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Death dilemma and organism recovery in ecotoxicology
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2 3
Roman Ashauera,b*, Isabel O’Connora,†, Anita Hintermeistera,‡ & Beate I. Eschera,c,d
4 5 6 7 8 9 10
a
Department of Environmental Toxicology, Eawag - Swiss Federal Institute of Aquatic Science and
Technology, 8600 Dübendorf, Switzerland b
Environment Department, University of York, Heslington, York YO10 5DD, United Kingdom
c
Cell Toxicology, Helmholtz Centre for Environmental Research – UFZ, Leipzig, Germany
d
Environmental Toxicology, Center for Applied Geosciences, Eberhard Karls University Tübingen,
Germany
11 12
* Correspondence to:
[email protected], phone: +44-1904-324052
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† Present address: Agroscope, Institute for Plant Production Sciences (IPS), Schloss 1, 8820
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Wädenswil, Switzerland.
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‡ Present address: Analytics Department, TESTEX AG, Swiss Textile Testing Institute,
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Gotthardstrasse 61, 8027 Zürich, Switzerland.
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Abstract: Why do some individuals survive after exposure to chemicals while others die? Either,
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the tolerance threshold is distributed amongst the individuals in a population, and its exceedance
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leads to certain death, or all individuals share the same threshold above which death occurs
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stochastically. The previously published General Unified Threshold model of Survival (GUTS)
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established a mathematical relationship between the two assumptions. According to this model
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stochastic death would result in systematically faster compensation and damage repair mechanisms
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than individual tolerance. Thus we face a circular conclusion dilemma because inference about the
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death mechanism is inherently linked to the speed of damage recovery.
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We provide empirical evidence that the stochastic death model consistently infers much slower
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toxicodynamic recovery than the individual tolerance model. Survival data can be explained by
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either, slower damage recovery and a wider individual tolerance distribution, or faster damage
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recovery paired with a narrow tolerance distribution. The toxicodynamic model parameters
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exhibited meaningful patterns in chemical space, which is why we suggest toxicodynamic model
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parameters as novel phenotypic anchors for in vitro to in vivo toxicity extrapolation. GUTS appears
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to be a promising refinement of traditional survival curve analysis and dose response models.
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Keywords: Survival analysis, dose response, ecotoxicology, chemical assessment, hazard model
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Introduction
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Why don’t all individuals die at the same dose?
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The sigmoidal shape of concentration-response curves raises the question: why don’t all individuals
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in the tested population die at the same concentration or time? Either, the tolerance threshold is
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distributed amongst the individuals in a population, and its exceedance leads to certain death, or all
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individuals share the same threshold above which death occurs stochastically1, 2. Recent theoretical
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advances have established a mathematical relationship between the two assumptions and resulted in
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the General Unified Threshold model of Survival (GUTS)3. Both assumptions lead to the typically
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observed sigmoidal concentration-response curves, but the time course of mortality differs
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markedly. More importantly, stochastic death would result in systematically faster compensation
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and damage repair mechanisms than individual tolerance. Thus we face a circular conclusion
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dilemma because inference about the death mechanism is inherently linked to the speed of damage
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recovery. Two complementary assumptions describe the limit cases of what is, probably, a mix of
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both in reality: (i) the tested individuals share a common tolerance threshold and when that is
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exceeded they die at random (stochastic death), or (ii) each individual has its own tolerance
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threshold above which it dies immediately, and the tolerances of many individuals follow a
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statistical distribution in the tested population (individual tolerance)3 (Figure 1A).
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Mathematical models of both assumptions have been unified in GUTS; however, inference about
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the prevalent nature of death in a given set of mortality or survival data is impossible without
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considering the rate of toxicodynamic recovery. The classic example from Newman & McCloskey2
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illustrates the challenge: Consider the hypothetical example of 100 fish exposed to a pulse of
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toxicant that kills half of them. The surviving fish are transferred to clean water for a duration that
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is long enough to allow full recovery and then they are exposed to the exact same pulse of toxicant
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again. How many fish will survive the second pulse? The answer depends: Stochastic death (SD)
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would predict that 25 fish survive, whereas assuming an individual tolerance (IT) distribution
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predicts that all 50 fish survive the second pulse (Figure 1A). Crucially, this thought experiment
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requires full organism recovery between the pulses otherwise carry-over toxicity could cause 25
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fish to die also under the assumption of IT. The experiment with the two pulses might seem like a
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good test for carry-over toxicity and organism recovery, but the only unambiguous outcome would
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be the observation of all 50 fish surviving the second pulse, which can be rationalised by IT. All
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other outcomes can be explained by different combinations of the nature of death and organism
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recovery (Figure 1B). This is the ‘death dilemma’. A constant exposure to a toxicant or other
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stressor will also lead to different outcomes: any exposure that kills at least one individual will
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eventually kill the whole population when assuming SD, whereas the assumption of IT will result in
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mortality levelling off at toxicokinetic and toxicodynamic steady-state (Figure 1C, aka: incipient
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lethal level4).
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How to study toxicodynamic recovery?
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Toxicodynamic recovery is a result of cellular and physiological compensating mechanisms and
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repair in an organism’s stress response to the chemical insult. However, when we quantify
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toxicodynamic recovery in a model, the above considerations imply slower organism recovery in
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the case of IT, and faster recovery in the case of SD (Figure 1). Thus when analysing survival data
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we face the dilemma of having to infer the stochastic or deterministic nature of death and at the
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same time quantifying the speed of toxicodynamic recovery. This entanglement requires explicit
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representation of recovery and assumptions about death in the toxicodynamic model.
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The toxicodynamic clustering hypothesis
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In 2007 we hypothesised that “compounds with the same mode of action cluster together in the
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first. In 2009 Jager & Kooijman demonstrated patterns in the parameters of GUTS-SD for fish, but
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without clear separation of toxicokinetics and toxicodynamics6. The GUTS framework provides the
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theory to solve the ‘death dilemma’ and enables systematic experimentation to test two related
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hypotheses in this study: (i) assuming individual tolerance results in slower toxicodynamic
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recovery, and (ii) toxicodynamic parameters cluster according to the chemical mode of action. In
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other words: to better understand toxicodynamic parameters we mapped them across chemicals and
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toxic modes of action, analysed patterns in their values and tested if the differences in recovery
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rates between IT and SD as predicted by theory manifested themselves in survival data.
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Study overview and rationale
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The first step is to quantitatively differentiate toxicokinetic processes (uptake, biotransformation
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and elimination) from toxicodynamic processes (interaction with biological target and toxic effect).
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In previous work we experimentally quantified the uptake, biotransformation and elimination rates
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of 14 synthetic organic chemicals in the aquatic invertebrate Gammarus pulex and built a
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toxicokinetic model7. With the additional toxicity experiments presented here we are able to
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construct a toxicokinetic-toxicodynamic model for each compound where the toxicokinetic part
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simulates the time course of the internal concentrations. The sums of internal concentrations of the
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toxicologically active chemicals over time are the biologically effective doses and serve as inputs
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for the new toxicodynamic model part (Figure S3). The toxicodynamic model links the biologically
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effective dose to the survival data. In a second step we fitted two toxicodynamic models for each of
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the 14 compounds: GUTS-IT assumes individual tolerance, and GUTS-SD assumes stochastic
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death3, 8. This analysis enables us to learn about the nature of death and its relation to
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toxicodynamic recovery; and extract mechanistic signals from survival data.
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Materials and methods
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Chemicals, test organisms & experiments
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We measured the time-course of survival of the freshwater amphipod Gammarus pulex when
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exposed to 14 toxicants separately (listed below) in repeated pulsed toxicity tests 8, 9. G. pulex were
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collected from a headwater stream [Itziker Ried, 20km southeast of Zürich, Switzerland, E 702150,
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N 2360850], acclimatized to laboratory conditions (pre-aerated artificial pond water (APW), 13°C,
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12:12 light:dark) and fed horse-chestnut leaf discs (pre-conditioned with the fungi Cladiosporium
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herbarum) 10. Experimental treatments consisted of seven or eight replicate beakers (600 mL) filled
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with 500 mL APW, ad libitum leaf discs and initially ten individual G. pulex per beaker. Survival
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was usually measured daily (see Model Fits: Figures S6-S19 & raw data file). We dosed a mixture
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of 14C-labelled and unlabelled material and frequently measured the actual exposure concentration
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during the experiments by Liquid Scintillation Counting (LSC) in 1 ml aliquots of the test
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solutions8, 9. G.pulex were exposed to each test chemical in separate experiments.
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Additional survival data was taken from four day toxicity tests with constant exposure11 and
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previous studies9,
12
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Dichloroaniline,
1,2,3-Trichlorobenzene,
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Trichlorophenol, 4,6-Dinitro-o-cresol, Aldicarb, Carbofuran, Carbaryl, Diazinon, Malathion,
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Chlorpyrifos, Sea-nine and 4-Nitrobenzyl-chloride. The CAS numbers can be found in Table S2.
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We used the same batches of
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labelled Chlorpyrifos, Pentachlorophenol, Carbaryl, Malathion, Aldicarb, Carbofuran, Imidacloprid
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were supplied by the Institute of Isotopes, Budapest, Hungary. 2,4-Dichloroaniline, 2,4-
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Dichlorophenol, 1,2,3-Trichlorobenzene, 4,6-Dinitro-o-cresol, 2,4,5-Trichlorophenol, Ethylacrylate,
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4-Nitrobenzyl-chloride were supplied by American Radiolabeled Chemicals, St. Louis, USA. Sea-
(Table S1). Overall we analysed data for fourteen compounds: 2,4-
14
2,4-Dichlorophenol,
Pentachlorophenol,
C-labelled compounds as in the toxicokinetic studies
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7, 9
2,4,5-
. The
14
C-
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nine (4,5-Dichloro-2-octyl-3-isothiazolone) was supplied by Amersham (GE Healthcare), UK.
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Unlabelled material of these compounds was of analytical grade and purchased from Sigma-
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Aldrich, Buchs, Switzerland, except for Sea-Nine (>97% purity, Rohm and Haas), which was a gift
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of Christ Chemie AG, Rheinach, Switzerland.
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The pulsed toxicity tests generally followed the design established previously8, 9, in which test
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organisms were exposed to pulses of toxicant of one day duration, then transferred to clean medium
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for intervals of varying duration (treatment), followed by a second pulse of the same concentration
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and duration. Survival was measured daily throughout the experiment, including a follow-up period
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after the last pulse. This design allows for depuration of toxicant and different degrees of recovery
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between pulses. The overall durations of the pulsed toxicity tests were between 6 and 28 days
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(Table S1). Raw data is provided in the supplemental material, including measured time series of
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exposure concentrations and survival in the pulsed toxicity tests (Figures S6-S19).
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Modelling approach
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The time-course of the sums of internal concentrations of toxicologically active chemicals in the
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tested organisms (Table S3) was simulated using previously established toxicokinetic models7, 9 and
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served as input for GUTS-IT and GUTS-SD3, 8. Scaled damage was the dose metric in both
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toxicodynamic models (for an explanation of scaled damage see the original GUTS publication3).
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Toxicodynamic parameters were estimated by maximising the likelihood (see equation (8) below)
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with a combination of Monte-Carlo sampling of the parameter space and optimization with the
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downhill simplex algorithm.
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The models were implemented in ModelMaker (version 4, Cherwell Scientific Ltd., Oxford, UK).
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First the background hazard rate was fitted to the control survival data from each experiment,
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assuming constant background hazard through time (this can be replaced with a different model for Page 7 of 29
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background hazards that change through time, e.g. Weibull13). Then the toxicodynamic parameters
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were fitted to the survival data from all the treatments. Wherever possible we used data from the
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pulsed toxicity tests in conjunction with data from standard toxicity tests11 because the combination
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of pulsed and constant exposures maximises the information gain for this type of model14.
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History and assumptions of GUTS
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GUTS is the current synthesis of a range of assumptions and toxicokinetic-toxicodynamic models
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traditionally used to describe survival data in (eco)toxicology3,
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evolved out of the need to understand and describe the time course of toxicity data and they have
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been reviewed previously3, 15, 23, 24. Common to these models is that they relate a dose metric to
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mortality, where the dose metric is allowed to vary over time. Common dose metrics are external
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concentrations (i.e., concentration in experimental media), scaled internal concentrations, internal
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whole body concentrations, scaled damage and damage. GUTS does not prescribe the use of any of
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these dose metrics, it can be used with any dose-metric as long as there is consistency within one
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study. Here, we chose to simulate internal whole body concentrations and use the scaled damage as
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dose metric because we want to quantify toxicodynamic parameters without confounding them with
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toxicokinetics.
15
. Historically these models16-22
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Traditionally effect models relate mortality to the maximum concentration, critical body residue or
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the area under the curve. Inherent in these choices are assumptions about the speed of
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toxicodynamic recovery, for example using the maximum concentration assumes very fast
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toxicodynamic recovery and using the area under the curve assumes very slow toxicodynamic
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recovery. It has been shown that these assumptions, when expressed mathematically, translate into a
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sub-set of the traditionally used toxicodynamic models3,
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certain groups of chemicals and are difficult to ascertain as discussed in the introduction, the
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suitability of the corresponding models is often not given or unclear. GUTS resolves this problem
15
. As these assumptions hold only for
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because it does not require a priori assumptions about the speed of toxicodynamic recovery3. This is
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why it has been suggested that GUTS is applicable to a wide range of chemicals with diverse modes
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of action and speeds of toxicodynamic recovery3. However GUTS requires the assumption that
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toxicodynamic recovery can be approximated with first order kinetics, and that the link between the
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dose metric and mortality can be modelled with a proportionality constant (killing rate constant, see
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below) between the dose metric and the hazard rate and a distribution for the threshold3. Here we
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assumed a log-logistic distribution of the threshold (see Eq. 6 below), but other distributions are
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possible too. Further we assume time-invariable model parameters, which implies that organisms do
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not change substantially during the experiment (e.g., no physiological adaptation) and we ignore
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variability in toxicokinetics between organisms.
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Toxicokinetic model
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The time-course of internal concentrations in G. pulex was simulated using a previously established
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toxicokinetic model7, 9:
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, ( )
(1)
199 200
= () × , − , () × , − ∑" , () × ! ," #
,$ ( )
= , () × ! ," − ," () × ,"
(2)
201
Where Cinternal,p(t) is the concentration of the parent compound in the organism [nmol/kgw.w.], Cw(t)
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is the concentration of the parent compound in the water [nmol/L], Cinternal,j(t) is the concentration of
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biotransformation product j in the organism [nmol/kgw.w.], kin,p is the uptake clearance coefficient
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[L/(kgw.w.×d)], kout,p is the elimination rate constant of the parent compound [1/d], kmet,j is the first-
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order biotransformation rate constant for formation of metabolite j [1/d] and kout,j is the elimination
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rate constant of the biotransformation product j.
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As there was a maximum of three different biotransformation products, j took values between 1 and
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3. For some parent compounds we did not detect any biotransformation7 and for others we modelled
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the toxicity using the sum of the internal concentrations of parent compound and biotransformation
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products as driving variable for the toxicodynamic model (e.g. for baseline toxicity, see Table S3).
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In both those cases the toxicokinetic model reduces to equation (1) without the biotransformation
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term.
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Dose metric
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The dose metric is the state variable which is compared with the threshold (Figure S2). We used the
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two limit cases of GUTS, GUTS-SD and GUTS-IT, both with scaled damage as dose metric. The
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scaled damage is a proxy for the toxicodynamic state of the organism3 and is calculated based on
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the sums of the internal concentrations of the toxicologically active chemicals (Table S3):
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dDscaled (t ) = k r × (Csum tox, organism (t ) − Dscaled (t ) ) dt
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Where Dscaled(t) is the time course of the scaled damage [nmol/kgw.w.], t is time [d], Csum tox, organism(t)
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is the time course of the sums of the internal concentrations of the toxicologically active chemicals
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in the organism [nmol/kgw.w.] and kr is the damage recovery rate constant [1/d]. The damage
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recovery rate constant captures the time course of toxicodynamics and we use two different
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parameters kr SD and kr IT for the two limit cases of GUTS.
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Effects on survival in GUTS-SD
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Here, the hazard rate is the probability of an organism dying at a given point in time and, assuming
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it increases linearly with the damage above the threshold, is calculated as3, 8, 22:
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%( )
= & × '()(*+, () − -, 0) + ℎ_2345367
(3)
(4)
229
Where dH(t)/dt is the hazard rate [1/d], kk is the killing rate constant [kgw.w./(nmol×d)], Dscaled(t) is
230
the time course of the scaled damage [nmol/kgw.w.], t is time [d], z is the threshold [nmol/kgw.w.] and Page 10 of 29
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h_controls is the background hazard rate (control mortality rate, assumed to be constant through
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time) [1/d]. The survival probability, i.e. the probability of an individual to survive until time t, is
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given by:
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S (t ) = e − H (t )
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Where S(t) is the survival probability [unitless].
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Effects of survival in GUTS-IT
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Here we assume a log-logistic distribution of the threshold in the tested population (individual
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tolerance)3, 8. Then the cumulative log-logistic distribution of the tolerance threshold in the test
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population, which changes over time as individuals die, is calculated as:
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F (t ) =
241
Where F(t) is the cumulative log-logistic distribution of the tolerance threshold over time [unitless],
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Dscaled(t) is the time course of the scaled damage [nmol/kgw.w.], t is time [d], τ is time [d], α is the
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median of the distribution [nmol/kgw.w.] and β is the shape parameter of the distribution [unitless].
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Under the assumption of individual tolerance the survival probability is then given by 3, 8:
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S (t ) = (1 − F (t ) ) × e − h _ controls×t
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Where S(t) is the survival probability [unitless] and h_controls is the background hazard rate
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(control mortality rate, assumed to be constant through time) [1/d].
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Likelihood function and parameter estimation
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The parameters for GUTS-SD and GUTS-IT were found by maximising the ln(likelihood)
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function3:
(5)
1 max Dscaled (τ ) 1 + 0< τ