* CIIT Centers for Health Research, Research Triangle Park, North Carolina 27709; and
Department of Toxicology, University of Würzburg, 97078 Würzburg, Germany
Received May 6, 2003; accepted September 28, 2003
ABSTRACT
Dose-response curves for the first interaction of a chemical with a biochemical target molecule are usually monotonic; i.e., they increase or decrease over the entire dose range. However, for reactions of a complex biological system to a toxicant, nonmonotonic (biphasic) dose-effect relationships can be observed, showing a decrease at low dose followed by an increase at high dose, or vice versa. We present four examples to demonstrate that nonmonotonic dose-response relationships can result from superimposition of monotonic dose responses of component biological reactions. Examples include (i) a membrane-receptor model with receptor subtypes of different ligand affinity and opposing downstream effects (adenosine receptors A1 vs. A2), (ii) androgen receptor-mediated gene expression driven by homodimers, but not mixed-ligand dimers, (iii) repair of background DNA damage by enzymatic activity induced by adducts formed by a xenobiotic, (iv) rate of mutation as a consequence of DNA damage times rate of cell division, the latter being modulated by cell-cycle delay at low-level DNA damage, and cell-cycle acceleration due to regenerative hyperplasia at cytotoxic dose levels. Quantitative analyses based on biological models are shown, and factors that affect the degree of nonmonotonicity are identified. It is noted that threshold-type dose-response curves could in fact be nonmonotonic. Our analysis should promote a scientific discussion of biphasic dose responses and the concept termed "hormesis," and of default procedures for low-dose extrapolation in toxicological risk assessment.
Key Words: dose-response relationship; hormesis; mechanisms; models.
There is much debate over the shape of the dose-response curve in the low-dose zone in the fields of toxicology and human health-risk assessment. Common default models of extrapolation include a no-effect threshold for noncarcinogens and linear extrapolation for DNA-reactive carcinogens. However, numerous toxicological studies show a nonmonotonic (biphasic) dose-response curve, with either a decrease in the response below control at low dose followed by an increase at high dose (called a U-shape or J-shape), or vice versa (an "inverted U" or ß-shape). The first such observation was published in 1888, showing that low concentrations of fungicidal chemicals such as mercuric chloride increased the fermentation capacity of yeast (Schulz, 1888), while high concentrations were cytotoxic and abolished this activity. This observation was followed by numerous experiments showing that low levels of toxic chemicals or ionizing radiation stimulated various physiological processes such as growth and reproduction, while high dose had the opposite effect (review by Luckey, 1975
, 1980
).
For toxicological risk assessment and extrapolation to low dose, the idea was not well received. Besides concerns about statistical significance of the low-dose effects, one major question was whether the low-dose deviation from control could be considered to be truly beneficial. While this is obvious for most quantal endpoints of toxicity such as cancer incidence or malformation, it is not so clear for continuous data such as organ weights. The fact is that, as of today, more than 1600 toxicological dose-response relationships have demonstrated evidence consistent with the hormesis hypothesis (Calabrese and Baldwin, 2001a). While this number supports the old idea that biphasic dose responses could represent a general biological phenomenon (Stebbing, 1982
), little effort has so far been devoted to mechanistic explanation and modeling of underlying reactions.
Here, we analyze two pharmacological data sets and two toxicological examples to propose a number of biologically founded mechanisms that explain biphasic shapes of dose-response curves. For further insight and for the generation of hypotheses to be tested experimentally, we model the respective dose responses and probe the influence of changing selected kinetic parameters.
Example #1.
In the course of investigating the effect of the adenosine analog phenylisopropyladenosine (PIA) on adenylyl cyclase activity in rat brain mediated by adenosine receptor binding, a clearly nonmonotonic dose-response curve was demonstrated for the formation of cAMP in the striatum (Ebersolt et al., 1983). The biphasic dose response was explained by the antagonistic action of two adenosine receptor subtypes that regulate adenylyl cyclase in opposite directions, given appropriate differences in ligand affinity and in efficacy of signal transduction.
Example #2.
A nonmonotonic dose-response curve for androgen receptor-mediated gene transcription by hydroxyflutamide (HOF) was seen in HepG2 human hepatoma cells (Maness et al., 1998). Low HOF concentrations partially antagonized the effect of a priming dose of dihydrotestosterone (DHT), while agonistic activity was observed with a further increase in the HOF concentration. The biphasic dose response was explained by the hypothesis that receptor dimers that carry two DHT or two HOF ligands, but not mixed-ligand dimers, are transcriptionally active.
Example #3.
We take up the understanding that DNA adducts formed by an exogenous carcinogen induce DNA repair, and put forward the hypothesis that the induced repair capacity not only repairs the incremental exogenous DNA adducts, but also the background DNA damage. At low dose, the beneficial effect of repair induction could overcompensate the incremental damage. Once repair induction is saturated, the total DNA damage (background plus exogenous) observed at the high dose of the xenobiotic, will be higher than background. A nonmonotonic dose response is the result.
Example #4.
Here, we finally investigate cell division as a modulating factor for the fixation of primary DNA lesions as permanent mutations. Low-level DNA damage is assumed to slow down the cell cycle, to enable more complete DNA repair before replication. High levels of DNA-damage, on the other hand, are cytotoxic, and cell division is accelerated as a result of regenerative hyperplasia. The rate of cell division, and with this the rate of mutation, show a biphasic response with an increase in the dose of the DNA-damaging agent.
MATERIALS AND METHODS
Modeling Tools and Programming
The computational models were written in MATLAB® (The MathWorks, Inc., Natick, MA) as systems of differential and algebraic equations. Dose-response curves were built by incrementing the xenobiotic dose and simulations were run to steady state on Pentium III® PC computers, using the Windows XP® operating system. Only steady-state results are reported. The governing equations are available as a supplement linked to the on-line manuscript. The programs are available from Rory Conolly (rconolly{at}ciit.org).
RESULTS
Example #1: Membrane receptor subtypes with opposite downstream effect
Model assumptions: (1) All interactions of the adenosine analog phenylisopropyladenosine (PIA) with the adenosine receptors A1 and A2 are reversible and are described by forward and backward differential equations. Rate constants for forward reactions were set to 105 and the rates of the backward reactions were adjusted to obtain dose-response relationships as described (Ebersolt et al., 1983). (2) A1 and A2 receptors are present in equal amounts, set arbitrarily to 1. (3) PIA binding to A1 decreases the basal rate of cAMP formation by up to 25% while binding to A2 increases cAMP formation by up to 57%.
The result of our modeling analysis is shown in Figure 1. Part A shows the dose response for the occupancy of the two adenosine receptor subtypes A1 and A2, given the known dissociation constants for phenylisopropyladenosine binding. B shows the increase in cAMP formation based on A2 binding, with the experimentally established maximum effect of +57%. C shows the decrease in cAMP formation by A1 binding at various levels, including the experimentally established maximum of -25% (= curve 0.4). D combines B and C: in the absence of an effect exerted by A1 (curve 0), the curve coincides with the curve in B, showing the effect of A2 exclusively; with increasing effectiveness of A1, the dose response shows an increasingly nonmonotonic shape. In summary, non-monotonic dose-response curves can be generated for receptor-mediated effects, if the receptor is expressed with two subtypes that produce opposite effects and differ with respect to affinity and maximum effect.
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Example #2: Androgen receptor-mediated gene expression
Model assumptions: (1) all interactions (ligand-androgen receptor binding, dimer formation, binding of dimer to DNA) are reversible and are described by forward and backward differential equations. (2) The amount of androgen receptor was arbitrarily set to 1 and the amount of DNA binding capacity to 10-10. (3) Mixed-ligand AR-receptor dimers (DHT-AR||AR-HOF) were considered to be devoid of activity for gene transcription. The highest efficacy for gene transcription was attributed to the homodimer DHT-AR||AR-DHT, the homodimer HOF-AR||AR-HOF was attributed an efficacy range.
The results of our modeling are shown in Figure 2. Part A was based on the available information on androgen receptor affinity of the DHT and HOF and shows that the formation of each of the dimers has a unique dependence on the concentration of HOF. The DHT homodimer generated from the priming dose predominates at low concentrations of HOF. As HOF concentrations increase, the DHT homodimer is replaced by the mixed-ligand dimers ("heterodimers"), which in turn is replaced by the xenobiotic homodimer at even higher HOF concentrations. The DHT and the HOF homodimers are assumed to be able to promote gene transcription while mixed-ligand dimers are not. Under these conditions, the relative abundance of the three kinds of dimer, together with their assigned efficacies for promotion of gene transcription, allow the generation of nonmonotonic curves for gene transcription (B). The family of curves was obtained by varying the efficacy of HOF homodimers for promotion of gene transcription, with 1.0 representing an efficacy equivalent to DHT homodimers and the fractional values indicating decreasing efficacy. The bottom curve, with efficacy 0, describes a classical competitive inhibition curve.
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Another nuclear receptor model that can produce nonmonotonic dose responses was recently published (Kohn and Melnick, 2002). It is not based on receptor-dimer formation, but allows insight into the competition of endogenous and exogenous ligand binding.
Example #3: Induction of DNA repair and "co-repair" of background DNA damage
Model assumptions: (1) Background DNA adducts are formed at a zero-order rate and repaired with first-order kinetics. Basal repair activity is an inducible function of the background adduct level. (2) A xenobiotic forms DNA adducts with a rate proportional to the dose of xenobiotic. (3) DNA adducts formed by the xenobiotic induce a repair capacity in a saturable manner (i.e., repair can be induced only up to some maximum value). Xenobiotic-induced repair acts on both the background damage and exogenous adducts. (4) The total adduct level is the sum of background and exogenous adducts.
Part A of Figure 3 shows a monotonic increase of the exogenous DNA adduct level with increasing dose. The numbers 1 to 7 indicate the relative efficiency of the exogenous adducts for induction of repair, "efficiency 1" being the efficiency of the background adducts to induce repair on their own. The exogenous adducts induce DNA repair capacity in a saturable manner, as illustrated in B (also shown as a function of the dose of xenobiotic). (C) As a result of repair induction and co-repair of background damage, the level of background adducts is reduced with increasing doses of the xenobiotic. The level of reduction is highest when the efficiency of the exogenous adducts to induce repair is maximal (assumed to be seven-fold). D finally shows the superimposition of B and C, indicating a monotonic increase in adducts when the efficiencies of repair induction are equal for background and exogenous adducts, but exhibiting threshold-like, then nonmonotonic shapes of the dose-response curve with increasing efficiency of repair induction. A threshold-like dose-response curve arises when the rates of DNA damage and repair approximately balance out over a certain dose range.
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The hypothesis that repair processes could be responsible for nonmonotonic dose responses had been set up a long time ago (Downs and Frankowski, 1982). It did not have a sound biological foundation, however, in that it ignored defense mechanisms such as metabolic detoxification.
Example #4: Modulation of the cell cycle and effect on rate of mutation
Model assumptions: (1) the xenobiotic forms DNA adducts with a rate proportional to the dose of xenobiotic. Potencies range from 1 to 5. (2) Adducts are repaired at a first-order rate, which means the total adduct level is proportional to dose. (3) The rate of cell division is reduced as a saturable function of the adduct level, with a maximum reduction of 50%. (4) The cell-death rate is a sigmoidal function of the adduct burden. (5) The rate of regenerative proliferation as a function of adduct burden is the same as the rate of cell death due to the adduct burden. (6) The effect of adducts in slowing the rate of cell division is maintained, even at the high adduct burdens associated with an increased rate of cell death.
This example is based on the assumption of a dose-linear adduct burden (Fig. 4A). DNA adducts are assumed to result in a cell-cycle delay (part B, curve x) with a maximum effect of doubling the cell cycle time. B (curve y) shows a sigmoidal dose response for cytotoxicity and regenerative hyperplasia that accompanies higher adduct levels. Upon combination of curves x and y (= curve z), a nonmonotonic shape of the dose-response curve for the rate of cell division is the result. (C) The result of multiplication of adduct levels (A) with the rate of cell division (B, curve z) is shown, which is indicative of the rate of mutation. Curves 15 correspond to the increasing potency of the xenobiotic for DNA adduct formation, as shown in A.
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Agents that increase DNA damage usually are cytotoxic at higher doses, and tumor incidence may be increased only at cytotoxic dose levels, as a result of regenerative hyperplasia. The first data showing a nonmonotonic dose response for cell division was with caffeic acid, where the labeling index in the target organs for tumor induction showed a J-shaped dose response (Lutz et al., 1997). These data also formed the basis for modeling the dose response for tumor induction, using the two-stage carcinogenesis model with clonal expansion (Kopp-Schneider and Lutz, 2001
; Lutz and Kopp-Schneider, 1999
). The most prominent example for this type of situation is formaldehyde. It increases nasal tumor incidence only at cytotoxic dose levels. Interestingly, at low exposure levels, the labeling index was below control, so that the full dose response was nonmonotonic (Conolly et al., 2002
).
Since most cancer models include cell birth and death, it is no surprise that the respective modulation has stimulated other types of analysis of nonmonotonic dose responses. Besides the ones cited above, a model that permits a controlled birth-and-death process for precursor cells has recently been presented (Whitaker and Portier, 2002). It extends the analysis of the cell cycle to aspects of cell differentiation and development.
DISCUSSION
Our examples illustrate that nonmonotonic dose-response relationships can be explained by straightforward biochemical processes (Examples #1 and 2) or postulated on the basis of reasonable biological hypotheses (Examples #3 and 4). Numerous additional mechanisms can be put forward, e.g., overshooting homeostatic feedback control or shifts in immune responses, to name just two. Some may simply be derived from superimposition of counteracting monotonic dose responses (Examples #1 and 4) (Lutz, 1998), others may be more complex, involving modulation of the activity of endogenous factors (Example #2) or of the background DNA damage (Example #3).
For a nonmonotonic dose response to be detectable, a control measure or a background incidence at dose 0 is a prerequisite. In Example #1, a constitutive receptor activity was responsible for background adenylyl cyclase activity. In Example #2, a given concentration of endogenous dihydrotestosterone was the starting point. Example #3 was based on the presence of background DNA damage. Example #4 also included a background rate of cell turnover. The study of mechanisms of action of toxic chemicals should therefore no longer be limited to the interaction of the chemical with its first line reaction partner. Modulation by the xenobiotic of processes that govern a control level or a spontaneous incidence might be a clue to the understanding of low-dose effects. As the topic of our companion publication (Gaylor et al., 2003), we examine whether a decrease of the background measure at low dose can be assessed in a statistically significant manner.
For a low-control activity and a small decrease at low dose, the nonmonotonic shape of the dose response might not be evident. The curve can appear as threshold. Numerous toxicological data sets show this type of dose response, which is also seen in some of the curves shown in our figures. Changing critical model parameters can lead to a group of curves that often include a threshold-like example. Since a "true" threshold in a mathematical definition cannot be explained in the context of toxicity data (Slob, 1999), some of the observed threshold-like dose responses in toxicity testing may be nonmonotonic (Calabrese and Baldwin, 2003b
). This hypothesis could reconcile diverging interpretations of such data (Lutz et al., 2002
, 2000
).
Concepts Supporting Low-Dose Linearity Questioned
The first interaction of a toxic agent with its primary biological target molecule follows the law of mass action, which results in a monotonic dose response. For a receptor-ligand complex-formation reaction R + L < = > RL; for instance, the dose response is described by [RL]/[Rtot] = [L]/([L] + KD). With decreasing ligand concentration [L], the denominator tends to KD, so that the equation becomes quasi-linear with [L]. Therefore, a linear default extrapolation to low dose appears to be appropriate. In fact, low-dose linear behavior has been assumed by the U.S. EPA (2000) for receptor-mediated toxicity; for example, for the toxicity of dioxin mediated through binding to the Ah receptor.
Similar arguments can be put forward for the formation of DNA adducts. All processes that govern the rate of adduct formation are first-order reactions, as long as the concentration is far below the dissociation constant of enzymatic reactions involved (Lutz, 1990). However, DNA adducts are not mutations, mutations are not cancer, so the fact that the rate of adduct formation is proportional to dose at low levels does not, per se, mean that cancer incidence is proportional to dose. An "additivity to background" hypothesis was the basis for justification of linear low-dose extrapolation of cancer risk for DNA-damaging carcinogens (Crump et al., 1976
) "...if carcinogenesis by an external agent acts additively with any already ongoing process, then under almost any model the response will be linear at low dose." In view of the fact that DNA damage is unavoidable (Gupta and Lutz, 1999
) this assumption originally (Krewski et al., 1995
) made sense also to the corresponding author of this paper.
The additivity-to-background concept for tumor induction by DNA-damaging carcinogens was based on one single mode of action, i.e., formation of DNA adducts, and no distinction was made between background DNA damage and the incremental adducts with regards to the overall response. Today, new information on the consequences of adducts has to be considered. DNA adducts formed by exogenous carcinogens may not be equated with background adducts. Differences are expected when the capability of an adduct induces DNA repair and/or delays the cell cycle. Furthermore, DNA is only one of many possible reaction partners for a reactive carcinogen. The majority of adducts formed by genotoxic carcinogens occurs on protein. Protein damage could, in its own right, result in a cellular-defense reaction and have an effect on the background process of carcinogenesis by causing changes in gene expression. In view of these differences, the additivity-to-background argument may no longer be a generally acceptable concept for a complex toxic response of an organism.
Low-dose linearity, as a default assumption, might be appropriate in the absence of data and with the need to protect the public health (U.S. EPA, 1986, 1999
). Risk assessments that depend heavily on default assumptions are inevitably uncertain, and low-dose-linear extrapolations are expected to overestimate the actual risk most of the time. This means that the costs of compliance with default-based regulations may be greater than is actually needed to protect the public health. In view of the large number of experimental data that indicate nonmonotonic dose responses (Calabrese and Baldwin, 2003b
), mathematical extrapolation models such as the linearized multi-stage model of carcinogenesis should allow for negative values of the coefficient of the linear term and include a lower limit of the respective confidence interval.
Our biologically based models indicate that the linear default assumption cannot reflect the complexity of responses of a biological system. A ligand does not interact exclusively with one receptor, and gene transcription is not simply proportional to the concentration of one type of receptor-ligand complex; a DNA-reactive carcinogen does not simply form promutagenic DNA lesions. Therefore, endocrine disruption should no longer be described simply by the formation of a receptor-ligand complex; carcinogenesis is not adequately described by the formation of DNA adducts alone. Actions of a toxic agent in an organism are multifaceted, the reaction of the organism accordingly is pleiotropic, the dose response is the result of a superimposition of all interactions that pertain.
Nonmonotonic dose-response curves are increasingly dealt with under the name "hormesis." This is the term originally given to describe stimulatory effects of low levels of potentially toxic agents or ionizing radiation. For most historical examples, the stimulation was measured in the form of growth or reproduction; toxicity at high dose was usually registered as death of a cell or organism (Luckey, 1975, 1980
). The hormetic reaction was interpreted as an adaptive response to counteract perturbing effects of environmental variables with a switch to maximal growth, in an attempt to secure survival of the species. Overshooting of a homeostatic feedback mechanism was the usual explanation of the phenomenon (Stebbing, 1987
).
More recently, hormesis has been postulated as a generalizable and unifying hypothesis for all endpoints of toxicity (Calabrese and Baldwin, 2003a,c
). While our analysis may provide a mechanistic basis for a number of nonmonotonic dose-response curves, we do not consider this to indicate universality for mechanisms of toxicity. While growth stimulation at low external stress may indeed be a generalizable phenomenon, we consider it premature to extrapolate the phenomenon to all endpoints of toxicity. For this to hold, response axes of dose-response curves would have to be assigned both adverse and beneficial directions. While this appears to be possible for incidence measures such as for tumor formation or malformation, it is by far not obvious for continuous measuresfor instance, for hormone levels or activity of immune cells or cytokines. The fundamental problem of how to assign adversity to a measured change has to be addressed before a more general interpretation of a nonmonotonic dose response can be considered for toxicology.
Extrapolation of a toxic response from high dose to low is a fundamental problem in toxicology and human health-risk assessment. Toxicity testing and mechanistic research with laboratory animals typically uses doses well in excess of the doses received by people. Since the shape of the dose-response curve is determined by complex toxicokinetic and toxicodynamic processes, and since the underlying mechanisms are usually not well characterized, the laboratory data in most cases tell us little or nothing about the actual risks associated with low-level human exposures. A science-based approach to this extrapolation problem is needed. It should not be limited to the first line interaction of the chemical with a target molecule but should include a comprehensive approach, following the ideas of systems biology (Kitano, 2002) and taking advantage of adequate modeling (Csete and Doyle, 2002
).
ACKNOWLEDGMENTS
This work was funded in part by the United States Air Force through subcontract number 740889.3000-00 with Parsons Engineering Science, Inc., and in part by the Long-Range Research Initiative of the American Chemistry Council through a grant to the CIIT Centers for Health Research.
NOTES
1 To whom correspondence should be addressed at the Department of Toxicology, University of Würzburg. 9 Versbacher St., 97078 Würzburg, Germany. Fax: +49 931 20148446. E-mail: lutz{at}toxi.uni-wuerzburg.de.
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