A Universal Delayed Difference Model Fitting Dose-response Curves

Purpose Dose-response curves, which fit a multitude of experimental data derived from toxicology, are widely used in physics, chemistry, biology, and other fields. Although there are many dose-response models for fitting dose-response curves, the application of these models is limited by many restrictions and lacks universality, so there is a need for a novel, universal dynamical model that can improve fits to various types of dose-response curves. Methods We expand the hormetic Ricker model, taking the delay inherent in the dose-response into account, and develop a novel and dynamic delayed Ricker difference model (DRDM) to fit various types of dose-response curves. Furthermore, we compare the DRDM with other dose-response models to confirm that it can mimic different types of dose-response curves. Data analysis By fitting various types of dose-response data sets derived from drug applications, disease treatment, pest control, and plant management, and comparing the imitative effect of the DRDM with other models, we find that the DRDM fits monotonic dose-response data well and, in most circumstances, the DRDM has a better imitative effect to non-monotonic dose-response data with hormesis than other models do. Results The MSE of fits of the DRDM to S-shaped dose-response data (DS2-G) is not lower than those for four other models, but the MSE of fits to U-shaped (DS7) and inverted U-shaped dose-response data (DS10) were lower than for two other models. This means that the imitative effect of the DRDM is comparable to other models of monotonic dose-response data, but is a significant improvement compared to traditional models of non-monotonic dose-response data with hormesis. Conclusion We propose a novel dynamic model (DRDM) for fitting to various types of dose-response curves, which can reflect the dynamic trend of the population growth compared with traditional static dose-response models. By analyzing data, we have confirmed that the DRDM provides an ideal description of various dose-response observations and it can be used to fit a wide range of dose-response data sets, especially for hormetic data sets. Therefore, we conclude that the DRDM has a good universality for dose-response curve fitting.

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A General Measure of In Vitro Phototoxicity Derived from Pairs of Dose-Response Curves and its Use for Predicting the In Vivo Phototoxicity of Chemicals

Alternatives to Laboratory Animals ◽

10.1177/026119299702500407 ◽

1997 ◽

Vol 25 (4) ◽

pp. 445-462 ◽

Cited By ~ 4

Author(s):

Hermann-Georg Holzhütter

Keyword(s):

Dose Response ◽

Uv Light ◽

Test System ◽

Maximal Response ◽

Response Curves ◽

General Measure ◽

Absolute Change ◽

Response Data ◽

Dose Response Curves ◽

The Absolute

In pharmacology, it is common to evaluate the influence of external effectors (for example, temperature, pH, and presence of a second drug) on dose-response relations by the potency factor (PF50): [Formula: see text] where ED50 (± effector) denotes the 50% effective dose in the presence and in the absence of the effector, respectively. In this paper, the external effector is ultraviolet (UV) light, and PF50 is referred to as the photoirritancy factor (PIF). There are two parameters which limit the applicability and toxicological reliability of the PIF. Firstly, the physical properties (for example, water solubility) of the chemical tested and the constraints of the biological test system may make it difficult, or even impossible, to achieve sufficiently high doses to observe 50% of the maximal response. In such cases, no numeric value of the potency factor can be computed. Secondly, the potency factor does not take into account the absolute change in response induced by UV light, i.e. depending on the shape of the ±UV dose-response curves, the absolute change in response may be small although the PIF is large, and vice versa. This paper proposes a more general measure of phototoxicity, the mean photo effect (MPE), which can be assessed from pairs of dose-response curves, even if the 50% response level is not reached in one curve or in both. The MPE is a weighted average of PIFd values across different dose levels (d being common to both dose-response curves). The absolute response changes, ΔRd, i.e. the differences between the -UV curve and the +UV curve are used as weighting factors. The numerical computation of the MPE is based on theoretical curves obtained by fitting a mathematical model to the experimental dose-response data. Plotting PIFd and ΔRd versus the corresponding doses permits differences in the shapes of the two curves to be assessed, and possible alterations in the toxic mechanisms induced by UV light to be revealed. The variance of MPE is estimated by a bootstrap procedure. The use of the MPE is illustrated by its application to dose-response data obtained with a human keratinocyte assay of fibroblasts in the EU/COLIPA international validation project on photoirritancy.

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Solving the Problem of Assessing Synergy and Antagonism for Non-Traditional Dosing Curve Compounds Using the DE/ZI Method: Application to Nrf2 Activators

Frontiers in Pharmacology ◽

10.3389/fphar.2021.686201 ◽

2021 ◽

Vol 12 ◽

Author(s):

Elizabeth M. Repash ◽

Kaitlin M. Pensabene ◽

Peter M. Palenchar ◽

Aimee L. Eggler

Keyword(s):

Dose Response ◽

Nearest Neighbor ◽

Antioxidant Response ◽

Pharmacological Intervention ◽

Data Sets ◽

Response Curves ◽

Data Set ◽

Dose Response Curves ◽

Small Molecule Modulators ◽

Antagonistic Interactions

Multi-drug combination therapy carries significant promise for pharmacological intervention, primarily better efficacy with less toxicity and fewer side effects. However, the field lacks methodology to assess synergistic or antagonistic interactions for drugs with non-traditional dose response curves. Specifically, our goal was to assess small-molecule modulators of antioxidant response element (ARE)-driven gene expression, which is largely regulated by the Nrf2 transcription factor. Known as Nrf2 activators, this class of compounds upregulates a battery of cytoprotective genes and shows significant promise for prevention of numerous chronic diseases. For example, sulforaphane sourced from broccoli sprouts is the subject of over 70 clinical trials. Nrf2 activators generally have non-traditional dose response curves that are hormetic, or U-shaped. We introduce a method based on the principles of Loewe Additivity to assess synergism and antagonism for two compounds in combination. This method, termed Dose-Equivalence/Zero Interaction (DE/ZI), can be used with traditional Hill-slope response curves, and it also can assess interactions for compounds with non-traditional curves, using a nearest-neighbor approach. Using a Monte-Carlo method, DE/ZI generates a measure of synergy or antagonism for each dosing pair with an associated error and p-value, resulting in a 3D response surface. For the assessed Nrf2 activators, sulforaphane and di-tert-butylhydroquinone, this approach revealed synergistic interactions at higher dosing concentrations consistently across data sets and potential antagonistic interactions at lower concentrations. DE/ZI eliminates the need to determine the best fit equation for a given data set and values experimentally-derived results over formulated fits.

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A critique of the use of hormesis in risk assessment

Human & Experimental Toxicology ◽

10.1191/0960327105ht520oa ◽

2005 ◽

Vol 24 (5) ◽

pp. 249-253 ◽

Cited By ~ 16

Author(s):

Kirk T Kitchin ◽

J Wanzer Drane

Keyword(s):

Risk Assessment ◽

Dose Response ◽

A Priori ◽

Assessment Process ◽

Data Sets ◽

Response Curves ◽

Dose Response Curves ◽

Post Hoc ◽

Public Health Protection ◽

Default Assumption

There are severe problems and limitations with the use of hormesis as the principal dose-response default assumption in risk assessment. These problems and limitations include: (a) unknown prevalence of hormetic doseresponse curves; (b) random chance occurrence of hormesis and the shortage of data on the repeatability of hormesis; (c) unknown degree of generalizability of hormesis; (d) there are dose-response curves that are not hormetic, therefore hormesis cannot be universally generalized; (e) problems of post hoc rather than a priori hypothesis testing; (f) a possible large problem of ‘false positive’ hormetic data sets which have not been extensively replicated; (g) the ‘mechanism of hormesis’ is not understood at a rigorous scientific level; (h) in some cases hormesis may merely be the overall sum of many different mechanisms and many different dose-response curves - some beneficial and some toxic. For all of these reasons, hormesis should not now be used as the principal dose-response default assumption in risk assessment. At this point, it appears that hormesis is a long way away from common scientific acceptance and wide utility in biomedicine and use as the principal default assumption in a risk assessment process charged with ensuring public health protection.

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STUDIES ON THE PITUITARY MELANOPHORE-EXPANDING HORMONE WITH REFERENCE TO ITS IDENTITY WITH ACTH

Journal of Endocrinology ◽

10.1677/joe.0.0110007 ◽

1954 ◽

Vol 11 (1) ◽

pp. 7-13 ◽

Cited By ~ 8

Author(s):

B. KETTERER ◽

ELIZABETH REMILTON

Keyword(s):

Linear Regression ◽

Dose Response ◽

Progressive Increase ◽

Regression Curve ◽

Response Curves ◽

Experimental Conditions ◽

Response Data ◽

The Mean ◽

Dose Response Curves ◽

Linear Regression Curve

SUMMARY 1. The standard Xenopus method for the assay of pituitary melanophore-expanding hormone has been critically examined, and the results from various assay procedures are statistically analysed. 2. Log dose-response data are well fitted by a linear regression curve. Responses at 3 hr give a steeper curve than those at 1½ hr. 3. Results collected 6 months apart show that the mean and slope of dose-response curves remain constant when Xenopus are given regular dosage; there is, however, a progressive increase of variance with time shown by the colony under these experimental conditions. 4. Evidence is presented to show that Xenopus must be minimally disturbed during assay, and that assay doses must be given not less than 1 day apart.

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Analysis and comparison of sigmoidal curves: application to dose-response data

AJP Gastrointestinal and Liver Physiology ◽

10.1152/ajpgi.1989.257.6.g982 ◽

1989 ◽

Vol 257 (6) ◽

pp. G982-G989 ◽

Cited By ~ 16

Author(s):

J. B. Meddings ◽

R. B. Scott ◽

G. H. Fick

Keyword(s):

Nonlinear Regression ◽

Dose Response ◽

Numerical Solutions ◽

Maximal Response ◽

Response Curves ◽

Experimental Conditions ◽

Response Data ◽

Accuracy And Precision ◽

Analysis Technique ◽

Dose Response Curves

A number of physiological or pharmacological studies generate sigmoidal dose-response curves. Ideally, data analysis should provide numerical solutions for curve parameters. In addition, for curves obtained under different experimental conditions, testing for significant differences should be easily performed. We have reviewed the literature over the past 3 years in six journals publishing papers in the field of gastrointestinal physiology and established the curve analysis technique used in each. Using simulated experimental data of known error structure, we have compared these techniques with nonlinear regression analysis. In terms of their ability to provide accurate estimates of ED50 and maximal response, none approached the accuracy and precision of nonlinear regression. This technique is as easily performed as the classic methods and additionally provides an opportunity for rigorous statistical analysis of data. We present a method of determining the significance of differences found in the ED50 and maximal response under different experimental conditions. The method is versatile and applicable to a variety of different physiological and pharmacological dose-response curves.

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A method to construct dose–response curves for a wide range of environmental factors and plant traits by means of a meta-analysis of phenotypic data

Journal of Experimental Botany ◽

10.1093/jxb/erp358 ◽

2010 ◽

Vol 61 (8) ◽

pp. 2043-2055 ◽

Cited By ~ 100

Author(s):

Hendrik Poorter ◽

Ülo Niinemets ◽

Achim Walter ◽

Fabio Fiorani ◽

Uli Schurr

Keyword(s):

Environmental Factors ◽

Dose Response ◽

Plant Traits ◽

Meta Analysis ◽

Response Curves ◽

Phenotypic Data ◽

Wide Range ◽

Dose Response Curves

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MELANOPHORE-STIMULATING HORMONE-MELATONIN ANTAGONISM IN RELATION TO COLOUR CHANGE IN XENOPUS LAEVIS

Journal of Endocrinology ◽

10.1677/joe.0.0490573 ◽

1971 ◽

Vol 49 (4) ◽

pp. 573-580 ◽

Cited By ~ 5

Author(s):

KAY DIERST-DAVIES ◽

F. W. LANDGREBE ◽

G. M. MITCHELL

Keyword(s):

Xenopus Laevis ◽

Dose Response ◽

Colour Change ◽

Response Curves ◽

Low Concentrations ◽

Wide Range ◽

Dose Response Curves ◽

Normal Light ◽

Melanophore Stimulating Hormone ◽

Stimulating Hormone

SUMMARY Experiments on colour change of Xenopus laevis were performed to investigate the possibility that melatonin is the physiological antagonist to melanophore-stimulating hormone (MSH). Various amounts of substandard (SS) extract of ox posterior pituitary plus melatonin were injected into the dorsal lymph sac of adult male Xenopus laevis. Normal light-adapted, completely hypophysectomized, and anterior lobectomized animals were used. Dose—response curves were obtained for different SS dosages over a wide range of melatonin concentrations. Melatonin at very low concentrations inhibited the darkening reaction to both injected SS and endogenous MSH. In all cases more melatonin was required to inhibit the effect of SS in hypophysectomized than in normal animals. The results indicate that melatonin may be a physiological MSH antagonist in Xenopus laevis and the pituitary either contains some lightening factor itself ( Hogben's 'W' substance?) or has control over another organ (pineal gland?) where a lightening factor may be present. The unusual linear-logarithmic dose—response curves are discussed.

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Dose-response Curves in the Fibrin Plate Assay Fibrinolytic Activity of Proteases

Thrombosis and Haemostasis ◽

10.1055/s-0038-1647705 ◽

1974 ◽

Vol 32 (02/03) ◽

pp. 356-365 ◽

Cited By ~ 12

Author(s):

F Haverkate ◽

D. W Traas

Keyword(s):

Dose Response ◽

Fibrinolytic Activity ◽

Enzyme Concentration ◽

Response Curves ◽

Agar Gel ◽

Porcine Tissue ◽

Plate Assay ◽

Fibrin Plate ◽

Different Types ◽

Dose Response Curves

SummaryIn the fibrin plate assay different types of relationships between the dose of applied proteolytic enzyme and the response have been previously reported. This study was undertaken to determine whether a generally valid relationship might exist.Trypsin, chymotrypsin, papain, the plasminogen activator urokinase and all of the microbial proteases investigated, including brinase gave a linear relationship between the logarithm of the enzyme concentration and the diameter of the circular lysed zone. A similar linearity of dose-response curves has frequently been found by investigators who used enzyme plate assays with substrates different from fibrin incorporated in an agar gel. Consequently, it seems that this linearity of dose-response curves is generally valid for the fibrin plate assay as well as for other enzyme plate bioassays.Both human plasmin and porcine tissue activator of plasminogen showed deviations from linearity of semi-logarithmic dose-response curves in the fibrin plate assay.

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BIOASSAY OF THYROID HORMONE USING HYPOTHYROID TADPOLES

Acta Endocrinologica ◽

10.1530/acta.0.0410143 ◽

1962 ◽

Vol 41 (1) ◽

pp. 143-153 ◽

Cited By ~ 2

Author(s):

U. Henriques

Keyword(s):

Thyroid Hormone ◽

Dose Response ◽

Developmental Rate ◽

Response Curves ◽

Sodium Salts ◽

Dose Response Curves

ABSTRACT A bioassay of thyroid hormone has been developed using Xenopus larvae made hypothyroid by the administration of thiourea. Only tadpoles of uniform developmental rate were used. Thiourea was given just before the metamorphotic climax in concentrations that produced neoteni in an early metamorphotic stage. During maintained thiourea neotoni, 1-thyroxine and 1-triiodothyronine were added as sodium salts to the water for three days and at the end of one week the stage of metamorphosis produced was determined. In this way identical dose-response curves were obtained for the two compounds. No qualitative differences between their effects were noted except that triiodothyronine seemed more toxic than thyroxine in equivalent doses. Triiodothyronine was found to be 7–12 times as active as thyroxine.

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