Using Various Nonlinear Response Surfaces for Mathematical Description of the Type of Combined Toxicity

Abstract

The article considers the problem of characterizing the type of combined action produced by a mixture of toxic substances with the help of nonlinear response functions. Most attention is given to second-order models: the linear model with a cross-term and the quadratic model. General propositions are formulated based on the data on combined toxicity patterns previously obtained by the Ekaterinburg nanotoxicology team in animal experiments and analyzed with the help of the linear model with a cross-term. It is shown now that the quadratic model features these general characteristics in full measure, but interpretation of combined toxicity types based on isobolograms obtained by the quadratic model is more difficult. This suggests that where both models ensure a comparable quality of combined toxicity type identification, it would be enough to use the linear model with a cross-term.

Mathematical properties of Hand Incremental Effect Additivity and other synergy theories

“…A logical error in this argument was discovered by Hand [21]. Perhaps more importantly, actual experiments with the joint action of drugs, toxins, and other agents without known interactions reveal that in many cases, isoboles are nonlinear; see, for example, Lederer et al and Varaksin et al [3,23]. This calls for alternative synergy theories.…”

A response-surface approach into the interactive effects of multiple stressors reveals new insights into complex responses

“…A suitable experimental design for such research is the 'response-surface' design (Inouye, 2001;Inouye, 2005;Rosenblatt and Schmitz, 2016). 'Response-surface' designs test the relationship between the response and a number of input (predictor) variables across a range of levels (Box and Wilson, 1951;Inouye, 2005;Lin and Peterson, 2006;Varaksin et al, 2018). Response-surface experiments have tended to be done in the laboratory with individual species or simplified assemblages, however, they have been criticized for lacking replicate combinations of treatments (Benedetti-Cecchi, 2005) and environmental relevance (Mayer-Pinto et al, 2010).…”

“…If, however, the more harmful stressor is one that would be expected to occur under climatic change such as increased temperature, acidification, etc., it may not be possible to modify its effects (Harley et al, 2006;Russell et al, 2009;Cheng et al, 2015). These sorts of scenarios could be examined using a 'response-surface' design and provide useful information to managers and policymakers who wish to avoid harmful multiple stressor scenarios, something that has previously been called for in the literature (Kroeker et al, 2017;Varaksin et al, 2018), but remains rare (but see Rindi et al, 2022 for experimental approaches on biofilms) due to the complexity of the task and remains a knowledge-gap (Orr et al, 2020;Jackson et al, 2021).…”

Comparative and Combined In Vitro Vasotoxicity of Nanoparticles Containing Lead and Cadmium

“…Alongside this line of research, our aspiration has been to advance the general theory of combined toxicity ( 11 - 16 and many others). In these studies, various acute, subchronic or chronic intoxications were modeled by exposing rats to repeated administration of dissolved salts or of nanoparticles of different toxic elements in different combinations.…”