Drug Action 65
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Appendix I
Kinetic analysis of drug–receptor reactions The classical analysis of drug responses depends on the assumption that each drug molecule combines with a re-ceptor in a reversible manner, forming a drug–rere-ceptor complex, i.e.
D+ R k1
k2 D R
where D is the number of free (unbound) drug molecules, R is the number of free receptors, DR is the number of occupied receptor sites, k1the association rate constant and k2the dissociation rate constant. At equilibrium, the rates of association and dissociation are equal; if D, R and DR are expressed as molar concentrations (i.e. [D], [R]
and [DR]), then k1[D][R]= k2[DR]
and k2
k1
=[D][R]
[DR] = Kd
where Kd is the equilibrium dissociation constant and reflects the affinity with which drugs bind to receptors.
When Kdis high, there is a low affinity for drug receptors, and when Kdis low, there is high receptor affinity. In nu-merical terms, Kdrepresents the concentration of the drug required to occupy half the receptor sites at equilibrium.
If Rtis the total number of receptors, [Rt]= [R] + [DR]
and
[R]= [Rt]− [D R]
thus
Kd=[D][R]
[D R] =[D]([Rt]− [D R]) [D R]
and
[D]([Rt]− [D R]) = Kd[D R]
thus
[D][Rt]− [D][D R] = Kd[D R]
and
[D][Rt]= Kd[D R]+ [D][D R]
= [D R](Kd+ [D]) consequently
[D R]
[Rt] = [D]
Kd+ [D]
and
f = [D]
Kd+ [D]
since the fraction of receptors occupied ( f ) is given by f =[D R]
[Rt]
This equation (the Langmuir or Hill–Langmuir equa-tion) was originally derived by A.V. Hill in 1909. A similar relationship was used by Langmuir to characterize the ab-sorption of gases to metal surfaces.
Appendix II
arranged in the same manner. Isoflurane and enflurane are a well-known example of structural isomerism. Both drugs have the same molecular formula (C3H2Cl F5O), but individual atoms are not arranged in the same manner in relation to the common carbon atom structure of the two agents.
The actions of structural isomers may be relatively sim-ilar (e.g. isoflurane and enflurane), or their actions and uses may be quite different (e.g. promethazine and pro-mazine). Structural isomers do not usually present prob-lems of identification, since they are easily recognized as entirely different drugs, with distinctive names.
Tautomerism
In tautomerism or dynamic isomerism, two unstable structural isomers are present in equilibrium.
One isomer can be reversibly and rapidly converted to the other by physical changes (e.g. pH changes). In alka-line solution (pH 10.5), sodium thiopental is ionized and water-soluble. On injection into plasma (pH 7.4), the drug becomes non-ionized and undergoes tautomerism, thus increasing its lipid-solubility (Chapter 7).
Stereoisomerism
Stereoisomers are two or more different substances with the same molecular formula and chemical structure, but a different configuration, i.e. their atoms or chemical groups occupy different positions in space, and thus differ in their spatial arrangements. Stereoisomers can be classified into two main groups:
rEnantiomers
rDiastereomers
Enantiomers
Enantiomers (literally, substances of opposite shape) are pairs of stereoisomers that are non-superimposable mirror-images of each other. This type of stereoisomerism is dependent on the presence of a chiral centre in the molecular structure of certain drugs, which is usually a single carbon atom with four different substituent atoms or groups. Drugs with this type of structure (chiral drugs) have a mirror-image that cannot be superimposed on their original configuration, and they therefore exist as R (rec-tus) and S (sinistra) isomers. These two forms are distin-guished by the orientation of different substituents around the chiral centre. Enantiomers are also optically active and can rotate polarized light to the right (the (+) or (d) form) or the left (the (−) or (l) form). Individual isomers are
therefore referred to as R(+), S(−), R(−) or S(+) isomers.
Equal mixtures of the two forms (racemic mixtures), with the prefixes (±) or (dl), have no optical activity.
Diastereomers
Diastereomers are pairs of stereoisomers that are not enan-tiomers (i.e. not mirror images). Diastereomers charac-teristically have different physical and chemical proper-ties. For example, they do not have the same melting point or solubility, and they do not take part in chemi-cal reactions in the same manner. Some of the stereoiso-mers of atracurium, mivacurium and tramadol are diastereomers.
Differences between stereoisomers
In terms of stereoisomerism, anaesthetic agents can be divided into four main groups (Table 3.11).
rAchiral drugs
rDrugs administered as single stereoisomers
rDrugs administered as mixtures of two stereoisomers
rDrugs administered as mixtures of more than two stereoisomers
There may be differences in the pharmacodynamic activ-ity and pharmacokinetic properties of individual isomers.
Although R and S isomers have the same structure, they have a different configuration, i.e. their substituent groups occupy different positions in space. Consequently, the two enantiomers may form different three-dimensional rela-tionships in the asymmetric environment of receptors and enzymes, which are almost entirely composed of l-amino acids with stereoselective properties. In these conditions, there may be differences between the R and S enantiomers, since their relationship with specific receptor sites and en-zymes may not be identical.
There are often differences in the potency of individual enantiomers, for example, S(+)-isoflurane is slightly more potent than its R(−) enantiomer, while S(+)-ketamine is 3–4 times more potent than R(−)-ketamine. Occasion-ally, one stereoisomer is almost inactive, and l-atropine, l-noradrenaline and l-adrenaline are approximately 50–
100 times more potent than their d-enantiomers. When differences in potency are present, they are often expressed by the stereo-specific index (eudismic ratio), which rep-resents the relation between the activity of the more ac-tive isomer (the eutomer) and its less acac-tive antipode (the distomer). Stereo-specific indices of 100 or more are not uncommon and may be due to differences in either the affinity or the intrinsic activity of individual enantiomers.
Drug Action 67
Table 3.11 Some achiral and chiral drugs that are commonly used in anaesthetic practice.
Chiral
Achiral One isomer Two isomers More than two isomers
Propofol Etomidate Thiopental Mivacurium
Nitrous oxide Ropivacaine Ketamine Atracurium
Tetracaine Levobupivacaine Halothane
Lidocaine Cisatracurium Isoflurane
Fentanyl Pancuronium Desflurane
Alfentanil Vecuronium Prilocaine
Remifentanil Morphine Bupivacaine
Pethidine Hyoscine Atropine
Neostigmine Tramadol
Edrophonium Dobutamine
Dopamine Glycopyrronium
Although some chiral drugs are administered as single isomers, most of them are used as equal, racemic mixtures of two enantiomers.
There may also be important differences in the type of pharmacological activity produced by the enantiomers.
Thus, one isomer may be an agonist, while its enantiomer is a partial agonist or competitive antagonist.
There are also differences in the metabolism and phar-macokinetics of individual stereoisomers, and one enan-tiomer may be more rapidly metabolized than its antipode.
R(+)-propranolol, R(−)-prilocaine and S(+)-ketamine are more rapidly metabolized than their enantiomers, and have a greater intrinsic hepatic clearance. Paradox-ically, the metabolism of S(+)-ketamine is inhibited by R(−)-ketamine, and this may account for the relatively prolonged action of the racemic mixture. Some inac-tive enantiomers undergo unidirectional metabolic con-version (‘incon-version’) to their antipodes. R(−)-ibuprofen and R(−)-ketoprofen are converted to their active S(+)-enantiomers in the intestine and the liver, which are 100–
160 times more potent than their R(−)-enantiomers. Both S(+)-ibuprofen and S(+)-ketoprofen are now used clin-ically as single isomer preparations (dexibuprofen and dexketoprofen).
Differences in the metabolism and disposition of the R and S enantiomers of many chiral drugs may affect their pharmacokinetics, and individual drug enantiomers may have different half-lives, clearances and volumes of distri-bution (Chapter 2).
Practical considerations
Many anaesthetic agents are normally administered as chi-ral mixtures of two stereoisomers or more complex iso-meric mixtures. In many instances, there are differences in the pharmacodynamic properties and pharmacokinetic behaviour of the individual isomers (e.g. ketamine, bupi-vacaine and atracurium). Occasionally, the enantiomers of chiral drugs have different but complementary actions, and both stereoisomers make an important contribution to the overall pharmacological profile of the drug (e.g.
tramadol, dobutamine). The use of these drugs as chiral mixtures is clearly essential.
In other instances, the use of stereoisomeric mixtures has been widely accepted, although it appears to have few practical advantages. Recent progress in chemical tech-nology has greatly simplified the separation and prepa-ration of individual stereoisomers by asymmetric chem-ical synthesis, or by chiral inversion of one enantiomer.
In addition, drug regulatory authorities in many coun-tries have encouraged the introduction of new drugs as single stereoisomers. Consequently, since 1990 most new drugs have been introduced as single enantiomers, and in some instances previously available mixtures have been re-introduced as single stereoisomers (e.g. atracurium, bupi-vacaine). In the future, it seems likely that this trend will continue.