Prodrug design

Pharmac. Ther. Vol. 14, pp. 25 53 © Pergamon Press Ltd 1981. Printed in Great Britain

0163-7258/81/090 -0025505 00,/0

Specialist Subject Editors: M, ROWLANDand G. TUCKER

PRODRUG

DESIGN

ROBERT E. NOTARI College of Pharmacy, The Ohio State University, 500 W. 12th Avenue, Columbus, Ohio 43210, U.S.A.

1. INTRODUCTION 1.1.

BACKGROUND AND DEFINITION

Although Albert (1958, 1964) and Harper (1959) discussed the concept of prodrugs in the late 1950's, it was in the early 1970's that marked world-wide attention was directed to this area, as a potential approach to improving drug therapy. There appears to be general agreement on the prodrug concept but there is no strict universal definition for a prodrug itself. In this review, it is assumed that a prodrug is an inactive compound, formed by intentionally linking a drug to an inert chemical by a covalent bond, which may be broken (by any mechanism) to yield drug itself in vivo (Fig. 1). This differs somewhat from other definitions which (a) have included poorly soluble salts or complexes, (b) have not ruled out prodrug activity, (c) have limited the reversal mechanism to metabolism, (d) have included formation of active metabolites from compounds thought to be drugs or (e) have included derivatives which were not intended to be prodrugs when devised. Other terms used interchangeably with prodrugs include reversible or bioreversible derivatives and latentiated drugs. While definitions are arbitrary, and to some degree irrelevant, it is significant that throughout this review prodrugs are assumed to be inactive. As is often pointed out, examples of prodru~s orecede the discussion and introductinn of the concept of prodrugs by at least 50 years. Metbenamlne dates back to the late 19th century and relies on the formation of formaldehyde in urine for its antiseptic effect. Although aspirin is also cited as an early prodrug of salicylic acid, it remains controversial whether or not the unhydrolyzed ester has analgesic properties itself. One of the major attractions of the prodrug concept is that (theoretically at least), if the prodrug itself is inactive and the disposable moiety is inactive, the pharmacology and toxicology should be limited to that of the original drug and are presumably already known. If reversal is either instantaneous in plasma or occurs before absorption then circulating prodrug may be negligible and only the inert chemical formed by reversal need be a concern. The advantage of improving on a drug by

I Drug

Bioreversible Link

In

Inert chemical

patient"

FIG. 1. The drug is covalently bonded to an inert chemical to form an inactive prodrug, which can be chemically or metabolically converted to drug and disposable moiety after administration to the patient. 25

26

ROBERT E. NOTARI

covalent linkage to an inert chemical, while maintaining the original drug action, may also be the source of the main limitation of the approach. That is, how many known drugs can be considered as candidates for prodrugs? Indeed, there are relatively few drugs which have the necessary functional groups to produce bioreversible bonds. In addition to the fact that improvements cannot always be expected from such linkages, there are also a limited number of chemical covalent bonds which can be considered bioreversible. (These are discussed below, Section 1.3). Thus, while the prodrug approach does offer one possible technique to improve the characteristics of a parent drug, it is not a universal approach. In spite of these limitations however, it can often be the optimum approach. 1.2. REASONS FOR PRODRUGS

The list of reasons for preparing prodrugs is just as long as the list of general pharmaceutical and pharmacokinetic problems associated with drugs. In most cases, at least one example of a prodrug can be found to justify each item being included in the list. A brief summary of typical goals is given in Table 1. The examples given are too simplistic in that the goals are often inter-related. For example, increasing stability to stomach acid might be a means of increasing oral bioavailability. Or, decreasing solubility might allow the formulation of an intramuscular depot form which increases duration. Regardless of the specific prodrug goal, one goal is common to all prodrug design. As soon as the prodrug has completed its job it should be TABLE 1. Brief Summary of Typical Goalsfor Prodru9 Design and Examples of Each~ Goal

Pharmaceutical Drug

Improve Taste

Chloramphenicol

Goal

Nicotonic Acid

amide

Ampicillin

Hetacillin

diaminoketal

Prednisolone

Prednisolone Sodium Succinate Erythromycin Ethyl Succinate

hemiester

Site Specificity Decreased Side Effects

Clindamycin

Erythromycin

Pharmacokinetic Drug

Increased Oral Absorption Increased Topical Penetration Extend Duration

Linkage

Chloramphenicol Palmitate Clindamycin Palmitate Clindamycin Phosphate Nicotinamide

Clindamycin Decrease Pain on Injection Decrease GI Irritation Increased Stability Increased Solubility Decreased Solubility (for suspension)

Prodrug

Prodrug

ester ester phosphate ester

hemiester

Linkage

Ampicillin

Pivampicillin

ester

Triamcinolone

Triamcinolone Acetonide Fluphenazine Decanoate Dromostanolone Propionate

ketal

Fluphenazine Dromostanolone (breast carcinoma) Chloral hydrate Aspirin and N-acetyl-paminophenol

ester ester

Dichloralphenazone

complex b

Benorylate

ester

aFor more complete lists of prodrugs see references in Section 1.3 particularly Sinkula and Yalkowsky (1975) and Notari (1973). bin this review only covalent linkages are considered as prodrugs.

Prodrug design

27

quantitatively converted to drug. If the specific goal is to resist stomach acid, then ideally the prodrug should revert to drug in the intestines. If the specific goal is to increase absorption in the GI tract, then the prodrug should convert to drug on entering the bloodstream. Inherent in these statements is the limitation imposed earlier, that prodrug p e r se is not the active species. Therefore, once the specific task is achieved, intact prodrug represents unavailable drug. 1.3. PRODRUG CANDIDATES AND PRODRUG CONVERSION

A known drug having a single disadvantage, which would be improved by achieving one of the goals in Table 1, represents an ideal prodrug candidate provided a reversible derivative can be synthesized. Sinkula and Yalkowsky (1975) have summarized the possible enzyme-reversible prodrug linkages as: aliphatic esters, carbonate esters, hemiesters, phosphate esters, sulfate esters, amides, amino acids, azo linkages, carbamates, phosphamides, glucosiduronates, N-acetylglucosaminides, and fl-glucosides. Although the list is short the list of prodrug linkages commonly employed is much shorter. By far the most widely used prodrug linkage is that of an ester wherein the original drug provides either the carboxylic acid or the hydroxyl group. Add to this the phosphates, carbonates and hemiesters and one has accounted for the large majority of prodrugs. Not included in this list, however, is the large number of derivatives which are capable of chemical conversion from drug precursor to drug (as in cyclocytidine and hetacillin). These prodrug linkages have not yet been cataloged but are discussed only as individual cases when they are observed. While enzyme-mediated conversion of prodrugs to drug appears to severely limit the possibilities, it is not yet possible to speculate as to the potential for chemically mediated prodrug reversal. As alluded to in the previous section the best site for prodrug reversal will depend upon the goal for which the prodrug was designed. Ideally, the prodrug should be converted to drug as soon as the goal is achieved. Obviously this ideal may need to be compromised. The various ester-hydrolyzing enzymes, for example, are widespread throughout the gut, intestinal mucosa, liver, blood, kidney and other tissues. The goal therefore becomes one of optimizing rate differences. An ester, for example, does not undergo hydrolysis at a constant rate throughout its passage from stomach to intestines to blood. These rate processes are subject to structural effects. If increased absorption is the goal, then esters are chemically modified and tested to find the prodrug which best survives the stomach and intestines, is absorbed to the greatest extent and then produces the most drug in the plasma. Conversely, if the duration of drug in the plasma is to be extended, then this optimization plan must be changed. Some of the pharmacokinetic schemes associated with the administration of prodrugs together with the optimization of rates to achieve specific goals are discussed in Section 2. 1.4. SYMPOSIA AND REVIEWS

This review is designed to provide an overview of prodrugs and particularly to present, for the first time, an orderly catalog of the possible pharmacokinetic schemes, equations and limiting cases (Section 2). It is not an attempt to survey all of the work that has been reported in the field of prodrugs. Several other reviews and symposia have already summarized that literature. Some of those are annotated here for those interested in more extensive surveys. Several chapters in the series 'Drug Design' consider prodrugs and report many case studies (Ariens, 1971). Ariens also discusses the concept referring to the inert portion of the prodrug as the disposable moiety. Several reviews by Sinkula (197.5 and 1979) and Sinkula and Yalkowsky (1975) present a large number of referenced examples together with reviews of structural relationships with partitioning theory

28

ROBERT E. NOTARI

which are not mentioned in this review. An early recognition of the pharmacokinetic aspects of prodrug design and evaluation can be found in the articles by Notari (1973, 1975). The presentation in Section 2 is an extension of that theory together with a detailed analysis of the pharmacokinetic aspects delineated later (Notari 1977, 1980). A symposium on Pharmacokinetics and Drug Effects, Stockholm, Nov. (~8, 1974 provided several papers which examined the role of structure on pharmacokinetic properties with some consideration of prodrugs. Abstracts have been published (Teorell, 1974). Interest generated by that meeting probably stimulated the 1976 symposium on Bioactivation and Controlled Drug Release, Stockholm, April 21 23, in which prodrugs played a prominent role (Danielsson, 1976). The American Chemical Society sponsored a symposium (Atlantic City, 1974) on Pro-drugs as Novel Drug Delivery Systems which was then published as a book (Higuchi and Stella, 1975). The text contains two chapters which are reviews and four chapters providing detailed discussions of prodrugs of phenytoin, epinephrine and cytotoxic agents for parenteral use. The American Academy of Pharmaceutical Sciences held a symposium on Design of Biopharrnaceutical Properties through Prodrugs and Analogs which was published as a book (Roche, 1977). Of the 15 chapters, 7 deal in part or wholly with prodrugs. Unique among the presentations that relate to prodrugs are chapters on enzyme-substrate specificities in prodrug design, physical organic approach to prodrugs, percutaneous delivery by prodrugs, and taste properties through structural modification. 2. PHARMACOKINETICS 2.1.

GENERAL SOLUTIONS FOR COMPARTMENTAL MODELS

Scheme I presents a general linear pharmacokinetic model for the absorption k,'l and subsequent conversion (kc) of intact prodrug where PD, represents the prodrug remaining at the site of administration

k~,,l

k',~

k'l. |

k'Lj /'h

Aa

X

>PDI Z - - - - "

PDa

kol

L

I I I

k~

>A1 (

,,4/

>Aj

k~,,l Scheme I

as a function of time following an initial extravascular (ev) dose, Dcv. Prodrug and drug in the blood (compartment 1) are represented by PDI and AI respectively. Elimination of drug by all routes is represented by kxo while k'lo represents loss of prodrug to any process other than conversion to drug. Loss of prodrug and drug from the absorption site to processes which compete for absorption is designated by k'ao, and kao, while prodrug conversion at the site of administration is kc,. The rate constants for distribution of drug and prodrug throughout n compartments are shown as k l j , kj.t and k~j, k)x respectively. To date, the use of this scheme (or part of it) has been adequate to describe the blood time course for drug (A1) and prodrug (PD1) following ev or intravenous (iv) administration of prodrug. In this section, equations will be derived for PD1 and A1 as a function of time under a variety of conditions arising from Scheme I. In Section 2.2 these equations will be simplified under limiting

Prodrug design

29

conditions which apply to ideal kinetics for specified goals. The application of the general models and the limiting cases in literature examples will be discussed in Section 3. This discussion will be limited to models behaving according to first-order kinetics (linear systems), where a rapid iv dose (D) of drug may be described by either a one-compartment model, wherein the amount of drug in the body is defined by A = D'e

-kt

(1)

or a two-compartment model A2

kl2 T+ k21 kJO AI

>

Scheme II wherein the amount of drug in compartment 1 is defined as A1 = Al.1 exp [-- ),it] + A1.2 exp [ - ,,].2/]

(2)

where 21, 22 are the large and small exponential coefficients. Additional variations, such as three-compartment models or elimination from other than compartment 1, will not be covered but may be derived by the reader through extension of the approaches illustrated here. Although the chemical similarity between drug and prodrug suggests that their pharmacokinetic behavior might be related, this is not a requirement. Presumably the prodrug has been designed to improve upon some pharmacokinetic (or other) limitation of the drug. It is therefore inherently different. If one assumes that a prodrug may be described by either a one- or two-compartment model and that it might be administered by either i.v. or e.v. routes, then eight models are required to describe all of the possible permutations and combinations. Since the molecular weight of the prodrug will be greater than that of the drug it will be assumed that mass is expressed on a molar basis. The derivations in this section result in equations for either the total mass in the body (PD or A) or the mass in compartment 1 (PD1 or AI) depending on the model. Conversion to molar concentration may be achieved by dividing the PD or A equations by the volume of distribution of prodrug (V') or drug (V), and the PD1 or A1 equations by the appropriate volume of compartment 1 (V~ or V~). Conversion of prodrug to drug will be assumed to behave kinetically as though it occurred in compartment 1. This would not apply to those prodrugs designed to be converted in specific organs or tissues. For simplicity, it will be assumed that absorption following ev administration of prodrug occurs primarily via the prodrug. 2.1.1. A One-compartment-model Druq Formed after an i.v. Dose of a One-compartmentmodel Prodru9 This is the simplest of the eight schemes. After administration of an i.v. bolus dose (D) D

L

>PD

Scheme III

k,

>A

ROI~ERT E. NOTARI

30

of prodrug (PD), the amount of prodrug remaining in the body (PD) is described by (3)

PD = D. e -k''

where D is the dose of prodrug administered, k' is the elimination rate constant of the prodrug, made up of kc the first-order rate constant for conversion to drug and k,c, the rate constant for loss of prodrug by other routes. The time course for drug may be described by k~.,PD(O)

A-

~[~ K ~

_

le k,_ e-k,,

(4)

where k is the elimination rate constant for the drug. The fraction of the dose which is converted to drug is defined f~

=

(5)

kj'k'

2.1.2, A One-compartment-model Drug with First-order Absorption of a One-compartmentmodel Prodrug A;

k,

PDa

) PD

)A

k.r,

Scheme IV Here the dose of prodrug, D, is administered by an ev route. The first-order absorption rate constant is k~ while k'~o represents competing first-order loss of prodrug at the absorption site. The amount of prodrug remaining at the site of administration (PD,t as a function of time is given by PD, = D.exp[-(k~, + k'~0)t]

(6)

If part of the initial dose is not available to participate in this rate expression then Eqn (6) becomes PD° = f . D .exp [ - (k'~ + k'~o)t]

(7)

where f is the fraction of the dose whiich is available to be absorbed or lost. Of that afnount available to participate, i.e. f,D, only f~ = k'J(k', + k'~o) is absorbed. Thus, the bioavailability fraction, F, of prodrug is defined (8)

f.k', F = f - f ~ - (k'o + k'~0)

For simplicity, throughout the remainder of this presentation, f will be assumed equal to unity so that F = f~. The time course for prodrug and drug in the body are respectively PD =

k'~D

[ e x p [ - k ' t ] - exp [ - (k', + k'~o)t] ~

(9)

(k'o + k'oo - k')

t

xpE2 tk,° + k'oolt3i k'~o)]

A = k'ok~D [k' - ~ - - k ~ o ] [ k ~ - ~ e - k "t

e - kt

)

+ [(k'~ + k'~o) - k'][k - k'] + [(k'~ + k'.o) - k][k' - k]~

(lO)

Prodrug design

31

Thus, fac, the fraction of the original dose, D, which is both absorbed and converted to drug is defined

k'ok~ f.c = f.f~ - k'(k'. + k'.o)

(11)

which is the product of Eqns (5) and (8) with f = 1. An example showing the time course for PDa, PD, A and the sum of (PD + A) is shown in Fig. 2. 2.1.3. A Two-compartment-model Druo Formed after an i.v. Dose of a One-compartmentmodel Prodrug A2 D,

k~

k12T~k21

I )PD

)A1

'

Scheme V The time course for prodrug in the body (PD) is described by Eqn (3). The equation for the amount of drug in compartment 1, AI is A1 = kcD~ (k21 - )oxle-Z" (k21- 22)e ~ a 2 ' (k11-,k')e -'k''', ~(22 - ~ - k ' Z ~ ) + (2, - 22)(k' - 22) + (2, Z k ) ~ 2 : k)J" where

(12)

)q,)t2 = 0.5[(k,2 + k21 + klo) +_ x/(k,2 + k2, + klo)2 - 4k21k,o] Equation (12) may be converted to concentration by dividing both sides of the equation by the volume of compartment 1 (VI). 2.1.4. A Two-compartment-model Drug with First-order Absorption of a One-compartmentmodel Prodrug A2

kl2 k'. eOa,, k'oO

k2t

k, ) PD

k~ lg

)A1

k~° ~

Scheme VI

I POo

O

Time FIG. 2. A typical example of an e.v. dose of prodrug as defined in Scheme |V. The molar a m o u n t is shown as a function of time for PD. [Eqn (6)], PD [Eqn (9)], A [Eqn (10)], and the total [T = A + PD] where f.c = 1 [Eqn (I1)] and the ratio of the rate constants (in time -1) is k'./kc/k = 4/2/1.

32

ROBERT E. NOTARI

The a m o u n t of p r o d r u g remaining at the ev site as a function of time, P D , , is defined by Eqn (6). The time course for p r o d r u g in the body, P D , is described by Eqn (9). The equation for the time course for A 1, the a m o u n t of drug in c o m p a r t m e n t 1, is (k21 - ) q ) e

+ (21 +

~''

(22 _ 21)[(k,] + k,o ) _ 21](k, _ 21)

A1 = k'~k~D

-

(k21 - 22)e ~ ' 22)(k'. + k'ao - 22)(k' - ).2)

(k21 - k'. - k ' . o ) e x p [ - ( k ' . + Go)t] [()q - (k'. + k'~o)] [22 - (k'. + k'~o)] [k' - (k'. + k'~o)] (k21

k')e -(k')' ,

-

l

(13)

+ (21 - k')(22 -- kO(k~+-k~o - k') ) 2.1.5. A T w o - c o m p a r t m e n t - m o d e l

D r u g F o r m e d a f t e r an i.v. D o s e o f a T w o - c o m p a r t m e n t -

model Prodrug PD2

A2

k~,

k~

i,, t

O

1,2~

i,

/

) A1

Scheme VII In Scheme VII the a m o u n t of p r o d r u g in the central c o m p a r t m e n t is represented by and that in the peripheral by P D 2 . First-order elimination of p r o d r u g from c o m p a r t m e n t 1 is designated by the rate constant k'lo and conversion by k¢. The time course for p r o d r u g in the central c o m p a r t m e n t is similar to that for drug in Eqn (2) and m a y be written PD1

PD1 = PDl,l exp[-2'lt

] + PD1,2 e x p [ -

(14)

2'2t]

where *t

P D I . 1 = (k'21

-

i

A1)/(A2

.t

~t

--

/41)

PD1,2 = (k'21 - 2'2)/().'2 - 2'1)

and

V

2'1,2 ~ = 0.5L(k'12 q- k~l + k'lo + k c ) + _ \

(k'12 + k21 + k'lo + kc) 2

] 4k21(k'lo + /,',)J

T h a t for drug in its central c o m p a r t m e n t is correspondingly given by + ((~2

- - J-1)(~-'l - - fi-lJ(')-2

'~1)

(k21 - 22)(k~1 - 22)e -;'~ 6:-1 - 22)(2'1 - 22)().~ - 5.2)

(k21 - 2'z)(k'zl - ;'/2)e - ~''~' (k2, - ,~'~)(k~ - 2'Oe -x~' + (,;-1 -- 2'1)(22 -- ).',)(2~ -- /-'l) q- (;.1 - ;/2)(22 - 2'2)(2'1 - ;.'2))

(15)

Prodrug design

33

2.1.6. A Two-compartment-model Drug with First-order Absorption o f a Two-compartmentmodel Prodrug PD2

A2

o+ o+ )PD 1

PD.

) A1

Scheme VIII The dose of prodrug remaining at the site of administration (PD.) as a function of time is described by Eqn (6). The corresponding equations for the amount of prodrug (PD1) and drug (A1) in their respectively central compartments are given by ik i ' ~ 2 ' , ) e x p [ _ 2 ' , t ] + (k~,-21)exp[-21t ] [ ( ~ + k.o 2- ),, )(z~ ~ ,.~) (k'. + k'.o - ;tl)(2' , - 21)

PD1 = k'.D~

+ % ,_- 5_ 5 _k'oo exj-(k;+ 'ooltl ()~, - k. - k~,o)(22

k'. 2 k~o) J

(16)

and A1 = k'okcD {(k'~

(ki~ - )~i )(k2~ - 2'~) exp [ - 2it] + k'ao -

;-'~)(;-i -

;~i)(;-,

-

;/,)(;~2

-

2i)

(k~x - 2~)(k2~ - 2~)exp [ - 2~t]

+

(k; + k'oo - ; . i ) ( ; . i - ;4)(;~, - ;4)(;~2 - ~ i )

(kll - ;q)(k21 - 2 1 ) e x p [ - ;qt]

+

(k'o + k'.o -

+

)~ )(;tl -

2~ )(;~i -

;-~ )(;~2 -

;~)

(k'21 - 22)(k21 - 2 2 ) e x p [ - 2 2 t ] (k'~ + k'~o - 22)(2'1 - 22)(2~ - 22)(21 - 22)

(k~,l -- sk'~ k', ~- k',o)exp[-(k,' - - -- , , k',o)(k21 - - ~ - - - ,-- - - . - - ~ - ~ - - - ~ - -+- k,'o)t ] + (;'

l

(17)

_2 k~ - kao)(X 2 - ka - kao)(Z ~ - ka - kao)(Z 2 -- ka - k'.o ) 1

2.1.7. A One-compartment-model Drug Formed after an i.v. Dose o f a Two-compartmentmodel Prodrug PD2 I,'..

th

Scheme IX In this scheme the time course for prodrug in the central compartment is given by Eqn 04). That for drug in the b o d y is: A J.P.r.

k

D[(< k'21 - ~'q ) e x p [ - ) - ' l t ] c

~4/1/ c

[

]-2~---2-~-22

2'~--)

(k21 - 2 ~ ) e x p [ - 2 ~ t ] +

(2', - 21)(k - 21)

(k~l - k ) e x p [ - k t ] ) > +

(2'1

~

--k-)

)

(18)

ROBERJ E. NOJARI

34

2.1.8. A One-compartment-model Drug with First-order Absorption of a Two-compartmentmodel Prodrug PD2

~"

)Pil

)i

Scheme X The amount of prodrug remaining at the site of administration is given by eqn (6), that for PDI by Eqn (16) and that for the amount of drug in the body, A, by t A

=

k'akcD

-

(k~l (k',, +

k)exp[-kt]

k',, o -

(k~t + (k'. + k'.o -

k)().',

-

k)(,~'2 -

k) +

(k' a

(k'2~ - Z D e x p [ - Z t t ] -F k'ao - /~',)(,~,~ - ,,~.'t)(k

-

~-'1)

;.~)exp[- ),~,t] ;j)I;/t

-

;~){k -

;~)

(k~, - k,~ - k;0)exp[-(k; + k,'0)t ] "~ + (k - k', ~ /~'a0J[),;t ~ k," - k'aOii2~ -- k f - k ~ o ) J~

(19)

2.2. RAPID SYSTEMIC CONVERSION

A prodrug intended for parenteral use may be designed to increase stability, solubility or patient acceptability (as in the case of decreased pain on injection). The prodrug approach may also be employed to increase the oral bioavailability of a poorly absorbed drug. In both cases, instantaneous systemic conversion of prodrug to drug would be ideal since circulating prodrug represents an inactive species which may also be eliminated intact (Fig. 3). Ideally, an orally administered prodrug should increase the amount and/or the rate of absorption relative to the parent drug. Therefore it should not result in significant presystemic conversion to the less bioavailable drug.

P

D

a

~

T

A

PD

F Time (a)

(b]

FK;. 3. Time course for molar amounts in Scheme 1V when absorption (k~,) and systemic conversion (k,) are both moderately rapid, ha',ing the rate constant ratio of k'.:k~ k = 50,'251 and 1., = 1 [Eqn (111]. The time scale for Fig. 3a has been expanded tenfold relative to that in Fig. 3b. f h e protile for PD versus time is apparent initially since k'. > k~. The total I T = A + PD] is indistinguishable from A after the initial period since kc > k. The condition kc > k'. > k [Eqn (25)] will be examined in Fig. 4.

Prodrug design

35

TABLE 2. Relationship between Equations Describing a Rapid i.v. Dose of Drug and the Approximate Equations for the Concentration of Drug in the Plasma (C) Following e.v. Administration o f a Prodrug which undergoes Rapid Absorption and Systemic Conversion or i.v. Administration of Prodrug with Rapid Systemic Conversion. a Scheme II1, IX V, VlI IV, X VI, VIII

Route

General Eqn. No.

C -

Approx. Eqn. No.

i.v. i.v. e.v. e.v.

(4), (18) (12), (15) (10), (19) (13), (17)

fcC(0)e -k' fc{C1 e -a'' + C21e-x*} f , cC(O)e -k' f.c{Cle -a'' + C2e-a211

(2t) b (22) ~ (25) b (26) ¢

aSee text preceding each approximate Eqn for detailed explanation of the assumptions leading to their derivation. bC(0) represents the expected intercept value following a rapid i.v. injection of a 1-compartment drug, wherein C(0) = D/V. cCl and C2 are the coefficients associated with 21 and 2 z when a 2-compartment-model drug is administered by rapid i.v. injection: Cl = D AH/I/~ ; C2 = D. A 1,2/V 1.

Imposing these restrictions on the general equations of Section 2.1 leads to the simplified forms summarized in Table 2. The following discussion describes the assumptions leading to these approximations. 2.2.1. Prodrugs for Rapid iv Administration with Rapid Conversion Schemes III (Section 2.1.1), V (Section 2.1.3), VII (Section 2.1.5) and IX (Section 2.1.7) represent the general cases for rapidly administered i.v. doses of prodrug. For maximum availability of drug, an ideal prodrug would convert immediately to drug so that the concentration of circulating prodrug would rapidly become insignificant in relation to that of drug. The limits that are possible for the fraction of prodrug converted to drug, fc = k~/(k'), are 0 ~
kcD {exp [ - kt] - exp [ - (k')t] } (k' - k)V

(20)

To achieve a high drug concentration, with an insignificant concentration of circulating prodrug, let kc >> k. Within a short period of time the concentration will be approximated by C--- (l ~ keD e x p ][ - k t ]

= , (f~DvI - /exp[-kt]

(21)

Dividing Eqn (1) by V gives C = C(O)e -k' where C(0) = D/V. This is related to the approximation (Eqn 21) by fc as shown in Table 2. Scheme V (Section 2.1.3) gives rise to Eqn (12) for drug in compartment 1. If prodrug conversion is much faster than the terminal exponential for drug itself (kc >> 22) and k~ >> 21, then as e x p [ - ( k ' t ) ] - * 0 , Eqn (12) approaches -

-(~22 Z ~

+

(/.1 - &)

J

(22)

36

ROBERTE. NOTARI

which may be expressed as concentration by dividing by VI. Dividing Eqn (2) by Va provides C = C~ e x p [ - Z l t ] + C 2 e x p [ - Z z t ] . The relationship of this expression to Eqn (22) is shown in Table 2. Scheme VII (Section 2.1.5) represents the case where both drug and prodrug are described by two-compartment models. The time course for drug in compartment 1 is given by Eqn (15) wherein the exponents are 21, 22, )-'1 and £~. Assuming that prodrug conversion is much faster than its distribution allows one to impose the condition (kc + k'10) ~ (k'12 + k~l). Substituting various numerical values for kc, k'lo, k'12 and k; 1 in Eqn (14) will quickly demonstrate that if (k~ + k'10) >> (k'lZ + k~l), then )L1 ", (k c 4- klo) >~ 22 - k21.Yhus, asz2---*k21,then(k21 - z/) 0, [(k~l - / ~ l ) / ( z / - 2 1 ) ] --~ 1, [(k~l - 22)/(2~ - Zz)] --~ 1 and Eqn (15) becomes A1

~-

~(k21- £,)exp[-)~it] ,:1)(,~, 2)~)~)

k~O I (Z2

( k 2 , - 22)exp[-)~2t]~ (2, 22)()Jl - ,-2) )

+

(23)

If it is further assumed that 2'1, (which is approximated by 2'1 -~ kc + k'lo ) is sufficiently large to satisfy the condition 2'1 >> 21, then Eqn (23) collapses to Eqn (22). Scheme IX (Section 2.1.7) gives rise to Eqn (18) which describes the amount of drug in the body as a function of time. Assuming that (kc + k'ao) >> (k'12 4- k~l ) results in 2'1 ~ (k~ + k'~o) ~ Z~ -~ k~l as discussed above in Eqn (23). As e x p [ - ) ) l t ] - - * 0 and (k~a - )~)---~0, Eqn (18) approaches the limit ~(

( k'21 - k)e-*'

~) _

A -~ k~,~ (2~ -- #)()-~z~ k ) J

k~D e - k '

(24)

(k~ + k;o)

since prodrug conversion is assumed to be much faster than drug elimination making k~ >> k. Dividing by V and substitutingfc = k~/(k~ + klo), yields Eqn (21). 2.2.2. Prodrugs f o r Increased Bioavailability and Rapid Conversion Schemes IV (Section 2.1.2), VI (Section 2.1.4), VIII (Section 2.1.6) and X (Section 2.1.8) represent the general cases for first-order absorption of an e.v. dose of prodrug. The previous discussion regarding the value for fc (Section 2.2.1) would also apply here. In addition, fa = k',/(k'~ + k'~o), would also have the limits 0 ~> k, k~ > k'a and dividing by V results in Eqn (10) approaching

C -

k, k c D e - k , (k'~ + k'oo)k'V

-

.f . L • D e --k, V

(25)

which approximates the drug time course after the initial period (Fig. 4). Equation (25) is related to C(0)e -kt by factors as previously shown for Eqn (22) (Table 2). Scheme VI (Section 2.1.4) gives rise to Eqn (13) for the time course of drug in compartment 1. Assuming k'~ >> ),1 and kc > k~ provides k'~kcD _(k21--)q)expEA1 - k'(k'a + k',,o) ((}-2 - 21)

Zxt] + (k21 = - - - ---

-~2) e x p [ - ) . 2 t ] t ./

(Zl - )-z)

(26)

and C, by dividing by V1. This equation may be related to the Eqn for i.v. administration of drug as shown in Table 2. Scheme VIII (Section 2.1.6) provides Eqn (17) which defines drug in compartment 1 as a function of time. Assuming k'~ >> 21, k~ > k,~ and (kc + k'~0) >> (k~2 + k~l ) yields A1

k'ok~D ~ ~ -),1! 4L (k21- £ 2 ) e x p [ - X 2 / ] } (k'o + k',o)(21(22 - )q) expE-)~lt] 2'1(21 - / - 2 )

(27)

Prodrug design

37

Da

I O Time

la)

(b)

FIG. 4. A comparison of the true time course for A in Scheme IV [Eqn (I0)] to that predicted by Eqn (25) where A* = CV. The time scale in Fig. 4a is tenfold that of Fig. 4b. The ratio of the rate constants is k'a/kc/k = 250/2500/1 and f = = 1. PD,,, PD and A are defined by Scheme IV. There is no observable difference between the time course for A and that for the total [ T = A + PD] after the initial period.

since 2'1 2 (kc + k'xo) >> 2~ - k~l. Substituting (kc + k'~o) for 2'1 again results in Eqn (26). Scheme X (Section 2.1.8) results in Eqn (19) for the time course of drug in the body. Assuming k'a >> k, kc > k',, and (kc + k'~o) >> (k'~2 + k~)yields

A ~- k'kcD

(k" -----'~7s7'~'+ k~o)(;q)(;~2 - k)

(28)

which may be divided by V and written as Eqn (25) since 2~-~ (kc + k~o) and (k~1 - k) --_ ().~ - k).

2.3. PRODRUGS DESIGNED TO PROLONG PLASMA D R U G CONCENTRATION DURATION

Byron and Notari (1976), in a systematic analysis of the 'flip-flop' phenomenon, determined that the first-order absorption rate constant, ka, should have the limit 3ka < 2z in order that the terminal phase of the time course for drug in plasma be a function of k a instead of 2~, the terminal exponent of drug, when given as an i.v. bolus dose. If a prodrug is meant to significantly extend the duration of drug, then the ratio R = krds/~.z, krd s being the rate constant of the rate-determining step, must be minimized (Byron et al., 1978). However, if the dose size is held constant then a plot of duration as a function of R passes through a maximum value. The value for R corresponding to this maximum represents an optimum ratio, Ropt, for that set of conditions. Either an increase or a decrease in R will result in a shorter duration (Fig. 5). Byron et al. (1978) and Notari et al. (1978) have established methods for calculating the optimum rate-determining prodrug input rate c o n s t a n t (kopt) to provide the maximum duration from a fixed bioavailable dose, when response can be associated with a minimum effective concentration (MEC) of drug in the plasma. In that treatment Ropt, defined as kopJ2z, may be estimated from the quotient (Q), Rop t ""

e/Q

(29)

provided Q >/8. When all of the prodrug is bioavailable in terms of formation of circulating drug then Q is defined

Q=

PD ..... [MEC] [ V]

(30)

38

ROBERT E. NOTARI 80

6O A

50

~4o 3o 2O D

E

10 0

=G 0

0.02

I 0.04

I

0.06

0.08

0.10

0.12

0.14

R = krd s / X z

FIG. 5. Duration of time during which arug concentration will be above various MEC values (increasing from A to G) following a fixed dose of prodrug as a function of t h e ratio. R = krd~/2~. This treatment assumes that either k', or kc is rate-determining and that the non-limiting rate constants are much greater than k~o~. Drugs conveying both one-compartment and two-compartment characteristics were described by the higher curve in each MEC simulation and the lower curve was required to accommodate the two-compartment-model for drug, wherein both k]2 and k2z were 0.1 k~o. Data adapted from Byron et al. (1978) with permission of the publisher.

where PDa,ma x is the mass of prodrug at the site of administration, following a single dose or the maximum accumulated during the steady state in multiple dose therapy of fixed dose and fixed interval r. As pointed out earlier (Section 2.1), all units of mass are normalized on a molar basis which also applied here both to PD . . . . . and MEC. The values for MEC and 2= are properties of the drug itself. The value of PDa . . . . is limited by practical considerations such as the largest acceptable accumulation of mass in the muscle (i.m.), or the largest mass that can dissolve and be absorbed before it is TABLE 3. Summary of Approximate Equations ~ for Concentration of Drug in the Plasma (C) followiny Administration of Prodruos, which extend Drug Duration through Rate-limiting Absorption (k',) or Systemic Conversion (k~). The approx. Eqn is:

C ~- XIR~Dv]exp[-kobJ]= X I ~ ] e x p [ - k o b J ] Eqn No. Gen Approx

Scheme

Route

III V

i.v. i.v.

(4) (12)

(32) (32)

VII

i.v.

(15)

(41)

IX

i.v.

(18)

(41)

IV, X VI, VIII IV VI

e.v. e.v. e.v. e.v.

(10),(19) (13), (17) (10) (13)

(44) (44) (46) (46)

VllI

e.v.

(17)

X

e.v.

(19)

kob~

R = (k~d~/2,)

X

CL

(kc + k,,,.) (kc + k,,,.)

kc/k kc/22 kc/22

1 1

kV 22 V 22 V

(kc + k'~0) (I+K) (kc + k'~o) (1 + K )

1 I+K 1 1 +K

kc/k

kV

(k'~ + k'~o) (k'a + k'~o) (kc + k,,~)

k',,/k k'a/.)~2 kc/k

fi fc .f,

kV ,)~2V kV

(kc + k,~)

kc/',;~2

f,

22 V

(54)

(kC(l++k'XO)K)

k~/22

,(1-+K "1~ ,)

)~2V

(54)

(k,+k'lO+)(l K)

kc/k

(

kV

aSee text accompanying the approximate Eqns for a detailed discussion of the assumptions.

Prodrug design

39

excreted (oral). Once P/),,m~ is set, Q is fixed and there is, only one optimum value for the rate-determining first-order input of drug, kop,, as estimated by Eqn (29). This kopt value must represent the rate-determining step in the scheme, krds. In terms of the models in Section 2.1, the input function which may be made k~d~ can be k~ (Schemes III, V, VII and IX) or either k', or k~ (Schemes IV, VI, VIII and X). By imposing the restriction that either k', or k c is rate-determining the general equations in Section 2.1 can be written in terms of R = krds/~.z where one ratio, namely Rop, = kopt/;t~, will provide the maximum duration for each set of PD ..... and MEC values. Table 3 summarizes the approximate equations which apply when either k', or kc r e p r e s e n t krd s. The details leading to these limiting cases are discussed in the following sections. 2.3.1. Prodrugs for Rapid i.v. Administration with Rate-determining Conversion (k~) Schemes III (Section 2.1.1), V (Section 2.1.3), VII (Section 2.1.5) and IX (Section 2.1.7) represent rapid i.v. injections of prodrug. In each case k~ would have to become krd ~ in order to prolong the duration, during which drug concentration would exceed the MEC. Ideally fc should approach 1 but this may not be required in order to gain an advantage. Obviously, iff~ ~ 0 then a suitable drug concentration may be impossible to attain. The following simplifications will assume that f~ is sufficiently large to provide an effective drug plasma level. This simplification is equivalent to prohibiting the condition wherein k,c ~> k~. Therefore, when it is stipulated that a rate constant, k~, has the relationship, k~ ,> k~, then it is also assumed that k~ ,> k,~ and therefore k~ ,> k'. Equation (4) represents the time course for drug in the body in Scheme III (Section 2.1.1). If k~ = k~d~then k ~> k~ and dividing by V gives

(k~D~

C - \k-V] exp[-(k'.t)]

= RC(O)e -(k'°

(31)

where (kc/k) = R and D/V = C(0) following a rapid i.v. dose. Equation (31) may also be written C -~

e -k'' = [ ~ - £ ] e -

(32)

since CL = kV, where CL is the total body clearance of the drug. Equation (12) defines drug in compartment 1 of Scheme V (Section 2.1.3). Setting ~-2 ~> kc means that ;~1 "> kc so that A1 will approach

A1 ~- k¢D{ (k21- k')e-k't} (33)

~1~ 2

Here as k21 > ~-2, it follows that k21 ~ k c. Using the identity by V1 and substituting ;t2 V for klo V1 yields C ~ [_ktoV1J e-(k'O

[2~FJ

/].1,~2 ~--- kE1klo ,

dividing

(34)

which may also be written as Eqn (32) where R = kc/22 and 3.2V = CL. Scheme VII (Section 2.1.5) results in Eqn (15) for drug in compartment 1. Assuming (ki2 + k'21) ,> (kc + klo) in Eqn (14) results in the following observations: ~-1 -----ki2 + k~l

(35)

2~ - (kc + klo)/(1 + K)

(36)

where K -- k'12/k'21. Therefore if kc = krd~ and (k'12 + k21) ~ (kr + k'lo), it follows that

40

ROBERT E. NOTARI

2'1 >>)~'z, 22 >>k,,, 21 > k~, 21 > 2~, 22 > 2~ and as e x p [ - 2 1 t ] , e x p [ - 2'1t] all approach zero, Eqn (15) becomes

exp[-£2

A1 ~- k~Dt(k21- 2'2)(k'zl - 2'2)exp[-£'2t] I 2~ 2z).'1

t]

and

(37)

Since k21 > 22 and 22 >> 2~, then k21 >> 2~. Dividing by V1 and applying the identity 2122 = klok21 yields

k~D fk~l - , ~ t exp [ _ 2 ~ t ]

C -~ klo V1 -

21

-

t

(38)

For clarity, R will be defined as krd~/2~ in all cases. Equation (381 can be made to comply by expressing it in terms of k~/2 z instead of k~/kao. Substitution for 2~ from Eqn (36) allows the following simplification

{k'2~-2'2.}k'zl{(k'~2+k'2,)-(k~+k~o)l 21

-

(k',2 + kl,)2'1

(39)

which is approximately equal to k'21/(k'zl + k'1z) since (k'12 + k~l) >2>(kc + k'lo) and 2] "~ (k'12 + k'zl) [Eqn (35)] and may be rewritten as 1 21

Substituting for 2h [Eqn (36)] and

--

1+ K

(k~x -- 2 ~ ) / 2 ' 1

(40)

[Eqn (40)] together with the identities

kloV 1 = 2zV = CL allows Eqn (38) to be rewritten as RD +

+ K )t~ = [(1 k~D K)CL]exp[-(ki

+ K ° ) t ] (41,

where R = kd2z. Equation (18) represents the time course for drug in the body in Scheme IX (Section 2.1.7). Assuming (k'12 + kh~) >> (k¢ + k'~o) provides the approximations given in Eqns (35) and (36) together with 2'1 >> 2~ and k >> 2~ since k >> k~. Therefore dividing by V yields

C - kcC(O)k I~k'2a2'1--2~} e x p [ - 2 ~ t ]

(42)

where C(0) = D/V. Applying the approximations given in Eqns (36) and (40) results in Eqn (41) where R = k~/k and CL = kV. 2.3.2. Prodrugs for Oral or i.m. Administration with Either Rate-determining Absorption (k'a)

or Systemic Conversion (kc) In a series of consecutive first-order rate processes one step may become rate-limiting if it is sufficiently slow relative to the others. In Section 2.3.1 the i.v. administration of prodrug prolonged drug duration by changing the rate-determining step from elimination of drug to the systemic conversion of prodrug. If a prodrug designed for increased duration is administered by an e.v. route then rate-determining absorption or conversion will extend drug duration. Thus, in Schemes IV, VI, VIII and X, either k'a or kc may become kras (Fig. 6). The following simplifications will assume reasonable values for f~ and f,. This prohibits k,~ >> k~ and also k',o >>k'a. Scheme IV (Section 2.1.2) results in Eqn (10) for the time course of drug in the body. Assuming that k >> k'~ ~ ke and dividing by V gives

C~- k'~kcOexP[k.k,.V-(k',,+ k'~o)t] = RfcC(O)exp [-(k'a + k'~o)t]

(43)

Prodrug design

41

2O

0 =E

210 0 0

TIME

FIG. 6. Illustration of effect of rate-limiting k,~ on the time course for drug (A) in Scheme IV, where f~c = 1 and the ratio of the rate constants is k'a/kc/k = 1/400/40. Curve 1, which represents A versus time following an i.v. dose of prodrug, shows the effect of kc/k = 10. The remaining curves represent e.v. doses of prodrug. The curves are labelled as to dose size relative to curve 1.

where R = k',/k,fc = kc/k' and C(0) = D / V . Equations (10) and (43) are compared in Fig. 7. Since C L = kV, Eqn (43) may be written C "~

e x p [ - ( k a + k'ao)t] =

L CL_l

e x p [ - ( k o + k'~0)t]

(44)

Similarly, assuming k >> kc < k'~ and dividing Eqn (10) by V yields k'akcD e - k't C ~- k(k'~ + k'.o)V - R f ~ C ( O ) e x p [ - k ' t ]

(45)

which may be written C "~

e -k't=

L~Je

(46)

where R = kc/k, C L = k V and C(0) = D / V . Scheme VI (Section 2.1.4) results in Eqn (13) for drug in compartment 1. Assuming 22 >> k'. < kc results in A1 _". k'akcO(k21 - k', - k'o0)exp[-(k'~ + k'ao)t]

k212z

~_.:PD

.,•P/D

A

0

(a)

Time

(b)

FIG. 7. Illustration of the use of Eqn (43) to approximate the time course for drug (A) in Scheme IV when k,> k~' < k c. Fig. 7a shows the time course for PDa, PD and A when f,c = 1 and the ratio k'/kc/k = 1/400/40. PD appears to be at the baseline since the ratio kc/k'~ = 400 is sufficient for steady state. The ordinate in Fig. 7b has been expanded 40-fold which allows comparison of the time course for A versus time in Fig. 7a [Eqn (10)] to the approximation, A*, obtained using Eqn (43) where A* = CV.

(47)

42

ROBERTE. NOTAR1

Since kza > 2 2 and 22 >> k'~ then k21 >> k'~. Using the identity 2122 = k21klo , dividing by V~ and substituting 22V for k~oV~ gives Eqn (44) where R = k'./22 and CL = 22V. Similarly, if22 >> kc ~ k'a then Eqn (13) approaches A1 -~

k'~kcD (k21 ) e - k',

(48)

213.2(k'. + k'~o)

which on similar treatment gives Eqn (46) where R = k J 2 2 and CL = 22 V. Equation (17) describes drug in compartment 1 in Scheme VIII (Section 2.1.6). Assuming 22 ~ k'a <~ 2~ leads to t

A1 -

t

k'.k~D(k'zl - k'a - k'.o)(k21 - k. - k ~ o ) e x p [ - ( k "

t

t

+ k.o)t]

(49)

;:12~).122

But k~a > 2~ and k21 > 22 so that k~a >> k, and k2~ >> k', which after dividing by Va and substituting based on the identities 2'~2~ = k'2~(k'lo + kc) and 2t22 = k21kxo gives C -~

k'~kcD

e x p [ - ( k ; + k'~o)t]

klo(k'lo + kc)Vl

(50)

After substituting 22 v for k l o V l Eqn (50) may be written as Eqn (44) where R = k'~/22 and C L = 22 V. Ifkc is rate-limiting in Scheme VIII then it may be assumed that (k'~2 + k~) ~> (k¢ + k'ao) which again provides the approximations associated with Eqns (35) and (36). Thus, 2~ -~ (kc + k'~o)/(1 + K) becomes rate-determining and Eqn (17) approaches A1 ---

k'~kcD(kl ~ - )~i)(k2,

~-i)exp [ - 2~t] (k'. + k'.o - 2~)(2', - 2~)(2, - 2~)(22 - hl) --

(51)

is further reduced by considering the relative magnitude of )~ to ~

"

'

A1 - f a k c O k z l ( k 2 1

-

,~i)

exp[-,:~t]

(52)

212122

Dividing by V1 and substituting using 1/(1 + K) -- (k~ 1 - 2~)/2'1 [Eqn (40)],)~122 and 22 V = k~o V~ provides C

~--

(1 +okcD2vJeXpL_ 1 F

ff i +T-2 klo)tJ]

=

k 10k21

(53)

which may be expressed as C-~

(1 +K-)

exp

--k i~ ~)tj

=

(1 + K ) C L

exp -

i ; K/tJ

(54)

where R = kc/22 and CL = 22 V. Scheme X (Section (2.1.8) results in Eqn (19) for amount of drug in the body. Assuming k >> k'~ ~ 2~ provides A ~- k'akcD(k'21 - k'~ - k'ao)exp[-(k'~ + k'ao)t]

(55)

k2121 Since k~l > 2~ and 2~ >i> (k'a + k'ao) then k~l >> (k'a + k',o). Combining this with the identity 2'12~ = k'21(kc + klo) and dividing by V yields F f c k " D 1 exp[-(k'a + k'.o)t] = f ~ R C ( O ) e x p [ - ( k ' .

c'" L kv]

+ k'.o)t ]

(56)

where R = k'a/k and C(0) = D / V . This may also be written as Eqn (44) where C L = kV.

Prodrug design

43

If kc is rate-limiting in Scheme X then Eqns (35), (36), (40) and the associated limits once again apply. Thus, 2~ --- (kc + k'lo)/(1 + K) becomes rate-limiting and Eqn (19) approaches A ~-

k'akcO(k'2x - 2~,)exp[- 2'2t] k(k'~ + k',,o)(2'1)

(57)

Appropriate substitutions using Eqns (36), (40) and fa = k'a/(k'a + k'ao) together with dividing by V yields Eqn (54) where R = k~/k and C L = kV. 2.4. OPTIMUM LABILITY OF PRODRUG LINKAGE FOR MAXIMUM ORAL BIOAVAILABILITY OF DRUG

A drug may show poor bioavailability following oral administration due to either presystemic* metabolism or inadequate absorption of the drug. In either case, premature conversion of prodrug will reduce bioavailability of drug due to the original problem. Conversely, if the prodrug linkage is too stable, the value of ]~, will be too small and drug bioavailability will again decrease. These extremes suggest that for a given drug an optimum value for k~ should exist which would provide the maximum bioavailability of drug. While these two absorption problems are not mutually exclusive it is instructive to conceptualize them individually in simplified forms, remembering that the final observations will apply to more complex situations. Scheme IV (Section 2.1.2) can be modified to represent the situation whereby a dose of orally administered prodrug may be either absorbed (k,]) or converted in the GI tract (kca) to a drug having relatively negligible absorption characteristics (Aa). k',

PD a

k,

)A

>PD

A.

PDe

loss due to poorly absorbed drug

loss due to elimination of intact prodrug

Scheme XI A similar kinetic situation can exist when drug undergoes significant first-pass metabolism. For simplicity this may be represented by the following scheme O k-

PDLiver~

k . PD

k,, I ALive r "

I kc ' A

Metab

Ae

k;o ' PDe

Scheme XII wherein the dose of prodrug is absorbed but first-pass metabolism of prodrug (k'c) results primarily in metabolism of drug while conversion of circulating prodrug (k3 results in a smaller fraction of drug metabolism. *Pre-systemic metabolism is used as a general term to include first-pass, intestinal or intestinal membrane metabolism.

44

ROBERT E. NOTARI

Assuming linear kinetics both schemes can behave kinetically according to the general form L~

k~

D

>PD

>A

Scheme XIII since, in the extreme case, premature conversion (k'~) represents loss of drug. The bioavailability of the drug is related to AUC

=

(58)

A dt

which may be solved to give 1 AUC

= k'~k~D

(k a -F k'~)(k' -

k'~ -

k'~)(k -

k'~ -

k'~)

1 + k'(k'a + k'~ -

, k')(k -

k') + k ( k a + k'~ -

} k)(k'

-

k)

(59)

The value for k will be a property of the drug itself. All other constants relate to the prodrug. The following assumptions are made for the sake of illustration. They are not prerequisite to observing an optimum value of kc for maximum bioavailability of drug. Let us assume that the prodrug absorption (k'a) and elimination (k.c) rate constants are relatively insensitive to the lability of the prodrug linkage, which is reflected primarily in the kc value. Let us further assume that as the prodrug bond becomes more stable both k~ and k'~ values decrease. It is reasonable to expect a linear relationship between k~ and k'~ if conversion is chemically mediated. If conversion is Q

CONVERSION

CONSTANT

FIG. 8. The A U C values for d r u g in b l o o d as a function of the c o n v e r s i o n constant, k'c, following the a d m i n i s t r a t i o n of p r o d r u g a c c o r d i n g to Scheme XIII where k'a = 10, k = 2, k ' n c = 4 (all in t i m e - l ) , D = 100 a n d c u r v e 1: k c = 2 k ' c ; curve 2: k'c = k C a n d curve 3: kc = 0.5 k'c.

Prodrug design

45

metabolic then the relationship may or may not be linear. A linear relationship will be employed for illustration but it is only necessary that increased bond strength will retard both processes (kc and k'c) in order to observe an optimum. Thus, as bond strength is increased an increase in A U C would be anticipated due to an increase in f,. But if the bond is too stable, fc will decrease due to competitive elimination, k,~. This behavior is illustrated in Fig. 8 where A UC can be seen to pass through a maximum value as the value for the conversion constant is increased.

2.5. MULTIPLE

D O S E EQUATIONS IN PRODRUG ADMINISTRATION

According to the principle of superposition, the plasma level of drug during multiple dosing may be predicted by successively adding a single-dose curve to what remains of the preceding plasma level curve each time a new dose is given (Notari, 1980). It is assumed that the single dose curve will be repeated following each new dose. Assuming that blood levels are proportional to dose, the method may be adjusted for variable doses. In the case of a graphical solution, it can also accommodate variable dosage intervals, z. The commonly used equations, however, which allow rapid calculations of drug plasma levels after dose, N, from a single dose curve are based on constant dosage and z values. Under these conditions, a single-dose equation may be converted to its corresponding multiple-dose equation by multiplying each term containing t in the exponent by the factor X, defined as (1

-

e x p [ - N2iz]'~

16o)

where hi is the observed exponential coefficient and N is the dose number. The conversion of Eqn (17), the most complex in Section 2, to the multiple dose equation is given here for illustration. Dividing through Eqn (17) by 1/1 and applying Eqn (60) provides the time course for drug concentration in plasma following dose N: CN =

Gl(-f~) G2(I - f~) exp[--2'lt] + --exp[-2~t] (1 - f l ) (1 - f 2 ) +

G4(1 - f 4N) (1 - f4)

exp [ - 22t] +

G5(1 -- f sN)

fs)

(1 -

+

G3(1 - f f ) exp[-2xt] (1 - f a )

exp [ - (k~ + k~o)t]

(61)

where

k'.kcD(k'21

-

21 )(k21 -

2'1 )

G1 = (k'a + k'ao - 21)(21 -/'[i)(~l -- ~tl)(,~2 I ~rl)

and where fl = e - / l t , f 2 = exp[-2~z], f3 = exp[-21z], f4 = exp[-22z] and f5 = exp [ - (k, + k,o)t]. If, for example, absorption and conversion were very fast, then Jl, J2 and fs approach zero and their corresponding X values [Eqn (60)] approach unity. As discussed in connection with Eqn (27) Eqn (61) would then approach Cu - G3(1 - f~) exp [ - 2, t] + G4(1 - f,u) exp [ - 22 t] (1 - f3) (1 - ./'4)

(62)

The limiting cases are summarized in the following sections. General equations can be written by applying Eqn (60) to the single dose equations as illustrated above for Eqn (17).

46

ROBERT E. NOTAR!

2.5.1. Multiple Dosing of Prodrugs Which Undergo Rapid Absorption, Conversion or Both Table 2 summarizes the approximate equations for the concentration of drug in plasma (C) when the supply constants, k',, kc or both are very fast relative to the rate constants for other processes. Two forms of multiple-dose equations will accommodate the table. Equations (21) and (25) may be written CN -

Ge-~,(1 _ e-N~) Ge-~.,(1 __fU) (1 - e -~'~) = (1 - f )

(63)

where f = e-'L G = f~C(0) [for Eqn (21)] and G = f , fcC(O) [for Eqn (25)]. After division by V1, Eqns (22) and (26) may be written as

C N ~_

G l e x p [ - ) . l t ] ( 1 - exp[-N,Zqr]) G2 e x p [ - 2 z t ] ( 1 - e x p [ - N 2 2 t ] ) + (1 - e -~''~) (1 - e - ~ ) =

G ~ e x p [ - 2 , t ] ( 1 - f x u) (1 - f a )

+

G2exp[-22t](1 -f~) (1 - f 2 )

(64)

where f l = e-X~¢, f2 = e -x~¢, and Ga = f~Ca, G2 = f~C2 for Eqn (22)while G1 = fof~C1, G2 = f.f~C2 for Eqn (26). 2.5.2. Multiple Dose Equations for Prodrugs with Either Rate-limiting Absorption (k',) or Systemic Conversion (k c) Table 3 provides the approximate equations for drug plasma concentration in Schemes III-X under the condition of rate-limiting input. All cases may be written in the form

where kobs is a function of either (k', + k',o) or (kc + k'lo) (which allows for competitive loss by routes k'~o or k'lo. Scheme i, Section 2.1), R = k~as/2z and X is a coefficient which depends upon the Scheme and the rate-limiting step (k', or kc). These approximations represent primarily observed monoexponential loss of log-linear negative slope, kobs. As illustrated by Byron et al. (1978) and Notari et al. (1978), the equations do not describe the early time course when C is increasing with time. This period (designated t'p) decreases in significance as the inverse ratio (r =- 1/R = ,~.z/krds) and r increases. One set of simulations showed t'p to be 33~o of r at r = 5, r = 1.7 hr whereas t'p was only 3~o when r = 100, r = 140hr. Depending upon the conditions therefore, Eqn (65) can describe most of the time course for drug in plasma and, providing k', or kc is ratelimiting, it will always describe the terminal log-linear slope for loss of drug. In the previously published work k', was used to signify krds = k', or kc and the bioavailable fraction was taken as unity. In Table 3, the fraction of prodrug absorbed and converted to drug is represented by the product R X , recalling that loss of bioavailable prodrug has been limited to either k',o or k'~o in this treatment as discussed under Eqn (8). One equation (in two forms) can therefore be written for the multiple-dose conversion of Eqn (65). exp [ - kobst](1 -- exp[-- NkobsT]) (1 - e x p [ - kobsZ])

(66)

or

[-k~osD] e x p [ - kobst](1 - exp[-- NkobsZ])

j where X, krds, R, and kob s a r e defined in Table 3.

koT,

(67)

Prodrug design

47

3. P R O D R U G DESIGN AND EVALUATION 3.1. PHARMACOKINETICANALYSES Most reported prodrugs appear to have been intended to increase oral absorption, prolong shelf-life of injectables, decrease pain on injection, improve taste or produce i.m. depot injections. In these instances rapid systemic conversion is desired so that blood samples should assay predominantly for drug alone. In the case of depot injections, prolongation of drug levels by rate-determining ka is the primary goal. Research workers in these areas have tended to report either rapid or prolonged drug blood levels without detailed kinetic analyses of individual species. A notable exception is that of Ikeda et al. (1972) who employed Scheme VII together with Eqns (14) and (15) to solve all six rate constants in rabbits. The rate constants, k12, k2z and kto were determined by independent i.v. administration of the sodium salt of the sulfonamide itself. The prodrugs (methanesulfonic acid derivatives) were inactive and the conversion rate constants (kc) to active sulfonamide were estimated by hydrolysis studies in whole blood. The pharmacokinetic analysis provided (kc + k~o) -

(68)

and k'10 was assigned the difference between this total and the observed hydrolysis rate constant. An alternative approach would have been to calculate f~ and f~ = (AUC)pa/ (AUC)d where (AUC)v d is the area under the concentration-time curve for drug following i.v. administration of prodrug and (AUC)a is that following i.v. administration of an equimolar dose of drug. Then k~ =f~ZiZ2/k'21 should agree with" the values obtained from the in vitro studies. Of the six prodrugs studied iti vitro, two were examined in rabbits. Although the k~ values were of the same magnitude as kto values, causing significant prodrug levels, the terminal slopes for drug loss ()-z) were similar from both drug and prodrug administration. A typical plot is shown in Fig. 9. Assay specificity becomes critical in pharmacokinetic analyses wherein circulating prodrug concentration is significant relative to drug. Since the prodrug disposition may be different from that of the drug, a non-specific assay can cause totally misleading conclusions in comparing various plasma time profiles. Examination of the total of drug plus prodrug [T = A + PD] in Figs. 2 and 3a will demonstrate the magnitude of error that may be encountered. This problem has previously been discussed in detail (Notari, 1977, 1980).

~,g/rnl tO0'

,o f

l

rain

FIG. 9. Semilogarithmic plot of the concentration-time course in blood for the prodrug (SaMeS) and drug from prodrug (SavD) following i.v. administration of SaMeS compared to the time course of drug (Sa) following i.v. administration of Sa. Redrawn from data reported by lkeda et al. (1972).

48

ROBERT E. NOTARI

3.2. PRODRUGS FOR INCREASED ORAL ABSORPTION Ideally, these prodrugs would have rapid and complete absorption characteristics with immediate conversion to drug in the blood. The time course for the total of drug and prodrug would thus be primarily drug alone. In the extreme case, the shape of the drug time course would approach that of a rapid i.v. injection of drug, as is seen from the limiting case equations in Table 2 and illustrated in Figs. 3b and 4b. Antibiotic prodrugs represent the largest number of examples developed to improve oral absorption, with penicillins being by far the most common. Pivampicillin (Loo et al., 1974; Lune et al., 1976) talampicillin (Clayton et al., 1974; 1976; Shiobara et al., 1974) and bacampicillin (Swahn, 1974; Rozencweig et al., 1976; Bodin et al., 1975) all prodrugs of ampicillin, appear to be nearly completely bioavailable whereas ampicillin itself is roughly 50 per cent absorbed (Loo et al., 1974; Swahn 1974; Modr and Dvoracek 1970; Jusko and Lewis 1973). All three prodrugs appear to undergo rapid conversion. A similar approach has been attempted using pivmecillinam which, following a 400mg dose, provided approximately 45 per cent oral absorption of mecillinam (Roholt 1977; Ball et al., 1978) with roughly the same percent excreted as mecillinam. In contrast, orally administered mecillinam showed a maximum urinary recovery of 5 per cent (Roholt, 1977). Incomplete and variable ampicillin absorption may be attributed to its zwitterionic character. The pKa of the protonated amine and carboxylic acid functions are roughly 7.2 and 2.6 (Bundgaard 1976; Tsuji et al., 1977). Thus, ampicillin exists as both an anion and a cation in the pH region 3-7. Esterification of the carboxylic acid eliminates one of the charges while the substituent group itself can be tailored to enhance absorption characteristics. An analogous situation exists with reference to the dicarboxylic acids, ticarcillin and carbenicillin. Poor bioavailability limits their use to parenteral routes, presumably due to the poor membrane permeability of the dicarboxylates together with acid instability of the fl-lactam. Esterification of the side chain carboxyl group in carbenicillin has resulted in two prodrugs which are orally absorbed; carbenicillin indanyl ester (carindacillin, Butler et al., 1971; Wallace et al., 1970) and carbenicillin phenyl ester (carfecillin, Clayton et al., 1975). Both prodrugs show increased chemical stability of the fi-lactam, relative to carbenicillin, of the order of threefold at pH 1, sixfold at pH 2 and 17-fold at pH 3 (Tsuji et al,, 1979). At pH < 3, fl-lactam degradation occurred before significant ester hydrolysis was detected. Above pH 7, ester hydrolysis to carbenicillin superseded fl-lactam degradation. Predicted ester cleavage under intestinal pH conditions between 5-7 was considered negligible. Half-lives for carbenicillin formation at pH 7, 3 7 were 17 hr for the indanyl ester and 8.5 hr for the phenyl ester. The acid-instability of erythromycin has probably contributed to its poor and variable bioavailability. Welling (1977) has reviewed the factors influencing the bioavailability of erythromycin esters. Many prodrug esters of erythromycin have been reported. Erythromycin estolate and erythromycin ethylsuccinate are employed orally. A comparison of the estolate to the salt (erythromycin stearate) showed higher total plasma levels from the ester but higher erythromycin base levels from the salt (Welling et al., 1979). The estolate is therefore an example of a prodrug designed for increased absorption wherein kc is not sufficiently fast to prevent significant accumulation of circulating intact prodrug. However, absorption from the estolate was increased in the presence of food while that from the stearate was inhibited. Erythromycin ethylsuccinate is stated to provide reliable absorption with comparable erythromycin serum concentrations in fasting and non-fasting states (Physicians' Desk Reference, 1980). An interesting study has been reported by Sinkula (1974) who made erythromycin prodrugs by esterifying the sugar 2'-hydroxyl to make diesters. If the prodrug hydrolyzes in the body at the erythromycin oxygen it yields free erythromycin. However, if hydrolysis first occurs at the terminal end of the ester, the carboxylic acid would be formed and these compounds are known to be rapidly excreted. This study, which compared the oxygen

• Prodrug design

49

ester to the thio ester and the more stable amides, was designed to reflect an increased bioavailability of free erythromycin from the amides, which allow a greater chance for hydrolysis to occur at the erythromycin oxyester. The bioavailability from the oxygen and thio esters was poor compared to the erythromycin itself as was the observed activity of those compounds. However, both the N-ethyl glutaramate and the N-dodecylsuccinamate showed an A U C value equivalent to that of the base and equivalent or greater activity. Note that drug profiles with equivalent A U C values can differ in biological response since the shape of the curves can differ without altering the A U C . An early example of a nucleoside prodrug for improved oral absorption appeared in 1969 (Hocksema et al.). Psicofuranine tetracetate was well absorbed in humans whereas the parent drug gave no detectable plasma concentrations after oral administration. 3.3. PRODRUGS FOR INCREASED DURATION As discussed in Section 2.3, the duration of drug plasma levels may be increased by causing either prodrug conversion or prodrug absorption to become rate-limiting. The more practical of the two is rate-limiting absorption from an i.m. injection of prodrug. Notable examples of these so-called depot i.m. injections of prodrugs are fluphenazine enanthate and fluphenazine decanoate. Comparison of these-esters given to dogs (i.m. in sesame oil) to that of fluphenazine base itself showed that initial plasma levels from the base were roughly 30 times higher than that from the enanthate and 130 times that from the decanoate (Dreyfuss et al. 1976). However, after 1.2 days both prodrugs provided plasma levels that were roughly twice that achieved b y the free base. Since most of the i.v. dose of either prodrug was hydrolyzed within 30min in the dog, it is reasonable to assume that kc ~> k'a. This is supported by the shape of the time course over 12 days which implies that absorption is still occurring. In humans, the usual dosage interval is 2 weeks for the enanthate and 3 weeks for the decanoate. Schooler and Levine (1976) reported that 25 mg of ftuphenazine decanoate given i.m. every 3 weeks was equivalent to 20 mg/day of fluphenazine hydrochloride given orally. The impracticality of employing rate-limiting conversion to extend duration is due to loss of intact prodrug by the competing rate of elimination. (k'~0). In order to achieve a very long duration by this mechanism it would be necessary to design prodrugs which are largely distributed to sites of minor conversion (thus mimicking a depot injection) or which are not significantly eliminated by routes other than conversion to drug. In spite of these unlikely restrictions a prodrug with rate-limiting conversion can still prolong plasma drug levels especially if the drug itself is of short duration. In man, the prodrug cyclocytidine (cyclo-C) hydrolyzes to the antineoplastic agent, arabinosylcytosine (ara-C). The effectiveness of ara-C is limited by its very short duration in plasma primarily due to rapid deamination to the inactive metabolite, arabinosyluracil (ara-U). The achievement of therapeutic blood levels of ara-C from cyclo-C depends upon the rate of prodrug hydrolysis relative to prodrug renal clearance, which is very high. In man, cyclo-C is not deaminated but more than 80 per cent of the parenterally administered dose is excreted unchanged. In spite of this problem i.v. administration of cyclo-C produced reduced initial ara-C plasma levels, but slightly prolonged levels after 4hr (Ho et al., 1975). Depot injections of 5'-adamantoate and 5'-acylate ester prodrugs were shown to prolong immunosuppressive, antiviral and antitumor activities of ara-C in experimental animal models (Gray et al., 1972). Later, the 5'-adamantoyl hydrochloride salt administered orally was shown to be nearly as effective as ara-C in i.p. tests against L1210 (Wechter et al., 1976). 3.4. PRODRUGS FOR IMPROVED FORMULATIONS

The time course for ampiciUin in plasma following i.v. administration of the prodrug hetacillin is nearly identical to that following i.v. administration of ampicillin itself J.P.T. 14/I

O

50

ROBERT E. NOTARI

I00

0 ~AMPICH_I.IN

~

i.v. •

' ~ HEYACILLIN

~,

i .v.

2C

g~

~o

g

i (J

o

o.i TIME, NOQleS

Fie. 10. Comparison of the plasma concentration time course of ampicillin (ej and the urinary excretion rate of ampicillin (©) following i.v. administration of ampicillin to that followingi.v.administrationof hetacillin.The short durationof hetacillinin plasma is also shown ('k). Taken from Jusko et al. (1973) with permissionof the publisher. (Jusko and Lewis, 1973 and Jusko et al., 1973) as shown in Fig. 10. Apparently the rate of conversion of hetacillin to ampicillin is so rapid that the prodrug and drug may be regarded as nearly indistinguishable from a pharmacokinetic point of view. Ampicillin, like other aminopenicillins, undergoes degradation by /3-1actam hydrolysis and, in concentrated solutions at pH values which allow free amine, by self aminolysis in the form of dimerization (Bundgaard, 1976, 1977a, 1977b). For example, analysis of a 10 per cent w/v solution of ampicillin at pH 8.1, 35 ° shows that 93 per cent of the initial degradation rate is due to dimerization with only 7 per cent due to hydrolysis. Hetacillin, a condensation product of ampicillin and acetone, effectively inhibits the dimerization reaction. Concentrated parenteral solutions of hetacillin, therefore, have a longer useful shelf-life than do those of ampicillin. At 250 mg/ml ampicillin solutions should be used within 1 hr whereas hetacillin is useful for 6 hr (Schwartz and Hayton, 1972). Esters of lincomycin and clindamycin have been prepared in an effort to mask undesirable taste and maintain (or improve) oral absorption (Sinkula and Lewis, 1973)• Esters have been compared for activity by subcutaneous and oral routes in mice. The 2-hexanoate, 2-1aurate, and 2-palmitate esters appear to be absorbed as well or better than clindamycin itself when all are administered as hydrochloride salts equivalent to 25 mg/kg clindamycin base. These prodrugs appear to hydrolyze either prior to or just after absorption. Clindamycin palmitate hydrochloride, for oral solution, is a prodrug product with more acceptable taste characteristics than a solution of the drug itself. The clindamycin phosphate ester is a rapidly reversing prodrug for parenteral use. The phosphate prodrug ester is intrinsically inactive. Although some intact ester is measured in plasma following i.m. administration of prodrug, the drug represents most of the plasma total assay (De Haan et al., 1973). While clindamycin hydrochloride solutions are irritating by both i.v. and i.m. injection the phosphate prodrug showed no signs of irritation or local intolerance by either route. Cephalosporin pharmacokinetics have been reviewed (Notari 1980, and Nightingale et al., 1975). Like the penicillins, the biological half-life values are roughly 0.5-1.0hr. Cefamandole nafate is a sodium salt of a formate ester prodrug of cefamandole for parenteral use. The pH of freshly reconstituted solutions range from 6.0-8.5 and the t+ for hydrolysis to parent drug at pH 8.5 is roughly 17min. Intravenous injections of the prodrug solutions therefore provide biological half-life values for cefamandole that are similar to i.v. injections of the drug itself. The primary advantage of the

Prodrug design

51

prodrug appears to be stability of the dry powder. Cefazolin sodium and cephalothin sodium are typical of the cephalosporins with dry form stability periods of roughly 2 years (90 per cent potency). Cefamandole nafate is stable in dry form for 3 years. 3.5. SITE SPECIFICITY

Site specificity is perhaps one of the most important and elusive goals in drug design. Theoretically, prodrugs offer one approach to this problem. If the prodrug itself is void of biological activity then designing a bond which can only undergo conversion at the site of action would previde specificity provided delivery to the site is assured. In practice this is probably never achieved in the absolute sense bttt may at least be approached. Most enzymes involved in metabolizing prodrug bonds used to date are rather ubiquitous. Differences in chemical conversion can rely only on pH differences and these are quite limited throughout the body. One common example of pH dependence is the prodrug methamine which requires an acidic pH (pH < 5) before it is converted to the urinary antiseptic drug, formaldehyde. Protecting the prodrug from the stomach pH and acidifying the urine thus restricts the formaldehyde to the urine. N-t-butylarterenol (tBA) is an active fl-adrenoceptor agonist structurally related to isoproterenol. Both compounds are potent bronchodilators of short duration. Rapid metabolism following oral administration is probably responsible for the limited duration. Bitolterol is the di-p-toluate prodrug ester of tBA. Studies in man, dog and rat indicate that the prodrug, bitolterol, is absorbed intact orally and retained primarily in the lung as the intact prodrug. The observed prolonged bronchodilation is attributed to slow release of the ester from lung with hydrolysis to tBA. Pharmacological activity is terminated by tBA metabolism via conjugation or 3-O-methylation (Shargel and Dorrbecker, 1976). This successful concentration of a bronchodilator prodrug in the lungs may have been fortuitous, in that the prodrug was reportedly synthesized to give slow hydrolysis thus prolonging tBA plasma levels (Shargel et al., 1976). It does represent an interesting example of site specificity albeit a posteriori. REFERENCES ALBERT, A. (1958)Chemical aspects of selective toxicity. Nature 182: 421-426. ALBERT, A. (1964) Selectit, e Toxicity. Wiley, New York. ARIENS, E. J. (Ed) (1971) Drug Design V. l, p. 2-270. Academic Press, London. BALL, A. P., VISWAN, A. K., MITCHARD, M. and WISE, R. (1978) Plasma concentrations and excretion of mecillinam after oral administration of pivmecillinam in elderly patients. J. Antimicrob. Chemother. 4: 241 246. BODIN, N-O., EKSTROM, B., FORSGREN, U., JALAR, L-P., MAGNI, L., RAMSAY, C-H. and SJOBERG, B. (1975) A new orally well-absorbed derivative of ampicillin. Antimicrob. A#. Chemother. 8: 518-525. BUNDGAARD, H. (1976) Polymerization of penicillins: kinetics and mechanisms of di- and polymerization of ampicillin in aqueous solution. Acta. Pharm. Suec. 13: 9-26. BUNDGAARD, H. (1977a) Polymerization of penicillins. II. Kinetics and mechanism of dimerization and selfcatalyzed hydrolysis of amoxycillin in aqueous solution. Acta. Pharm. Suec. 14: 47-66. BUNDGAARD, H. (1977b) Polymerization of penicillins. II1. Structural effects influencing rate of dimerization of aminopenicillins in aqueous solution. Acta. Pharm. Suec. 14: 67-80. BUTLER, K., ENGLISH, A. R., KNIRSCH, A. K. and KORST, J. J. (1971) Metabolism and laboratory studies with indanyl carbenicillin. Del. Med. J. 43: 366-343. BYRON, P. R. and NOTARI, R. E. (1976) Critical analysis of "flip-flop" phenomenon in two-compartment pharmacokinetic model. J. Pharm. Sci. 65:1140-1144. BYRON, P. R., NOTARI, R. E. and HUANG, M-Y. (1978) Pharmacokinetic predictions of optimum drug delivery rates from prodrugs designed for maximum duration. Intl. J. Pharm. 1: 219-231. CLAYTON, J. P., COLE, M., ELSON, S. W. and FERRES, H. (1974) BRL 8988 (Talampicillin): A well absorbed oral form of ampicillin. Antimicrob. Ag. Chemother. 5: 670-671. CLAYTON, J. P., COLE, M., ELSON, S. W., HARDY, K. D., MIZEN, L. W. and SUTHERLAND, R. (1975) Preparation, hydrolysis and oral absorption of ~t-carboxy esters of carbenicillin. J. Med. Chem. lg: 172-177. CLAYTON, J. P., COLE, M., ELSON, S. W., FERRES, H., HANSON, J. C., MIZEN, L. W, and SUTHERLAND, R. (1976) Preparation, hydrolysis and oral absorption of lactonyl esters of penicillins. J. Med. Chem. 19: 1385-1391. DANIELSSON, B. (Ed.) (1976) Symposium on bioactivation and controlled drug release, Stockholm (Abstracts). Acta. Pharm. Suec. 13: (suppl.) 148.

52

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DE HAAN, R. M., METZLER, C. M., SCHELLENBERG, D. and VANDENBOSCH, W. D. (1973~ Pharmacokinetic studies of clindamycin phosphate. J. Clin. Pharmacol. 13: 190-209. DREYFUS. J., SHAW, J. M. and Ross, J. J. (1976) Fluphenazine enanthate and fluphenazine decanoate: intramuscular injection and esterification as requirements for slow release characteristics in dogs. J. Pharm. Sci. 65: 131~ 1315. GRAY, G., NICHOL, E. R., MICKELSON, M. M., CAMIENER,G. W., G1SH, D. T., KELLY, R. C., WECHTER, W. J., MOXLEY,T. E, and NEIL, G. L. (1972) Immunosuppressive, antiviral and antitumor activities of cytarabine derivatives. Biochem. Pharmacol. 21 : 465 475. HARPER, N. J. (1959) Drug latentiation. J. Med. Pharm. Chem, I : 467 500. HIGUCHI, T. and STELLA, V, (Eds.) (1975) Pro-drugs as Not'el Drug Delil,er)' Systems. Amer, Chem. Soc., Washington, D.C. Ho, D. H., ROORIGUEZ, V., LOG, T. L., BODEY, G. P. and FREIRE1CH, E. J. (1975) Clinical pharmacology of 0 2, 2'-cyclocytidine. Clin. Pharmacol. Therap. 17: 66-72. HOCKSEMA, H., WHITFIELD, G. B. and RHULAND, L. E. (1961) Effect of acylation on the oral absorption of a nucleoside by humans. Biochem. and Biophys. Res. Comm. 6: 213--216. IKEDA. K., KVRONO,Y. and TUKAMOm,T. (1972) Methanesulfonic acid derivative of sulfonamides. I. Hydrolysis rate in vitro and pharmacokinetics in ~-it'o. Chem. Pharm. Bull. 20:863 870. JUSKO, W. J. and LEwis, G. P (1973) Comparison of ampicillin and hetacillin pharmacokinetics in man. J, Pharm. Sci. 69:69-76. JUSKO, W. J., LEWIS, G. P. and SCHMITT, G. W. (1973) Ampicillin and hetacillin pharmacokinetics in normal and anephric subjects. Clin. Pharmaeol. Ther. 14: 9(~99. LoG, J. C. K., FOLTZ, E. L., WALLICK, H. and KWAN, K. C. (1974) Pharmacokinetics of pivampicillin and ampicillin in man. Clin. Pharmacol. Therap. 16: 35- 43. LUND, B., KAMPMANN,J, P., LINDAHL, F. and HANSEN,J. M. (1976) Pivampicillin and ampicillin in bile, portal and peripheral blood. Clin. Pharmacol. Ther. 19:587 591. MODR, Z. and DVORACEK, K. (19701 Pharmacokinetics in clinical drug research. In: Adt'ances in Bioscienees p. 219 230, RASPE,G. (Ed). Pergamon Press, New York. NIGHTINGALE, C. H., GREENE, D. S. and QUINTILIANI, R. (1975) Pharmacokinetics and clinical use of cephalosporin antibiotics. J. Pharm. Sci. 64: 1899-1927. NOTARI, R. E. (1973) Pharmacokinetics and molecular modification: implications in drug design and evaluation. J. Pharm. Sci. 62:865 881. NOTARI, R. E. (1975) Effects of molecular structure on biopharmaceutic and pharmacokinetic properties of drugs. Pharmaceut. Weekblad. 110:577 588. NOrARI, R. E. (1977) Alteration of pharmacokinetics through structural modification. In: Design of BiGpharmaceutical Properties through Prodrugs and Analogs p. 68-97, ROCHE, E. B. (Ed). Amer. Pharm. Assoc., Washington. D.C. NOTARI, R. E. (1980) Biopharmaeeutics and Clinical Pharmacokineties, An Introduction. Marcel Dekker, New York. NOTARI, R. E,, HUANG, M-Y. and BYRON, P. R. (1978) Calculations of optimum pharmacokinetic drug supply rates for maximum duration during multiple dose thereapy by prodrug administration. Intl. J. Pharm. 1:233 247. Physicians" Desk Reh'rence(1980) p. 516. Medical Economics Co., Oradell, New Jersey. ROCHe, E. B. (Ed.) (1977) Design ~{fl Biopharmaeeutical Propertie,s through Prodrugs and Analog.s. Amer. Pharm. Assoc., Washington, D.C. ROHOLT, K. (1977) Pharmacokinetic studies with mecillinam and pivmecillinam. J. Antimicrob. Chemother 3: (suppl. B) 71 81. ROZENCWEIG, M., STAQUET, M. and KLASTERSKY, J. (1976) Antibacterial activity and pharmacokinetics of bacampicillin and ampicillin. Clin. Pharmaeol. Ther. 19:592 597. SCHOOLER, N. R. and LEVINE,J. (1976) The initiation of long-term pharmacotherapy in schizophrenia: dosage and side effect comparisons between oral and depot fluphenazine. Pharmakopsychiatr. Neuropsychopharmakol. 9 : 159-169. SCHWARTZ, M. A. and HAYTON, W. I. (1972) Relative stability of hetacillin and ampicillin in solution. J, Pharm. Sci. 61 : 906-909. SHARGEL, L. and DORRBECKER, S. (1976) Physiological disposition and metabolism of bitolterol in man and dogs. Drug Metah. and Disp. 4: 72-78. SHARGEL, L., DORRBECKER, S. A. and LEVITT, M. (1976) Physiological disposition and metabolism of N-t-butylarterenol and its Dl-p-toluate ester (bitolterol) in the rat. Drug Metab. and Disp. 4: 65-71. SHIOBARA, Y., TACHIBANA, A., SASAKI, H., WATANABE, T. and SADO, T. (1974) Phthalidyl D-z~-aminobenzylpenicillinate hydrochloride (PC-183): a new orally active ampicillin ester. J. Antibiot. 27:665 673. SINKULA, A. A. (1974) Chemical modification of erythromycin: synthesis and preliminary bioactivity of selected amides and esters. J. Pharm. Sci. 63:842 848. SINKULA,A. A. (1975) Prodrug approach in drug design. Ann. Rep. Meal. Chem. 10: 306-316. SINKULA, A. A. (1979} Methods to achieve sustained drug delivery, the chemical approach. In: Sustained and Controlled Release Drug Delirery Systems p. 411-555, ROBINSON, J. R. (Ed.). Marcel Dekker, New York. SINKULA,A. A. and LEWIS,C. (1973) Chemical modification of lincomycin: synthesis and bioactivity of selected 2, 7-dialkylcarbonate esters, J. Pharm. Sci. 62:1757-1760. SINKULA, A. A. and YALKOWSKY,S. J. (1975) Rationale for design of biologically reversible drug derivatives: prodrugs. J. Pharm. Sci. 64: 181-210. SWAHN, A. (1974) On the Absorption and Metabolism of Some Penicillins in Man, Ph.D. thesis, p. 13, Department of Medicine and Clinical Pharmacology, Karolinska Institutet. Stockholm. TEORELL, T. (Pres.) (1974) Symposium on pharmacokinetics and drug effects, Stockholm (Abstractsl. Acta. Pharm. Suec. I 1 : 629-668.

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