BIOINF 4372 Drug Design 2 Oliver Kohlbacher & Jens Krüger

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1 BIOIN 4372 Drug Design 2 Oliver Kohlbacher & Jens Krüger Summer QSAR Part I: MoCvaCon, Basics, Descriptors Overview A"ri%on rate in drug discovery Relevant pharmacokine%c proper%es log P, pka, solubility Predic%on of molecular proper%es (QSPR) Examples: ClogP, AlogP Descriptors Classifica%on 0D and 1D descriptors Topological (2D) descriptors 3D and 4D descriptors Predic%on of drug- likeness 2 ailure in Late Development Discovery Number of Candidates 10 Preclinical Clin. Phase I 8 Clin. Phase II 6 Clin. Phase III Market years After: Lipper, Modern Drug Discovery, 1999, 2 (1),

2 ailure in Late Development Number of Candidates Discovery Preclinical Clin. Phase I Clin. Phase II Clin. Phase III Market years After: Paul et al. Nat Rev Drug Discov, 2010, 9, ailure in Late Development 90% of all drug candidates fail between discovery and introduc%on to the market The late development phases are the most expensive phases In a study from 1988, Pren%s et al. found that in more than 60% of the cases, poor pharmacokinecc (PK) or toxicological properces were the cause Reason for ailure 6% 31% 22% 41% Market Toxicity PK Efficacy Prentis et al., Br. J. Clin. Pharmacol. 1988, 25, ailure in Late Development More recent studies find that this problem has changed since Currently PK and bioavailability play a minor role This is mostly due to improved tes%ng, but quite likely also due to improved computa%onal models for these proper%es The problem of toxicity has increased as well, we will discuss methods for addressing this issue later Kola & Landis, Nat Rev Drug Discov. 2004;3(8):

3 Consequences for Discovery Biol. Data Target ID Lead ID Optimization Trials Approval Lead ID Restrict search space to candidates with good pharmacokinecc properces Exclude compounds with poor proper%es from virtual screening campaigns Lead opcmizacon Improve efficacy (µm! nm) Reduce side effects Improve pharmacokineccs 7 Reduce AXriCon Rate ail early, fail cheap The earlier unsuitable candidates are removed from the pipeline, the more money can be saved. If drugs with unsuitable proper%es can be removed in an earlier development phase, the a"ri%on rate in the late (expensive) development phases can be reduced Which properces does a good drug need? How to predict these proper%es? 8 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 9

4 AbsorpCon and EliminaCon Gehirn Parenteral Blood-Brain Barrier Biliary Central Compartment Renal Absorption Elimination Enteral Membranes of the GI Tract 10 Experimental QuanCCes An important pharmacokine%c property is the distribucon coefficient n- octanol/water P: P = k 1 /k 2 where k 1 and k 2 are rate constants for the transi%on 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 11 DeterminaCon of log P log P is a measure of lipophilicity of a compound log P can be determined by measuring the change of concentracon in a three- phase system H 2 O/octanol/H 2 O Compound is ini%ally dissolved in water (A) and distributes over the octanol phase (B) into the second water phase (C) In equilibrium, concentra%ons of the compound are constant in all three phases BKK, p

5 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 13 log P and log k Biological barriers are not simply lipid membranes Distribu%on 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 permea%on 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 respec%ve biological barrier 14 log P and log k In experiments, one observes more or less well- defined maxima for log P as a func%on of log k Each barrier has an opcmal lipophilicity, where log k is maximal or this log P uptake across the barrier is most effec%ve or 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 Intestinal absorption Organic membrane BKK, p

6 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 protona%on 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 Absorp%on of a drug thus dras%cally depends on the protona%on state Bioavailability is consequently influenced by the ph of the surrounding medium 16 Acid- Base Equilibrium Protona%on/deprotona%on is an equilibrium process as well and it is coupled to the distribu%on equilibrium Protona%on is described by the protonacon constant K a and its respec%ve nega%ve 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 17 ph Profiles Acid AH Amino acid protonated base B + Ion pair Anion A - Dibasic acid Plolng log P as a func%on of ph yields ph- dependent absorp%on profiles These profiles indicate ph ranges that are suitable for absorp%on BKK,p

7 Enteral AdministraCon Most common route of administra%on, easiest for pa%ents Absorp%on through gastrointes%nal (GI) tract Oral cavity 0.02 m 2 Stomach m 2 Small intestine m 2 Different parts of the GI tract differ in their surface area Strong dependence on stomach content Colon m 2 Rectum m 2 After HRS, p Enteral AbsorpCon 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 intes%ne differ in their ph Uptake of acids and bases thus occurs in different regions of the gastrointes%nal tract Distribu%on and protona%on of a compound depend on the pk a /pk b of its protonatable groups BKK p Solubility Solubility of a compound is important, because it limits its bioavailability Insoluble substances are not taken up aner the disintegra%on of a dosage form Substances with low solubility might be unable to achieve sufficient (effec%ve) concentra%on in vivo Solubility of a substance is typically given as log S, the logarithm of its maximum concentra%on (in mol/l) log S depends on Polarity of the compound (solva%on free energy) MelCng point T M, because dissolu%on of a substance implies breaking its crystal lalce (= mel%ng) as a first step ph (different solva%on free energies of ionic/neutral form) 21

8 Simple Solubility Models A simple solubility model was suggested by Yalkowski and Valvani This simple model describes log S as a func%on of log P and T M : log S = log P 0.01 (T M 25) T M measures the contribu%on of mel%ng/lalce energies, log P es%mates the solva%on free energy This simple equa%on is reasonably accurate, however, it requires the experimental determina%on of T M and log P for every compound Computa%onal predic%on of T M is rather difficult Yalkowski, Valvami, J. Pharm. Sci. (1980), 69, PharmacokineCc ProperCes log P, pk a (for acids/bases), and log S play a key role in the predic%on of the pharmacokine%c proper%es of a compound Predic%ng pharmacokine%c proper%es is a non- trivial, but worthwhile, task Experimental determina%on of these proper%es is too expensive for large libraries (e.g., HTS libraries!) or many of these proper%es, simple addi%ve models (increment models) have been developed These models assume that the property is given as the sum of the proper%es of the structural fragments contained in the compound 23 PredicCon of log P We assume that the property of a molecule (e.g., log P) can be expressed as the contribu%ons 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 contribu%on to log P This trivial approach works surprisingly well and can be further improved through the inclusion of correccon factors These factors compensate for effects like interac%ons between fragments ujita et al., J. Am. Chem. Soc. (1961), 86,

9 ClogP One of the most widely used approaches for log P predic%on is ClogP ClogP uses a library of fragment proper%es and correc%on factors ragments are generated by decomposing the structures at isola%ng carbon atoms These atoms have neither double nor triple bonds to heteroatoms OH NH O Leo, Chem. Rev. (1993), 93, ClogP ClogP now adds the contribu%ons of the ragments Isola%ng C atoms H- atoms on isola%ng C atoms Correc%on factors Correc%ons are introduced for special bonds or certain geometric correc%ons log P exp = 0.86 NH O 6 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, ClogP ClogP now adds the contribu%ons of the ragments Isola%ng C atoms H- atoms on isola%ng C atoms Correc%on factors Correc%ons are introduced for special bonds or certain geometric correc%ons log P exp = 1.66 OH 3 aliphatic isolating C H on isolating C x OH x Branching w/ polar group Rotatable bonds x X-C-X interactions x X-C-C-Y interactions Sum Leo, Chem. Rev. (1993), 93,

10 AlogP ClogP has problems with unusual fragments: there are no tabulated group contribu%ons for those! Ghose and Crippen developed a method that is not based on fragment contribu%ons, but on atom contribu%ons ALOGP Each atom of the molecule is assigned one of 120 atom types log P is then simply the sum of all atom contribu%ons ALOGP = i n i a i where n i is the number of atoms of type i in the structure and a i the contribu%on 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, AlogP vs. ClogP AlogP and ClogP yield comparable performance There are some differences with respect to molecular mass ClogP slightly be"er 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, PredicCon of Other ProperCes pk a values can be predicted in a similar fashion, although performance is worse Solubility is very difficult to predict Based on pk a predic%on (ions usually have very nega%ve solva%on free energies) Solva%on free energy is influenced dras%cally by the lalce energy Predic%on of lalce energies is very tricky 30

11 QSPR Computa%onal predic%on of molecular proper%es is a field of its own within chemoinforma%cs: QSPR Quan7ta7ve Structure- Property Rela7onships The approaches discussed so far for the predic%on of log P fall into this category A special case of QSPR is QSAR Quan7ta7ve Structure- Ac7vity Rela7onships here we try to predict pharmacological proper%es in par%cular biological accvity Both approaches require an encoding of the structure in a special form (e.g., number of fragments, atoms) 31 QSPR Representa%on of a structure by so- called descriptors Descriptors encode proper%es or aspects of the structures as numbers Based on these numerical representa%ons of the structures, mathema%cal func%ons for the desired property are derived Structure Property Deskriptoren Descriptors 32 Descriptors Descriptors aim at encoding relevant features of a structure Simple descriptors are, for example, based on the presence, absence or number of certain funcconal groups or certain atom types = generaliza%on of fingerprints (! lectures on 2D similarity) Other descriptors correspond to experimental properces of a compound, e.g., AlogP or ClogP, refrac%on index, Also experimental data of compounds is some%mes used as descriptors Disadvantage: data is onen incomplete, cannot be computed 33

12 Descriptor Classes There are numerous (10,000+) descriptors that have been used in the literature Many of these descriptors are just minor varia%ons of others Descriptors can be subdivided into roughly five classes 0D Simple counts (e.g., atom counts) 1D ragment counts (2D fingerprints) 2D Topological (graph- based) 3D Geometrical and surface- based 4D 3D + sampling of conformacons Both quality of the descriptors and computa%onal cost increase from 0D to 4D 34 0D Descriptors The simplest descriptors count trivial proper%es 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 aroma%c rings... Although simple, these descriptors are very powerful and part of many QSPR models (MW, for examples, is essen%al for bioavailability!) Advantages Easy to compute Disadvantages No informa%on on topology, geometry, D 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 proper%es based on increment models (AlogP is an example for this) 36

13 2D Descriptors 2D descriptors account for topological properces They are derived from the molecular graph of the structure They encode informa%on on Size Branching Shape (topological, not geometrical!)... of the structures They are more expensive to compute than 1D descriptors, but s%ll rather cheap 37 Wiener Index In 1947, H. Wiener observed that the boiling point of alkanes can be predicted based on their topology or n- alkanes this is trivial based on chain length alone, but not for branched alkanes or example, different nonanes have boiling points between 122 C (2,2,4,4- tetramethyl- pentane) and 150 C (n- nonane) Wiener proposed to model the boiling point as a linear funccon of two variables, p and w: T B = a p + b w + c with constants a, b, c Based on this simple model, he could predict boiling points with an accuracy of about 1 K T B / C Chain Kettenlänge length Boiling points of n-alkanes 38 Wiener Index p is called polarity number, a 1D descriptor, coun%ng 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 In acyclic alkanes this corresponds to the product of all atoms to the len 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 39

14 Wiener Index There is a large number of generaliza%ons of the Wiener index to make it applicable for cyclic structures as well A widely used defini%on 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 onen used if the degree of branchedness is relevant for a property It is also relevant for predic%ng pharmacological ac%vi%es, e.g., there are models for carboanhydrase II inhibitor ac%vity based on the Wiener index Saxena, Khadikar, Acta Pharm. 49 (1999) 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 defini%ons for δ i, however, we will not go into those details here. Note: this simple defini%on 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, 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: Summa%on 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,

15 Chi Indices Structure # paths of length χ 1 χ 2 χ Topological Indices There is a whole range of addi%onal topological indices that have been applied successfully Topological indices are usually easy to compute Calcula%on is onen based on the distance matrix of the molecular graph A disadvantage of topological indices is that they are unrelated to observable physical quancces They are par%cularly suitable, if proper%es like shape or degree of branching are expected to have an influence on the property predicted Other physical quan%%es (e.g., hydrophobicity, electrosta%c proper%es) can be easily combined with topological indices 44 3D Descriptors 3D descriptors also consider molecular geometries They are typically based on a selected, energy- minimized conforma%on Choice of this conformacon 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 onen also the distribu%on of proper%es with respect to the geometry (e.g., polarity of a surface) 45

16 3D Descriptors RD The distribu%on of all intramolecular distances is captured by the radial distribucon funccon (RD) Because the distances are typically discrete, they are turned into a density funccon: B is a constant describing the width of the Gaussian contribu%on to the density func%on RD is a one- dimensional descripcon of the three- dimensional geometry of a molecule 46 3D Descriptors RD GE, p D Descriptors RD Isomers and even conformers (which, by defini%on, yield iden%cal 2D descriptors) can be dis%nguished using the RD Disadvantage: RD is a vector, not a single number Similar to Rigit, physicochemical proper%es can also be integrated into RDs: where p i, p j are the respec%ve values for the property of atoms i and j 48

17 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) Proper%es of the surface are determined by the atoms beneath the surface Simple examples for descriptors Total surface area of the SES or vdw surface rac%on of the surface formed by H- bond donors D 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 contribu%ons as for AlogP PSA (red) for aspirin 50 4D Descriptors 4D descriptors compute the value of a 3D descriptor not just for one conforma%on, but for an ensemble of conformacons Conforma%ons are usually created by a simula%on (molecular dynamics, Monte Carlo) Values obtained for the individual conforma%ons are weighted by energies Advantage Not based on a single (arbitrary) conforma%on, thus more robust Disadvantage Computa%onally expensive, onen li"le difference to the corresponding 3D descriptor 51

18 QSPR Not all descriptors are directly derived from the structure One can also use (QSPR- )predicted proper%es to predict other proper%es Deskriptoren Descriptors Eigenschaft Property Structure Property Deskriptoren Descriptors 52 PredicCon of Drug- Likeness Based on descriptors one can develop simple models for a wide range of molecular proper%es In order to minimize a"ri%on rate, one can predict the proper%es that are relevant for all relevant pharmacological proper%es These proper%es 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 proper%es 53 Lipinski s Rule of ive A compound has most likely unsuitable pharmacokine%c proper%es, if one of the following condi%ons 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,

19 Oral Bioavailability and PSA Another rule is based on an observa%on by Palm et al. Plolng oral bioavailability (frac%on of the drug arriving in the blood aner oral administra%on) shows a sigmoidal rela%onship with PSA Palm et al. suggested that compounds with good bioavailability should have a PSA below 140 Å 2 A dyn. PSA [A 2 ] A: fractional oral bioavailability (0 100%) Palm et al., Pharm. Res. (1997), 14, Drug- Likeness Sadowski et al. and Ajay et al. independently developed the concept of drug- likeness Idea Something has to dis%nguish drugs from non- drugs Why predict individual proper%es 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 classifica%on between drugs and non- drugs Sadowski, Kubinyi, J. Med. Chem. (1998), 41, 3325 Ajay, Walters, Murcko, J. Med. Chem. (1998), 41, 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 57

20 Drug- Likeness Classifica%on into drug/non- drug based on ACD/WDI is not exact ACD contains deriva%ves of known drugs HO ACD O OH COOH HO WDI O OH COOH Cl O O Some compounds from the WDI are rather unusual and not drug- like in the classical sense; instead they are very similar to fine chemicals EtO O OEt O 2 N NO 2 O 58 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 classifica%on into drugs and non- drugs COOH O O CH Drug- Likeness Predic%on based on an arcficial 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 ACD ANN Score 60

21 Drug- Likeness 83% of ACD and 77% of WDI are classified correctly! 61 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, ) Classifica%on was done based on an ar%ficial neural network as well Descriptors were the 166- bit ISIS keys (structural fingerprints) and seven addi%onal descriptors Ajay et al., J. Med. Chem. (1998), 41, Drug- Likeness Descriptors ISIS keys contain informa%on 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 drug- likeness: ClogP MW (molecular weight) # H- bond donors # H- bond acceptors # freely rotatable bonds Aroma%c density (# aroma%c 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 63

22 Drug- Likeness Results Ar%ficial Neural Network (173 x 5 x 1) Trained on ACD/CMC Results: 90% of CMD classified correctly 90% of ACD classified correctly Good generaliza%on Test with external dataset: MDDR (MACCS- II Drug Data Report) 80% of the MDDR structures were classified correctly 64 Drug- Likeness Results Design of a combichem library: 10,000 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! 65 Summary During lead iden%fica%on and op%miza%on, candidates with poor pharmacokine%c proper%es need to be recognized early on Key proper%es in this context are log P, log S, and pk a Proper%es of compounds can be predicted using quan%ta%ve structure- property rela%onships (QSPR) QSPR models require the encoding of structures as numeric descriptors Simple models permit the modeling of some of the proper%es relevant for lead ID and op%miza%on Other models permit the predic%on of more complex proper%es (e.g., drug- likeness, which is useful in the design of screening libraries) 66

23 References Books [BKK] Böhm, Klebe, Kubinyi: Wirkstoffdesign, Spektrum 2002 [HR] orth, Henschler, Rummel, Starke: Allg. und spez. Pharmakologie und Toxikologie, BI Wissenschansverlag, 1992 [GE] Gasteiger, Engel (Hrsg.), Chemoinforma%cs A Textbook, Wiley, 2003 [Lea] Andrew Leach: Molecular Modelling: Principles and Applica%ons, 2nd ed., Pren%ce Hall, 2001 [LG] Andrew Leach, Valerie Gillet: An Introduc%on to Chemoinforma%cs, Kluwer, 2003 [Mut] Mutschler, Geisslinger, Kroemer, Schäfer- KorCng: Mutschler Arzneimi"elwirkungen, WVG, Stu"gart, 8. Aufl.,