Computational Design of a Time-Dependent Histone Deacetylase 2 Selective Inhibitor

Jingwei Zhou, Min Li, Nanhao Chen, Shenglong Wang, Hai-Bin Luo, Yingkai Zhang , and Ruibo Wu

Histone deacetylases (HDACs) are a family of enzymes involved in gene expression and post-translational modifications. HDACs are very important targets for drug development due to their roles in cancer and other diseases. Several HDAC inhibitors have been developed, however, many known inhibitors produce side-effects because of their poor selectivity. This paper presents a striking example of how state-of-the-art QM/MM-MD calculations can be used for computer-aided drug design (CADD). 

Based on their previous calculations on the mechanism of the wild-type enzyme, Zhou and co-workers hypothesized that a selective inhibitor could be created by developing a molecule that would undergo an HDAC-catalyzed intra-molecular reaction. To this end, the authors proposed several candidates and used QM/MM-MD simulations to study the mechanism in gas-phase, solution and in the enzyme active site. The most promising candidates ( –hydroxymethyl and –aminomethyl substituted chalcones) were subsequently synthesized and characterized in vivo. The authors further analyzed the mechanism of inhibition via QM/MM-MD for the most promising candidate to understand how this molecule acts as an HDAC2-selective, time-dependent inhibitor.

 Reprinted with permission from ACS Chem. Biol., Article ASAP DOI: 10.1021/cb500767c . Copyright (2014) American Chemical Society.

A simple, exact DFT embedding scheme

Fredrick R. Manby, Martina Stella, Jason D. Goodpaster and Thomas F. Miller III

JCTC, 2012, 8, 2564-2568

 

Embedding methods have become a useful tool to perform molecular electronic structure calculations on large systems at relatively modest computational cost, and (hopefully) acceptable accuracy, compared to full blown calculations on the entire system. These methods rely on the short-range nature of chemical interactions between molecular fragments, which allows (most) systems to be subdivided. 

Manby and co-workers have developed embedding schemes that enforce Pauli exclusion by a projection technique to ensure orthogonality of the orbitals of the interacting subsystems. The authors use the fact that Kohn-Sham density functional theory (KS-DFT) provides a framework to perform exact calculations on a subsystem embedded in its full QM environment. This is achieved by partitioning the total density into subsystem densities. If the subsystem densities are constructed with non orthogonal orbitals, a non-additive term arises in the kinetic energy.  However, if the orbitals are orthogonal, this term vanishes. Methods to enforce orthogonality have been employed previously. Manby et al exploit one of these methods to formulate a formally exact DFT embedding scheme. To this end they employ a level shifting operator to keep the orbitals of  a subsystem orthogonal to those of other subsystems. They show that increasing the value of the level shifting parameter reduces the error in energy up to a point (numerical instabilities arise at very large values). The  interesting innovation comes in the use of perturbation theory to eliminate the dependence on the level shifting parameter.

The authors present applications with different embedding schemes combining DFT and wave-function methods. The first example consists of embedding the hydroxyl moiety of ethanol in the environment of the ethyl backbone. DFT-in-DFT embedding calculations at the PBE/6-31G* level with the level-shift and perturbation correction agree with the full DFT calculation to 7 pEH. The second example consists of the deprotonation reaction of ethanol in gas-phase. The PBE result on the full system is 10 mEH lower than the CCSD(T) reference. This can be compared with CCSD(T)-in-PBE embedding results which are as close as 1.5 mEH. Similar trends are observed for the activation barrier for the SN2 reaction of chloride with propyl chloride and water trimer.

As the authors note, this method is "limited to applications for which the electronic structure can be reasonably described using KS theory". However, it provides a simple and straightforward method to perform embedding calculations and can be easily implemented in most electronic structure programs.

Resolution of identity approach for the Kohn-Sham correlation energy within exact-exchange random-phase approximation

 P. Bleiziffer, A. Hesselman, A. Gorling, J. Chem. Phys., 136, 134102, (2012)

Hesselman and Gorling recently introduced exact-exchange random phase approximation (EXXRPA) methods. These Kohn Sham (KS) based methods treat the correlation energy via the random phase approximation (RPA) based on TDDFT using the exact frequency-dependent exchange kernel (Mol. Phys. 108, 359 (2010) and PRL 106, 093001 (2011)). Results from these EXXRPA methods for closed shell organic molecules showed results with accuracy on par with CCSD for total energies and slightly less accurate for reaction energies compared to CCSD but better than MP2.

In this paper, the authors report the development and implementation of the resolution of the identity EXXRPA. This results in two new methods: RI-EXXRPA and RI-EXXRPA+. Both methods make use of RI and auxiliary basis sets to reduce the formal scaling from N⁶ to N⁵. The computational speedup allows the inclusion of previously neglected terms giving rise to RI-EXXRPA+.

Results for total energies for 21 molecules show RMSD values of around 10 kcal/mol for RI-EXXRPA and CCSD, and below 10 kcal/mol for RI-EXXRPA+ (using CBS extrapolated CCSD(T) as reference). RMSD for 16 reaction energies gives values around 1.7 kcal/mol compared to 2.5 for MP2 using the same reference. Overall, this proof of principle paper presents two methods that employ RI to reduce the computational scaling. These methods, albeit more computationally costly than conventional DFT, could provide alternatives to post-HF methods using a Kohn-Sham based approach after more extensive testing.