Basic Concepts of the Dose-Response Relationship - ACS Publications

4 Basic Concepts of the Dose-Response Relationship ROBERT SNYDER

Downloaded by CORNELL UNIV on September 19, 2016 | http://pubs.acs.org Publication Date: January 13, 1984 | doi: 10.1021/bk-1984-0239.ch004

Joint Graduate Training Program in Toxicology, Rutgers, The State University of New Jersey, and College of Medicine and Dentistry of New Jersey, Piscataway, NJ 08854

The dose-response relationship is the cornerstone of Pharmacology/Toxicology. It quantitatively defines the role of the dose of a chemical in evoking a biological response. In the absence of chemical no response is seen. As chemical is introduced into the system the response is initiated at the threshold dose and increases in intensity as the dose is raised. Ultimately a dose is reached beyond which no further increase in response is observed. The dose-response relationship can be demonstrated for interactions of chemicals with biological receptors leading to physiological responses, therapeutic effects of drugs, or for toxic, lethal, teratogenic, mutagenic or carcinogenic effects of chemicals. The data from these studies can be expressed as dose-response curves which can take the form of linear plots or a variety of reciprocal or logarithmic transformations. Two types of dose-response relationships are observed. The first is the incremental change in response of a single system or individual as the dose is increased. The second is the distribution of reponses in a population of individuals given different doses of the agent. The former are frequently used for the determination of the mechanism of interaction between the chemical and the biological system. The latter describe the response of a population of individuals and can also be used to determine multimodal responses indicative of genetic variations. The dose-response relationship is of key importance when attempting to define allowable exposure of humans to chemicals in the workplace, consumer products or the environment. Usually initial studies are done in animals and, where 0097-6156/ 84/ 0239-0037S06.00/ 0 © 1984 American Chemical Society

Rodricks and Tardiff; Assessment and Management of Chemical Risks ACS Symposium Series; American Chemical Society: Washington, DC, 1984.

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possible, they are compared with data derived from recorded human exposure. The reliability of extrapolations from these data is compromised by the inherent inaccuracy of the data observed in the high and, more importantly, the low dose regions of the dose-response curves since these usually demonstrate the fewest reponses. It is essential that we develop new approaches to understanding responses to low doses of chemicals if we are to define safe limits of exposure with accuracy.

The e a r l y h i s t o r y of Pharmacology and Toxicology was charact e r i z e d by e x p l o r a t i o n of q u a l i t a t i v e d e s c r i p t i o n s of the actions of drugs and t o x i c agents. Eventually a more q u a n t i t a t i v e approach had to be taken t o pave the way f o r mechanistic studies. The n e c e s s i t y f o r q u a n t i t a t i o n of b i o l o g i c a l data was argued by A . J . C l a r k (1) who attempted t o c h a r a c t e r i z e c e l l s as physico-chemical systems. He d i s c u s s e d the dose-response r e l a t i o n s h i p i n terms of c o n t r o l l i n g f a c t o r s such as e q u i l i b r i a and k i n e t i c s i n c e l l - d r u g i n t e r a c t i o n s , and i n t r a c e l l u l a r b i n d i n g of drugs. I t i s c l e a r that i n t e r a c t i o n s between chemicals and biological systems demonstrate s i m i l a r i t i e s r e g a r d l e s s of the chemical s t u d i e d . The f i r s t necessity i s a chemical to be s t u d i e d ; the second is a b i o l o g i c a l assay system i n which to study the chemical. In the absence of the chemical no response i s observed. Upon a d d i t i o n of the chemical at a c r i t i c a l dose or c o n c e n t r a t i o n the response begins to be observed and t h i s i s c a l l e d the " t h r e s h o l d . " As the dose increases the response increases, however, the quantitative relationship between the increased dose and increased response may vary among chemicals and systems. E v e n t u a l l y the dose reaches a magnitude beyond which no f u r t h e r increment i n response i s seen. Beyond that dose only the maximum a c t i v i t y i s observed. At extremely high doses f o r the responses being observed, the response i s e i t h e r l o s t or cannot be seen because a t o x i c e f f e c t of the chemical may come i n t o play. However, over a reasonable c o n c e n t r a t i o n range the dose-response r e l a t i o n s h i p i s maintained. Modern g r a p h i c a l analyses of dose-response phenomena are l a r g e l y d e r i v e d from the p i o n e e r i n g e f f o r t s of Trevan ( 2 ) , B l i s s (3_) and Gaddum ( 4 ) . This d e s c r i p t i o n , which makes l i b e r a l use of d e s c r i p t i v e m a t e r i a l compiled by G o l d s t e i n et. a l . (5) and Hayes (6), w i l l i n v e s t i g a t e the modes of expression of dose-response curves making use of a v a r i e t y of data t r a n s f o r m a t i o n s . Both incremental and quantal responses w i l l be d i s c u s s e d . The application of these concepts to lethality, toxicity, c a r c i n o g e n e s i s , t e r a t o g e n e s i s and mutagenesis w i l l be d e s c r i b e d .


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Dose-Response Relationship

F i n a l l y problems of the dose-re»punse r e l a t i o n s h i p low dose exposure w i l l be explored.

r e l a t i v e to


Bioassay Systems The s i n g l e most important e n t i t y i n the study of the doseresponse relationship i s the bioassay system i n which the chemical w i l l be s t u d i e d . Since the most e s s e n t i a l f e a t u r e of the r e s u l t s w i l l be the q u a n t i t a t i v e data which are d e r i v e d , the r u l e s governing the accuracy and p r e c i s i o n of the assay should approach as n e a r l y as p o s s i b l e those achieved i n measurements i n chemical systems. Since b i o l o g i c a l systems are not machines, accuracy and p r e c i s i o n can be d i f f i c u l t problems i n b i o a s s a y 8 . However, b i o l o g i c a l systems f r e q u e n t l y are the match of chemical eye terns when i t comes to s e n s i t i v i t y since the dose or concentration of chemical to which the bioassay systems may respond i s o f t e n exceedingly low. In chemical analyses the l i m i t s of accuracy r e l a t e to the r e l a t i o n s h i p between the value observed and the a c t u a l v a l u e . The l i m i t i n g f e a t u r e i s the method or the instrument used f o r the measurement. Since the a c t u a l value i s o f t e n not known i n an experimental s i t u a t i o n , the determination w i l l be based on the r e s u l t of m u l t i p l e measurements. I f the d i f f e r e n c e s between the results obtained i n repeated determinations i s small the measurement can be considered to be p r e c i s e , i . e . r e p r o d u c i b l e . The l i m i t s to accuracy and p r e c i s i o n i n b i o l o g i c a l systems can be explored u s i n g three l e v e l s of b i o l o g i c a l o r g a n i z a t i o n as examples: whole animals, i s o l a t e d organ systems, and p u r i f i e d enzymes. Whole animals are used i n many bioassay systems. The s t a r t of most s a f e t y e v a l u a t i o n s t u d i e s i n v o l v e s determining the median l e t h a l dose of the chemical, i . e . the LD50. Since many animals are necessary f o r these s t u d i e s s m a l l , r e l a t i v e l y inexpensive rodents are u s u a l l y used, e.g. mice or r a t s . Furthermore, outbred, i . e . g e n e t i c a l l y heterogeneous animals of the same s t r a i n , r a t h e r than the more e x o t i c i n b r e d , s t r a i n s are used. T h i s not only reduces the cost but avoids cases of g e n e t i c a l l y determined unusual s e n s i t i v i t y or r e s i s t a n c e to the chemical. To be sure, the major problem i n these s t u d i e s i s the assumption that one can e x t r a p o l a t e from the s e n s i t i v i t y of animals to the s e n s i t i v i t y of humans. While examples can be c i t e d f o r unexpected d i f f e r e n c e s i n s e n s i t i v i t y between humans and s p e c i f i c animal s t r a i n s t o the l e t h a l i t y of a chemical, f o r the most part comparative l e t h a l i t y i n animal s t r a i n s t o v a r i o u s chemicals i s s i m i l a r to the r e l a t i v e s e n s i t i v i t y of humans t o the v a r i o u s chemicals. Thus, to use an extreme example, i n r a t s and mice as w e l l as i n humans, sucrose i s l e s s t o x i c than cyanide. That does not mean that the LD50 f o r any given chemical i s the same i n a l l s p e c i e s . I t i s f o r t u n a t e , however, that except f o r unusual examples, t o x i c i t y c l a s s e s , i . e . ranges of



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doses i n which chemicals are l e t h a l , do not vary widely among species. The accuracy of LD50 determinations cannot be v e r i f i e d i n a given experiment since i t can only be done once with one group of animals. Provided that normal healthy animals are used and the c o r r e c t doses are administered by the proper route, the r e s u l t must be accepted. The p r e c i s i o n i s another matter. R e p e t i t i o n of the study with animals of the same s t r a i n , sex, age, e t c . , may lead to somewhat d i f f e r e n t values because of b i o l o g i c a l v a r i a b i l i t y . T h i s can be d e a l t with by expressing the r e s u l t s i n terms of confidence l i m i t s d e r i v e d from a s t a t i s t i c a l e v a l u a t i o n of the data. These d i f f e r e n c e s between experiments may not be great but i t would not be unexpected i f they were greater than those observed i n chemical determinations. As a p r a c t i c a l matter they are u s u a l l y s u f f i c i e n t l y accurate and p r e c i s e f o r t h e i r intended purpose which i s to i n d i c a t e the r e l a t i v e l e t h a l i t y of the compound. The more d i f f i c u l t problem with whole animals concerns events which occur over long periods of time. The LD50 value must a 1way β be accompanied with an i n d i c a t i o n of the time over which the animals were observed before the experiment is terminated. I f not, every treatment would be considered l e t h a l since every animal d i e s e v e n t u a l l y , or no chemical would be considered l e t h a l since both c o n t r o l and t r e a t e d animals would die eventually. Thus, o b s e r v a t i o n periods of 24 hours or two weeks are o f t e n chosen as end p o i n t s . When d e a l i n g with c a r c i n o g e n e s i s , however, the time of the study i s considered the l i f e time of the animal which i n the case of mice or r a t s may extend to two years or more. Furthermore, since c o n t r o l animals may d i s p l a y spontaneous tumors and the tumor i n c i d e n c e i n both t r e a t e d and c o n t r o l animals may be s m a l l , the t o t a l number of animals i n the experiment o f t e n plays a key r o l e i n determining the accuracy of the r e s u l t s . The responses d i s c u s s e d here are c l a s s i f i e d as quantal since each animal provides only one p i e c e of d a t a . The animal e i t h e r d i e s or i t does not; i t develops tumors or i t does not. The same o b s e r v a t i o n cannot be repeated i n the same animal and the e f f e c t of a higher dose i n that animal cannot be i n v e s t i g a t e d . In contrast a number of i s o l a t e d organ p r e p a r a t i o n s have been used as bioassay systems. H i s t o r i c a l l y bioassay systems were developed when the nature of the chemicals themselves were o f t e n unknown and/or the s e n s i t i v i t y of chemical methods was i n s u f f i c i e n t to measure the extremely small concentrations of chemicals necessary to produce responses i n bioassay systems. Thus, these systems could be used not only to measure the e f f e c t of the chemical on the system, but once the system was c a l i b r a t e d the c o n c e n t r a t i o n of a s o l u t i o n of the chemical could be determined based on the response i t produced i n the system. Furthermore, bioassay systems allowed f o r the demonstration of specific principles. For example, the demonstration by Loewi



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(7) that a chemical mediator c o n t r o l l e d heart r a t e depended upon the demonstration that blood flowing from one f r o g heart contained a substance which could slow down the r a t e of a second heart. This was a bioassay system i n which two i s o l a t e d f r o g heartβ were used. Other systems such as the response of muscle preparations i n tissue baths to direct stimulants of c o n t r a c t i o n , such as the i s o l a t e d clam heart, or the i s o l a t e d cat spleen are based on the a b i l i t y t o measure changes i n c o n t r a c t i o n of the organs i n réponse t o chemicals. The l a t t e r w i l l be used f o r some of the examples c i t e d below. The f e a t u r e which d i s t i n g u i s h e s these systems from the whole animal systems described above i s that the responses which can be measured are incremental. Thus, the a d d i t i o n of a given c o n c e n t r a t i o n can produce a response of a given magnitude but the same preparations can then be t r e a t e d with a higher c o n c e n t r a t i o n and a greater response observed. C l e a r l y , there a r e advantages t o observing changes i n response i n the same system t o e i t h e r d i f f e r e n t chemicals or the same chemical at d i f f e r e n t doses. Q u a l i t a t i v e d i f f e r e n c e s and s i m i l a r i t i e s a r e emphasized and q u a n t i t a t i v e d i f f e r e n c e s can be be evaluated with greater certainty. F i n a l l y , i s o l a t e d enzymes, which come c l o s e s t t o working with pure chemicals can be used t o study the mechanisms of the effects of chemicals. The i n t e r a c t i o n of chemicals with biological receptors f o l l o w much the same laws as the i n t e r a c t i o n of substrates with enzymes. Thus, p a r a l l e l s can be drawn between the i n t e r a c t i o n of chemicals with receptors and mechanisms of enzyme c a t a l y z e d r e a c t i o n s . The main d i f f e r e n c e is that receptors d i s s o c i a t e from chemicals l e a v i n g the chemicals unchanged whereas enzymes a l t e r the chemicals. G r a p h i c a l P r e s e n t a t i o n o f the Dose-Response R e l a t i o n s h i p The dose-response r e l a t i o n s h i p can be expressed g r a p h i c a l l y using a v a r i e t y of mathematical transformations. I n the simplest expression the dose i s p l o t t e d on the a b c i s s a and the response on the o r d i n a t e . Both are expressed i n appropriate u n i t s on an a r i t h m e t i c b a s i s (Figure 1 ) . Although the data a r e expressed without f u r t h e r transformation the r e s u l t i s not a straight line throughout. The i n i t i a l slope tends t o be s t r a i g h t and i s o f t e n the s e c t i o n of the curve which i s of greatest i n t e r e s t . Thus, Figure 2 shows the s t r a i g h t lines obtained expressing an increase i n mutagenesis when e i t h e r s t r a i n s TA 1535 or TA 100 of Salmonella typhimurium are exposed to i n c r e a s i n g concentrations o f sodium azide ( 8 ) . Figure 1 i s t y p i c a l of an incremental dose-response curve observed using a p r e p a r a t i o n i n which a muscle i s f i x e d i n a bath with one end t i e d t o a device f o r r e c o r d i n g changes i n t e n s i o n and the dose of chemical agent, i . e . an a g o n i s t , which modifies t e n s i o n i s v a r i e d . I f i t i s assumed that (1) the



ASSESSMENT A N D M A N A G E M E N T OF C H E M I C A L RISKS

Dose F i g u r e 1. The r e l a t i o n s h i p between dose and response plotted arithmetically.

5ooor

i

yui [ R A ]

(1)

*2 B

If r e p response and R s p ^ x » equation can be d e r i v e d : rsp -

maximum

response

the f o l l o w i n g

Rspmax^A K +A

(2)

A

T h i s i s the equation f o r the curve seen i n F i g u r e 1. I t i s i n most respects i d e n t i c a l t o the Michaelis-Menton equation: ν -

Vmax-S K + S

(3)

M

The only d i f f e r e n c e i s that i n enzymatic r e a c t i o n s described by the Michaelis-Menton equation substrate i s consumed and, therefore, i s not a true d i s s o c i a t i o n constant whereas i n equation (2) K i s a true d i s s o c i a t i o n constant. In Figure 1 the d i s s o c i a t i o n constant can be obtained by determining the dose of agonist necessary to give h a l f of the maximal response. Because we are d e a l i n g with a curve, however, i t i s d i f f i c u l t t o determine t h i s value with accuracy from the a r i t h m e t i c dose-response p l o t . The data can be expressed as a straight l i n e most r e a d i l y by applying the technique of Lineweaver and Burk (9) and p l o t t i n g the data as the r e c i p r o c a l of both dose and response (Figure 3 ) . The equation d e s c r i b i n g the r e s u l t i n g s t r a i g h t l i n e i s : A

1 « rsp The

K Rspmax A

.

I A

t

- 1 Rspmax

maximum response can be derived from the point on the



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o r d i n a t e that i n t e r s e c t s the s t r a i g h t l i n e . The dose g i v i n g h a l f of the maximum response can then be e a s i l y d e r i v e d and i s the d i s s o c i a t i o n constant. The double r e c i p r o c a l p l o t has been used e x t e n s i v e l y i n the study of enzymatic r e a c t i o n s to c h a r a c t e r i z e the r a t e of the r e a c t i o n , the M i c h a e l i s constant, and the mode of a c t i o n of i n h i b i t o r s . I t can a l s o be used t o study the i n t e r a c t i o n of chemicalβ with b i o l o g i c a l systems. The simplest types of i n t e r a c t i o n s can be i l l u s t r a t e d i n Figures 4 and 5. The lowest l i n e β i n each represent the dose-response r e l a t i o n s h i p f o r a h y p o t h e t i c a l system. When the a c t i o n of the agonist i s i n h i b i t e d by another chemical, i . e . an antagonist, the response i s reduced and two upper l i n e s represent the degree of antagonism as a f u n c t i o n of dose of the a g o n i s t , each l i n e r e p r e s e n t i n g a d i f f e r e n t dose of antagonist. In F i g u r e 4 a l l three l i n e s i n t e r s e c t at the o r d i n a t e . These data are i n t e r p r e t e d to mean that the agonist and antagonist are probably r e a c t i n g at the same s i t e . The r e a c t i o n of each with the receptor s i t e i s r e v e r s i b l e because by i n c r e a s i n g the dose of the agonist i t i s p o s s i b l e to completely overcome the e f f e c t s of the antagonist. Thus, the maximum response i s not a l t e r e d . This i s c a l l e d competitive antagonism s i n c e the two agents compete f o r the same receptor s i t e . The d i s s o c i a t i o n constant can be c a l c u l a t e d f o r the a g o n i s t - r e c e p t o r i n t e r a c t i o n from the p o i n t where the s t r a i g h t l i n e obtained i n the absence of antagonist crosses the abcissa. In contrast Figure 5 demonstrates the double r e c i p r o c a l p l o t c h a r a c t e r i s t i c of non-competitive antagonism. Note that the three l i n e s i n t e r c e p t at the a b c i s s a rather than at the o r d i n a t e at a point which i s the negative r e c i p r o c a l of the d i s s o c i a t i o n constant. On the o r d i n a t e the maximum response i n the presence of antagonist i s i n each case smaller than that produced by the agonist alone. Thus, r e g a r d l e s s of the s i z e of the dose of agonist the e f f e c t s of the antagonist cannot be completely overcome. M e c h a n i s t i c a l l y t h i s suggests that e i t h e r the antagonist r e a c t s at a s i t e remote from the s i t e at which the agoniet acts or the antagonist r e a c t s i r r e r e v e r s i b l y with the receptor and thereby decreases the t o t a l number of a c t i v e receptor s i t e s . A s p e c i f i c example of a competitive antagonist i n a f i g u r e taken from a paper by Chen and R u s s e l l (10) can be seen i n the effect of diphenhydramine, an anti-histaminé on the hietamine-induced decrease i n blood pressure i n the dog (Figure 6 ) . Note that with i n c r e a s i n g dose of diphenhydramine the e f f e c t of histamine i s decreased but by i n c r e a s i n g the dose of histamine the a n t a g o n i s t i c e f f e c t s are e v e n t u a l l y overcome. In contrast they showed that when ergotamine, a v a s o c o n s t r i c t o r , which r a i s e s blood pressure by a mechanism remote from the effect of histamine, i s adminstered with histamine, the antagonism cannot be completely overcome by i n c r e a s i n g the dose. T h i s type of antagonism i s not competitive.




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A S S E S S M E N T A N D M A N A G E M E N T O F C H E M I C A L RISKS

'/Dose Figure 5. Schematic p r e s e n t a t i o n of non-competitive antagonism u s i n g a double r e c i p r o c a l p l o t .

ι 0.15

ι O.SO

ι 0.1S

1 ι. ο

F i g u r e 6. Double r e c i p r o c a l p l o t demonstrating a n t a g o n i s m o f d i p h e n y h y d r a m i n e and e r g o t a m i n e t o t h e blood pressure lowering e f f e c t s of histamine i n the dog. ( R e p r i n t e d w i t h p e r m i s s i o n from R e f . 10.)



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In a d d i t i o n t o a r i t h m e t i c r e p r e s e n t a t i o n s of the data and r e c i p r o c a l transformation, i t i s common t o p l o t b i o l o g i c a l data using l o g a r i t h m i c transformations. Expression of the dose i n l o g a r i t h m i c terms allows f o r the d e s c r i p t i o n of the e f f e c t s over a wide range of doses on a simple scale. An i d e a l i z e d semi-log-dose-response curve i s shown i n Figure 7. The ordinate represents the percent of maximum response a t t a i n a b l e i n the bioassay system, which f o r the purposes of t h i s d i s c u s s i o n produces an incremental response, and the a b c i s s a i s the dose p l o t t e d i n l o g a r i t h m i c u n i t s over a range covering three orders of magnitude. The dose producing h a l f of the maximal response i s c a l l e d the ED50, i . e . the dose g i v i n g 50% of the maximal response. An example of the p r a c t i c a l a p p l i c a t i o n of t h i s technique i s taken from a paper by Bicker ton (11) who i n v e s t i g a t e d the e f f e c t s of catecholamines on the i s o l a t e d c a t spleen. The spleen c o n t r a c t s when stimulated by epinepherine ( e p i ) or norepinepherine ( n - e p i ) . The degree of c o n t r a c t i o n can be measured on a s t r a i n gauge and increases as the c o n c e n t r a t i o n of catecholamine i n the system i s r a i s e d . F i g u r e 8 shows a dose-response curve comparing the r e l a t i v e a c t i v i t y of e p i and n-epi i n t h i s system. The dose expressed l o g a r i t h m i c a l l y covers more than a 10,000 f o l d c o n c e n t r a t i o n range. Both appear t o produce the same maximum response, i . e . both have the same efficacy. The e f f e c t s o f e p i appear to be produced at lower doses and, thus, f o r t h i s system, e p i i s s a i d t o be more potent than n - e p i . The shape of the curve, i . e . "S" shaped, i s c h a r a c t e r i s t i c o f these transformations. Generally speaking f o r curves of t h i s type the middle p o r t i o n of the curve tends t o approximate a s t r a i g h t line. The slope of the curved i s determined by the dosage range r e q u i r e d t o observe the e n t i r e dose-response r e l a t i o n s h i p . Anatagonism can be explored using semi-log transformations. Thus B i c k e r t o n (11) examined the e f f e c t s of two types of antagonists on the the e f f e c t s of n-epi on the c a t spleen. F i g u r e 9 shows the log dose-response curve f o r n-epi at the l e f t and the dose response curves obtained with the same doses of n-epi when t o l a z o l i n e was added at e i t h e r of two concentrations at the r i g h t . The e f f e c t s o f n-epi can s t i l l be observed but higher doses o f n-epi were r e q u i r e d t o produce the same e f f e c t . When the dose o f n-epi was r a i s e d s u f f i c i e n t l y high the e f f e c t of t o l a z o l i n e was completely overcome. Thus, t o l a z o l i n e i s a competitive antagonist o f n - e p i . I n c o n t r a s t , F i g u r e 10 shows the effect o f a d d i t i o n of dibenamine at e i t h e r of two c o n c e n t r a t i o n s . Again n-epi i s l e s s potent i n the presence of the antagonist, but i n a d d i t i o n i t i s not p o s s i b l e t o overcome the e f f e c t s of dibenamine r e g a r d l e s s of how high the dose of n o r - e p i i s made. Dibenamine i s a non-competitive antagonist and i t i s known that i t binds i r r e v e r s i b l y to r e c e p t o r s , thereby causing i n a c t i v a t i o n and hence reducing the t o t a l number of receptors a v a i l a b l e f o r s t i m u l a t i o n by n - e p i .

American Chemical Society Library 1155 16th St. N. W.

Rodricks and Tardiff; Assessment and Management of Chemical Risks Washington. D. C. Society: 20036Washington, DC, 1984. ACS Symposium Series; American Chemical


ASSESSMENT AND MANAGEMENT OF CHEMICAL RISKS

L03 Figure 7. Schematic dose-response curve.

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Norepinephrine Cone, (xio ) 7

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Basic Concepts of the Dose-Response Relationship - ACS Publications

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