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COSMO Polarization Charge Densities as Key Information for

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1 COSMO Polarization Charge Densities as Key Information for
Solubility and Partitioning Property Prediction and 3D-QSAR Andreas Klamt COSMOlogic GmbH&Co.KG Leverkusen, Germany & Inst. of Physical and Theor. Chemistry, Univ. of Regensburg

2 Let us look for an alternative representation
The molecular electrostatic potential MEP / ESP Polarity, i.e. electrostatics, is generally accepted as most important for the interactions of molecules, and thus for the understanding and prediction of the behaviour drug molecules. Hydrogen bonding is considered as a special flavor of polarity. Molecular electrostatic potentials are the most widely used concept to quantify and visualize molecular polarity. But it has a few nasty aspects: 1) It diverges at the positions of the atomic nuclei, 2) It decays only slowly with the distance from the molecule. 3) There is no clear recipe, at which place or on which surface the MEP should be considered. 4) On the same surface, MEPs of ions on a different scale than those of neutral compounds. They are hardly comparable. Let us look for an alternative representation of molecular polarity.

3 The conductor polarization charge density
The conductor can be taken into account during the quantum chemical calculation using the Conductor-like Screening Model (COSMO, Klamt, Schüürmann, 1993) electron density polarization charge density s = polarization charge / area conductor energy, geometry, polarization charge density and conformations in conductor The COSMO embedding already gives an approximate representation of a polar solvent. For less polar solvents it can be scaled by a simple function f(e) = (e-1)/(e+0.5).  COSMO has become one of the most popular continuum solvation models But all dielectric continuum models are fundamentally wrong, and COSMO-RS follows a different concept !

4 Interactions of molecules swimming in a conductor
There are no long-range interactions of molecules in conductor!!! We only get an energy change DE, if the two cavities contact each other. Basic idea of COSMO-RS: Quantify interaction energies as local interactions of COSMO polarization charge densities s and s‘ s s‘ DEcontact = E(s,s‘)

5 Linear dependence of EHB on s
DFT-HB-cluster calculations for a week and a strong donor s (e/nm²) donor=HCN) DFT/COSMO hydrogen bond energies donor=HF) s is the better local interaction descriptor! Polarization charge densities provide a predictive quantification of hydrogen bond energies Klamt, Reinisch, Eckert, Hellweg, Diedenhofen, Phys. Chem. Chem. Phys., 2012,14, 955ff

6 exp. hydrogen bond enthalpies
Phys. Chem. Chem. Phys., 2013,15, Interpretation of experimental hydrogen-bond enthalpies and entropies from COSMO polarisation charge densities Klamt, Reinisch, Eckert, Graton, Le Questel

7 Interaction energy of individual contacts:
In a dense liquid all surface pieces are bound in surface pairs, and the total interaction energy can be expressed as a sum of surface interactions Eint(s,s‘). But for liquid phase properties we need free energies, i.e. contact probabilities of all possible contacts!

8 For an efficient statistical thermodynamics we reduce the ensemble of molecules to an ensemble of pair-wise interacting surface segments. For handling this we need histograms of surface polarity. Screening charge distribution on molecular surface reduces to "s-profile"

9 Screening charge distribution on molecular surface
reduces to "s-profile"

10    Why does it get warm when you mix acetone and?
Qualitative thermodynamics based on s-profiles Why does it get warm when you mix acetone and? Because their s-profiles are almost complementary!

11 potential of a segment of
Next we need the solve the statistical thermodynamics of an ensemble of surface pieces with a composition: I.e. we need to calculate chemical potentials and contact probabilities of the pairwise interacting surface pieces. “Three weeks of sleepless nights“ led to the exact equation: s-potential, i.e. “pseudo“- chemical potential of a segment of polarity s in solvent S free energy costs of getting partner s‘ available solvent s-profile, i.e. compostion of solvent S wrt s interaction energy of s and s‘ requires iterative solution: µS(s‘)=0

12 representative liquids
-profiles and -potentials of representative liquids hydrophobicity affinity for HB-donors HB-acceptors

13 Molecules can be flexible!
For getting the chemical of a soluteX in a solvent we project the solvent s-potential back to the solute surface: „size correction“ or combinatorial contribution (“lended from chem. eng.“): depends on solute and solvent volumes and areas (e.g. from COSMO cavity) This is the central equation of COSMO-RS, since knowing the chemical potential as a function of composition and temperature we do have almost the entire liquid phase thermodynamics in our hands. But stop, I sheated you: Molecules can be flexible!

14 For flexible molecules there are multiple local minima (conformations)
2fold For flexible molecules there are multiple local minima (conformations) COSMO-RS knows the internal energy (from DFT) and the individual free energy from central COSMO-RS eq. At every temperature and composition COSMO-RS can calculate the total free energy of the compound (from the partition function) and the exp. values of the all properties.

15 chemical potential of solute X in the gasphase:  vapor pressures

16 chemical potential of solute X in S:
Property Calculation chemical potential of solute X in S: chemical potential of solute X in the gasphase:  vapor pressures partition coefficients activity coefficients  arbitrary liquid-liquid equilibria vapor pressure

17 COSMO-RS Flow Chart of DFT/COSMO COSMOtherm Chemical Structure
Phase Diagrams Equilibrium data: activity coefficients vapor pressure, solubility, partition coefficients Quantum Chemical Calculation with COSMO (full optimization) s-potential of mixture s-profiles of compounds ideally screened molecule energy + screening charge distribution on surface Fast Statistical Thermodynamics Database of COSMO-files (incl. all common solvents) other compounds s-profile of mixture DFT/COSMO COSMOtherm

18 alkanes alkenes alkines alcohols ethers carbonyls esters aryls diverse amines amides N-aryls nitriles nitro chloro water COSMOtherm currently is the most accurate tool for DGsolv prediction: Accuracy (kcal/mol) on 2343 data COSMOtherm 0.48 SM (fitted on this data set!) PCM ~ (only 3 solvents) A. Klamt, B. Mennucci, J. Tomasi, V. Barone, C. Curutchet, M. Orozco and F. Javier Luque, "On the Performance of Continuum Solvation Methods. A Comment on “Universal Approaches to Solvation Modeling”" Acc. Chem. Res., 2009, 42 (4), pp 489 ------ SAMPL 2009 blind test for prediction of DGsolv of very demanding compounds 45 entries from molecular dynamics, Monte Carlo, Continuum Solvation Models, and other methods: COSMO-RS error is about 0.5 kcal/mol smaller than the that of the second best entry. Results of parametrization based on DFT (DMol3: BP91, DNP-basis 650 data 17 parameters rms = 0.41 kcal/mol A. Klamt, V. Jonas, J. Lohrenz, T. Bürger, J. Phys. Chem. A, 102, 5074 (1998) meanwhile: COSMOtherm2.1_0110 with Turbomole BP91/TZVP rms = 0.29 kcal/mol Residuals Limited by accuracy of DFT!

19 Applications to Phase Diagrams and Azeotropes
Winner of the 1st,5th,6th IFPSC (AICHE/NIST) Applications to Phase Diagrams and Azeotropes miscibility gap

20 COSMOtherm prediction of drug solubility in diverse solvents (blind test performed with Merck&Co., Inc., Rahway, NJ, USA) all predictions are relative to ethanol solvents: Water 1-Propanol 2-Propanol DMF Ethyl Acetate Methanol Heptane Toluene Chlorobenzene Acetone Ethanol Acetonitrile (Triethylamine) Butanol triethylamine heptane

21 Example Absolute solvent screening with estimated DGfus Artemisinin:
All data are simulated / measured at 20°C Yellow points indicate alternative experimental measurements, the experimental range is additionally visualized by black lines. Data and DGfus are extracted from Lapkin A., Peters M., Greiner L., Chemat S., Leonhard K., Liauw M., Leitner M., Screening of new solvents for artemisinin extraction process using abinitio methodology, Green Chem., 2010, DOI: /b922001a Artemisinin:

22 „Conformational analysis of cyclic acidic a-amino acids
in aqueous solution - an evaluation of different continuum hydration models." by Peter Aadal Nielsen, Per-Ola Norrby, Jerzy W. Jaroszewski, and Tommy Liljefors, for JACS Method Solvent rms rms (4 points) Max Dev Model (kJ/mol) (kJ/mol) (kJ/mol) AM SM5.4A PM SM5.4P AM SM HF/6-31+G* C-PCM HF/6-31+G* PB-SCRF AMBER* GB/SA MMFF GB/SA BP-DFT/TZVP COSMO-RS COSMO-RS was evaluated as a blind test !!!

23 latest results for bases (pKb): similar rms
formicacid aceticacid chloroaceticacid dichloroaceticacid0 trichloroaceticacid n-pentanoicacid 2,2-dimethylpropanoicacid benzoicacid oxalicacid0 maleicacid3 fumaricacid carbonicacid0 phenol pentachlorophenol ethanol 2,2,2-trichloroethanol hypochlorousacid hypobromousacid hypoiodousacid nitrousacid sulfurousacid phosphoricacid2 boricacid 5-fluorouracil 5-nitrouracil cis-5-formyluracil thymine trans-5-formyluracil Uracil and others latest results for bases (pKb): similar rms

24 COSMO-RSol has rmse of 0.6 on pesticide test set,
Competing method shows 1.3 on that dataset.

25 s-moment regressions enable a range of other ADME predictions
logBB logK_IA logK_HSA logK_OC

26 COSMOflat: Simulation of molecules at a flat interface
Concept: Just a flat interface between two arbitrariry user-defined liquids, (typically one his hydrophobic and other is water) construct a total partition sum get the probability to find the solute in a certain depth and orientation. get the total free energy change of the solute at this interface (conformations can be taken into account, e.g. stretched vs. collapsed  surface activity - surface and interfacial tension

27 COSMOmic: Simulation of molecules in micelles and membranes (2)
COSMOmic: A Mechanistic Approach to the Calculation of Membrane-Water Partition Coefficients and Internal Distributions within Membranes and Micelles, J. Phys. Chem. B, 2008 Andreas Klamt, Uwe Huniar, Simon Spycher, and Jörg Keldenich|

28 Micelle and Interface Properties: COSMOmic
Example: Free energy profiles through DMP (dimethylphthalate) membrane MD-simulations*,** COSMOmic (5 minutes calc. time) * Simulation results of Daniele Bemporad and Jonathan W. Essex University of Southampton, UK and ** see also Claude Luttmann, J. Phys. Chem. B 2004, 108, 4875ff

29 Cocrystal-Screening with COSMOtherm excess heat of mixing!
Initial tests gave better results than current state-of-the-art method [1] (6 false positive results versus only 2 with COSMOtherm!) Fast screening against large databases with harmless food ingredients (EAFUS, GRAS) within minutes with COSMOfrag technology. [1] Hunter et al., Chem. Sci. 2011, 2, 883–890.

30 Probability of cocrystallization

31 So far all COSMO-RS application examples were relevant for drug-development. Now to drug-design:
- the interactions of ligands with receptors are exactly of the same type as those of solutes and solvents (electrostatics, hydrogen bonding, vdW – and all in the liquid state) ! but position plays a far more important role than in liquids: The right polarity must be at the right place! nevertheless, it is a necessary criterium that the molecules have the right polarities, i.e. a suitable s-profile is a necessary, but not sufficient condition for strong binding. Retinal

32 COSMOsim bio-isoster search based on s-profiles
If physiological distribution and drug-receptor binding are to a large degree determined by s-surfaces and s-profiles, it makes sense to screen for drug-candidates s-profile-similarity: search is based on surface polarity (s) and not on structure => scaffold hopping either search over full COSMO-files of COSMOfrag-DB (60000 compounds) screen millions of candidate compounds using the COSMOfrag method see also: Thormann M, Klamt A, Hornig M, Almstetter M COSMOsim: bioisosteric similarity based on COSMO-RS sigma profiles. [J Chem Inf Model. 2006, 46: ]

33 CCC(=O)O ZFQCMUCKI 1 OC(=O)C=C ITPZMBCLI 0.8169 CCCC(=O)O IAVMXKDKI 2 0.7996 CC=CC(=O)O RGQGEAHMI 3 0.791 CC(=C)C(=O)O WCMTTAFLI 4 0.765 VGZSDPDLI 5 0.7584 CC(C)C(=O)O DGWQYNDKI 6 0.7487 OCC1CO1 SDLNNSMIA 7 0.7269 CC(O)C#N HTYYARCJZ 8 0.7233 Oc1nnns1 NBAKLRQLI 9 0.7171 CC(O)C(=O)O WOJBMNDKV 10 0.7109 CC(=O)O CZWYICCKI 11 0.7052 Clc1nnn[nH]1 JMAKWZALI 12 0.7041 CC(=NO)C EZHYEWAJI 13 0.6983 OCCC(=O)O FFBMJKDKI 14 0.6978 CC(=O)C=NO HOMSZUGLI 15 0.6919 Oc1csnn1 UMBRJEKLI 16 0.6885 OC(=O)C1CCC1 CUOCJIGKI 17 0.6817 OCCS HLKLSJLHI 18 0.6804 CC1CC1C(=O)O GXSEIQGKP 19 0.6767 But COSMOsim was not widely used, since drug modelers do not want to waste 3D-information! p7 p9 p8 p12 p13 p15

34 COSMOsim3D bio-isoster search based on s-surfaces idea and initial implementation by Dr. M. Thormann, Origenis AG presented as CUBEsim on COSMO-RS symposium 2009 places s-surfaces of target and probe on a grid alignes probe on target different start orientations ( first 21 systematic), ~ 5s – 30s gives 3D simlarity measure (CS3D) - search for molecules with maximum similarity of 3D-s-surfaces

35 M.Thormann, Origenis Separation of true and random bioisosteric pairs

36 Enrichment of active drugs
in MDDR activity classes

37 PharmBench introduction
Alignment performance: PharmBench PharmBench introduction A benchmark for alignment/pharmacophore elucidation methods was recently proposed on J. Chem. Inf. Model. PharmBench, namely a benchmark for alignment/pharmacophore elucidation methods was recently proposed on J. Chem. Inf. Model. The authors collected all available X-ray structures for 81 different protein targets, they superimposed the proteins using their alpha carbons and then they extracted the co-crystallized ligands. The collection of ligands for each target constitute a gold standard for alignment. In fact, judging the quality of an alignment of ligands is always a bit elusive in the absence of an experimental reference. By using the PharmBench collection, the quality of the alignments can be objectively evaluated by the RMSD from the crystallographic poses. The quality of the alignments is evaluated by the RMSD from the crystallographic poses

38 PharmBench performance
PharmBench: reproducing X-ray alignments (performed by Paolo Tosco, Univ. Turino) Tthe same procedure as the one described by Cruciani in the PharmBench papers was used; namely, the crystallographic conformations were extracted from the respective PDB files, then for each dataset, each ligand was aligned to each of the others in their X-ray position. Then each of the aligned ligands was compared to its X-ray position, and the RMSD was computed. For each of the ligands, the template which gives the lowest RMSD from the crystallographic pose was taken into consideration (see page D of the PharmBenchI paper). Here the results for 5 of the 81 datasets are reported for Open3DALIGN (O3A) and COSMOsim3D (CS3D), and compared to the results obtained by the authors of the PharmBench publication with FLAP, namely their own software distributed by Molecular Discovery. While Open3DALIGN performs slightly worse than FLAP, COSMOsim3D achieves a significantly lower RMSD from the X-ray poses.

39 COSMOsim3D based Molecular Field Analysis:
COSMOsar3D: COSMOsim3D based Molecular Field Analysis: PLS The most predictive and robust MFA method presented ever! COSMOsim3D: 3D-Similarity and Alignment Based on COSMO Polarization Charge Densities J. Chem. Inf. Model., 2012, 52,2149 COSMOsar3D: Molecular Field Analysis Based on Local COSMO σ-Profiles, J. Chem. Inf. Model., 2012, 52 ,2157

40 COSMOsar3D: COSMOsim3D based Molecular Field Analysis:
do alignment with COSMOsim3D use the grid of local s-profiles as descriptor array by the local s-profiles you have high quality local information about - electrostatics hydrogen bonding - hydrophobic interactions - shape the ~2Å grid spacing represents some local flexibility and fuzzyness, i.e. it mimics that the ligand and receptor can slightly adjust to each other. If we just assume that the virtual receptor provides a local s-potential at each grid point, then the binding free energy (including desolvation) should be a linear functional of the local s-profiles! Hence a multi-dimensional regression analysis (as PLS) should have a very good chance to generate a predictive model for binding constants. COSMOsim3D based Molecular Field Analysis should be favorable compared to standard MFA methods! (patent application submitted)

41 out off the box COSMOsar3D outperforms all 7 standard methods

42 Robustness of COSMOsar3D
compared to standard MFA and no cutoff-values are required!

43 COSMOfrag: A fast shortcut of COSMOtherm
suited for HTS-ADME prediction 1) large database of precalculated drug-like compounds (about , incl. ions) 2) for new compound find most similar fragments in database 3) compose approximate COSMO surface from surface fragments 4) write a meta-cosmo-file or a full 3D fcos-file for 3D-QSAR COSMOfrag requires less than 0.5 sec/compound  HTS

44 CF-COSMO files (.fcos):
COSMOsim3D usually would require one quantum-chemical calculation for each conformation of a ligand which shall be tested. That is doable, but quite time-consuming for screening ~ 5 min. on AM1/SVP level COSMOfrag was able to generate s-profiles for new compounds in less than a second based on finding the most similar atoms in a big database of ~60000 pre-calculated drug-like compounds. NEW: COSMOfrag now can generate in a second an approximate 3D-COSMO file (*_cf.cosmo) by searching for the most similar atoms, transforming the respective COSMO segments into the new local atomic coordinate system. CF-cosmo files do not provide a nice closed COSMO surface, but have the polarity roughly in the right spatial reagion. But they are sufficient for COSMOsim3D screening.

45 Summary: The Conductor polarization charge density s provides rich information about molecular interactions! The COSMO-RS statistical thermodynamics converts s into free energies in liquid phases and thus yields activity coefficients, solubility … This enables many useful applications in drug development and formulation: solvent screening, co-crystal screening, reaction media selection and optimization, ADME predictions, … s-profiles and local 3D- s-profiles are very useful for the description of ligand-receptor binding.

46 Information content of s-surfaces
The electrostatic potential ESP calculated by DFT with (or without) COSMO is dominated by dipole moment. Almost no local features (lone pair directions, structure on halogen atoms) can be seen. The conductor polarization charge density s, calculated from DFT/COSMO, shows lone pair directions and many polarity details (e.g. on halogen atoms). It is a very good local measure of polarity. If s is calculated from ESP-fitted point charges, the picture looks similar on the first glance, but all details get lost, because a point charge representation is unable to reflect sub-atomar orbital features!


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