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Force Field

In their 2003 review on force fields protein simulations (Adv. in Protein Chem. 2003, 66, 27) Ponder and Case concluded that “An increase in computer power of at least two orders of magnitude should occur over the next decade. Without further research into the accuracy of force field potentials, future macromolecular modeling may well be limited more by validity of the energy functions, particularly electrostatic terms, than by technical ability to perform the computations.”

We aim to address this issue by systematically scrutinizing the way that well-known force fields (AMBER, CHARMMm, GROMOS,…) are constructed. This is of course a long-term goal but important steps have already been taken. Although point charges are popular they are inherently limited and best replaced by multipole moments. In the study of crystal polymorphism for example multipole moments provide a much needed accurate description of the electrostatic interaction.

The topological approach divides molecules into atoms in a natural and unbiased way, following the construction of the gradient vector field. As such it generates unique atoms, carved out of their molecular environment. The first three-dimensional pictures of topological atoms were produced in 1994 [13], in a paper that stressed that the topological approach is a departure from the conventional way of defining molecular fragments in the Hilbert space of the basis functions. Because each topological atom is unique there are millions of atoms but transferability enables them to be grouped in atom types by similarity. We have generated a data set of all atoms occurring in one conformation of each natural amino acid and smaller derived molecules. Cluster analysis revealed atom types for carbon [64], hydrogen, nitrogen, oxygen and sulfur [65]. These atom types are constructed in the opposite way to the construction of atom types in force fields. In force field design one starts from a single atom type per atomic number and gradually introduces new types according to the need for accuracy from the force field. We spent much attention to the question how much the integration error influences atomic properties [38]. To our knowledge this is the first time that atom types are being computed rather than postulated. They may guide the design of future force fields [67].

Molecular Similarity / QSAR / PKa Prediction

The long-term purpose of this research effort is to provide a new angle of approach to rational drug design and any area where Quantitative-Structure-Activity/Property-Relationships are relevant. We are developing a new method, which we called Quantum Topological Molecular Similarity (QTMS) [44]. This method is under continuous development and has originated from the PhD work of Dr. SE O’Brien sponsored by EPSRC grant GR/L65895 (final report). The basic idea goes back to 1995 [18] where a molecular representation was proposed based on properties evaluated at the so-called bond critical points (BCP). This (hyper)space of properties is called the BCP space. A molecular similarity measure can then be constructed as a distance in BCP space and molecules can be ranked according to their activity. The first successful QSAR using BCP space was set up for the acidity of benzoic acids [36]. Later it became clear that BCP space was also useful for several other systems of medicinal [53][81][87], physical organic [85] and ecological [57] interest.

The QTMS sequence

  • Data generation: This is where the raw data on the molecules are generated, i.e. their optimised geometries and wave functions. This is done preferentially at several levels of ab initio theory, but semi-empirical calculations can be included (just for geometries).
  • Localisation: This is where the topological approach extracts local information from the wave functions. The molecules are represented in BCP space and/or via their atomic properties. For semi-empirical data, the topological approach just reduces to bond lengths.
  • Interpretation: The topological descriptors are contrasted with experimental data in order to obtain a predictive model. We use tools such as Partial Least Squares (PLS), Neural Networks and Genetic Algorithms.