One of the principal physical forces affecting molecular structures and the interactions between molecules is electrostatics. When covalent bonds between atoms are formed to create molecules, the electrons shared in the bonds are usually shared unequally. Atoms with less electron density than in their uncombined states take on partial positive charges. Atoms with an excess of electrons become partially negative. Attractions and repulsions among charged atoms cause them to arrange themselves into geometrical structures that maximize the forces of attraction and minimize the forces of repulsion. The structure of molecules and their behaviors are intimately related. In the case of the large biological molecules (proteins, nucleic acids, carbohydrates, and lipids), their functions in the support of living systems are directly related to their structures. Predicting molecular structures and properties computationally is a standard way of interpreting behaviors since computations reveal details that experiments cannot disclose.

The 15 papers in this book were presented in the international meeting on Computational Electrostatics for Biological Applications held in Italy in 2013. The editors identify two main topics of the conference as the solution of the Poisson-Boltzmann equation and geometric approaches to the creation of the molecular surfaces. The scope of the conference is wider, as shown by the papers selected. The Poisson-Boltzmann equation is a theoretical approach for representing the distribution of charge in a continuum model of the solvent. The solvent is represented as a continuum instead of as a collection of the discrete molecules in order to keep the computation manageable and to focus attention on the molecule of interest. The continuum model is based on the physical approximation that the discrete behavior of individual molecules is less important than the properties of the solvent in an averaged sense in the presence of the field generated by the partial positive and negative charges borne by its constituent atoms of the solute.

The geometrical problem of the molecular surfaces has a built-in uncertainty in how the molecule’s surface is defined. The sizes of atoms in a box of plastic models are usually based on van der Waals atomic radii. These are not the only possible values. Depending on various physical properties, other size parameters may be selected and justified. When the atoms are combined to form molecules, the surfaces are not smooth but are lumpy. Not every region of a molecule may be accessible to the solvent since the solvent really consists of molecules of definite shapes and sizes that may not fit into crevices and cavities in the solute molecule. The geometrical modeling of the molecular surface affects also the partitioning of the near portion of the continuum solvent by requiring a dense partition of layers of solvent close to the solute using a grid model with larger grid partitions further away from the solute as the modification of the solvent properties closer to the solute makes the transition to bulk properties. At the surface of the solute, there is an abrupt transition between the solute and the solvent, a discontinuity that must be grappled with. To further complicate the calculation, the grid generated in the solvent must move and adapt following the motions of the atoms in the molecules as they twist and turn in molecular mechanics calculations.

The first paper is an overview of electrostatics models for biological molecules. The second through seventh papers form a cluster of papers that primarily review the solution of the Poisson-Boltzmann equation, with the exception of two papers whose topics are the alternative models of density functional theory and generalized Born forces. The eighth through eleventh papers emphasize the geometrical representation of the molecular surfaces. The description and use of different software packages characterize these papers. The software systems described are open-source, and the URLs of the websites of the underlying packages and tools are given. The final four papers describe applications to biological systems. Three of the four papers look at proteins and one at a carbohydrate, cyclodextrin.

The authors of the papers in this book do not shy away from the underlying uncertainties in model choice, software implementation, and geometry and surface description. They are aware of the sensitivity of results to the choices made in designing calculations and the difficulty in making firm connections between causes and effects in the results obtained. Their approach is self-critical and cautious.