Interaction energy of DNA base pairs and amino acid pairs: DFT, DFTB and WFT calculations

Transcription

1 Interaction energy of DNA base pairs and amino acid pairs: DFT, DFTB and WFT calculations Tomáš Kubař, Petr Jurečka, Jirka Černý, Honza Řezáč, Michal Otyepka, Haydée Valdés and Pavel Hobza* Institute of Organic Chemistry and Biochemistry Czech Academy of Sciences Prague * hobza@uochb.cas.cz

2 Biomolecules

3 Biomolecular interactions Contribution of non covalent interactions to the 3D structure Interaction motifs: hydrogen bonding stacking Similar strength ( E ~< 25 kcal/mol) Balanced and reasonably accurate description of non covalent interactions required

4 Computational methods Hydrogen bonding interaction electrostatic and charge transfer origin good description by all methods (HF, DFT, ) electron stacking interaction London dispersive forces HF and DFT approaches fail (correlation missing or incorrect) MP2 overestimates Eint, CCSD(T) desirable basis set dependence (polarization and diffuse functions, complete basis set limit)

5 Computational methods Correct prediction of the entire PES necessary, not only the interaction energy in minima Reason: minimization and dynamics Example: minimization of the GC stacked complex using DFT (X3LYP/cc pvtz) Error: no minimum on the PES for the stack this complex is unstable and H bonding prevails

6 Computational methods Modern QCh offers DFT reliable except the treatment of dispersion energy excellent timing (use of RI / density fitting) needs adaptation to describe non bonded interactions 1. Modification of the XC density functional 2. Full DFT calculation with empirical correction for dispersion energy (DFT D) 3. Density functional tight binding with empirical contribution of dispersion energy (SCC DFTB D)

7 DFT based approaches 1 Modification of the XC density functional blending of various functionals eg. Zhao, Schultz, Truhlar J Chem Theor Comput 2, 364 (2006) reliable interaction energy in the minima the inclusion of exact exchange functional decreased speed the exchange functional drives the complex formation incorrect distance dependence of energy for the dispersion bound complexes (r1 or r3 instead of r6)

8 DFT based approaches 2 Full DFT calculation with empirical correction to dispersion energy (DFT D) eg. Grimme our implementation Jurečka, Černý, Hobza, Salahub J Comp Chem 25, 1463 (2004) J Comp Chem, in press r6 function damped at middle to short distances r (nm) E (kcal/mol)

9 DFT based approaches 2 Full DFT calculation with empirical correction to dispersion energy (DFT D) our implementation Jurečka, Černý, Hobza, Salahub J Comp Chem, in press r6 function damped at middle to short distances no extra computational cost RI approximation in DFT leads to favorable timing (2) parameters fitting on extensive CCSD(T) data extrapolated to the CBS limit testing on a large & balanced class of complexes best performance with TPSS / TZVP facility to calculate normal mode frequencies

10 DFT based approaches 3 Density functional tight binding self consistent charges and empirical contribution of dispersion energy first introduction of empirical Edisp into a DFT like framework Elstner, Hobza, Frauenheim, Suhai, Kaxiras J Chem Phys 114, 5149 (2001) (surprisingly) good results extremely fast compared to other approaches for non bonded complexes, no failure found yet slightly inaccurate in the description of H bonding

11 DNA interaction of bases Testing Both H bonded and stacked base pairs Minimized geometry Interaction energy (kcal/mol) B3 LYP AT W B3 LYP GC W mamt H mgmc W AT S GC S mamt S mgmc S often used to describe biomolecular systems strong H bonded complexes; stacking weak interaction

12 DNA interaction of bases Testing Both H bonded and stacked base pairs Minimized geometry Interaction energy (kcal/mol) B3 LYP 20 CCSD(T)/CBS AT W GC W mamt H mgmc W AT S GC S mamt S mgmc S B3 LYP incorrect for stacked complexes, there is strong attraction

13 DNA interaction of bases Testing Both H bonded and stacked base pairs Minimized geometry Interaction energy (kcal/mol) B3 LYP 20 DFT D SCC DFTB D CCSD(T)/CBS AT W GC W mamt H mgmc W AT S GC S mamt S mgmc S Generally perfect performance of D methods Slightly weaker H bonding by SCC DFTB D

14 DNA interaction of bases Application Analysis of 128 double helical DNA octamers Interaction energy for 3 types of base pairs H bonded, intra and interstrand stacked Massive amount of calculation efficiency is crucial Avg. total interaction energy per octamer: kcal/mol Hydrogen bonded Intrastrand stacked Interstrand stacked DFT D DFTB D Idea of relative importance of these interactions Methods compare well Řezáč et al., Chem Eur J, submitted

15 DNA interaction of bases Application Comparison of interaction energy due to inter and intrastrand stacking (DFT D, kcal/mol) Hypothesis: complementarity of stabilization stemming from these two interaction modes

16 DNA interaction with ligand Ligands bind to DNA in various modes Interaction energy ~ strength of binding ~ ~ biological activity of the drug drug design Ellipticine (anti tumor drug) and a DNA tetramer Kubař et al., in preparation

17 DNA interaction with a ligand Neutral and protonated ellipticine molecule bound to DNA Interaction energy: (kcal/mol) Ligand Method Intercalated Minor groove DFT uncharged DFT D DFTB D DFT protonated DFT D DFTB D Dispersion bound complex DFT fails DFT D and DFTB D: excellent agreement of results DFTB D much faster (12 min vs 1137 hours); slow convergence of both SCF and SCC

18 Interactions inside proteins Testing Complexes of amino acids (and the model of peptide bond); geometry from experiment Interaction energy: (kcal/mol) Aromatic amino acid w/ non polar Aromatic w/ peptide bond Strong salt bridges 1BRF 1BRF 1BRF 1BRF 1BRF 1IU5 1BQ9 1BRF Phe30 Lys46 Phe30 Leu33 Phe30 Tyr13 Phe49 PB(4 5) Phe49 PB(5 6) Glu47 Lys6 Glu49 Lys6 Glu50 Lys30 DFT DFT D DFTB D CCSD(T)/CBS

19 INK4 tumor suppressor hydrophobic core protein with a hydrophobic core consisting of 10 helices EDFTB D = 513 kcal/mol interaction energy of every pair of neighboring helices: Interaction energy (kcal/mol) DFT D SCC DFTB D Otyepka et al., J Phys Chem B 110, 4423 (2006)

20 Small peptide molecular dynamics MD simulation of Trp Gly Gly using SCC DFTB D Goal to find conformers coexisting in the gas phase to calculate IR spectra & compare with expt. SCC DFTB D used for MD/Q then, DFT D used for minimization (superior to MP2) DFT DFT D MP2 Valdés et al., J Phys Chem B 110, 6385 (2006)

21 DFT D and SCC DFTB D Balanced and reliable description of the interactions inside biomolecules No failure found yet Very efficient SCC DFTB D useful for MD simulations Universal DFT D works even for less common elements

22 Thanks further to Eva Mrázková, Dominik Horinek, Filip Ryjáček, for control statement, Iwona Dąbkowska, Jarda Rejnek, Jindra Fanfrlík, Kristýna Pluháčková, Lada Bendová, Martin Kabeláč, Michal Hanus, Míša Kolář, Petr Dobeš, Petr Sklenovský, trinity at matrix, Vojta Klusák, VOND (last but not least).