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Hormesis is a biphasic dose (concentration)-response phenomenon characterized by low dose stimulatory and high dose inhibitory effects exerted by stressors on living organisms. Recently, there has been increased interest in the phenomenon and statistical models for its exploration in toxicological studies. The bilogistic model of Beckon et al. is one of such models for modeling biphasic dose-response relationships in toxicological studies. However, there is no explicit formula for the estimation of effective doses (ED K ) with the model. In this study, a simple general approach was suggested to reparameterize the model, leading to a range of mathematical models for determination of effective doses at both stimulatory and inhibitory ranges in inverted U-shaped hormetic dose-response relationships. The reparameterized models were tested on experimental data from three different in vitro experimental systems obtained from literature and our experiment. They were successfully applied to test for significance of hormesis and estimate effective doses and their statistical properties. In addition, reparameterization of the model for a particular effective dose (ED K ) did not affect estimation of other parameters (such as x 1, x 2 , β 1 , β 2 and M). The reparameterized models provided useful tools for adequate exploration of the tested hormetic dose-response relationships. The extended models could hopefully be versatile in characterization of variable hormetic dose response relationships in many toxicological disciplines.

Background: Otamiri river server as a source of water for domestic activities, urban farming, recreation, aquatic foods in Owerri and environs. It also receives untreated domestic, industrial and agricultural waste water and run offs from the municipality. Seepages from solid wastes dumps at the river banks and sand mining activity going on in the river could also constitute environmental hazards Aims: This study aims at evaluating the interactive effects of the ternary mixtures of sodium dodecyl sulfate (SDS) and some divalent metals on preponderant bacterium (Serratia marcescens (SerEW01)) from the river. Study Design: Fixed ratio ray design was used for the study, with inhibition of dehydrogenase activity as end point. Place and Duration of Study:    Owerri, Imo State, Nigeria, June – December, 2019. Methodology: The bacterium was earlier isolated as the preponderant bacterium isolate from the river water. Fixed ratio ternary mixtures (Equieffect concentration (EEC50) and arbitrary concentration (ABCR) ratios), SDS + Pb + Zn, SDS + Cd +Zn, SDS + Pb +Ni, SDS + Ni + Cd, SDS + Co + Pb and SDS + Co + Cd were designed to evaluate the combined toxicities of these toxicants. Toxicities predicted by concentration addition (CA) and independent action (IA) models were compared with the experimentally observed toxicities. Results: The EC50S observed ranged from 0.046 ± 0.003 mM (Zn) to 2.329 ± 0.092 mM (SDS). The EC50S of the toxicants were statistically different from each other (P<0.05). The order of increasing toxicities were SDS >Pb >Ni > Co > Cd(II) >Zn. Concentration-dependent toxicities with progressive inhibition of the dehydrogenase activity as the concentration increased were observed.. In all ternary mixtures, both the experimentally derived, CA and IA-predicted EC50S were statistically different from each other. Both models predicted lower toxicities compared to the experimental data. The Toxic Index and Model Deviation Ratio indicated synergistic interaction of SDS and metal ions against S. marcescens (SerEW01) Conclusion: This study could constitute base line information towards assessing the possible environmental hazards associated with co-contamination of the environment by SDS and divalent heavy metals, more so when both pollutants are common aquatic pollutants.

Toxicities of sodium dodecyl sulfate (SDS) + Pb(II), SDS + Cd(II), SDS + Ni(II), SDS + Zn(II), and SDS + Co(II) binary mixtures to Serratia marcescens (SerEW01) isolated from Otamiri river water, Owerri, Imo State, Nigeria were undertaken, using dehydrogenase activity as a response. Inhibitions of dehydrogenase activity by the individual toxicants were concentrationdependent, increasing steadily as the concentration increases. The observed EC50S ranged from 0.046 ± 0.003 mM for Zn(II) to 2.329 ± 0.092 mM for SDS. Duncan tests indicated that the EC50S of the individual toxicants differed significantly from each other. The order of decreasing toxicities was Zn(II) > Cd(II) > Co(II) > Ni(II) > Pb(II) > SDS. Fixed ratio mixtures [Arbitrary concentration ratio (ABCR) and EC50 equieffect concentration ratio (EECR 50)] were used to study the joint action of the binary mixtures. The mixtures progressively inhibited dehydrogenase activity in S. marcescens as the concentration increases. However, SDS 98.08% + Co(II) 1.92% mixture ratio was biphasic. The effects of the mixtures on the dehydrogenase activity were assessed using Toxic Index, Model Deviation Ratio and Isobolographic analyses. In addition, the toxicities of the mixtures were predicted with concentration addition (CA) and independent action (IA) models. In SDS+Ni(II) binary mixture, both models predicted similar toxicities. In all binary mixtures, both models greatly underestimated the mixture toxicities compared to the experimentally-observed data. Similarly, both the experimentally-observed, CA and IA-predicted EC50S were statistically different from each another. Furthermore, the binary mixtures were generally synergistic against S. marcescens (SerEW01). This demonstrates the potential danger of co-contamination of the aquatic system by SDS and heavy metals

Toxicities of sodium dodecyl sulfate (SDS) and heavy metals, Pb(II), Cd(II), Ni(II), Zn(II) and Co(II), as individuals and ternary mixtures of two heavy metals and SDS to Acinetobacter seifertii isolated as preponderant bacterium from Otamiri river sediment, were assessed, using inhibition of dehydrogenase activity as end point. Among the individual toxicants, the EC50S observed ranged from 0.011 ± 0.000 mM for Cd(II) to 2.810 ± 0.140 mM for SDS. The EC50S of the toxicants were statistically different from one another and the order of increasing toxicities were SDS > Ni(II) > Pb(II) > Zn(II) > Co(II) >Cd(II). The responses of the bacterium were concentration -dependent. Arbitrary (ABCR) and EC50 equieffect (EECR) fixed ratio mixtures were used to evaluate the combined toxicities of the toxicants. The concentration-response relationships of all mixtures and individual toxicants were sigmoidal and fitted with logistic function. The observed toxicities (EC50S) were compared with toxicities predicted from concentration addition (CA) and independent action (IA) models. In ABCR1 and ABCR3 mixture ratios of SDS+Ni(II)+Cd(II) and SDS+Co(II)+Cd(II) ternary mixtures, both CA- and IA-predicted EC50S were not statistically different from each other. Furthermore, in all ternary mixtures, both models underestimated the mixture toxicities to A. seifertii, except in ABCR1 of SDS+Ni(II)+Cd(II) mixture, where both models almost correctly predicted the toxicities. Basically, synergistic interaction of the mixture components observed against A. seifertii, indicates their possible toxicological effects on the bacterial population of the aquatic ecosystems.