3.4 Summary and perspective
4.1.3 Point charges
Angiogenesis inhibitors prevent blood vessel growth and since cancer cells multiply at a faster speed than normal cells, they are good candidates for possible anti-cancer drug molecules.[165] Usually the angiogenesis inhibitor drug has to be combined with other chemotherapeutic drugs that can actually kill and not only limit growth of tumor cells.
For treatment of different types of cancer a variety of substances have been developed.
Their mechanisms of action fall into different classes. Two big categories can be distin-guished: monoclonal antibodies like the popular drug bevacizumab and smaller organic molecules. In this study the focus was on small-molecule inhibitors that prevent func-tioning of vascular-endothelial growth factor receptor tyrosin kinase.[166] The reason why monoclonal antibodies were avoided was their size, which rendered them unsuitable for performing quantum chemical computations and thus the procedures used for validation of the developed point charges.
4.1.3 Point charges
Atomic charges in a molecule are not a clearly defined property.[167] Nevertheless, atomic point charges are a widely used concept in chemically or biologically motivated computa-tional modeling. This is mostly due to their ease of use and conceptual simplicity.
Bader charges[18] are one of the most rigorously defined atomic charges in quantum chemistry. They are not as basis-set dependent as Mulliken charges,[168,169] an advantage shared by charges from natural population analysis.[170] Alternatively, Hirshfeld partition-ing[41] is an equally elegant way of obtaining charges. However, the disadvantage of all these approaches lies in the requirement of having a molecular EDD available. Ususally the source of the EDD is a QM calculation except for Bader charges. Like Monopole-κ charges, Bader charges can be derived from XRD experiments and have therefore found use in crystallography.[171]
Several procedures[172–176]have been established to obtain atomic point charges for force-field parametrization. They are efficient, well-tested and robust. Alongside other force-force-field parameters those charges have been used for molecular mechanics and dynamics simula-tions, in programs like amber[177],charmm[178] and gromacs.[179] Such point charges, however, still require at least a semi-empirical computation of the whole molecule of inter-est if it is not a common amino acid, nucleotide, carbohydrate or lipid. Thus the size of systems that are possible to study is limited. Partitioning a system into smaller fragments more amenable to computation is required as soon as systems become larger (>150 atoms), e.g. metalloproteins or supramolecular structure assemblies.
1pqrfiles are similar in format to protein database files,[5]but the column of site occupancy factors is replaced by atomic charges; the column with the WilsonB factor contains thevan-der-Waals radii.
Table 4.1: Overview of small-molecule angiogenesis inhibitors used as test-set. API stands for active pharmaceutical ingredient. c reprinted with permission from Wiley.
API Molecular formula API Molecular formula
afatinib N O
Therefore a look-up table of atomic point charges fitted to a molecular ESP[173] (Section 4.1.3.1) was recently developed.[180] Look-up tables offer direct access to charges, thus reducing computing time and overcoming the limitation in the size of a system. This general idea of the Transferable Partial Atomic Charge Model (TPACM4) is followed, but not the procedural details. Atomic point charges derived according toMerz andKolman[181]
(MK) from a fit to the ESP of the model compounds in the generalized invariom database[81]
are presented here.
4.1.3.1 Point charges for force-field applications
The parameter set ’amberff’[182] provides very specific charges for peptides, sugars and nucleotides for the popular molecular dynamics program amber.[177] The same applies to the charmm additive all-atom force field[178] which additionally contains parameters for lipids.[183] Charges for unparameterized compounds can be computed by several suggested procedures:
• An established way is the computation of RESP[173] charges. It is the same method which was applied for the parameterization of ’amberff’. A HF/6-31G(d) quantum chemical computation is required for the complete target molecule, followed by a calculation of the molecular ESP from the obtained wave function. The atomic point charges are then fitted to reproduce this ESP by a restrained least-squares algorithm. The restraints ensure that the inner, less well defined atomic charges stay close to neutral. After the quantum-mechanics program has calculated the ESP from the wave function, the programAntechamber[184] can fit the RESP charges, while the unrestrained MK method[181,185] is implemented in many programs, e.g. in gaussian09[103]. The disadvantage of this approach is the computation and time demand for the study of large molecules.2
• Bond-Charge Correction (BCC) is a semi-empirical method introduced by Bayly et
al.[176] in 2000. This procedure derives molecule specific atomic point charges from
AM1[187] semi-empirical point charges[188,189] via scaling by bond-charge correction
factors from a table. They are designed to reproduce the RESP charges at a lower computational cost.3
• The general amber force field (GAFF)[191] mainly provides all other force field pa-rameters, because its use for charges has been superseded by the two methods above.
The computing time required for those two options depends on molecular size. In the inter-est of procedure speed up, the look-up table TPACM4 for RESP charges was developed.[180]
Its implementation is similar to the website of pdb2pqr.[192,193] Both work on a web server that converts a pdb file, into a pqr file. Typically the molecules for TPACM4 are organic.
Another database designed to store RESP and MK point charges is REDDB.[194] Differently to other methods described above, the main purpose of REDDB is just the storage and not
2HF as well as DFT methods asymptotically scale as order N2 for large systems with N being the number of basis functions.[186]
3Semi-empirical methods are in general a thousand times faster than DFT, but still "several orders of magnitude slower than molecular-mechanics treatments".[190]
assignment of atomic point charges to atoms in a molecule of biological interest. Moreover, it contains less than 200 molecules and fragments as of September 2016.[195]
4.1.3.2 ESP-reproducing point charges in crystallography
One of the main goals of crystallography is, to provide structure models with accurate atomic coordinates. Once this is achieved, understanding inter- and intramolecular interactions within the crystal lattice often is the new focus of interest. In small-molecule structure models4 such an interaction analysis is based on geometric criteria. Adding electrostatic information is logically the next step, since electrostatic forces have a longer range than van-der-Waals interactions. Therefore, electrostatic complementarity is discussed in several studies[196–199] and it would be very useful to facilitate rapid access to ESPs for models from single-crystal X-ray structure determination.
The ESP is frequently discussed in the context of recognition processes involving biolog-ical macromolecules.[197,200–202] There are several charge sets and programs that calculate and/or display the molecular ESP for these structures.
Point charges in macromolecular crystallography
The ESP generated by the apbs[203] plug-in to pymol[204] is discussed often for pro-tein structures. The charges apbs reads have usually been assigned by the program pdb2pqr[192,193] and are communicated via a pqr file. In pdb2pqr users can specify different charges to be assigned: parse[205,206], amber[182], charmm[178], peoepb[207], swanson[208] and tyl06[209]. In spite of this flexibility only charges for nucleic acids and proteins can be assigned automatically. Otherwise a file (mol2 format) which includes the atomic point charges has to be supplied.
coot[210] and ccp4mg[211] contain functions to assign atomic charges for standard proteins and nucleic acids as well. They can also map an ESP onto a molecular surface (a graphical overview is given in Figure 4.1). Regrettably, with respect to charges, neither pdb2pqr nor the ccp4 programs[212] or cootcover charges for small-molecules such as ligands, co-factors or other pharmaceutically active molecules.
ESP modeling in charge density
Charge density is worth special mention[24], since this branch of crystallography focuses on modeling the molecular charge-density distribution that best fits high-resolution5 XRD data.
Thus the subsequent ESP can be obtained from comparably demanding experiments[214]
and least-squares refinements[50,51] of multipole populations. However, minor disorder can already lead to misleading results.[79] Therefore, accurate ESPs can only be obtained for non-disordered crystal structures. Moreover, attention should be given to possible additional polarization for molecules in a crystal compared to their gas-phase counterparts.[215,216]
4from data with a resolution ofd ≈0.83Å orsinθ/λ≈0.6Å−1
5d ≤0.5 Å or sinΘ/λ≥1.0 Å
Figure 4.1:Overview of ways to an ESP mapped on a molecular surface for trialanine. Blue boxes indicate file formats and ellipsoids programs. * symbolizes aPoisson-Boltzmannpotential[213]that models solvents and ions in the peripherie instead of an isolated molecule. The different ESP were generated as follows: a) Invariom point charges via APD-Toolkit on a VDW·1.5 surface in esp_mcq, b) AM1-BCC charges fromAntechamber on a VDW·1.5 surface inesp_mcq, c) Invariom point charges on a solvent accessible surface in Jmol, d) Invariom point charges on a VDW+2.4 Å surface inJmol, e) Invariom point charges on a normal surface inapbsinPymol, f) TPACM4 charges on a normal surface in apbs in Pymol, g) Amberff charges via pdb2pqr on the deafault surface in apbs(Pymol) different protonation, h) Invariom point charges on a solvent excluded surface inChimera.
More sophisticated methods to study interactions in a crystal[217–219] have become avail-able in computational crystallography. Both require QM wave functions and thus consid-erable expertise. In contrast, a molecular ESP can easily be generated from atomic point charges, which should be more useful for a broader group of scientists.
Invariom point charge project
Therefore, this project’s overall aim is :
1. introducing a database of ’invariom point charges’ that reproduce the ESP obtained from gas-phase quantum mechanics,
2. reporting validation and application of these atomic charges by a comparative study for a test set of angiogenesis inhibitor molecules, and
3. providing a tool that allows assignment of these charges to molecules with atomic coordinates from sources like molecular mechanics or single crystal XRD.