TOXICOKINETIC-TOXICODYNAMIC MODELING OF QUANTAL AND GRADED SUBLETHAL ENDPOINTS: A BRIEF DISCUSSION OF CONCEPTS ROMAN ASHAUER,*y ANNIKA AGATZ, z CARLO ALBERT, y VIRGINIE DUCROT,§ NIKA GALIC, k JAN HENDRIKS,# TJALLING JAGER, yy ANDREAS KRETSCHMANN, y ISABEL O’CONNOR, y #MASCHA NADINE RUBACH, kzz ANNA-MAIJA NYMAN, y §§ WALTER SCHMITT,## JULITA STADNICKA, y §§ PAUL J. VAN DEN BRINK, k and THOMAS G. PREUSS## yEawag, Swiss Federal Institute of Aquatic Science and Technology, Du ¨bendorf, Switzerland zThe University of York, Heslington, York, United Kingdom §INRA, E ´ quipe E ´ cotoxicologie et Qualite ´ des Milieux Aquatiques, Rennes, France kAlterra and Wageningen University, Wageningen, The Netherlands #Radboud University, Nijmegen, The Netherlands yyVrije Universiteit, Amsterdam, The Netherlands zzSyngenta Crop Protection, Basel, Switzerland §§ETH Zu ¨rich, Institute of Biogeochemistry and Pollutant Dynamics, Zu ¨rich, Switzerland kkBayer CropScience, Monheim, Germany ##RWTH Aachen University, Aachen, Germany (Received 17 March 2011; Returned for Revision 5 May 2011; Accepted 17 June 2011) Abstract —We report on the advantages and problems of using toxicokinetic-toxicodynamic (TKTD) models for the analysis, understanding, and simulation of sublethal effects. Only a few toxicodynamic approaches for sublethal effects are available. These differ in their effect mechanism and emphasis on linkages between endpoints. We discuss how the distinction between quantal and graded endpoints and the type of linkage between endpoints can guide model design and selection. Strengths and limitations of two main approaches and possible ways forward are outlined. Environ. Toxicol. Chem. 2011;30:2519–2524. # 2011 SETAC Keywords —Toxicity Dynamic energy budget Dose–response Adverse outcome pathway Mechanistic effect model INTRODUCTION Toxicokinetics (TK) and toxicodynamics (TD) are concepts that explain the patterns of toxic effects on organisms over time by simulating the underlying processes. The strengths of TK and TD in ecotoxicological research and risk assessment of chemicals have recently received increasing attention [1–3]. Toxicokinetics deals with the time course of the toxicant concentration at the site of toxic action, encompassing the processes of absorption (uptake, bioaccumulation), distribution, biotransformation, and elimination of a toxicant within an organism (what the organism does with the chemical). Tox- icodynamics deals with the processes that lead from the toxic action at the target site to effects on the individual organism (what the chemical does to the organism). Models that link TK and TD processes and translate exposure into time course of effects are TKTD models, which can include a range of endpoints, from survival to various sublethal effects. Toxic effects simulated with TKTD models could range from the molecular level to the life-history traits of the individual. Each level of biological organization could possibly require a differ- ent TK or TD model approach. Conceptually separating TK and TD has many benefits for ecotoxicology and risk assessment [1–4]. Applications include assessing the toxic effects for fluctuating and pulsed exposures [5–9] or time-dependent toxicity [10,11], understanding differ- ences in species’ sensitivities [12], and developing quantitative structure–activity relationships [13], as well as understanding or predicting mixture toxicity [7,14–17]. Despite the diverse and potentially very powerful applica- tions and benefits of TKTD modeling, progress has been hindered by inconsistent use of terminology, a wide range of seemingly unconnected models, and a lack of agreement among researchers about underlying assumptions. To address these issues, a technical workshop on TKTD modeling was held at Eawag, Kastanienbaum, Switzerland, in May 2010. A frame- work for modeling survival was developed that clarifies implicit model assumptions, unifies a diverse range of models within one TKTD framework, and combines the formerly exclusive concepts of stochastic death and individual tolerance distribu- tion [18]. Insights into optimal experimental design for TD parameter estimation are reported in Albert et al. [19], which was presented at the workshop. Here we focus on the advan- tages of, and problems with, TKTD modeling for the analysis, understanding, and simulation of sublethal effects. The dis- tinction between quantal and graded endpoints is discussed, followed by a brief overview of TD approaches for sublethal effects, the strengths and limitations of the two main approaches, and possible ways forward. TYPES OF SUBLETHAL EFFECTS Lessons learned from modeling survival The use of TK and TD in quantitative models requires rigorous definitions of variables and endpoints. For example, Environmental Toxicology and Chemistry, Vol. 30, No. 11, pp. 2519–2524, 2011 # 2011 SETAC Printed in the USA DOI: 10.1002/etc.639 * To whom correspondence may be addressed (roman.ashauer@eawag.ch). Published online 30 July 2011 in Wiley Online Library (wileyonlinelibrary.com). 2519