A challenge for estimating cumulative risks across multiple chemicals is determining whether the responses generated from exposures to multiple chemicals simultaneously are different from estimates based on the addition of individual responses. The hypothesis of dose additivity among chemicals in a mixture is typically evaluated through empiricism. If a greater response from the mixture is observed than expected from the sum of the individual chemicals, the mixture response is described as synergism or potentiation (Figure 1). If a lower mixture response is observed than expected, the mixture response is described as antagonism or inhibition (Figure 1). To better distinguish additivity and non-additivity, many efforts have concentrated on improving the analytical capability to more accurately measure responses or on developing statistical methods to properly test the null hypothesis of dose additivity [1]. Even with the most advanced analytical and statistical tools, however, determining the cumulative risk from exposure to environmental chemicals is still a difficult challenge.

In the absence of toxicity data on the mixture of concern, data on similar/related mixtures or data on individual chemicals in the mixture may be used for assessing cumulative risk from mixture exposures. Examples of methods for conducting cumulative risk assessment include the Hazard Index (HI) approach, weight-of-evidence modification of the HI approach, the toxicity equivalency factor approach, and the relative potency factor approach [2–4]. These methods, however, lack a mechanistic basis and thus are of limited utility for high-to-low dose or animal-to-human extrapolations. For example, a study on a quaternary mixture of trihalomethanes (THMs) showed that the rat venous blood concentrations of each THM following the mixture exposure were significantly higher compared to blood concentrations observed after exposures to single chemicals [5]. This finding is consistent with the occurrence of mutual inhibition of hepatic metabolism from THMs. Without considering this kinetic information (i.e., competitive inhibition), one may not recognize that this non-additive result is unlikely to occur in humans since the threshold for significant metabolic inhibition is not reached at environmental concentrations.

When assessing the toxicity and the resulting risk of chemical mixtures, a more mechanistic approach should be taken to characterize the interactions among individual chemicals in a mixture. In this article, two types of interactions will be discussed: Pharmacokinetic (PK) and pharmacodynamic (PD) interactions [6]. Interactions related to cell signaling networks that can affect a common physiological process are also important when assessing cumulative risk, but are not the focus of this article. Simply put, PK depicts the process of chemicals being absorbed, distributed to, metabolized within, and eliminated (ADME) from various organs and tissues. The term ‘PK interaction’ refers to the case in which one unit of applied dose to chemical “X” in the presence of other chemicals leads to more or less than one unit of target tissue dose compared to exposure to chemical “X” by itself (Figure 2). Most interactions studied to date are PK interactions. On the other hand, PD describes how chemicals bring about tissue responses. The term “PD interaction” refers to the case which one unit of target tissue dose brought about by chemical “X” in the presence of other chemicals leads to more or less than one unit of tissue response compared to response caused by chemical “X” by itself (Figure 3). With the proper identification of interactions occurring at various levels, a more integrated systems approach can then be applied to provide a better perspective on how both biology and biochemistry impact mixture toxicity and cumulative risk.

The knowledge on PK or PD interactions can be integrated in a quantitative manner with a mechanistic model. A mechanistic model for chemical mixtures is composed of three major elements: (1) The interaction among individual chemicals in the mixture at the level of PK and PD; (2) Quantitative descriptions of both temporal (i.e., concurrent or sequential exposures) and dose relationships among individual chemicals; and (3) Each chemical’s mode of action. Mode of action is the sequence of events by which the active form of the chemical (parent or metabolites) interacts with the target tissue and leads to responses. A commonly used computational model that consists of all three elements described above is a physiologically based pharmacokinetic/pharmacodynamic (PBPK/PD) model.

PBPK modeling involves the development of mass-balance differential equations to describe the ADME processes of chemicals as a function of their physiochemical (e.g., tissue:blood partition coefficient), biochemical (e.g., metabolic rate constant), and physiological (e.g., tissue volume) characteristics. Typically, a PBPK model consists of a series of biologically relevant compartments, each receiving the chemical via the arterial blood and returning the free chemical via the venous blood. These compartments may represent a single tissue or a group of tissues with similar blood flow and solubility characteristics.

PBPK models of chemical mixtures involve the change of rates of ADME for one or more chemicals. The alteration of the absorption/excretion rate of a chemical as a result of the presence of other chemicals is often caused by interference with an active uptake/excretion process or by modulation of critical biological determinants of uptake (e.g., breathing rate) or excretion (e.g., glomerular filtration). The distribution rate can change when multiple chemicals compete for binding to the same macromolecules (e.g., hemoglobin, albumin, metallothionein) or proteins. The enhancement of metabolic rate (induction) can occur in the case when specific isoenzymes are induced by prior exposures to certain chemicals, leading to an increase in the enzyme capacity to metabolize other chemicals. The reduction of metabolic rate (inhibition) is a result of two or more chemicals competing for biotransformation mediated by the same enzyme. With environmental chemicals, the most common single mechanism of interaction investigated is inhibition or induction of hepatic cytochrome P450 by mixtures of chemicals [7,8]. Metabolism plays an important role in the toxicity of many chemicals, either by the detoxification of a directly toxic compound or by the formation of a metabolite that is more reactive than the parent compound [9].

Besides simulating the ADME processes, PBPK models also have the capability to simulate target tissue dose, which is the determinant of tissue reactions leading to toxicity [10]. Thus, a PBPK model can be connected to a PD model to simulate the time course of tissue response as a function of target tissue dose. The quantitative descriptions of PK and PD of individual chemicals in PBPK/PD models allows one to investigate the possibility and degree of interactions among chemicals in the PK and PD processes at different exposure scenarios. This modeling approach provides a means to evaluate mixture interactions and associated cumulative risk that are not readily available from observing the temporal and dose-response relationship of co-existing chemicals (i.e., empiricism). In addition, modeling approach has the capability to answer questions for experiments that would be too costly and complex to perform.

Another advantage of analyzing mixture interactions with a PBPK model is that mixture exposure may result in altering one biomarker while other biomarkers of the same chemical remain unchanged. For example, Tardif and Charest-Tardif exposed rats for 4 h to 1,1,1-trichloroethane or m-xylene alone or as a mixture and found that the blood concentration of 1,1,1-trichloroethane was not affected whereas that of m-xylene was increased [11]. They also found that the excretion of 1,1,1-trichloro-ethane metabolites (trichloroethanol and trichloroacetic acid) during a period of 48 h following the onset of exposure was significantly reduced [11]. These results were successfully simulated using a PBPK model with a description of competitive inhibition in the liver [7]. This example highlights the importance of conducting quantitative analysis of PK and PD interactions before selecting appropriate biomarkers to study mixture interactions. In the following sections, examples will be provided to further illustrate mixture interactions at the PK and PD levels. In addition, these examples will demonstrate how computational models can be used to enhance our ability to evaluate cumulative risk following mixture exposures by incorporating the interaction mechanisms.

Most studies reviewed in Sections 3 and 4 were conducted in animals. Only a few studies used computational models to examine the effects of PK interactions among chemicals in a mixture for human health risk assessment. These studies were all conducted in occupational settings, in which potential exposure concentrations may be high enough for interactions to occur. Some examples are presented below.

Occupational health and safety professionals use a “unity calculation” to evaluate whether over-exposure occurs when workers are exposed to mixtures of chemicals that share a common mechanism of toxicity [52]. The unity calculation first converts the exposure concentration of each chemical in the mixture to a fraction of the corresponding reference occupational exposure limit (OEL) (i.e., exposure concentration divided by the OEL). If the sum of these fractions (denoted as EM) exceeds unity (1.0), then the exposures should be reduced. This method assumes dose additivity, and it does not take into account PK or PD interactions. In a study conducted by Dennison and colleagues, the effect of PK interactions was factored in by using a human PBPK model for a mixture of toluene, ethylbeneze, and xylene to predict venous blood concentrations for a variety of exposure concentrations, as well as for different activity levels [53]. The predicted blood concentrations, instead of inhaled concentrations, were then used to derive an ‘internal dose-based EM’, which is the sum of each chemical’s blood concentration at the exposure concentration divided by that chemical’s blood concentration at the OEL. They found that the traditional unity calculation that omits PK interactions can lead to significant over-exposures [53]. For example, in an exposure scenario based on exposure to one-third of the permissible exposure limit (PEL) for each chemical, the traditional unity calculation would result in an EM of 1.0 (= 1/3 + 1/3 + 1/3). However, the EM calculated based on blood concentrations was 2.9, suggesting that the cumulative blood concentrations of the three chemicals would be three times the concentration allowed by the PELs [XX]. Dennison and colleagues also found that workers with higher activity levels may experience significantly higher absorbed doses [53].

In another study, Jang and colleagues used PBPK modeling to investigate the interaction effects of a binary exposure to ethylbenzene and xylene for male workers who had been exposed to this mixture during painting and solvent mixing [54]. The PBPK model-predicted urinary excretion of methylhippuric acid (a metabolite of xylene) were 4.94 and 1.55 g/g creatinine when workers were exposed to 100 ppm of pure xylene and a mixture of 100 ppm of xylene and 25 ppm of ethylbenzene, respectively. The predicted result was consistent with that (1.96 g/g creatinine) calculated using the linear regression equation obtained from measured xylene and ethylbenzene concentrations in air and measured methylhippuric acid in urine [54]. Jang and colleagues concluded that PK interactions due to mixture exposures can significantly complicate the interpretation of biomonitoring data, and thus, PK interactions should be considered when developing biological limit values (BLVs) for mixture exposures [54].

As reviewed in Section 3.1.1, Dobrev and colleagues used a rat PBPK model to investigate the reduction of TCE metabolism caused by co-exposure to PERC and MC [14]. Dobrev and colleagues later scaled up the rat model to a human model for evaluating the impact of metabolic interactions in humans and its implications for risk assessment [55]. They found that inhibition of TCE metabolism in the presence of PERC and MC resulted in decreased formation of oxidative metabolites, but increased the formation of conjugative metabolites, S-1,2-dichlorovinylcysteine (S-1,2-DCVC) and S-2,2-DCVC. Both oxidative and conjugative metabolites of TCE have been associated with adverse effects in animals [56]. This study clearly demonstrated that human health risk associated with exposures to chemical mixtures is complexly related to the mechanism of interactions and the identity of the toxic moiety (e.g., parent or metabolite) [55].

A similar conclusion was reached in a study that used a PBPK model for DBTEX to conduct both non-cancer and cancer risk assessments [57]. In this study, Haddad and colleagues scaled up a rat DBTEX model (reviewed in Section 3.1.2; [24]) to a human model to account for the effects of PK interactions on tissue dose metrics [57]. For the non-cancer risk assessment, the PBPK model predicted AUC of D, B, T, E, and X in the richly perfused tissue compartment (representing brain) were used as dose metrics for CNS effects; and the PBPK model predicted AUC of carboxyhemoglobin in blood was used as a dose metric for hypoxia [57]. These dose metrics were used to calculate an ‘interaction-based’ hazard index (HI) for comparison with the conventional HI based on dose addition. Haddad and colleagues showed that, at high exposure concentrations, the interaction-based estimates of HI were higher for CNS effects, but lower for hypoxia [57]. For cancer risk assessment, Haddad and colleagues used the PBPK model-predicted amount of GSH conjugates as the dose surrogate for D and predicted the amount metabolized as the dose surrogate for B. Their analyses showed that in the presence of competitive inhibitors of P450 metabolism (B/D, T, E, X), cancer risk attributed to D exposure increased; but cancer risk attributed to B exposure decreased [57].

Human PBPK models presented in the above examples were all scaled up from existing animal models. Human PBPK models can also be developed using in vitro data. For example, Haddad and colleagues developed a “physiologically based” liver model based on in vitro data to describe the inhibition, metabolism, transport, and partitioning of R-bufuralol, bunitrolol, and debrisoquine in the liver [XX]. The model was used to simulate the perfusate kinetics of each drug in an isolated perfused rat liver for the single and paired drugs. In Comparison with empirical models, the physiologically based liver model, overall, performed the best [58]. Although this work was on drug-drug interactions, the approach for the development and subsequent application of a PBPK model for investigating chemical interactions is also applicable to environmental chemicals. The use of PBPK modeling in predicting drug-drug interactions can be found elsewhere (e.g., [59–61]).

The above examples represent experience with applying human PBPK models for chemical mixtures in cumulative risk assessment for predicting conditions under which PK interactions are likely to alter the assumption of dose additivity. Human PD models, however, are yet to be utilized with PBPK models to assess responses associated with exposures to chemical mixtures that have common modes of action (e.g., cholinesterase inhibited by chlorpyrifos and carbaryl [Section 4.1]). Furthermore, the emerging discipline systems biology may assist in understanding how mixtures of chemicals affect a common physiological endpoint (e.g., interference with endocrine) by either similar or diverse modes of action in the body [6]. Systems biology studies biological systems by globally monitoring the gene, protein, and pathway responses to perturbations, integrating these data and formulating mathematical models to describe the structure of the system and its response dynamics [62]. Since the mode of action is related to the perturbation of biological systems, systems biology can help ascertain modes of actions that involve different pathway targets within cells, tissues, or organs [6]. Using PBPK/PD models of these perturbations allows us to expand the current cumulative risk assessment paradigm to focus on the biology of responses more than on the kinetics of the chemicals [6].

Environmental exposure to multiple chemicals simultaneously or sequentially is the rule rather than an exception. When conducting cumulative risk assessment for chemicals in a mixture, the PK and PD interactions among chemicals need to be characterized since these interactions may cause alterations in the toxicity predicted based on the summation of the effects of each chemical. PK interactions occur when one chemical alters the absorption, distribution, metabolism, and/or excretion of other chemical(s). PD interactions occur when one chemical alters the tissue response of other chemical(s). The knowledge on PK and/or PD interactions can be integrated in a quantitative manner with a PBPK/PD model. A PBPK model can be used for dose, route and interspecies extrapolations of the target tissue concentration of the toxic moieties. A PD model can be used for describing mechanisms of action and tissue responses. An integrated PBPK/PD model for studying chemical interactions at both the level of PK (e.g., metabolic interactions) and PD (e.g., receptor interactions) is imperative to achieve the ultimate goal of assessing the health risks associated with human exposure to complex chemical mixtures. More than a science of observation, toxicology should be a science of observation and analysis.