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Defining an additivity framework for mixture research in inducible whole-cell biosensors.

Martin-Betancor K, Ritz C, Fernández-Piñas F, Leganés F, Rodea-Palomares I - Sci Rep (2015)

Bottom Line: A novel additivity framework for mixture effect modelling in the context of whole cell inducible biosensors has been mathematically developed and implemented in R.Specifically, the extension accounts for differential maximal effects among analytes and response inhibition beyond the maximum permissive concentrations.The biosensor was found to respond in a near additive way to heavy metal mixtures except when Hg, Co and Ag were present, in which case strong interactions occurred.

View Article: PubMed Central - PubMed

Affiliation: Departament of Biology, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain.

ABSTRACT
A novel additivity framework for mixture effect modelling in the context of whole cell inducible biosensors has been mathematically developed and implemented in R. The proposed method is a multivariate extension of the effective dose (EDp) concept. Specifically, the extension accounts for differential maximal effects among analytes and response inhibition beyond the maximum permissive concentrations. This allows a multivariate extension of Loewe additivity, enabling direct application in a biphasic dose-response framework. The proposed additivity definition was validated, and its applicability illustrated by studying the response of the cyanobacterial biosensor Synechococcus elongatus PCC 7942 pBG2120 to binary mixtures of Zn, Cu, Cd, Ag, Co and Hg. The novel method allowed by the first time to model complete dose-response profiles of an inducible whole cell biosensor to mixtures. In addition, the approach also allowed identification and quantification of departures from additivity (interactions) among analytes. The biosensor was found to respond in a near additive way to heavy metal mixtures except when Hg, Co and Ag were present, in which case strong interactions occurred. The method is a useful contribution for the whole cell biosensors discipline and related areas allowing to perform appropriate assessment of mixture effects in non-monotonic dose-response frameworks.

No MeSH data available.


Related in: MedlinePlus

Applicability of Loewe additivity.Typical dose-response profiles for (a) classical monotonic dose-response curves for chemicals A and B showing identical maximal effects, (b) classical monotonic dose-response curves for chemicals A and B presenting differential maximal effects, and (c) biosensor type biphasic dose-response curves for chemicals A and B presenting differential maximal effects and toxicity threshold. The meanings of the terms presented in the figure can be found in theory section.
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f1: Applicability of Loewe additivity.Typical dose-response profiles for (a) classical monotonic dose-response curves for chemicals A and B showing identical maximal effects, (b) classical monotonic dose-response curves for chemicals A and B presenting differential maximal effects, and (c) biosensor type biphasic dose-response curves for chemicals A and B presenting differential maximal effects and toxicity threshold. The meanings of the terms presented in the figure can be found in theory section.

Mentions: The prediction of the expected effect of chemical mixtures when only the effect of individual components is known is a hot topic in pharmacology, toxicology, and ecotoxicology123. A central element in mixture research is the definition and mathematical formulation of additivity245. At present, there are two sound pharmacological definitions of additivity: Loewe additivity6 and Bliss independence7, which are the foundations of the so-called Concentration addition (CA) and Independent Action (IA) additivity models, respectively8. Departures from Loewe additivity can be quantitatively studied based on the Combination Index (CI)49. The crucial prerequisite for the applicability of any additivity model is to fulfill certain mathematical assumptions5. The basic mathematical feature of Loewe additivity is that the effects of the mixture components could be formulated in terms of a common effective dose (EDp). For instance, this requisite is trivially met when all individual mixture components present identical maximal effects, (see Fig. 1a). An important complication occurs with mixtures of chemicals that show differential maximal effects: When this happens, additivity hypothesis can only be formulated up to the effect levels achieved by the less potent compound present in the mixture due to inherent mathematical features of the additivity definition5 (Fig. 1b). An additional challenge for formulating the additivity hypothesis occurs when the studied response is susceptible to result in non-monotonic biphasic dose-response patterns (see Fig. 1c). Besides, in biphasic dose-response curves, two different concentrations can result in the same fractional effect (Fig. 1c), resulting in misleading conclusions5. These problems have hampered the applicability of additivity models in important areas where differential maximal effects and biphasic dose-response patterns are commonly observed, such as in hormetic effects10, hormone agonists/antagonists research11, AhR agonists/antagonists activity research5, endocrine disrupters activity research1213, and in general in the field of inducible (turn-on) whole cell biosensors.


Defining an additivity framework for mixture research in inducible whole-cell biosensors.

Martin-Betancor K, Ritz C, Fernández-Piñas F, Leganés F, Rodea-Palomares I - Sci Rep (2015)

Applicability of Loewe additivity.Typical dose-response profiles for (a) classical monotonic dose-response curves for chemicals A and B showing identical maximal effects, (b) classical monotonic dose-response curves for chemicals A and B presenting differential maximal effects, and (c) biosensor type biphasic dose-response curves for chemicals A and B presenting differential maximal effects and toxicity threshold. The meanings of the terms presented in the figure can be found in theory section.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4660423&req=5

f1: Applicability of Loewe additivity.Typical dose-response profiles for (a) classical monotonic dose-response curves for chemicals A and B showing identical maximal effects, (b) classical monotonic dose-response curves for chemicals A and B presenting differential maximal effects, and (c) biosensor type biphasic dose-response curves for chemicals A and B presenting differential maximal effects and toxicity threshold. The meanings of the terms presented in the figure can be found in theory section.
Mentions: The prediction of the expected effect of chemical mixtures when only the effect of individual components is known is a hot topic in pharmacology, toxicology, and ecotoxicology123. A central element in mixture research is the definition and mathematical formulation of additivity245. At present, there are two sound pharmacological definitions of additivity: Loewe additivity6 and Bliss independence7, which are the foundations of the so-called Concentration addition (CA) and Independent Action (IA) additivity models, respectively8. Departures from Loewe additivity can be quantitatively studied based on the Combination Index (CI)49. The crucial prerequisite for the applicability of any additivity model is to fulfill certain mathematical assumptions5. The basic mathematical feature of Loewe additivity is that the effects of the mixture components could be formulated in terms of a common effective dose (EDp). For instance, this requisite is trivially met when all individual mixture components present identical maximal effects, (see Fig. 1a). An important complication occurs with mixtures of chemicals that show differential maximal effects: When this happens, additivity hypothesis can only be formulated up to the effect levels achieved by the less potent compound present in the mixture due to inherent mathematical features of the additivity definition5 (Fig. 1b). An additional challenge for formulating the additivity hypothesis occurs when the studied response is susceptible to result in non-monotonic biphasic dose-response patterns (see Fig. 1c). Besides, in biphasic dose-response curves, two different concentrations can result in the same fractional effect (Fig. 1c), resulting in misleading conclusions5. These problems have hampered the applicability of additivity models in important areas where differential maximal effects and biphasic dose-response patterns are commonly observed, such as in hormetic effects10, hormone agonists/antagonists research11, AhR agonists/antagonists activity research5, endocrine disrupters activity research1213, and in general in the field of inducible (turn-on) whole cell biosensors.

Bottom Line: A novel additivity framework for mixture effect modelling in the context of whole cell inducible biosensors has been mathematically developed and implemented in R.Specifically, the extension accounts for differential maximal effects among analytes and response inhibition beyond the maximum permissive concentrations.The biosensor was found to respond in a near additive way to heavy metal mixtures except when Hg, Co and Ag were present, in which case strong interactions occurred.

View Article: PubMed Central - PubMed

Affiliation: Departament of Biology, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain.

ABSTRACT
A novel additivity framework for mixture effect modelling in the context of whole cell inducible biosensors has been mathematically developed and implemented in R. The proposed method is a multivariate extension of the effective dose (EDp) concept. Specifically, the extension accounts for differential maximal effects among analytes and response inhibition beyond the maximum permissive concentrations. This allows a multivariate extension of Loewe additivity, enabling direct application in a biphasic dose-response framework. The proposed additivity definition was validated, and its applicability illustrated by studying the response of the cyanobacterial biosensor Synechococcus elongatus PCC 7942 pBG2120 to binary mixtures of Zn, Cu, Cd, Ag, Co and Hg. The novel method allowed by the first time to model complete dose-response profiles of an inducible whole cell biosensor to mixtures. In addition, the approach also allowed identification and quantification of departures from additivity (interactions) among analytes. The biosensor was found to respond in a near additive way to heavy metal mixtures except when Hg, Co and Ag were present, in which case strong interactions occurred. The method is a useful contribution for the whole cell biosensors discipline and related areas allowing to perform appropriate assessment of mixture effects in non-monotonic dose-response frameworks.

No MeSH data available.


Related in: MedlinePlus