The Hill equation and the origin of quantitative pharmacology

Gesztelyi, Rudolf; Zsuga, Judit; Kemény-Beke, Ádám; Varga, Balázs; Juhász, Béla; Tósaki, Árpád

doi:10.1007/s00407-012-0098-5

Cited by 310 publications

(301 citation statements)

References 27 publications

(41 reference statements)

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“…The model below was used to describe the anxV-membrane binding reaction under fixed concentration of calcium (Gesztelyi et al 2012;Goutelle et al 2008;Yen et al 2010): where P is the anxV-EGFP protein present at variable concentration; M is the apoptotic cell membrane with exposed PS, defined as a unit accommodating an anxV-EGFP molecule exactly; [P] and [PM] are the concentrations of free anxV-EGFP and PM complex, respectively; [M] and [M 0 ] are the free and total concentrations of M, respectively; B is the protein occupancy of the membrane (for the sake of simplicity and operability, B refers to the PBI value); and K D is the dissociation equilibrium constant.…”

Section: Anxv-membrane Binding Assay and Data Analysismentioning

confidence: 99%

Quantitative analysis of annexin V–membrane interaction by flow cytometry

Wang

Chen

et al. 2015

Eur Biophys J

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We constructed a green fluorescent phosphatidylserine (PS)-binding probe, which was generated by fusing enhanced green fluorescent protein (EGFP) to the C terminus of human annexin V (anxV). With this probe, we investigated anxV-membrane interaction under different calcium and anxV-EGFP concentrations through flow cytometry (FCM). A mathematical description of the binding characteristics is proposed and validated to quantify the relationship concerning the relative concentration of membrane-bound anxV (B), calcium concentration ([C]), and protein concentration ([P]). Further analyses reveal that [Formula: see text] is linear with [Formula: see text] or [Formula: see text] when [P] and [C] are fixed, respectively, which indicates that the anxV-membrane binding reaction may involve sequential multiple steps. Our study provides a reference for application of anxV in apoptosis detection. The mathematical expression facilitates exploration of the possible interactions between calcium, anxV, and membrane. The corresponding mathematical analysis strengthens the interpretation of the interaction data.

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Section: Anxv-membrane Binding Assay and Data Analysismentioning

confidence: 99%

Quantitative analysis of annexin V–membrane interaction by flow cytometry

Wang

Chen

et al. 2015

Eur Biophys J

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“…The Hill equation is a three-parameter equation that results in sigmoid functions that provide good fits to a wide range of pharmacological and physiological data. It is considered the basis of quantitative pharmacology (33,58,62). The form of the equation is…”

Section: Indeterminate Loewe Additivity Solutionsmentioning

confidence: 99%

Understanding synergy

Geary¹

2013

American Journal of Physiology-Endocrinology and Metabolism

136

181

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Analysis of the interactive effects of combinations of hormones or other manipulations with qualitatively similar individual effects is an important topic in basic and clinical endocrinology as well as other branches of basic and clinical research related to integrative physiology. Functional, as opposed to mechanistic, analyses of interactions rely on the concept of synergy, which can be defined qualitatively as a cooperative action or quantitatively as a supra-additive effect according to some metric for the addition of different dose-effect curves. Unfortunately, doseeffect curve addition is far from straightforward; rather, it requires the development of an axiomatic mathematical theory. I review the mathematical soundness, face validity, and utility of the most frequently used approaches to supra-additive synergy. These criteria highlight serious problems in the two most common synergy approaches, response additivity and Loewe additivity, which is the basis of the isobole and related response surface approaches. I conclude that there is no adequate, generally applicable, supra-additive synergy metric appropriate for endocrinology or any other field of basic and clinical integrative physiology. I recommend that these metrics be abandoned in favor of the simpler definition of synergy as a cooperative, i.e., nonantagonistic, effect. This simple definition avoids mathematical difficulties, is easily applicable, meets regulatory requirements for combination therapy development, and suffices to advance phenomenological basic research to mechanistic studies of interactions and clinical combination therapy research.

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“…The experimental data concerning the increase of an emulsion concentration versus time in the fragments of sorbent were approximated by equation based on fundamental descriptive-deterministic models such as Hill (Goutelle et al 2008;Gesztelyi et al 2012) and MichaelisMenten (Johnson and Goody 2011) relating the reaction velocity as a function of the substrate concentration, and Langmuir adsorption model (Zhang and Wang 2010). The models were chosen due to their mathematical form and common use in the fields of sorption processes description during which changes of a concentration occur.…”

Section: Determination Of the Maximal Mass Of The Imbibed Emulsionsmentioning

confidence: 99%

“…where V is the rate of reaction per unit time, S is the substrate concentration (Goutelle et al 2008;Gesztelyi et al 2012). In the presently discussed case, the parameter of the reaction rate was substituted by a dimensionless parameter of concentration C DPn (t), and the substrate concentration, correspondingly by the time of an imbibition, t im [s].…”

Section: Determination Of the Maximal Mass Of The Imbibed Emulsionsmentioning

confidence: 99%

Analysis of emulsions concentration changes during imbibition in porous sorbents

Shtyka

Błaszczyk

Sęk

2016

Int. J. Environ. Sci. Technol.

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The stabilized emulsions removal from the aqueous systems is supposed to be an issue as important as the free oil products recovery. This work was conducted to investigate the mechanisms of oil-in-water emulsions sorption in a non-woven oleophilic/hydrophobic material forced by the capillary suction pressure, and the saturation level of such material during this process. It ensures the effective application of the sorbents and facilitates the development of alternative high-performance sorptive materials that can contribute to diminishing of the negative consequences of the aquatic environment contamination. The main aspect investigated in this research work was kinetics of the imbibition process in the porous media to define the optimal time of sorption and the height of the emulsions penetration. The measurement of the dispersed phase concentration changes with the increase in an emulsion front in the porous medium using the nephelometrical method is the advanced approach in the field of assessment of sorbents efficiency. The tendency of the imbibed emulsion concentration decrease versus the height was observed, which depended strongly on the viscosity and the initial composition of a penetrating liquid. The observed process was described by the mathematical model based on Hill equation.

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The Hill equation and the origin of quantitative pharmacology

Cited by 310 publications

References 27 publications

Quantitative analysis of annexin V–membrane interaction by flow cytometry

Quantitative analysis of annexin V–membrane interaction by flow cytometry

Understanding synergy

Analysis of emulsions concentration changes during imbibition in porous sorbents

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