J Mol Model (2003) 9:77-83 DOIl 0.1007/s00894-002-0111 -z Tore Brinck 9 Ping Jin. Yuguang Ma- Jane S. Murray- Peter Politzer Segmental analysis of molecular surface electrostatic potentials: application to enzyme inhibition Received: 19 August 2002 / Accepted: 12 November 2002 / Published online: 21 February 2003 9 Springer-Verlag 2003 Abstract We have recently shown that the anti-HIV activities of reverse transcriptase inhibitors can be related quantitatively to properties of the electrostatic potentials on their molecular surfaces. We now introduce the technique of using only segments of the drug molecules in developing such expressions. If an improved correla- tion is obtained for a given family of compounds, it would suggest that the segment being used plays a key role in the interaction. We demonstrate the procedure for three groups of drugs, two acting on reverse transcriptase and one on HIV protease. Segmental analysis is found to be definitely beneficial in one case, less markedly so in another, and to have a negative effect in the third. The last result indicates that major portions of the molecular surfaces are involved in the interactions and that the entire molecules need to be considered, in contrast to the first two examples, in which certain segments appear to be of primary importance. This initial exploratory study shows that segmental analysis can provide insight into the nature of the process being investigated, as well as possibly enhancing the predictive capability. Keywords Molecular surface electrostatic potentials Segmental analysis 9 Enzyme inhibition Introduction The electrostatic potential V(r) that is created in the space around a molecule by its nuclei and electrons, defined by Eq. (1), is well established as a guide to molecular interactive behavior. [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] T. Brinck Department of Physical Chemistry, Royal Institute of Technology, 100 44 Stockholm, Sweden P. Jin 9 Y. Ma 9 J. S. Murray - P. Politzer (~) Department of Chemistry, University of New Orleans, New Orleans, LA, 70148, USA e-mail: ppolitze@ uno.edu ZA / p(r')dr' V(r) = A~IRA_ rl ~TZ~ (1) In Eq. (1), Za is the charge on nucleus A, located at RA, and p(r) is the electronic density function of the molecule. V(r) is a physical observable, which can be determined experimentally, by diffraction methods, as well as com- putationally. [4, 7] Its sign at any point in space depends upon which of the two terms on the right side of Eq. (1) dominates; the first describes the contribution of the nuclei and is positive, while the second reflects the effect of the electrons and is therefore negative. The electro- static potential is most effective in indicating the favored initial path of approach of an electrophile, and in analyzing noncovalent interactions or the early stages of processes that may eventually involve bond-breaking/ forming; the separations in such situations are sufficient to minimize complications due to polarization and/or charge transfer. [3, 5, 10, ti, 12, t3] For these purposes, attention has increasingly focused upon the potential computed on the molecular surface, Vs(r), since this is what other reactants initially encounter. This of course poses the question of how to define a molecular surface, for which there is no rigorous basis. One approach involves intersecting spheres centered on the nuclei, having van der Waals or other suitable radii. [14, 15, 16] We normally prefer to follow Bader et al. [17] in taking the surface to be some outer contour of the electronic density, e.g. p(r)=0.001 or 0.002 electrons bohr -3. It then reflects the specific features of the particular molecule, such as lone pairs or strained bonds. We have shown that the most negative and most positive values of the surface potential, Vs,mi n and Vs,max, correlate with empirically developed scales of hydrogen bond basicity and acidity, respectively. [18, 19, 20] However, while Vs,min and Vs,ma• are certainly key features of Vs(r), they are site-specific, and cannot possibly convey all the information contained in it. Accordingly, we have sought to develop mechanisms for more adequately describing and quantitatively character- izing the electrostatic potential over the entire molecular