The Signature molecular descriptor [1] is a type of topological index that encodes all atoms a pre-defined height h away from the root atom.  The adjustable height parameter allows Signature to be applied in quantitative structure-activity relationships (QSARs) with a tunable degeneracy.  QSARs provide a description of the correlation between the structure of a molecule and a specific molecular property of interest.  Typically QSARs are employed to refine the search for molecules matching a desired property by screening an existing database, but ideally one would like to identify potential compounds outside the database through solving the inverse-QSAR (I-QSAR) problem.  A distinctive feature of Signature is the ability to solve the I-QSAR problem, and success has previously been achieved at height 1 [2,3]  Focused libraries of compounds with desired predicted values are created from which a high-quality lead compound can be developed.  In this study, we explore an improvement in solving the I-QSAR problem by working at height 2 for the first time to design stronger trypsin inhibitors. 

Trypsin is a protease found in the digestive system.  A database of 39 known trypsin inhibitors with inhibition constant (K_i) data was obtained to create a QSAR.  Examples of compounds from this database [4,5]   are provided below in Figure 1.

Figure 1:  Sample training set compounds from the trypsin database. 

The general I-QSAR process is provided in Figure 2, where it begins with a literature search for known trypsin inhibitors to form the training set.  These structures are translated to Signatures for derivation of the constraint equations.  The purpose of this set of equations is to enforce restrictions on how the unique Signatures from the training set can be combined in all possible ways to form new compounds for high-throughput screening.  Next, the solutions are filtered based on number of cycles, Lipinski Rule of Fives [6], and predicted K_i.  The occurrences of the unique Signatures for each training set compound are correlated with the experimental log(K_i) values via a forward stepping multiple linear regression to construct the QSAR.  Structures are enumerated from all solutions predicted to be more active than the strongest inhibitor in the training set.  The inverse structures generated are evaluated for energetic stability by calculating the optimized 3D Dreiding energy from the Marvin Beans software package. [7]

Figure2:  The overall I-QSAR process begins with a training set from the literature, and ends with a focused database suitable for further study. 

Preliminary work indicated that working at height 2 resulted in a QSAR with enhanced predictive capability.  In addition, the degeneracy at height 2 was lower, which reduced the number of inverse structures generated to a manageable amount.  The tradeoff for working at height 2 is additional constraint equations and unique Signatures, which makes solving the I-QSAR problem more challenging.  Note that solving the problem in this manner generates new compounds without merely modifying substituent groups around a scaffold.  Accordingly, we report some preliminary candidates in Figure 3 that are currently being studied for synthesis and experimental confirmation.  As a compliment to the QSAR predictions, docking studies were also performed on these structures which indicate similar energies to the training set compounds.

Figure 3:  Compounds generated by solving the I-QSAR problem are promising candidates for stronger inhibitors of trypsin. 

[1] J. F. Faulon, D. P. Visco, Jr. and R. S. Pophale, “The Signature Molecular Descriptor. 1. Extended Valence Sequences vs. Topological Indices in QSAR and QSPR studies”, J. Chem. Inf. Comput. Sci., 43, 707 – 720 (2003).

[2] C. Churchwell, M. D. Rintoul, S. Martin, D. P. Visco, Jr., A. Kotu, R. S. Larson, L.O. Sillerud, D. C. Brown and J. L. Faulon , “The Signature Molecular Descriptor. 3. Inverse Quantitative Structure-Activity Relationship of ICAM-1 Inhibitory Peptides”, J Molecular Graphics and Modelling, 22, 263 – 273 (2004).

[3] D. Weis, J. L. Faulon, R. LeBone, D. Visco, “The Signature Molecular Descriptor. 5. The Design of Hydrofluoroether Foam Blowing Agents Using Inverse-QSAR”, Ind. Eng. Chem. Res, 44, 8883-8891 (2005).

[4] M. Whitlow, D. O. Arnaiz, B. O. Buckman, D. D. Davey, B. Griedel, W. J. Guilford, S. K. Koovakkat, A. Liang, R. Mohan, G. B. Phillips, M. Seto, K. J. Shaw, W. Xu, Z. Zhao, D. R. Light, M. M. Morrissey, “Crystallographic analysis of potent and selective factor Xa inhibitors complexed to bovine trypsin”, Acta Cryst. D55, 1395-1404 (1999).    

[5] Herbert Nar, Margit Bauer, Angela Schmid, Jean-Marie Stassen, Wolfgang Wienen, Henning W. M. Priepke, Iris K. Kauffmann, Uwe J. Ries, Norbert H. Hauel, “Structural Basis for Inhibition Promiscuity of Dual Specific Thrombin and Factor Xa Blood Coagulation Inhibitors”, STRUCTURE V. 9, 29-37 (2001).

[6] C. Lipinski, ACD/LogP – Rule of 5, http://www.acdlabs.com/products/phys_chem_lab/logp/ruleof5.html. 2005

[7] ChemAxon, http://www.chemaxon.com/marvin/doc/user/molconvert.html, 2007.