scholarly journals Critical Re-evaluation of the Slope Factor of the Operational Model of Agonism Short Title: Slope Factor of the Operational Model of Agonism

2021 ◽  
Author(s):  
Jan Jakubík ◽  
Alena Randáková ◽  
Dominik Nelic
Keyword(s):  
Substrate Inhibition ◽  
Theoretical Data ◽  
Hill Coefficient ◽  
Response Curves ◽  
Operational Model ◽  
Relative Term ◽  
Slope Factor ◽  
Operational Efficacy ◽  
The Hill ◽  
Operational Model Of Agonism

Abstract Although being a relative term, agonist efficacy is a cornerstone in the proper assessment of agonist selectivity and signalling bias. The operational model of agonism (OMA) has become successful in the determination of agonist efficacies and ranking them. In 1985, Black et al. introduced the slope factor to the OMA to make it more flexible and allow for fitting steep as well as flat concentration-response curves. Functional analysis of OMA demonstrates that the slope factor implemented by Black et al. affects relationships among parameters of the OMA. Fitting of the OMA with Black et al. slope factor to concentration-response curves of experimental as well as theoretical data (homotropic allosteric modulation, substrate inhibition and non-competitive auto-inhibition) resulted in wrong estimates of operational efficacy and affinity. In contrast, fitting of the OMA modified by the Hill coefficient to the same data resulted in correct estimates of operational efficacy and affinity. Therefore OMA modified by the Hill coefficient should be preferred over Black et al. equation for ranking of agonism and subsequent analysis, like quantification of signalling bias, when concentration response curves differ in the slope factor.

scholarly journals On slope factor of the operational model of agonism

2021 ◽  
Author(s):  
Jan Jakubik
Keyword(s):  
Hill Coefficient ◽  
Response Curves ◽  
Operational Model ◽  
Relative Term ◽  
Slope Factor ◽  
The Hill ◽  
Operational Model Of Agonism

Although being a relative term, agonist efficacy is a cornerstone in the proper assessment of agonist selectivity and signalling bias. The operational model of agonism (OMA) has become successful in the determination of agonist efficacies and ranking them. In 1995, Black et al. introduced slope factor to the OMA that makes the OMA more flexible and allows for fitting steep as well as flat concentration-response curves. Here I opinion drawbacks of the slope factor implemented by Black et al. that affects relationships among parameters of the OMA. Instead, I propose the implementation of the Hill coefficient in the OMA that does not affect observed parameters. The OMA modified by the Hill coefficient is more practical in the determination of operational efficacies for agonism ranking and subsequent analysis, like quantification of signalling bias.

Effect of asymmetry of concentration–response curves on the results obtained by the receptorial responsiveness method (RRM): an in silico study

2010 ◽  
Vol 88 (11) ◽  
pp. 1074-1083 ◽  
Author(s):  
Maria Grenczer ◽  
Judit Zsuga ◽  
Laszlo Majoros ◽  
Akos Pinter ◽  
Adam Kemeny-Beke ◽  
...  
Keyword(s):  
Hill Equation ◽  
Richards Equation ◽  
High Concentration ◽  
Response Curves ◽  
Operational Model ◽  
In Silico Study ◽  
Slope Factor ◽  
Agonist Concentration ◽  
The Hill ◽  
Advanced Model

The receptorial responsiveness method (RRM) was proposed to estimate changes in the concentration of an agonist in the microenvironment of its receptor. Usually, this is done by providing the equieffective concentration of another agonist for the same receptor or for a largely overlapping postreceptorial signaling (“test agonist”). The RRM is a special nonlinear regression algorithm to analyze a concentration–response (E/c) curve that represents the simultaneous actions of a single agonist concentration to be estimated and of increasing concentrations of the test agonist. The aim of this study was to explore whether asymmetry of the E/c curve to be analyzed influences the reliability of the RRM. For this purpose, computer simulation was performed by constructing symmetric and asymmetric E/c curves using the operational model of agonism, and then these curves were analyzed with the RRM. To perform the RRM, 2 types of equations were used: one involving the Hill equation, the simplest model of the E/c relationship, and one containing the Richards equation, an advanced model properly handling E/c curve asymmetry. Results of this study indicate that E/c curve asymmetry does not significantly influence the accuracy of the estimates provided by the RRM. Thus, when using the RRM, it is not necessary to replace the Hill equation with the Richards equation to obtain useful estimates. Furthermore, it was found that estimation of a high concentration of a high-efficacy agonist can fail when the RRM is performed with a low-efficacy test agonist in a system characterized by a small operational slope factor.

scholarly journals Pharmacodynamics of TRPV1 Agonists in a Bioassay Using Human PC-3 Cells

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Daniel Alvarez-Berdugo ◽  
Marcel Jiménez ◽  
Pere Clavé ◽  
Laia Rofes
Keyword(s):  
Sensory Neurons ◽  
Fluorescence Emission ◽  
Hill Equation ◽  
Hill Coefficient ◽  
Response Curves ◽  
Trpv1 Receptor ◽  
Specific Antagonist ◽  
Emission Changes ◽  
The Hill

Purpose. TRPV1 is a multimodal channel mainly expressed in sensory neurons. We aimed to explore the pharmacodynamics of the TRPV1 agonists, capsaicin, natural capsaicinoids, and piperine in anin vitrobioassay using human PC-3 cells and to examine desensitization and the effect of the specific antagonist SB366791.Methods. PC-3 cells expressing TRPV1 were incubated with Fluo-4. Fluorescence emission changes following exposition to agonists with and without preincubation with antagonists were assessed and referred to maximal fluorescence following the addition of ionomycin. Concentration-response curves were fitted to the Hill equation.Results. Capsaicin and piperine had similar pharmacodynamics (Emax204.8 ± 184.3% piperine versus 176.6 ± 35.83% capsaicin,P=0.8814, Hill coefficient 0.70 ± 0.50 piperine versus 1.59 ± 0.86 capsaicin,P=0.3752). In contrast, capsaicinoids had lowerEmax(40.99 ± 6.14% capsaicinoids versus 176.6 ± 35.83% capsaicin,P<0.001). All the TRPV1 agonists showed significant desensitization after the second exposition and their effects were strongly inhibited by SB366791.Conclusion. TRPV1 receptor is successfully stimulated by capsaicin, piperine, and natural capsaicinoids. These agonists present desensitization and their effect is significantly reduced by a TRPV1-specific antagonist. In addition, PC-3 cell bioassays proved useful in the study of TRPV1 pharmacodynamics.

Suppression by Zinc of AMPA Receptor-Mediated Synaptic Transmission in the Retina

2002 ◽  
Vol 88 (3) ◽  
pp. 1245-1251 ◽  
Author(s):  
Dao-Qi Zhang ◽  
Christophe Ribelayga ◽  
Stuart C. Mangel ◽  
Douglas G. McMahon
Keyword(s):  
Glutamate Receptor ◽  
Ampa Receptors ◽  
Bipolar Cells ◽  
Horizontal Cells ◽  
Hill Coefficient ◽  
Receptor Desensitization ◽  
Patch Clamp Recording ◽  
Response Curves ◽  
Peak Current ◽  
The Hill

Zinc is strikingly co-localized with glutamate-containing vesicles in the synaptic terminals of retinal photoreceptors, and it is thought to be co-released with glutamate onto postsynaptic neurons such as horizontal cells and bipolar cells. Here we examined exogenous zinc modulation of glutamate receptors on cultured retinal horizontal cells using patch-clamp recording and endogenous zinc effect on intact horizontal cells using intracellular recording techniques. Application of 3, 30, and 300 μM zinc reduced the whole cell peak current of response to 200 μM glutamate by 2, 30, and 56%, respectively. Zinc suppression of glutamate response persisted in the presence of 10 μM cyclothiazide (CTZ). Glutamate responses of outside-out patches were completely abolished by 30 μM 1-(4-aminophenyl)-4-methyl-7,8-methylenedioxy-5H-2,3-benzodiazepine (GYKI 52466), and the receptor desensitization was blocked by 30 μM CTZ, indicating that receptor target for the zinc action on horizontal cells is α-amino-3-hydroxy-5-methyl-4-isoxazoleproponic acid (AMPA) receptors. Zinc decreased the amplitude of outside-out patch peak current without an effect on either its 10–90% rise time or the rate of receptor desensitization. Dose-response curves for glutamate show that zinc reduced the maximal current evoked by glutamate and increased EC50 from 50 ± 3 to 70 ± 6 μM without changing the Hill coefficient. Chelation of endogenous zinc with 1 mM Ca-EDTA depolarized horizontal cells in the intact retina by 3 mV, consistent with relief of the partial glutamate receptor inhibition by zinc. Overall, the results describe a unimodal form of zinc modulation of AMPA-type glutamate receptor responses not previously described in native neuronal preparations and a novel role for endogenous zinc in modulating neurotransmission.

The γ Subunit Determines Whether Anesthetic-induced Leftward Shift Is Altered by a Mutation at α1S270 in α1β2γ2LGABAAReceptors

2001 ◽  
Vol 95 (1) ◽  
pp. 123-131 ◽  
Author(s):  
Michaela Scheller ◽  
Stuart A. Forman
Keyword(s):  
Volatile Anesthetics ◽  
Hill Coefficient ◽  
Mammalian Brain ◽  
Wild Type ◽  
Gaba Concentration ◽  
Response Curves ◽  
Gaba A ◽  
Leftward Shift ◽  
The Hill ◽  
The Impact

Background A major action of volatile anesthetics is enhancement of gamma-aminobutyric acid receptor type A (GABA(A)R) currents. In recombinant GABA(A)Rs consisting of several subunit mixtures, mutating the alpha1 subunit serine at position 270 to isoleucine [alpha1(S270I)] was reported to eliminate anesthetic-induced enhancement at low GABA concentrations. In the absence of studies at high GABA concentrations, it remains unclear whether alpha1(S270I) affects enhancement versus inhibition by volatile anesthetics. Furthermore, the majority of GABA(A)Rs in mammalian brain are thought to consist of alpha1, beta2, and gamma2 subunits, and the alpha1(S270I) mutation has not been studied in the context of this combination. Methods Recombinant GABA(A)Rs composed of alpha1beta2 or alpha1beta2gamma2L subunit mixtures were studied electrophysiologically in whole Xenopus oocytes in the voltage clamp configuration. Currents elicited by GABA (0.03 microM to 1 mM) were measured in the absence and presence of isoflurane or halothane. Anesthetic effects on GABA concentration responses were evaluated for individual oocytes. Results In wild-type alpha1beta2gamma2L GABA(A), anesthetics at approximately 2 minimum alveolar concentration (MAC) shifted GABA concentration response curves to the left approximately threefold, decreased the Hill coefficient, and enhanced currents at all GABA concentrations. The alpha1(S270I) mutation itself rendered the GABA(A)R more sensitive to GABA and reduced the Hill coefficient. At low GABA concentrations (EC5), anesthetic enhancement of peak current was much smaller in alpha1(S270I)beta2gamma2L versus wild-type channels. Paradoxically, the leftward shift of the whole GABA concentration-response relation by anesthetics was the same in both mutant and wild-type channels. At high GABA concentrations, volatile anesthetics reduced currents in alpha1(S270I)beta2gammaL GABA(A)Rs. In parallel studies on alpha1beta2 (gamma-less) GABA(A)Rs, anesthetic-induced leftward shifts in wild-type receptors were more than eightfold at 2 MAC, and the alpha1(S270I) mutation nearly eliminated anesthetic-induced leftward shift. Conclusions The results support a role for alpha1S270 in alpha1beta2gamma2L GABA(A)R gating and sensitivity to inhibition by volatile anesthetics. The alpha1S270 locus also modulates anesthetic enhancement in alpha1beta2 GABA(A)R. The presence of the gamma2L subunit reduces anesthetic-induced left shift of wild-type GABA(A)R and nullifies the impact of the alpha1(S2701) mutation on anesthetic modulation. Thus, the gamma2L subunit plays a significant role in GABA(A)R modulation by volatile anesthetic compounds.

The influence of affinity, efficacy, and slope factor on the estimates obtained by the receptorial responsiveness method (RRM): a computer simulation study

2010 ◽  
Vol 88 (11) ◽  
pp. 1061-1073 ◽  
Author(s):  
Maria Grenczer ◽  
Akos Pinter ◽  
Judit Zsuga ◽  
Adam Kemeny-Beke ◽  
Bela Juhasz ◽  
...  
Keyword(s):  
Computer Simulation ◽  
Simulation Study ◽  
Proper Choice ◽  
Concentration Effect ◽  
Simultaneous Action ◽  
Computer Simulation Study ◽  
Operational Model ◽  
Slope Factor ◽  
Operational Efficacy

The receptorial responsiveness method (RRM) was proposed to characterize changes in the concentration of degradable agonists in the microenvironment of their receptors. The characterization is done by providing concentrations of a stable agonist for the same receptor that is equieffective with the change in concentration to be characterized. RRM is based on the analysis of concentration–effect (E/c) curves reflecting the simultaneous action of the degradable and the stable agonist. In the present study, we investigated whether dissimilar affinity and (or) efficacy of the coacting agonists as well as the steepness of the E/c curves influence the reliability of RRM. E/c curves were simulated based on the operational model and then analyzed with RRM. We found that dissimilarity in affinity of the coacting agonists did not affect the accuracy of RRM estimates. In contrast, accuracy of the estimation depended on the magnitude of the concentration to be assessed, the operational slope factor, and the operational efficacy ratio of the coacting agonists. However, our results suggest that proper choice of a stable agonist for a degradable one can help to ensure reliable results, since information about the change in concentration of a degradable agonist is otherwise difficult to obtain.

On the Measurement of Cooperativity and the Physico-Chemical Meaning of the Hill Coefficient

2019 ◽  
Vol 20 (9) ◽  
pp. 861-872 ◽  
Author(s):  
Andrea Bellelli ◽  
Emanuele Caglioti
Keyword(s):  
Ligand Binding ◽  
Hormone Receptors ◽  
Fundamental Property ◽  
Statistical Correlation ◽  
Hill Coefficient ◽  
Biological Macromolecules ◽  
Physico Chemical ◽  
Physiological Relevance ◽  
Minimum Estimate ◽  
The Hill

Cooperative ligand binding is a fundamental property of many biological macromolecules, notably transport proteins, hormone receptors, and enzymes. Positive homotropic cooperativity, the form of cooperativity that has greatest physiological relevance, causes the ligand affinity to increase as ligation proceeds, thus increasing the steepness of the ligand-binding isotherm. The measurement of the extent of cooperativity has proven difficult, and the most commonly employed marker of cooperativity, the Hill coefficient, originates from a structural hypothesis that has long been disproved. However, a wealth of relevant biochemical data has been interpreted using the Hill coefficient and is being used in studies on evolution and comparative physiology. Even a cursory analysis of the pertinent literature shows that several authors tried to derive more sound biochemical information from the Hill coefficient, often unaware of each other. As a result, a perplexing array of equations interpreting the Hill coefficient is available in the literature, each responding to specific simplifications or assumptions. In this work, we summarize and try to order these attempts, and demonstrate that the Hill coefficient (i) provides a minimum estimate of the free energy of interaction, the other parameter used to measure cooperativity, and (ii) bears a robust statistical correlation to the population of incompletely saturated ligation intermediates. Our aim is to critically evaluate the different analyses that have been advanced to provide a physical meaning to the Hill coefficient, and possibly to select the most reliable ones to be used in comparative studies that may make use of the extensive but elusive information available in the literature.

Effect of adrenomedullin on the production of endothelin-1 and on its vasoconstrictor action in resistance arteries: evidence for a receptor-specific functional interaction in patients with heart failure

2001 ◽  
Vol 101 (1) ◽  
pp. 45-51 ◽  
Author(s):  
Chris HILLIER ◽  
Mark C. PETRIE ◽  
Michael P. LOVE ◽  
Fiona JOHNSTON ◽  
Margaret R. MACLEAN ◽  
...  
Keyword(s):  
Heart Failure ◽  
Hill Coefficient ◽  
Receptor Interaction ◽  
Resistance Arteries ◽  
Functional Interaction ◽  
High Potassium ◽  
Endothelin 1 ◽  
Patients With Heart Failure ◽  
Small Resistance ◽  
The Hill

Endothelin-1 (ET-1) and adrenomedullin (ADM) are both produced in the arterial wall, but have opposing biological actions. Evidence from experimental animals suggests a functional interaction between ET-1 and ADM. We have tested this in humans. Small resistance arteries were obtained from gluteal biopsies taken from patients with chronic heart failure (CHF) due to coronary heart disease (CHD), or with CHD and preserved ventricular function. The contractile responses to big ET-1 and to ET-1 in both sets of vessels were studied in the absence (control) and presence of ADM at 20 pmol/l (low ADM) or 200 pmol/l (high ADM), using wire myography. ADM did not affect the conversion of big ET-1 into ET-1 in vessels from patients with either CHD or CHF. Low ADM did not alter the contractile response to ET-1 in vessels from patients with CHF. Low ADM was not tested in vessels from patients with CHD, but high ADM did not affect this response in arteries from these patients. High ADM did, however, significantly reduce the vasoconstrictor effect of ET-1 in vessels from patients with CHF. The maximum response, as a percentage of the response to high potassium, was 199% (S.E.M. 25%) in the control experiments (n = 14), 205% (27%) in the low-ADM (n = 7) studies and 150% (17%) in the high-ADM (n = 6) experiments (P < 0.001). Furthermore, the Hill coefficient increased from 0.57±0.05 in the absence of ADM to 1.16±0.15 in the high-ADM experiments, indicating that ADM at 200 pmol/l specifically antagonized one receptor type in vessels from patients with CHF. We conclude that there is a one-site receptor interaction between ADM and ET-1 that is specific for vessels from patients with CHF. This functional interaction between ADM and ET-1 in resistance arteries may be of pathophysiological importance in CHF.

scholarly journals Activation and Two Modes of Blockade by Strontium of Ca2+-activated K+ Channels in Goldfish Saccular Hair Cells

1998 ◽  
Vol 111 (2) ◽  
pp. 363-379 ◽  
Author(s):  
Izumi Sugihara
Keyword(s):  
Dissociation Constant ◽  
Time Constant ◽  
Hair Cells ◽  
Single Channel ◽  
Hill Coefficient ◽  
K Channels ◽  
Voltage Dependent ◽  
Time Courses ◽  
The Hill ◽  
Inside Out

Effects of internal Sr2+ on the activity of large-conductance Ca2+-activated K+ channels were studied in inside-out membrane patches from goldfish saccular hair cells. Sr2+ was approximately one-fourth as potent as Ca2+ in activating these channels. Although the Hill coefficient for Sr2+ was smaller than that for Ca2+, maximum open-state probability, voltage dependence, steady state gating kinetics, and time courses of activation and deactivation of the channel were very similar under the presence of equipotent concentrations of Ca2+ and Sr2+. This suggests that voltage-dependent activation is partially independent of the ligand. Internal Sr2+ at higher concentrations (&gt;100 μM) produced fast and slow blockade both concentration and voltage dependently. The reduction in single-channel amplitude (fast blockade) could be fitted with a modified Woodhull equation that incorporated the Hill coefficient. The dissociation constant at 0 mV, the Hill coefficient, and zd (a product of the charge of the blocking ion and the fraction of the voltage difference at the binding site from the inside) in this equation were 58–209 mM, 0.69–0.75, 0.45–0.51, respectively (n = 4). Long shut events (slow blockade) produced by Sr2+ lasted ∼10–200 ms and could be fitted with single-exponential curves (time constant, τl−s) in shut-time histograms. Durations of burst events, periods intercalated by long shut events, could also be fitted with single exponentials (time constant, τb). A significant decrease in τb and no large changes in τl−s were observed with increased Sr2+ concentration and voltage. These findings on slow blockade could be approximated by a model in which single Sr2+ ions bind to a blocking site within the channel pore beyond the energy barrier from the inside, as proposed for Ba2+ blockade. The dissociation constant at 0 mV and zd in the Woodhull equation for this model were 36–150 mM and 1–1.8, respectively (n = 3).

Endotoxin administration alters the force vs. pCa relationship of skeletal muscle fibers

2000 ◽  
Vol 278 (4) ◽  
pp. R891-R896 ◽  
Author(s):  
G. Supinski ◽  
D. Nethery ◽  
T. M. Nosek ◽  
L. A. Callahan ◽  
D. Stofan ◽  
...  
Keyword(s):  
Skeletal Muscle ◽  
Muscle Force ◽  
Fiber Type ◽  
Contractile Proteins ◽  
Hill Coefficient ◽  
Control Group ◽  
Fiber Types ◽  
Endotoxin Administration ◽  
Generating Capacity ◽  
The Hill

Recent work indicates that endotoxemia elicits severe reductions in skeletal muscle force-generating capacity. The subcellular alterations responsible for these decrements have not, however, been fully characterized. One possibility is that the contractile proteins per se are altered in endotoxemia and another is that the mechanism by which these proteins are activated is affected. The purpose of the present study was to assess the effects of endotoxin administration on the contractile proteins by examining the maximum calcium-activated force (Fmax) and calcium sensitivity of single Triton-skinned fibers of diaphragm, soleus, and extensor digitorum longus (EDL) muscles taken from control and endotoxin-treated (8 mg/kg) rats. Fibers were mounted on a force transducer and sequentially activated by serial immersion in solutions of increasing Ca2+ concentration (i.e., pCa 6.0 to pCa 5.0); force vs. pCa data were fit to the Hill equation. All fibers were typed at the conclusion of studies using gel electrophoresis. Fmax, the calcium concentration required for half-maximal activation (Ca50), and the Hill coefficient were compared as a function of muscle and fiber type for the control and endotoxin-treated animals. Control group Fmax was similar for diaphragm, soleus, and EDL fibers, i.e., 112.34 ± 2.64, 111.55 ± 3.66, and 104.05 ± 4.33 kPa, respectively. Endotoxin administration reduced the average Fmax for fibers from all three muscles to 80.25 ± 2.30, 72.47 ± 2.97, and 78.32 ± 2.43 kPa, respectively ( P < 0.001 for comparison of each to control). All fiber types in diaphragm, soleus, and EDL muscles manifested similar endotoxin-related reductions in Fmax. The Ca50 and the Hill coefficient for all fiber types and all muscles were unaffected by endotoxin administration. We speculate that these alterations in the intrinsic properties of the contractile proteins represent a major mechanism by which endotoxemia reduces muscle force-generating capacity.

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