is used to derive partial differential equations. Energies and dissipations of different components are combined in EnVarA and Euler-Lagrange equations are then derived. These partial differential equations are the unique consequence of the contributions of individual components. The form and parameters of the partial differential equations are determined by algebra without additional physical content or assumptions. The partial differential equations of mixtures automatically combine physical properties of individual (unmixed) components. If a new component is added to the energy or dissipation, the Euler-Lagrange equations change form and interaction terms appear without additional adjustable parameters. EnVarA has previously been used to compute properties of liquid crystals, polymer fluids, and electrorheological fluids containing solid balls and charged oil droplets that fission and fuse. Here we apply EnVarA to the primitive model of electrolytes in which ions are spheres in a frictional dielectric. The resulting Euler-Lagrange equations include electrostatics and diffusion and friction. They are a time dependent generalization of the Poisson-Nernst-Planck equations of semiconductors, electrochemistry, and molecular biophysics. They include the finite diameter of ions. The EnVarA treatment is applied to ions next to a charged wall, where layering is observed. Applied to an ion channel, EnVarA calculates a quick transient pile-up of electric charge, transient and steady flow through the channel, stationary "binding" in the channel, and the eventual accumulation of salts in "unstirred layers" near channels. EnVarA treats electrolytes in a unified way as complex rather than simple fluids. Ad hoc descriptions of interactions and flow have been used in many areas of science to deal with the nonideal properties of electrolytes. It seems likely that the variational treatment can simplify, unify, and perhaps derive and improve those descriptions.

Nonspecific DNA-protein interaction: why proteins can diffuse along DNA

Recent single molecule experiments have reported that DNA binding proteins (DNA-BPs) can diffuse along DNA. This suggests that interactions between proteins and DNA play a role during the target search even far from their specific site on DNA. Here we show by means of Monte Carlo simulations and analytical calculations that there is a counterintuitive repulsion between the two oppositely charged macromolecules at a nanometer range. For the concave shape of DNA-BPs, and for realistic protein charge densities, we find that the DNA-protein interaction free energy has a minimum at a finite surface-to-surface separation, in which proteins can easily slide. When a protein encounters its target, the free energy barrier is completely counterbalanced by the H-bond interaction, thus enabling the sequence recognition.

Coarse-graining in suspensions of charged nanoparticles

A coarse-grain description of nanocolloidal suspensions in the presence of an added salt is presented here. It enables us to simulate trajectories of the nanoparticles from effective functions that depend on average densities of salt ions. In practice, the ion-averaged effective potential is used as input of a Brownian dynamics (BD) simulation. This potential may be derived by various methods, ranging from purely analytical to fully numerical ones. For the description of dynamical properties, this simulation also requires an effective diffusion coefficient that must be calculated or experimentally determined, and that accounts for the effects of microions on the mobility of the nanoparticles. The different versions of our coarse-graining procedure are applied to the case of a maghemite suspension, for which an explicit description of all ions would be very time-consuming.