Stochastic Model of Solvent Exchange in the First Coordination Shell of Aqua Ions.

Ion microsolvation is a basic, yet fundamental, process of ionic solutions underlying many relevant phenomena in either biological or nanotechnological applications, such as solvent reorganization energy, ion transport, catalytic activity, and so on. As a consequence, it is a topic of extensive investigations by various experimental techniques, ranging from X-ray diffraction to NMR relaxation and from calorimetry to vibrational spectroscopy, and theoretical approaches, especially those based on molecular dynamics (MD) simulations. The conventional microscopic view of ion solvation is usually provided by a "static" cluster model representing the first ion-solvent coordination shell. Despite the merits of such a simple model, however, ion coordination in solution should be better regarded as a complex population of dynamically interchanging molecular configurations. Such a more comprehensive view is more subtle to characterize and often elusive to standard approaches. In this work, we report on an effective computational strategy aiming at providing a detailed picture of solvent coordination and exchange around aqua ions, thus including the main structural, thermodynamic, and dynamic properties of ion microsolvation, such as the most probable first-shell complex structures, the corresponding free energies, the interchanging energy barriers, and the solvent-exchange rates. Assuming the solvent coordination number as an effective reaction coordinate and combining MD simulations with enhanced sampling and master-equation approaches, we propose a stochastic model suitable for properly describing, at the same time, the thermodynamics and kinetics of ion-water coordination. The model is successfully tested toward various divalent ions (Ca2+, Zn2+, Hg2+, and Cd2+) in aqueous solution, considering also the case of a high ionic concentration. Results show a very good agreement with those issuing from brute-force MD simulations, when available, and support the reliable prediction of rare ion-water complexes and slow water exchange rates not easily accessible to usual computational methods.

Spherical-harmonics mode decomposition of neural field equations.

Large-scale neural networks can be described in the spatial continuous limit by neural field equations. For large-scale brain networks, the connectivity is typically translationally variant and imposes a large computational burden upon simulations. To reduce this burden, we take a semiquantitative approach and study the dynamics of neural fields described by a delayed integrodifferential equation. We decompose the connectivity into spatially variant and invariant contributions, which typically comprise the short- and long-range fiber systems, respectively. The neural fields are mapped on the two-dimensional spherical surface, which is choice consistent with routine mappings of cortical surfaces. Then, we perform mathematically a mode decomposition of the neural field equation into spherical harmonic basis functions. A spatial truncation of the leading orders at low wave number is consistent with the spatially coherent pattern formation of large-scale patterns observed in simulations and empirical brain imaging data and leads to a low-dimensional representation of the dynamics of the neural fields, bearing promise for an acceleration of the numerical simulations by orders of magnitude.