Statistical Dose-Response Models with Hormetic Effects

Monotonically increasing or decreasing functions are often used to model the relationship between the response of an experimental unit and the dose of a given substance. Of late, there has been an increased interest in dose-response relationships that exhibit hormetic effects. These effects may be characterized by an increase in response at low doses instead of the expected decrease in response that is observed at higher doses. Herein, we study the statistical implications of hormesis in several ways. First, we present a broad class of parametric mathematical-statistical models, constructed from standard dose-response models, that allow the incorporation of hormetic effects in such a way that the presence of hormesis can be tested statistically. Second, we consider the impact of model misspecification on effective dose estimation, such as the ED50 and the limiting dose for stimulation, when the hormetic effect is present but ignored in the dose-response model by the researcher (model underspecification) and when an hormetic effect is not present but incorporated into the dose-response model (model overspecification). Our simulation study reveals that it is more damaging to the estimation of effective dose to ignore the hormetic effect through model underspecification than to include the hormetic effect in the model through model overspecification. Third, we develop a nonpara-metric regression technique useful as an exploratory procedure to indicate hormetic effects when present. Finally, both parametric and nonparametric methods are illustrated with an example.     

Hormesis provides a generalized quantitative estimate of biological plasticity

Phenotypic plasticity represents an environmentally-based change in an organism’s observable properties. Since biological plasticity is a fundamental adaptive feature, it has been extensively assessed with respect to its quantitative features and genetic foundations, especially within an ecological evolutionary framework. Toxicological investigations on the dose-response continuum (i.e., very broad dose range) that include documented evidence of the hormetic dose response zone (i.e., responses to doses below the toxicological threshold) can be employed to provide a quantitative estimate of phenotypic plasticity. The low dose hormetic stimulation is an adaptive response that reflects an environmentally-induced altered phenotype and provides a quantitative estimate of biological plasticity. Analysis of nearly 8,000 dose responses within the hormesis database indicates that quantitative features of phenotypic plasticity are highly generalizable, being independent of biological model, endpoint measured and chemical/physical stress inducing agent. The magnitude of phenotype changes indicative of plasticity is modest with maximum responses typically being approximately 30–60% greater than control values. The present findings provide the first quantitative estimates of biological plasticity and its capacity for generalization. Summary This article provides the first quantitative estimate of biological plasticity that may be generalized across plant, microbial, animal systems, and across all levels of biological organization. The quantitative features of plasticity are described by the hormesis dose response model. These findings have important biological, biomedical and evolutionary implications.     

N-acetyltyrosine-induced redox signaling in hormesis

A suite of adaptations allows insects to survive in hostile terrestrial environments for long periods of time. Temperature represents a key environmental factor for most ectothermic insects, and they rapidly acclimate to high and low temperatures. Vast amounts of data in this research field support the idea that an insect's ability to tolerate fluctuating temperatures can be regarded as a biphasic hormetic dose response. Observation indicates that their thermal hormetic response represents a conservative estimate of their intrinsic capacity for rapid adaptation to environmental changes in nature because they naturally experience diel or seasonal temperature fluctuations. It is therefore reasonable to suppose that the hormetic response in insects reflects a surplus physiological capacity to deal with temperature changes that they would experience naturally. Although it has been unknown how thermal acclimation is induced, a stress-dependent increase in N-acetyltyrosine (NAT) was recently found to occur in insect larvae who had endured high temperatures. NAT treatment was demonstrated to induce thermotolerance in several tested insect species. NAT was also identified in the serum of humans as well as mice, and its concentration in mice was shown to be increased by heat and restraint stress, with NAT pretreatment lowering the concentrations of corticosterone and peroxidized lipids in stressed mice. These recent findings may give us some hints about how long a hormetic response lasts. Here, I will discuss recent findings underlying hormetic responses induced by an intrinsic factor, NAT, and how the hormetic response may begin and end.     

Hormesis: from mainstream to therapy

This issue of the Journal of Cell Communication and Cell Signaling on hormetic mechanisms represents an important step in the evolution of the hormesis dose response concept. Since its modern resurgence in the late 1970s the widespread occurrence of hormesis has been in search of its underlying mechanisms. The present integrative set of papers builds upon significant recent advances in the elucidation of hormetic mechanisms and provides the reader with a deep and extensive view of the concept of hormesis from a broad range of researcher perspectives and in many biomedical applications.     

Detecting and Estimating Hormesis Using a Model-Based Approach

Hormesis is defined as a dose-response relationship that is stimulatory at low doses, but is inhibitory at higher doses. In a given experiment, it is not unusual to observe enhanced responses at low doses, however, such enhanced responses may not imply hormesis, but the random fluctuation of the data. Statistical tests can be developed to detect hormesis when enhanced responses at low concentrations are observed. We propose the use of a model-based approach to detect the presence of, and estimate the extent of, hormesis. This approach includes two steps: detection and estimation. In the detection step, we compare the full and the reduced models. The full model describes the dose-response relationship incorporating the hormetic effect; the reduced model describes the dose-response relationship without the hormetic effect. The full model is an extension of the reduced model and has an extra parameter that measures the amount of increase in response at low doses. A test of statistical significance of this extra parameter can essentially be a test for detecting hormesis. In the estimation step, we obtain the area under the best-fitted dose-response curve falling within the hormetic zone. Considering both the number of concentrations within the hormetic zone and the magnitude of the stimulatory response, we propose using the ratio of the area under the hormetic zone (AUC_H) and the area under the best-fitted curve from zero to zero equivalent point (AUC_ZEP) as an estimate of magnitude of the hormetic effect. Two numerical examples are used to illustrate the use of this model-based approach.     

Hormetic effects of curcumin: What is the evidence?

Curcumin (diferuloylmethane), a component of the yellow powder prepared from the roots of Curcuma longa or Zingiberaceae (known as turmeric) is not only widely used to color and flavor food but also used as a pharmaceutical agent. Curcumin demonstrates anti-inflammatory, anticarcinogenic, antiaging, and antioxidant activity, as well as efficacy in wound healing. Notably, curcumin is a hormetic agent (hormetin), as it is stimulatory at low doses and inhibitory at high doses. Hormesis by curcumin could be also a particular function at low doses (i.e., antioxidant behavior) and another function at high dose (i.e., induction of autophagy and cell death). Recent findings suggest that curcumin exhibits biphasic dose–responses on cells, with low doses having stronger effects than high doses; examples being activation of the mitogen-activated protein kinase signaling pathway or antioxidant activity. This indicates that many effects induced by curcumin are dependent on dose and some effects might be greater at lower doses, indicative of a hormetic response. Despite the consistent occurrence of hormetic responses of curcumin in a wide range of biomedical models, epidemiological and clinical trials are needed to assess the nature of curcumin’s dose–response in humans. Fortunately, more than one hundred clinical trials with curcumin and curcumin derivatives are ongoing. In this review, we provide the first comprehensive analysis supportive of the hormetic behavior of curcumin and curcumin derivatives.     

Testing threshold and hormesis in a random effects dose-response model applied to developmental toxicity data

Here we describe a random effects threshold dose-response model for clustered binary-response data from developmental toxicity studies. For our model we assume that a hormetic effect occurs in addition to a threshold effect. Therefore, the dose-response curve is based on two components: relationships below the threshold (hormetic u-shaped model) and those above the threshold (logistic model). In the absence of hormesis and threshold effects, the estimation procedure is straightforward. We introduce score tests that are derived from a random effects hormetic-threshold dose-response model. The model and tests are applied to clustered binary data from developmental toxicity studies of animals to test for hormesis and threshold effects. We also compare the score test and likelihood ratio test to test for hormesis and threshold effects in a simulated study.     

Modeling effective dosages in hormetic dose-response studies

Background

Two hormetic modifications of a monotonically decreasing log-logistic dose-response function are most often used to model stimulatory effects of low dosages of a toxicant in plant biology. As just one of these empirical models is yet properly parameterized to allow inference about quantities of interest, this study contributes the parameterized functions for the second hormetic model and compares the estimates of effective dosages between both models based on 23 hormetic data sets. Based on this, the impact on effective dosage estimations was evaluated, especially in case of a substantially inferior fit by one of the two models.

Methodology/Principal Findings

The data sets evaluated described the hormetic responses of four different test plant species exposed to 15 different chemical stressors in two different experimental dose-response test designs. Out of the 23 data sets, one could not be described by any of the two models, 14 could be better described by one of the two models, and eight could be equally described by both models. In cases of misspecification by any of the two models, the differences between effective dosages estimates (0–1768%) greatly exceeded the differences observed when both models provided a satisfactory fit (0–26%). This suggests that the conclusions drawn depending on the model used may diverge considerably when using an improper hormetic model especially regarding effective dosages quantifying hormesis.

Conclusions/Significance

The study showed that hormetic dose responses can take on many shapes and that this diversity can not be captured by a single model without risking considerable misinterpretation. However, the two empirical models considered in this paper together provide a powerful means to model, prove, and now also to quantify a wide range of hormetic responses by reparameterization. Despite this, they should not be applied uncritically, but after statistical and graphical assessment of their adequacy.     

Dose and litter allocations in the design of teratological studies for detecting hormesis

BACKGROUND: Hormesis is being recognized in the field of toxicology due to the stimulating effects of some toxic compounds at low exposure levels. Therefore, it is desirable that experimental designs for toxicological studies be flexible enough to aid in the detection of hormetic effects. Current designs may still not have enough power to do this. METHODS: A simulation study was conducted to determine teratological study designs that would yield more power over standard designs in detecting hormesis. Developmental toxicity endpoints of interest are the number of dead/resorbed or malformed fetuses in a litter. The simulation designs mimic teratological experiments in terms of sample size and number of dose levels. Modified designs with even dose spacing at low levels and reallocated litters are investigated to determine the power of hormetic detection. RESULTS: Designs with reallocated litters (with more litters at low exposure levels than at high levels) and even dose spacing have more power than those with equal litters per group and uneven dose spacing. CONCLUSIONS: Through appropriate modifications of current experimental designs, such as reallocation of litters and even dose spacing, we can better detect hormetic effects.     

Cellular stress responses, hormetic phytochemicals and vitagenes in aging and longevity

Modulation of endogenous cellular defense mechanisms represents an innovative approach to therapeutic intervention in diseases causing chronic tissue damage, such as in neurodegeneration. This paper introduces the emerging role of exogenous molecules in hormetic-based neuroprotection and the mitochondrial redox signaling concept of hormesis and its applications to the field of neuroprotection and longevity. Maintenance of optimal long-term health conditions is accomplished by a complex network of longevity assurance processes that are controlled by vitagenes, a group of genes involved in preserving cellular homeostasis during stressful conditions. Vitagenes encode for heat shock proteins (Hsp) Hsp32, Hsp70, the thioredoxin and the sirtuin protein systems. Dietary antioxidants, such as polyphenols and L-carnitine/acetyl-L-carnitine, have recently been demonstrated to be neuroprotective through the activation of hormetic pathways, including vitagenes. Hormesis provides the central underpinning of neuroprotective responses, providing a framework for explaining the common quantitative features of their dose response relationships, their mechanistic foundations, their relationship to the concept of biological plasticity as well as providing a key insight for improving the accuracy of the therapeutic dose of pharmaceutical agents within the highly heterogeneous human population. This paper describes in mechanistic detail how hormetic dose responses are mediated for endogenous cellular defense pathways including sirtuin, Nrfs and related pathways that integrate adaptive stress responses in the prevention of neurodegenerative diseases. This article is part of a Special Issue entitled: Antioxidants and Antioxidant Treatment in Disease.     

Interspecies Variability of Plant Hormesis by the Antiauxin PCIB in a Laboratory Bioassay

Chemical hormesis constitutes an alternative possible use of herbicidal agents for crop enhancement that is, however, compromised by the apparent variability of this low-dose stimulation phenomenon. Studies demonstrating the variability are rare and, therefore, this study investigated the interspecies variability of growth stimulation induced by the auxin-inhibitor PCIB [2-(p-chlorophenoxy)-2-methylpropionic acid] to determine if hormesis is generalizable enough and sufficiently stable between species/cultivars for practical use or which implications may have to be taken into account. In 85 complete dose–response bioassays with 23 cultivars of five species, the variability of PCIB effects was evaluated. The expression of PCIB hormesis proved to depend on the species/cultivar tested, ranging from a cultivar-dependent hormetic efficacy and an occasional lack of hormesis, to a complete lack of hormetic effectiveness in certain species/cultivars. Therefore, frequency estimations, as well as the pattern of dose-dependent variability of dose–response quantities, may inevitably depend on the biological model(s) used and, thus, apply only to the specific conditions for characterization. Comparing the frequency distribution of effective doses demonstrated a risk of a previously hormetic dose causing a loss of hormesis or inhibitory effects in another species/cultivar. Therefore, selecting a dose that will induce hormesis in every species/cultivar is unrealistic. This may limit the window for practical applications to stimulants with negligible varietal differences, to cultivar selective treatments, and/or to cultivars that enable a beneficial long-term use. Hence, efficient crop enhancement by chemical hormesis needs not only a good stimulant, but also a species/cultivar able to convert a specific low-dose treatment into an economic benefit.     

Hormesis, cellular stress response and vitagenes as critical determinants in aging and longevity

Understanding mechanisms of aging and determinants of life span will help to reduce age-related morbidity and facilitate healthy aging. Average lifespan has increased over the last centuries, as a consequence of medical and environmental factors, but maximal life span remains unchanged. Extension of maximal life span is currently possible in animal models with measures such as genetic manipulations and caloric restriction (CR). CR appears to prolong life by reducing reactive oxygen species (ROS)-mediated oxidative damage. But ROS formation, which is positively implicated in cellular stress response mechanisms, is a highly regulated process controlled by a complex network of intracellular signaling pathways. By sensing the intracellular nutrient and energy status, the functional state of mitochondria, and the concentration of ROS produced in mitochondria, the longevity network regulates life span across species by co-ordinating information flow along its convergent, divergent and multiply branched signaling pathways, including vitagenes which are genes involved in preserving cellular homeostasis during stressful conditions. Vitagenes encode for heat shock proteins (Hsp) Hsp32, Hsp70, the thioredoxin and the sirtuin protein systems. Dietary antioxidants, such as carnosine, carnitines or polyphenols, have recently been demonstrated to be neuroprotective through the activation of hormetic pathways, including vitagenes. The hormetic dose-response, challenges long-standing beliefs about the nature of the dose-response in a lowdose zone, having the potential to affect significantly the design of pre-clinical studies and clinical trials as well as strategies for optimal patient dosing in the treatment of numerous diseases. Given the broad cytoprotective properties of the heat shock response there is now strong interest in discovering and developing pharmacological agents capable of inducing stress responses. In this review we discuss the most current and up to date understanding of the possible signaling mechanisms by which caloric restriction, as well hormetic caloric restriction-mimetics compounds by activating vitagenes can enhance defensive systems involved in bioenergetic and stress resistance homeostasis with consequent impact on longevity processes.     

An illusion of hormesis in the Ames test: statistical significance is not equivalent to biological significance

A recent report (Calabrese et al., Mutat. Res. 726 (2011) 91-97) concluded that an analysis of Ames test mutagenicity data provides evidence of hormesis in mutagenicity dose-response relationships. An examination of the data used in this study and the conclusions regarding hormesis reveal a number of concerns regarding the analyses and possible misinterpretations of the Salmonella data. The claim of hormesis is based on test data from the National Toxicology Program using Salmonella strain TA100. Approximately half of the chemicals regarded as hormetic, and the majority of the specific dose-responses identified as hormetic, were actually nonmutagenic. We conclude that the data provide no evidence of hormetic effects. The Ames test is an excellent measure of bacterial mutagenicity, but the numbers of revertant (mutant) colonies on the plate are the result of a complex interaction between mutagenicity and toxicity, which renders the test inappropriate for demonstrating hormesis in bacterial mutagenicity experiments.     

The Concept of Hormesis in Developmental Toxicology

Animal bioassay experiments are frequently conducted to assess the toxicity of chemicals on the developing fetus. Experiments are normally conducted at dosage levels that are much higher than human exposure levels to elicit the toxic reproductive effect of the chemical in a limited number of litters. Recently there has been much discussion on the fact that some chemicals may have beneficial effects at low doses and become toxic at high doses. This concept, known as chemical hormesis, has been the focus of attention in many investigations. Here, we consider the prevalence of hormesis in developmental toxicology and show that current design of developmental toxicity testing does not accommodate the study of hormesis. If it can be proved that some developmental toxicants may have stimulatory low dose effects, then design and analysis of developmental toxicity experiments need to be revised by the scientific community and the regulatory agencies. Using a thorough analysis of an experimental data set, we further demonstrate that in order to establish the possible hormetic effects of a chemical in reproduction, often a multiple replication of the experiment may be necessary to examine such effects. Using a trend test, we illustrate that while it is possible that one replicate of a developmental toxicity experiment with a known teratogen shows strong evidence of hormesis, other replicates may show no sign of beneficial effects at low doses.     

Neoplastic transformation in vitro by low doses of ionizing radiation: role of adaptive response and bystander effects

The shape of the dose-response curve for cancer induction by low doses of ionizing radiation is of critical importance to the assessment of cancer risk at such doses. Epidemiologic analyses are limited by sensitivity to doses typically greater than 50-100 mGy for low LET radiation. Laboratory studies allow for the examination of lower doses using cancer-relevant endpoints. One such endpoint is neoplastic transformation in vitro. It is known that this endpoint is responsive to both adaptive response and bystander effects. The relative balance of these processes is likely to play an important role in determining the shape of the dose-response curve at low doses. A factor that may influence this balance is cell density at time of irradiation. The findings reported in this paper indicate that the transformation suppressive effect of low doses previously seen following irradiation of sub-confluent cultures, and attributed to an adaptive response, is reduced for irradiated confluent cultures. However, even under these conditions designed to optimize the role of bystander effects the data do not fit a linear no-threshold model and are still consistent with the notion of a threshold dose for neoplastic transformation in vitro by low LET radiation.     

Enhanced Anticancer Effect of Adding Magnesium to Vitamin C Therapy: Inhibition of Hormetic Response by SVCT-2 Activation

l-Ascorbic acid (vitamin C, AA) is known as an antioxidant, but at high concentrations, AA can kill cancer cells through a prooxidant property. Sodium-dependent vitamin C transporter family-2 (SVCT-2) determines the cellular uptake of AA, and the activity of SVCT-2 is directly related to the anticancer activity of AA. Cancer cells that showed high SVCT-2 expression levels were more sensitive to AA treatment than cancer cells with low SVCT-2 expression levels. Cells with low SVCT-2 expression showed a hormetic response to a low dose of AA. Magnesium ions, which are known to activate SVCT-2, could increase the V_max value of SVCT-2, so we investigated whether providing magnesium supplements to cancer cells with low SVCT-2 expression that had shown a hormetic response to AA would elevate the V_max value of SVCT-2, allowing more AA to accumulate. To evaluate the effects of magnesium on cancer cells, MgSO₄ and MgCl₂ were screened as magnesium supplements; both forms showed synergistic anticancer effects with AA. Taken together, the results of this study suggest that magnesium supplementation enhanced the anticancer effect of AA by inhibiting the hormetic response at a low dose. This study has also demonstrated that AA treatment with magnesium supplementation provided more effective anticancer therapy than AA treatment alone.     

Hormetic Effect of Berberine Attenuates the Anticancer Activity of Chemotherapeutic Agents

Hormesis is a phenomenon of biphasic dose response characterized by exhibiting stimulatory or beneficial effects at low doses and inhibitory or toxic effects at high doses. Increasing numbers of chemicals of various types have been shown to induce apparent hormetic effect on cancer cells. However, the underlying significance and mechanisms remain to be elucidated. Berberine, one of the major active components of Rhizoma coptidis, has been manifested with notable anticancer activities. This study aims to investigate the hormetic effect of berberine and its influence on the anticancer activities of chemotherapeutic agents. Our results demonstrated that berberine at low dose range (1.25 ~ 5 μM) promoted cell proliferation to 112% ~170% of the untreated control in various cancer cells, while berberine at high dose rage (10 ~ 80 μM) inhibited cell proliferation. Further, we observed that co-treatment with low dose berberine could significantly attenuate the anticancer activity of chemotherapeutic agents, including fluorouracil (5-FU), camptothecin (CPT), and paclitaxel (TAX). The hormetic effect and thereby the attenuated anticancer activity of chemotherapeutic drugs by berberine may attributable to the activated protective stress response in cancer cells triggered by berberine, as evidenced by up-regulated MAPK/ERK1/2 and PI3K/AKT signaling pathways. These results provided important information to understand the potential side effects of hormesis, and suggested cautious application of natural compounds and relevant herbs in adjuvant treatment of cancer.     

Lithium can mildly increase health during ageing but not lifespan in mice

Lithium is a nutritional trace element, used clinically as an anti‐depressant. Preclinically, lithium has neuroprotective effects in invertebrates and mice, and it can also extend lifespan in fission yeast, C. elegans and Drosophila. An inverse correlation of human mortality with the concentration of lithium in tap water suggests a possible, evolutionarily conserved mechanism mediating longevity. Here, we assessed the effects of lithium treatment on lifespan and ageing parameters in mice. Lithium has a narrow therapeutic dose range, and overdosing can severely affect organ health. Within the tolerable dosing range, we saw some mildly positive effects of lithium on health span but not on lifespan.