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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

The bi-dimensional fractional effect notation.(a) Fractional effective doses EDp in biphasic dose-response systems is proposed to be scaled as fractions (p) of the Emax defining the fractional effect scale (Ep). The empirical effect scale (E(τ), in the y axis) is decoupled from the fractional effect scale (Ep) which is projected in the z plane. This allows to define fractional effects covering the entire biphasic dose-response curve. (b) The proposed fractional effective notation allows to scale in a common fractional effect scale stimuli A and B showing differential maximal effects. (c) An additive biphasic dose response pattern “A + B” can be formulated for a theoretical mixture of A and B based on the univocal relationship of the fractional effect scale (Ep) with the other two dimensions: D(p) and E(p). For notation meanings in the Figures see section 2.
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f2: The bi-dimensional fractional effect notation.(a) Fractional effective doses EDp in biphasic dose-response systems is proposed to be scaled as fractions (p) of the Emax defining the fractional effect scale (Ep). The empirical effect scale (E(τ), in the y axis) is decoupled from the fractional effect scale (Ep) which is projected in the z plane. This allows to define fractional effects covering the entire biphasic dose-response curve. (b) The proposed fractional effective notation allows to scale in a common fractional effect scale stimuli A and B showing differential maximal effects. (c) An additive biphasic dose response pattern “A + B” can be formulated for a theoretical mixture of A and B based on the univocal relationship of the fractional effect scale (Ep) with the other two dimensions: D(p) and E(p). For notation meanings in the Figures see section 2.

Mentions: In the present work, a notation for fractional effective doses EDp scaled from the MPCs (hereafter, Emax) has been chosen (Fig. 2a). The novelty of the approach is that we maintain the empirical effect scale (E(τ)) in the y axis, and we project the fractional effect scale (Ep(p)) in the z plane (see Fig. 2a). Fractional effects (p) in the Ep scale are defined as follows: −100 ≤ p ≤ 100. For p < 0, fractional effects on the left side of the Emax are obtained (Fig. 2a) (the induction part of the curve), for p > 0, fractional effects on the right side of the Emax are obtained (the inhibition part of the dose-response curve). p = 0 = Emax = MPC. Decoupling the fractional effect scale (Ep(p)) from the empirical effect (E(τ)) allows to scale inverted v-shaped dose-response curves with differential maximum effects in a unique fractional scale independently of the maximum level of effect (Emax) attained (Fig. 2b). However, EDp needs to be dimensionally extended to account for differences in both the dose (D) and effect (E) scales (Fig. 2b). Therefore we define EDp as a two-dimensional vector (D(p), E(p)) where D(p)is the dose required to get the desired fractional effect (p) (i.e. 50%), and E(p) is the effect in the empirical effect scale (E (τ)) achieved at this fractional effect (p).


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)

The bi-dimensional fractional effect notation.(a) Fractional effective doses EDp in biphasic dose-response systems is proposed to be scaled as fractions (p) of the Emax defining the fractional effect scale (Ep). The empirical effect scale (E(τ), in the y axis) is decoupled from the fractional effect scale (Ep) which is projected in the z plane. This allows to define fractional effects covering the entire biphasic dose-response curve. (b) The proposed fractional effective notation allows to scale in a common fractional effect scale stimuli A and B showing differential maximal effects. (c) An additive biphasic dose response pattern “A + B” can be formulated for a theoretical mixture of A and B based on the univocal relationship of the fractional effect scale (Ep) with the other two dimensions: D(p) and E(p). For notation meanings in the Figures see section 2.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f2: The bi-dimensional fractional effect notation.(a) Fractional effective doses EDp in biphasic dose-response systems is proposed to be scaled as fractions (p) of the Emax defining the fractional effect scale (Ep). The empirical effect scale (E(τ), in the y axis) is decoupled from the fractional effect scale (Ep) which is projected in the z plane. This allows to define fractional effects covering the entire biphasic dose-response curve. (b) The proposed fractional effective notation allows to scale in a common fractional effect scale stimuli A and B showing differential maximal effects. (c) An additive biphasic dose response pattern “A + B” can be formulated for a theoretical mixture of A and B based on the univocal relationship of the fractional effect scale (Ep) with the other two dimensions: D(p) and E(p). For notation meanings in the Figures see section 2.
Mentions: In the present work, a notation for fractional effective doses EDp scaled from the MPCs (hereafter, Emax) has been chosen (Fig. 2a). The novelty of the approach is that we maintain the empirical effect scale (E(τ)) in the y axis, and we project the fractional effect scale (Ep(p)) in the z plane (see Fig. 2a). Fractional effects (p) in the Ep scale are defined as follows: −100 ≤ p ≤ 100. For p < 0, fractional effects on the left side of the Emax are obtained (Fig. 2a) (the induction part of the curve), for p > 0, fractional effects on the right side of the Emax are obtained (the inhibition part of the dose-response curve). p = 0 = Emax = MPC. Decoupling the fractional effect scale (Ep(p)) from the empirical effect (E(τ)) allows to scale inverted v-shaped dose-response curves with differential maximum effects in a unique fractional scale independently of the maximum level of effect (Emax) attained (Fig. 2b). However, EDp needs to be dimensionally extended to account for differences in both the dose (D) and effect (E) scales (Fig. 2b). Therefore we define EDp as a two-dimensional vector (D(p), E(p)) where D(p)is the dose required to get the desired fractional effect (p) (i.e. 50%), and E(p) is the effect in the empirical effect scale (E (τ)) achieved at this fractional effect (p).

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