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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.


Effect of mixture ratio.Experimental vs predicted (under additivity) dose-response patterns for the mixture Cu:Zn at 75:25 (a), 50:50 (b) and 25:75 (c) ratios based on the D0 concentration of the metals. Extended p-CI plots presenting departures from additivity (as CI values) as a function of the effect level (p) for the D dimension (d,f,h), and the E dimension (e,g,i). Extended p-CIwplots presenting weighted departures from additivity (as CIw values) as a function of the effect level (p) for the binary mixture Cu:Zn at 75:25 (j), 50:50 (k), 25:75 (l) mixture ratios. Error bars are standard errors (n = 3–4). Total free ion concentrations presented in the Figures are those presented as ED0 in Supplementary Material SM2 corrected by MINTEQ calculations due to the presence of the two metals used in each mixture.
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f6: Effect of mixture ratio.Experimental vs predicted (under additivity) dose-response patterns for the mixture Cu:Zn at 75:25 (a), 50:50 (b) and 25:75 (c) ratios based on the D0 concentration of the metals. Extended p-CI plots presenting departures from additivity (as CI values) as a function of the effect level (p) for the D dimension (d,f,h), and the E dimension (e,g,i). Extended p-CIwplots presenting weighted departures from additivity (as CIw values) as a function of the effect level (p) for the binary mixture Cu:Zn at 75:25 (j), 50:50 (k), 25:75 (l) mixture ratios. Error bars are standard errors (n = 3–4). Total free ion concentrations presented in the Figures are those presented as ED0 in Supplementary Material SM2 corrected by MINTEQ calculations due to the presence of the two metals used in each mixture.

Mentions: The effect of the metal ratio on the predictive power of the multivariative extension of Loewe additivity was addressed for selected binary mixtures. Figure 6a–c shows the experimental dose-response patterns and the respective additivity predictions for the three different metal ratios (75:25, 50:50, 25:75, respectively) of the binary metal mixture Cu:Zn. Extended p-CI plots for the D and E dimensions for the different metal ratios are presented in Fig. 6d–i. In addition, extended p-CIwplots are presented in Fig. 6j–l. The selection of metal ratios allows to specifically address the possibility of predicting the dose response patterns including metal combinations in which eventually one of the metal may be present below the MPC and the other above the MPC and vice versa. As can be seen in Fig. 6, the main features of the dose-response pattern of the 50:50 mixture of Cu:Zn (Fig. 6b), that is additivity in D, synergism in E, and overall additive effect (CIw > 0.5) is essentially conserved in the 25:75 and the 75:25 ratio. The only differences were the occurrence of a slight tendency to synergism in D in the 25:75 ratio (Fig. 6h), and a slight tendency to synergism in both the 75:25 and 25:75 ratios based on CIw (but still additive based on the management criterion: 0.5 < CIw < 2). Similar results were obtained for ratio variations for the mixture Zn:Cd (Supplementary Material SM4).


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)

Effect of mixture ratio.Experimental vs predicted (under additivity) dose-response patterns for the mixture Cu:Zn at 75:25 (a), 50:50 (b) and 25:75 (c) ratios based on the D0 concentration of the metals. Extended p-CI plots presenting departures from additivity (as CI values) as a function of the effect level (p) for the D dimension (d,f,h), and the E dimension (e,g,i). Extended p-CIwplots presenting weighted departures from additivity (as CIw values) as a function of the effect level (p) for the binary mixture Cu:Zn at 75:25 (j), 50:50 (k), 25:75 (l) mixture ratios. Error bars are standard errors (n = 3–4). Total free ion concentrations presented in the Figures are those presented as ED0 in Supplementary Material SM2 corrected by MINTEQ calculations due to the presence of the two metals used in each mixture.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f6: Effect of mixture ratio.Experimental vs predicted (under additivity) dose-response patterns for the mixture Cu:Zn at 75:25 (a), 50:50 (b) and 25:75 (c) ratios based on the D0 concentration of the metals. Extended p-CI plots presenting departures from additivity (as CI values) as a function of the effect level (p) for the D dimension (d,f,h), and the E dimension (e,g,i). Extended p-CIwplots presenting weighted departures from additivity (as CIw values) as a function of the effect level (p) for the binary mixture Cu:Zn at 75:25 (j), 50:50 (k), 25:75 (l) mixture ratios. Error bars are standard errors (n = 3–4). Total free ion concentrations presented in the Figures are those presented as ED0 in Supplementary Material SM2 corrected by MINTEQ calculations due to the presence of the two metals used in each mixture.
Mentions: The effect of the metal ratio on the predictive power of the multivariative extension of Loewe additivity was addressed for selected binary mixtures. Figure 6a–c shows the experimental dose-response patterns and the respective additivity predictions for the three different metal ratios (75:25, 50:50, 25:75, respectively) of the binary metal mixture Cu:Zn. Extended p-CI plots for the D and E dimensions for the different metal ratios are presented in Fig. 6d–i. In addition, extended p-CIwplots are presented in Fig. 6j–l. The selection of metal ratios allows to specifically address the possibility of predicting the dose response patterns including metal combinations in which eventually one of the metal may be present below the MPC and the other above the MPC and vice versa. As can be seen in Fig. 6, the main features of the dose-response pattern of the 50:50 mixture of Cu:Zn (Fig. 6b), that is additivity in D, synergism in E, and overall additive effect (CIw > 0.5) is essentially conserved in the 25:75 and the 75:25 ratio. The only differences were the occurrence of a slight tendency to synergism in D in the 25:75 ratio (Fig. 6h), and a slight tendency to synergism in both the 75:25 and 25:75 ratios based on CIw (but still additive based on the management criterion: 0.5 < CIw < 2). Similar results were obtained for ratio variations for the mixture Zn:Cd (Supplementary Material SM4).

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.