Drug Design 2. Oliver Kohlbacher. Winter 2009/ QSAR Part I: Motivation, Basics, Descriptors

Transcription

1 Drug Design 2 Oliver Kohlbacher Winter 2009/ QSAR Part I: Motivation, Basics, Descriptors Abt. Simulation biologischer Systeme WSI/ZBIT, Eberhard Karls Universität Tübingen

2 Overview Attrition rate in drug discovery Relevant pharmacokinetic properties log P, pk a, solubility Prediction of molecular properties (QSPR) Examples: ClogP, AlogP Descriptors Classification 0D and 1D descriptors Topological (2D) descriptors 3D and 4D descriptors Prediction of drug-likeness

3 Failure in Late Development 10 Discovery Preclinical Number of Candidates Clin. Phase I Clin. Phase II Clin. Phase III Market 6-12 years After: Lipper, Modern Drug Discovery, 1999, 2 (1),

4 Failure in Late Development 90% of all drug candidates fail between discovery and introduction to the market The late development phases are the most expensive phases In more than 60% of the cases, poor pharmacokinetic (PK) or toxicological properties are the cause Reason for Failure 6% 31% 41% 22% Market Toxicity PK Efficacy Prentis et al., Br. J. Clin. Pharmacol. 1988, 25,

5 Consequences for Discovery Lead ID Restrict search space to candidates with good pharmacokinetic properties Exclude compounds with poor properties from virtual screening campaigns Lead optimization Improve efficacy (µm! nm) Reduce side effects Improve pharmacokinetics

6 Reduce Attrition Rate Fail early, fail cheap The earlier unsuitable candidates are removed from the pipeline, the more money can be saved. If drugs with unsuitable properties can be removed in an earlier development phase, the attrition rate in the late (expensive) development phases can be reduced Which properties does a good drug need? How to predict these properties?

7 Overview of the Different Areas Pharmaceutical Phase Application Dissolution Pharmacokinetic Phase Absorption Biotransformation Storage Distribution Pharmacodynamic Phase Place of Action (Receptors) Pharmacological Effect Excretion Clinical Effect Toxic Effect After: Mut, p. 5

8 Absorption and Elimination Gehirn Blood-Brain Barrier Biliary Central Compartment Renal Absorption Elimination Enteral Membranes of the GI Tract

9 Experimental Quantities An important pharmacokinetic property is the distribution coefficient n-octanol/water P: P = k 1 /k 2 where k 1 and k 2 are rate constants for the transition between phases (H 2 O! octanol and vice versa). P is typically given as its logarithm, log P. log P is important, as it describes a drug s ability to cross a lipophilic membrane (lipophilicity of n-octanol is similar to that of biological membranes) H 2 O k 1 k 2 octanol

10 Determination of log P log P is a measure of lipophilicity of a compound log P can be determined by measuring the change of concentration in a three-phase system H 2 O/octanol/H 2 O Compound is initially dissolved in water (A) and distributes over the octanol phase (B) into the second water phase (C) In equilibrium, concentrations of the compound are constant in all three phases BKK, p. 401

11 log P and log k log k is the logarithm of the rate constants for crossing the membrane Crossing the membrane can be seen as a two-step mechanism: 1. water (inside)! membrane 2. membrane! water (outside) Obviously, this process can also be described in terms of rate constants k 1 and k 2 : log k = log k 1 + log k 2 + const. k H 2 O k 1 k 2 membrane k 2 k 1 H 2 O

12 log P and log k Biological barriers are not simply lipid membranes Distribution across biological barriers can only be described approximately by k 1 and k 2 In most models of log k, log P is used to model permeation across biological membranes A simple bilinear model generally reproduces log k reasonably well: log P = log k 1 log k 2 log k = a log P b log (c P + 1) + d a, b, c, d are constants that can be determined by regression for the respective biological barrier

13 log P and log k In experiments, one observes more or less well-defined maxima for log P as a function of log k Each barrier has an optimal optimal lipophilicity, where log k is maximal For this log P uptake across the barrier is most effective For lower and higher values of log P, log k is reduced Good bioavailability thus requires an average lipophilicity of the compounds Gastric absorption Placental barrier Organic Membrane Intestinal absorption BKK, p. 403

14 Acid-Base Equilibrium Many drugs are acids or bases HA + H 2 O A - + H 3 O + B + H 3 O + BH + + H 2 O Their protonation thus depends on the ph of the surrounding medium Charged species (A -, BH + ) possess log P-values that are about 3-5 above the values of the corresponding neutral species Absorption of a drug thus drastically depends on the protonation state Bioavailability is consequently influenced by the ph of the surrounding medium

15 Acid-Base Equilibrium Protonation/deprotonation is an equilibrium process as well and it is coupled to the distribution equilibrium Protonation is described by the protonation constant K a and its respective negative logarithm pk a : octanol HA A - P n P i There are thus two log P values: log P i for the ionized species and log P n for the neutral species In general, log P i is negligible when compared to log P n HA + H 2 O A - + H 3 O + buffer

16 ph Profiles Acid AH Amino acid Ion pair protonated base B + Anion A - Dibasic acid Plotting log P as a function of ph yields ph-dependent absorption profiles These profiles indicate ph ranges that are suitable for absorption BKK,p. 407

17 Enteral Adminstration Most common route of administration, easiest for patients Oral cavity 0.02 m 2 Stomach m 2 Small intestine m 2 Absorption through gastrointestinal (GI) tract Different parts of the GI tract differ in their surface area Strong dependence on stomach content Colon m 2 Rectum m 2 After FHRS, p. 31

18 Enteral Absorption Neutral compound Acid, pk a = 4 Weak base, pk a = 5 Strong base, pk a = 9 Stomach, ph = 1 Stomach, ph = 1 Stomach, ph = 1 Stomach, ph = 1 Blood, ph = 7.4 Blood, ph = 7.4 Blood, ph = 7.4 Blood, ph = 7.4 Intestine, ph = 6-8 Intestine, ph = 6-8 Intestine, ph = 6-8 Intestine, ph = 6-8 Stomach and intestine differ in their ph Uptake of acids and bases thus occurs in different regions of the gastrointestinal tract Distribution and protonation of a compound depend on the pk a / pk b of its protonatable groups BKK p.408

19 Solubility Solubility of a compound is important, because it limits its bioavailability Insoluble substances are not taken up after the disintegration of a dosage form Substances with low solubilities might be unable to achieve sufficient (effective) concentration in vivo Solubility of a substance is typically given as log S, the logarithm of its maximum concentration (in mol/l) log S depends on Polarity of the compound (solvation free energy) Melting point T M, because dissolution of a substance implies breaking its crystal lattice (= melting) as a first step ph (different solvation free energies of ionic/ neutral form)

20 Simple Solubility Models A simple solubility model was suggested by Yalkowski and Valvani This simple model describes log S as a function of log P and T M : log S = 0,5 - log P 0,01 (T M 25) T M measures the contribution of melting/lattice energies, log P estimates the solvation free energy This simple equation is reasonably accurate, however, it requires the experimental determination of T M and log P for every compound Computational prediction of T M is rather difficult Yalkowski, Valvami, J. Pharm. Sci. (1980), 69, 912

21 Pharmacokinetic Properties log P, pk a (for acids/bases), and log S play a key role in the prediction of the pharmacokinetic properties of a compound Predicting pharmacokinetic properties is a nontrivial, but worthwhile, task Experimental determination of these properties is too expensive for large libraries (e.g., HTS libraries!) For many of these properties, simple additive models (increment models) have been developed These models assume that the property is given as the sum of the properties of the structural fragments contained in the compound

22 Prediction of log P We assume that the property of a molecule (e.g., log P) can be expressed as the contributions of groups log P = i a i f i where a i is the number of fragments of type i occurring in the structure and f i the fragment s contribution to log P This trivial approach works surprisingly well and can be further improved through the inclusion of correction factors These factors compensate for effects like interactions between fragments Fujita et al., J. Am. Chem. Soc. (1961), 86, 5179

23 ClogP One of the most widely used approaches for log P prediction is ClogP ClogP uses a library of fragment properties and correction factors Fragments are generated by decomposing the structures at isolating carbon atoms These atoms have neither double nor triple bonds to hetero atoms Leo, Chem. Rev. (1993), 93, 1281

24 ClogP ClogP now adds the contributions of the Fragments Isolating C atoms H-atoms on isolating C atoms Correction factors Corrections are introduced for special bonds or certain geometric corrections log P exp = aromatic isolating C aliphatic isolating C H on isolating C NH-C=O fragment Ortho substitution on a ring Rotatable bonds (without fragments) Bond to a benzyl residue Sum Leo, Chem. Rev. (1993), 93, 1281

25 ClogP ClogP now adds the contributions of the Fragments Isolating C atoms H-atoms on isolating C atoms Correction factors Corrections are introduced for special bonds or certain geometric corrections log P exp = aliphatic isolating C H on isolating C x OH x -F Branching w/ polar group Rotatable bonds x X-C-X interactions x X-C-C-Y interactions Sum Leo, Chem. Rev. (1993), 93, 1281

26 AlogP ClogP has problems with unusual fragments: there are no tabulated group contributions for those! Ghose and Crippen developed a method that is not based on fragment contributions, but on atom contributions ALOGP Each atom of the molecule is assigned one of 120 atom types log P is then simply the sum of all atom contributions ALOGP = i n i a i where n i is the number of atoms of type i in the structure and a i the contribution of type i to log P a i were determined from a large database of experimental log P values Ghose et al., J. Phys. Chem. A (1998), 102, 3762

27 AlogP vs. ClogP AlogP and ClogP yield comparable performance There are some differences with respect to molecular mass ClogP slightly better for smaller molecules, AlogP for larger ones Both methods are standard methods in computer aided-drug design and are being used widely Ghose et al., J. Phys. Chem. A (1998), 102, 3762

28 Prediction of Other Properties pk a values can be predicted in a similar fashion, although performance is worse Solubility is very difficult to predict Based on pk a prediction (ions usually have very negative solvation free energies) Solvation free energy is influenced drastically by the lattice energy Prediction of lattice energies is very tricky

29 QSPR Computational prediction of molecular properties is a field of its own within chemoinformatics: QSPR Quantitative Structure-Property Relationships The approaches discussed so far for the prediction of log P fall into this category A special case of QSPR is QSAR Quantitative Structure-Activity Relationships here we try to predict pharmacological properties in particular biological activity Both approaches require an encoding of the structure in a special form (e.g., number of fragments, atoms)

30 QSPR Representation of a structure by so-called descriptors Descriptors encode properties or aspects of the structures as numbers Based on these numerical representations of the structures, mathematical functions for the desired property are derived Structure Property Deskriptoren Descriptors

31 Descriptors Descriptors aim at encoding relevant features of a structure Simple descriptors are, for example, based on the presence, absence or number of certain functional groups or certain atom types = generalization of fingerprints (! lectures on 2D similarity) Other descriptors correspond to experimental properties of a compound, e.g., AlogP or ClogP, refraction index, Also experimental data of compounds is sometimes used as descriptors Disadvantage: data is often incomplete, cannot be computed

32 Descriptor Classes There are numerous (10,000+) descriptors that have been used in the literature Many of these descriptors are just minor variations of others Descriptors can be subdivided into roughly five classes 0D Simple counts (e.g., atom counts) 1D Fragment counts (2D fingerprints) 2D Topological (graph-based) 3D Geometrical and surface-based 4D 3D + sampling of conformations Both quality of the descriptors and computational cost increase from 0D to 4D

33 0D Descriptors The simplest descriptors count trivial properties of the structure Molecular weight (MW) Number of atoms Number of carbon atoms Number of heavy atoms Number of bonds Number of 3-/4-/5-/6-membered rings Number of aromatic rings... Although simple, these descriptors are very powerful and part of many QSPR models (MW, for examples, is essential for bioavailability!) Advantages Easy to compute Disadvantages No information on topology, geometry,...

34 1D Descriptors These descriptors correspond to structural fingerprints They count the number of certain fragments or atom types Number of sp 3 carbons Number of each of the Ghose&Crippen atom types Number of hydroxyl groups Number of H-bond donors Number of amino groups... These descriptors capture some key chemical features of the structure They are sufficient to predict some key properties based on increment models (AlogP is an example for this)

35 2D Descriptors 2D descriptors account for topological properties They are derived from the molecular graph of the structure They encode information on Size Branching Shape (topological, not geometrical!)... of the structures They are more expensive to compute than 1D descriptors, but still rather cheap

36 Wiener Index In 1947, H. Wiener observed that the boiling point of alkanes can be predicted based on their topology For n-alkanes this is trivial based on chain length alone, but not for branched alkanes For example, different nonanes have boiling points between 122 C (2,2,4,4-tetramethylpentane) and 150 C (n-nonane) Wiener proposed to model the boiling point as a linear function of two variables, p and w: T B = a p + b w + c with constants a, b, c Chain length Boiling points of n-alkanes Based on this simple model, he could predict boiling points with an accuracy of about 1 K

37 Wiener Index p is called polarity number, a 1D descriptor, counting the number of carbon-carbon pairs separated by exactly three bonds (C C C C) W, the path number, is a topological descriptor and is also called Wiener index w is the sum of lengths of all pairwise paths in the molecular graph 5 In acyclic alkanes this corresponds to the product of all atoms to the left and to the right of any bond D 1,2 = 1, D 3,5 = 3,... w = (1 4) + (4 1) + (3 2) + (4 1) = 18

38 Wiener Index There is a large number of generalizations of the Wiener index to make it applicable for cyclic structures as well A widely used definition is half the sum of the entries of the distance matrix of the molecular graph (= sum of all minimal pair-wise paths) Wiener index is often used if the degree of branchedness is relevant for a property It is also relevant for predicting pharmacological activities, e.g., there are models for carboanhydrase II inhibitor activity based on the Wiener index Saxena, Khadikar, Acta Pharm. 49 (1999)

39 Chi Indices Kier and Hall suggested several topological indices, the so-called chi indices Chi indices are based on the δ-value of an atom, which considers the number of bonds and the number of neighboring hydrogen atoms: δ i = #bonds - #H-atoms There are more complex definitions for δ i, However, we will not go into those details here. Note: this simple definition corresponds to the node degree in the heavy atom graph Example: δ(-ch 3 ) = 1 δ(-ch 2 -) = 2 δ(-nh 2 ) = 1 Kier, Hall: Molecular Connectivity in Structure-Activity Analysis, New York, Wiley, 1986

40 Chi Indices The series of chi indices considers paths of different lengths They are a measure of branching in the structure 1 χ considers only paths of length 1, 2 χ paths of length 2 etc. Along these paths, the products of δ-values are computed: Summation is performed over all atoms for 0 χ, over all bonds along the path for 1 χ etc. Kier, Hall: Molecular Connectivity in Structure-Activity Analysis, New York, Wiley, 1986

41 Chi Indices Structure # paths of length χ 1 χ 2 χ

42 Topological Indices There is a whole range of additional topological indices that have been applied successfully Topological indices are usually easy to compute Calculation is often based on the distance matrix of the molecular graph A disadvantage of topological indices is that they are unrelated to observable physical quantities They are particularly suitable, if properties like shape or degree of branching are expected to have an influence on the property predicted Other physical quantities (e.g., hydrophobicity, electrostatic properties) can be easily combined with topological indices

43 3D Descriptors 3D descriptors also consider molecular geometries They are typically based on a selected, energyminimized conformation Choice of this conformation has a significant influence on the descriptor values! 3D descriptors consider for example Intramolecular distances Bond lengths Shape and size of the structure Molecular surface areas... They may consider the geometry alone, but often also the distribution of properties with respect to the geometry (e.g., polarity of a surface)

44 3D Descriptors RDF The distribution of all intramolecular distances is captured by the radial distribution function (RDF) Because the distances are typically discrete, they are turned into a density function: B is a constant describing the width of the Gaussian contribution to the density function RDF is a one-dimensional description of the threedimensional geometry of a molecule

45 3D Descriptors RDF GE, p.416

46 3D Descriptors RDF Isomers and even conformers (which, by definition, yield identical 2D descriptors) can be distinguished using the RDF Disadvantage: RDF is a vector, not a single number Similar to RigFit, physicochemical properties can also be integrated into RDFs: where p i, p j are the respective values for the property of atoms i and j

47 3D Descriptors Surfaces Quite a number of descriptors are defined and computed via molecular surfaces Key idea Surface is the part of the molecule that interacts with the molecule s surrounding (including solvent and receptors) Properties of the surface are determined by the atoms beneath the surface Simple examples for descriptors Total surface area of the SES or vdw surface Fraction of the surface formed by H-bond donors...

48 3D Descriptors PSA A very popular surface-based descriptor is the polar surface area (PSA) The PSA is the area of the molecular surface that corresponds to polar atoms (O, N, H connected to O/N) PSA is a measure for the polarity of the molecule PSA can be computed topologically (TPSA topological polar surface area) This can be computed by adding up atom-based contributions as for AlogP PSA (red) for aspirin

49 4D Descriptors 4D descriptors compute the value of a 3D descriptor not just for one conformation, but for an ensemble of conformations Conformations are usually created by a simulation (molecular dynamics, Monte Carlo) Values obtained for the individual conformations are weighted by energies Advantage Not based on a single (arbitrary) conformation, thus more robust Disadvantage Computationally expensive, often little difference to the corresponding 3D descriptor

50 QSPR Not all descriptors are directly derived from the structure One can also use (QSPR-)predicted properties to predict other properties Deskriptoren Descriptors Eigenschaft Property Structure Property Deskriptoren Descriptors

51 Prediction of Drug-Likeness Based on descriptors one can develop simple models for a wide range of molecular properties In order to minimize attrition rate, one can predict the properties that are relevant for all relevant pharmacological properties These properties can also interact in complex ways One can also try to predict directly, how drug-like a given structures is, i.e., how likely it is to have all required properties

52 Lipinski s Rule of Five A compound has most likely unsuitable pharmacokinetic properties, if one of the following conditions holds: Molecular mass above 500 g/mol Contains more than 5 H-bond donors Contains more than 10 H-bond acceptors Log P > 5 These rules make a lot of sense from a pharmacological point of view: Number of H-bond donors/acceptors and log P capture the polarity/lipophilicity of the molecule Molecules that are too large will not cross membranes Lipinski et al., Adv. Drug Delivery Rev. (1997), 23, 3-25

53 Oral Bioavailability and PSA Another rule is based on an observation by Palm et al. Plotting oral bioavailability (fraction of the drug arriving in the blood after oral administration) shows a sigmoidal relationship with PSA Palm et al. suggested that compounds with good bioavailability should have a PSA below 140 Å 2 FA: fractional oral bioavailability (0 100%) Palm et al., Pharm. Res. (1997), 14, 568

54 Drug-Likeness Sadowski et al. and Ajay et al. independently developed the concept of drug-likeness Idea Something has to distinguish drugs from non-drugs Why predict individual properties of which we do not know how they relate to drug-likeness? Instead, predict drug-likeness directly If a suitable encoding (i.e., descriptors) can be found, machine learning should allow classification between drugs and non-drugs Sadowski, Kubinyi, J. Med. Chem. (1998), 41, 3325 Ajay, Walters, Murcko, J. Med. Chem. (1998), 41, 3314

55 Drug-Likeness Sadowski and Kubinyi considered compounds from two databases ACD Available Chemicals Directory (commercially available chemicals, in their vast majority not drugs, about 160,000 compounds) WDI World Drug Index (about 38,000 known drugs) Compounds also contained in WDI were removed from ACD to avoid problems

56 Drug-Likeness Classification into drug/non-drug based on ACD/WDI is not exact ACD contains derivatives of known drugs ACD WDI Some compounds from the WDI are rather unusual and not drug-like in the classical sense; instead they are very similar to fine chemicals

57 Drug-Likeness Structures were encoded using the AlogP atom types Of the 120 atom types of Ghose & Crippen, 92 turned out to be relevant Each molecule is encoded as a vector containing the number of atoms of each of the 92 types in the structure This vector then serves as input for the classification into drugs and non-drugs

58 Drug-Likeness Prediction based on an artificial neural network (ANN) Input: atom type vector Output: drug-likeness (0 = non-drug, 1 = drug-like) Topology: 92 x 5 x 1 (simple feed-forward ANN) WDI ANN Score ACD

59 Drug-Likeness 83% of ACD and 77% of WDI are classified correctly!

60 Drug-Likeness Ajay et al. chose a slightly different approach to predict drug-likeness Their comprehensive study uses data from ACD and CMC (Comprehensive Medicinal Chemistry) They removed all compounds from CMC that are not drugs as such (spermicidal compounds, propellants, ) Classification was done based on an artificial neural network as well Descriptors were the 166-bit ISIS keys (structural fingerprints) and seven additional descriptors Ajay et al., J. Med. Chem. (1998), 41, 3314

61 Drug-Likeness Descriptors ISIS keys contain information on 166 different structural fragments and are very popular for 2D similarity analysis as well Ajay et al. complemented the structural descriptors with seven descriptors that are most likely relevant for druglikeness: ClogP MW (molecular weight) # H-bond donors # H-bond acceptors # freely rotatable bonds Aromatic density (# aromatic rings/molecular volume) 2 κ α (a topological index similar to 2 χ) Note: among these descriptors are also all descriptors relevant for Lipinski s Rule

62 Drug-Likeness Results Artificial Neural Network (173 x 5 x 1) Trained on ACD/CMC Results: 90% of CMD classified correctly 90% of ACD classified correctly Good generalization Test with external dataset: MDDR (MACCS- II Drug Data Report) 80% of the MDDR structures were classified correctly

63 Drug-Likeness Results Design of a combichem library: 1,000 compounds given Can we select 100 of those for the screening such that we test only those sufficiently drug-like? Experiment 9,900 compounds from the ACD 100 compounds from the CMC 1% of the library is thus drug-like (ACD is supposed to be low in drug-like compounds) When the top 100 compounds are selected from this dataset with respect to their drug-likeness, 72% of the compounds are compounds from CMC! ) enrichment factor 72!

64 Summary During lead identification and optimization, candidates with poor pharmacokinetic properties need to be recognized early on Key properties in this context are log P, log S, and pk a Properties of compounds can be predicted using quantitative structure-property relationships (QSPR) QSPR models require the encoding of structures as numeric descriptors Simple models permit the modeling of some of the properties relevant for lead ID and optimization Other models permit the prediction of more complex properties (e.g., drug-likeness, which is useful in the design of screening libraries)

65 References Books [BKK] Böhm, Klebe, Kubinyi: Wirkstoffdesign, Spektrum 2002 [FHR] Forth, Henschler, Rummel, Starke: Allg. und spez. Pharmakologie und Toxikologie, BI Wissenschaftsverlag, 1992 [GE] Gasteiger, Engel (Hrsg.), Chemoinformatics A Textbook, Wiley, 2003 [Lea] Andrew Leach: Molecular Modelling: Principles and Applications, 2nd ed., Prentice Hall, 2001 [LG] Andrew Leach, Valerie Gillet: An Introduction to Chemoinformatics, Kluwer, 2003 [Mut] Mutschler, Geisslinger, Kroemer, Schäfer-Korting: Mutschler Arzneimittelwirkungen, WVG, Stuttgart, 8. Aufl., 2001