Reaction within the coulomb-cage; science in retrospect.

The Coulomb-cage is defined as the space where the electrostatic interaction between two bodies is more intensive than the thermal energy (kBT). For small molecule, the Coulomb-cage is a small sphere, extending only few water molecules towards the bulk and its radius is sensitive to the ionic strength of the solution. For charged proteins or membranal structures, the Coulomb-cage can engulf large fraction of the surface and provides a preferred pathway for ion propagation along the surface. Similarly, electrostatic potential at the inner space of a channel can form preferential trajectories passage for ions. The dynamics of ions inside the Coulomb-cage of ions was formulated by the studies of proton-anion recombination of excited photoacids. In the present article, we recount the study of intra- Coulomb-cage reaction taking place on the surface of macro-molecular bodies like micelles, membranes, proteins and intra-protein cavities. The study progressed stepwise, tracing the dynamics of a proton ejected from a photo-acid molecule located at defined sites (on membrane, inter-membrane space, active site of enzyme, inside Large Pore Channels etc.). Accumulation of experimental observations encouraged us to study of the reaction mechanism by molecular dynamics simulations of ions within the Coulomb-cage of proteins surface or inside large pores. The intra-Coulomb-cage proton transfer events follows closely the fine structure of the electrostatic field inside the cage and reflects the shape of nearby dielectric boundaries, the temporal ordering of the solvent molecules and the structural fluctuations of the charged side chains. The article sums some 40 years of research, which in retrospect clarifies the intra-Coulomb-cage reaction mechanism.

Patient-specific prediction of SEEG electrode bending for stereotactic neurosurgical planning.

PURPOSE : Electrode bending observed after stereotactic interventions is typically not accounted for in either computer-assisted planning algorithms, where straight trajectories are assumed, or in quality assessment, where only metrics related to entry and target points are reported. Our aim is to provide a fully automated and validated pipeline for the prediction of stereo-electroencephalography (SEEG) electrode bending. METHODS : We transform electrodes of 86 cases into a common space and compare features-based and image-based neural networks on their ability to regress local displacement ([Formula: see text]) or electrode bending ([Formula: see text]). Electrodes were stratified into six groups based on brain structures at the entry and target point. Models, both with and without Monte Carlo (MC) dropout, were trained and validated using tenfold cross-validation. RESULTS : mage-based models outperformed features-based models for all groups, and models that predicted [Formula: see text] performed better than for [Formula: see text]. Image-based model prediction with MC dropout resulted in lower mean squared error (MSE) with improvements up to 12.9% ([Formula: see text]) and 39.9% ([Formula: see text]), compared to no dropout. Using an image of brain tissue types (cortex, white and deep grey matter) resulted in similar, and sometimes better performance, compared to using a T1-weighted MRI when predicting [Formula: see text]. When inferring trajectories of image-based models (brain tissue types), 86.9% of trajectories had an MSE[Formula: see text] mm. CONCLUSION : An image-based approach regressing local displacement with an image of brain tissue types resulted in more accurate electrode bending predictions compared to other approaches, inputs, and outputs. Future work will investigate the integration of electrode bending into planning and quality assessment algorithms.