Computational Drug Discovery - Hydration Behavior of De Novo Designed Pharmaceuticals

  • © Jenzig71 / Pixelio.de© Jenzig71 / Pixelio.de
  • © Jenzig71 / Pixelio.de
  • Fig. 1: Relationship between hydration free energy and other important physico-chemical properties.
  • Fig. 2: The error in calculated hydration free energy plotted against the experimental hydration free energy for molecules in both the training and test sets.
  • Dr. David S. Palmer, Max-Planck Institute for Mathematics in the Sciences, Leipzig
  • Dr. DSc. Maxim V. Fedorov, Max-Planck Institute for Mathematics in the Sciences, Leipzig

We report on an accurate computational method to calculate hydration free energies - a key property in predicting the pharmacokinetics of novel pharmaceutical molecules.

Introduction

In the past 20 years, developments in combinatorial chemistry, high throughput screening and robotics have revolutionized the drug discovery process, leading to a dramatic increase in the number of candidate drug molecules. However, despite this increase in experimental testing, the number of new pharmaceuticals approved per year in the developed countries has almost halved in the last decade [1]. One of the main causes of the unacceptable attrition rate in drug discovery is the failure of molecules to reach the market place because they have the wrong physico-chemical properties to allow them to be orally administered to patients [2].

Experimental high-throughput measurements of physico-chemical properties (solubility, pKa, logP, etc) are routinely used to screen candidate drug molecules. However, such experiments can only be applied to molecules that have already been synthesized, which makes them expensive and time-consuming. A complimentary approach is to use computer simulations to calculate the properties of putative drug molecules [3,4]. In a drug discovery setting, large computational databases of candidate drug molecules are screened prior to their synthesis, allowing medicinal chemists to prioritize which compounds to pursue, thus improving efficiency and reducing costs. The potential for computer simulations to improve the drug discovery process is enormous. However, there have traditionally been two main problems: (i) existing methods are not accurate or robust enough; (ii) the number of possible druglike molecules (the size of "druglike chemical space") is vast, which means that to use high-level methods, very large computational resources are required.

From a computational viewpoint, a key physico-chemical property in predicting the pharmacokinetics of putative drug molecules is the hydration free energy (ΔGhyd), which is the change in free energy observed when the molecule is transferred from the gas phase to aqueous solution (under standardized conditions).

Many of the pharmacokinetic properties of potential drug molecules are defined by their solvation and acid-base behaviour, which can be estimated from their hydration free energies (fig. 1).

Current computational methods to calculate hydration free energies are generally based on one of two distinct approaches to modelling solvent. Implicit solvent models treat the solvent as a dielectric field acting upon the solute (and hydration free energies are calculated by solving either the Generalized-Born or Poisson-Boltzmann equations). Although this approach has the benefit that it is computationally inexpensive, it ignores valuable information available in the microscopic solvent structure. By contrast, explicit solvent model simulations place a single solute molecule in a vast number of solvent molecules, each of which is modelled in fully atomistic detail. Although this approach is more rigorous, long computer simulations (e.g. molecular dynamics or Monte Carlo simulations) are required to calculate hydration free energies. Moreover, it has recently been shown that the best of these methods cannot calculate the hydration free energies of drug molecules with an accuracy much better than ~ 2.5 - 3.5 kcal/mol, which if used to calculate solubility, for example, will lead to at least a 100-fold error in maximum concentration. The consequence is that the current theoretical methods to calculate hydration free energy are not accurate enough for modern pharmaceutical research. For this reason, the pharmaceutical and agrochemical industries often rely upon purely empirical models for predicting physico-chemical properties. Although such Quantitative Structure-Property Relationships (QSPRs) have the benefit that they are computationally inexpensive, they provide only a loose relationship with the underlying physical chemistry and as such are often unreliable and difficult to systematically improve [5]. New accurate methods to calculate hydration free energies and related physico-chemical properties would have enormous scientific and economic value to both the pharmaceutical and agrochemical industries.

Integral Equation Theory

The Integral Equation Theory (IET) of Molecular Liquids is an alternative theoretical framework from which to calculate hydration free energies [6,7]. IET allows the hydration free energy to be calculated from a set of equations that describe the solute and solvent by way of correlation functions, which describe the average structure of the system. The benefit of this approach is that hydration free energies can be calculated without the need for long computationally expensive molecular simulations, as are normally required in explicit solvent methods. Moreover, IET retains information about the solvent structure unlike implicit continuum solvent models. Although the Integral Equation Theory of Molecular Liquids has been an active topic of academic research for over 40 years, it has traditionally been thought to be too inaccurate for most practical applications. The potential of IET for use in pharmaceutical drug discovery has recently been demonstrated by the Computational Physical Chemistry and Biophysics group led by Dr. DSc. Fedorov at the Max Planck Institute for Mathematics in the Sciences. We have shown that using a new model from IET it is possible to make accurate predictions of the hydration free energies of bioactive molecules [8]. The model was developed by combining new accurate mathematical expressions for the hydration free energy with quantum mechanics methods to calculate the electronic structure of the solute. The best model gave significantly more accurate predictions of the hydration free energies of drugs than other existing methods (RMSD ≈ 1.1 kcal mol-1, Fig. 2). Similar results have been reported by scientists from the Computational Physical-Chemistry and Biophysics group for the calculation of the hydration free energies of amino acids [9], and a large dataset of simple, non-druglike and pollutant molecules [10]. These results suggest that after further development the Integral Equation Theory of Molecular Liquids may be useful in pharmaceutical drug discovery. IET calculations are much less computationally expensive than fully atomistic simulations and would be applicable to virtual screening of large databases of compounds.

Future Horizons

The accuracy of available experimental data is of fundamental importance to testing and developing new computational methods for calculating physico-chemical properties. The European Union (through the FP7-PEOPLE program) has recently funded a new international network research program (the "BioSol" project Grant No 247500, Program: FP7-PEOPLE-2009-IRSES). The BioSol project will bring together theoreticians from the Computational Physical Chemistry and Biophysics group at the Max Planck Institute for Mathematics in the Sciences in Leipzig, Germany, with experimental chemists at leading research centres in Russia, France and Denmark to study solvation phenomena ranging from the solvation of drugs in supercritical fluids to crystal nucleation. As part of this project, hydration free energies and aqueous solubilities of druglike molecules will be measured by Prof. German Perlovich's group at the Institute of Solution Chemistry of the Russian Academy of Sciences in collaboration with Prof. Annette Bauer-Brandl's group at the University of Southern Denmark. It is anticipated that this international collaboration will help push back the barriers currently preventing widespread use of computational physical chemistry methods in practical applications such as, e.g. pharmaceutical drug discovery.

Acknowledgements
We would like to thank Ekaterina L. Ratkova for creating Figure 1.

References
[1] Munos B.: Nature Rev. Drug Disc. 8, 959 (2009)
[2] Lipinski C. A. et al.: Adv Drug Del Rev 23, 3 (1997)
[3] Palmer D. S. et al.: J. Chem. Inf. Model. 47, 150 (2007)
[4] Palmer D. S. et al.: Mol. Pharmaceutics 5, 266 (2008)
[5] Tropsha A.: Mol. Inf. 29, 476 (2010)
[6] Hansen J.-P. and McDonald, I. R.: Academic Press, London (1991)
[7] Hirata F. ed.: Molecular Theory of Solvation. Kluwer Academic, Dordrecht (2003)
[8] Palmer D. S. et al.: J. Chem. Phys. 133, 044104 (2010)
[9] Karino Y. et al.: J. Chem. Phys. Lett. 496 351 (2010)
[10] Ratkova E. et al.: J. Phys Chem. B. 114, 12068 (2010)

 

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