A theoretical study of polymorphism in VQIVYK fibrils.

The VQIVYK fragment from the Tau protein, also known as PHF6, is essential for aggregation of Tau into neurofibrillary lesions associated with neurodegenerative diseases. VQIVYK itself forms amyloid fibrils composed of paired ß-sheets. Therefore, the full Tau protein and VQIVYK fibrils have been intensively investigated. A central issue in these studies is polymorphism, the ability of a protein to fold into more than one structure. Using all-atom molecular simulations, we generate five stable polymorphs of VQIVYK fibrils, establish their relative free energy with umbrella sampling methods, and identify the side chain interactions that provide stability. The two most stable polymorphs, which have nearly equal free energy, are formed by interdigitation of the mostly hydrophobic VIY "face" sides of the ß-sheets. Another stable polymorph is formed by interdigitation of the QVK "back" sides. When we turn to examine structures from cryo-electron microscopy experiments on Tau filaments taken from diseased patients or generated in vitro, we find that the pattern of side chain interactions found in the two most stable face-to-face as well as the back-to-back polymorphs are recapitulated in amyloid structures of the full protein. Thus, our studies suggest that the interactions stabilizing PHF6 fibrils explain the amyloidogenicity of the VQIVYK motif within the full Tau protein and provide justification for the use of VQIVYK fibrils as a test bed for the design of molecules that identify or inhibit amyloid structures.

Polarization charge: Theory and applications to aqueous interfaces.

When an electric field is applied across an interface, a dielectric will acquire a polarization charge layer, assumed infinitely thin in the theory of macroscopic dielectrics and also in most treatments of electrokinetic phenomena in nanoscale structures. In this work we explore the polarization charge layer in molecular detail. Various formal relations and a linear response theory for the polarization charge are presented. Properties of the polarization charge layer are studied for three aqueous interfaces: air-water, a crystalline silica surface with water, and an amorphous silica surface with water. The polarization charge is calculated from equilibrium simulations via linear response theory and from non-equilibrium simulations, and the results are within statistical error. The polarization charge is found to be distributed within a region whose width is on the order of a nanometer.

Displacements, mean-squared displacements, and codisplacements for the calculation of nonequilibrium properties.

We study two situations in which nonequilibrium phenomena can be efficiently calculated using displacements, mean-squared displacements, or codisplacements instead of accumulating velocities or currents. The flow velocity profile for a fluid confined within a pore can be expressed as a sum of displacements within slabs from a molecular dynamics trajectory. In this form, an accurate flow profile is obtained from very sparse sampling of the trajectory. We also recast the linear response theory expression for the flow velocity profile in terms of mean codisplacements and demonstrate that this provides an efficient route for estimating the Green-Kubo expression for the velocity profile. Finally, we calculate the ionic contribution to the frequency-dependent electric susceptibility using dipolar displacements, instead of the conventional current-current correlation function. We expect these methods to be useful for generating transport properties from stored trajectories in very large systems or systems where relaxation times are long.