Electrostatic interactions are pervasive in the physical realm. Especially at nanoscopic and atomistic scales, they rule a plethora of relevant phenomena. For instance, biomolecular recognition and binding heavily rely on electrostatics, which acts at different levels. During recognition, its long-range nature allows the interacting partners to spend enough time in close proximity, so as to increase the probability of finding the right conformation for binding. During binding, electrostatics is the main component in tuning the delicate balance between the desolvation of the binding interfaces and the unscreened charged and polar interactions, providing specificity to the entire process [1].
Electrostatics is evaluated with different levels of approximation, depending on the specific application. Continuum models, for instance, represent the systems as low polarizable media embedded in a highly polarizable medium, possibly containing, a density-based description of the ionic species present in the solution. Among these approaches, Poisson-Boltzmann equation has been profitably used in the years to estimate interaction energies and the effect of ionic strength. More challenging, within this framework, proved to be the calculation of individual forces acting on the atoms. Alternative approaches describing the solvent implicitly, such as those based on Generalized Born, COSMO, classical density functional theory, or 3D-RISM, envision different types of approximations and solution strategies and have also been successfully used for studying solvation [2].
In Quanto-Mechanical calculations, electrostatics is not the bottleneck, due to the complexity of the QM part, still, a thorough calculation of the effects of the solvent on the QM system, possibly enabling the calculation of solvent-induced forces is relevant also in that field.
Depending on the available computational power, all degrees of freedom in a solute-solvent system can be represented by particles, which is often important if specific solvent properties, e.g. hydrogen bond network or ionic fluctuations including specific solvation properties, are considered. Classical Molecular Dynamics is a well-developed technique to treat systems on a particle basis. As the computation of electrostatic interactions increases the computational load considerably, research has focused on fast algorithms to, e.g., reduce the computational complexity from O(N2) to O(N-Nlog(N))[3], and to reduce the pre-factor so that the evaluation of electrostatics is not a limiting factor for complex systems simulations or to suggest implementations on hybrid architectures[4]. Fast methods for electrostatics include the Particle-Mesh-Ewald method (in various flavors, e.g. PME[5], SPME[6], P3M[7]), the Fast Multipole Method[8], Multigrid Methods[9] or Wavelet Methods[10]. Implementations for HPC are very specific and partly involved, but are available for several algorithms as library solution[3].
Devoting a workshop to this topic is timely because of:
-) the concurrent effort that is being made by the EU to go towards exascale computing[11], which requires, in addition to powerful hardware, suitable algorithmic and software implementations;
-) new experimental techniques such as Cryo-electron microscopy, that are starting to provide three-dimensional structures of the size of microns in near native conditions at close to atomic resolution, with the potential to reveal conformations of dynamic molecular complexes[12]. Computational methodologies must be ready to efficiently handle this information.