Inverse problem for the Hill equation. Numerical experiments

ABSTRACT The Clinical and Laboratory Standards Institute (CLSI) daptomycin MIC susceptibility breakpoint for the treatment of enterococcal infections is ≤4 μg/ml. However, patients receiving daptomycin for the treatment of infections caused by enterococci with MICs of ≤4 μg/ml may experience treatment failures. We assessed the pharmacodynamics of daptomycin against enterococci in a neutropenic murine thigh infection model and determined the exposures necessary for bacteriostasis and a 1-log10-CFU reduction of Enterococcus faecalis and Enterococcus faecium. We further characterized daptomycin efficacy at clinically achievable exposures. Six E. faecium and 6 E. faecalis isolates (daptomycin MICs, 0.5 to 32 μg/ml) were studied. Daptomycin was administered at various doses over 24 h to achieve area under the free drug concentration-time curve-to-MIC ratios (fAUC0–24/MIC) ranging from 1 to 148. Daptomycin regimens that simulate mean human exposures following doses of 6, 8, and 10 mg/kg of body weight/day were also studied. Efficacy was assessed by the differences in the number of log10 CFU per thigh at 24 h. The Hill equation was used to estimate the fAUC0–24/MIC required to achieve bacteriostasis and a 1-log10-CFU reduction. For E. faecium, a 1-log10-CFU reduction required an fAUC0–24/MIC of 12.9 (R2 = 0.71). For E. faecalis, a 1-log10-CFU reduction was not achieved, while the fAUC0–24/MIC required for stasis was 7.2 (R2 = 0.8). With a human-simulated regimen of 6 mg/kg/day, a 1-log10-CFU reduction was observed in 3/3 E. faecium isolates with MICs of <4 μg/ml and 0/3 E. faecium isolates with MICs of ≥4 μg/ml; however, a 1-log10-CFU reduction was not achieved for any of the 6 E. faecalis isolates. These results, alongside clinical data, prompt a reevaluation of the current breakpoint.

Download Full-text

Effect of osmotic swelling and shrinkage on Na(+)-K+ pump activity in mammalian cardiac myocytes

AJP Cell Physiology ◽

10.1152/ajpcell.1993.265.5.c1201 ◽

1993 ◽

Vol 265 (5) ◽

pp. C1201-C1210 ◽

Cited By ~ 48

Author(s):

D. W. Whalley ◽

L. C. Hool ◽

R. E. Ten Eick ◽

H. H. Rasmussen

Keyword(s):

Ventricular Myocytes ◽

Pump Current ◽

Hill Equation ◽

Cell Swelling ◽

Intracellular Na Activity ◽

Single Ventricular Myocytes ◽

Hyperosmolar Solutions ◽

Hill Coefficients ◽

The Hill ◽

The Relationship

The effect on the sarcolemmal Na(+)-K+ pump of exposure to anisosmolar solutions was examined using whole cell patch clamping and ion-selective microelectrodes. Na(+)-K+ pump currents were measured in single ventricular myocytes by using pipette Na+ concentrations ([Na]pip) of 0-70 mM. The relationship between [Na]pip and pump current was well described by the Hill equation. The [Na]pip for half-maximal pump current (K0.5) was 21.4 mM in isosmolar (310 mosM) solution. K0.5 was 12.8 mM during cell swelling in hyposmolar solution (240 mosM) and 39.0 mM during cell shrinkage in hyperosmolar solution (464 mosM). The maximal pump currents, derived from the best fit of the Hill equation, and the Hill coefficients were similar in isosmolar, hyposmolar, and hyperosmolar solutions. A sustained (> 20 min) decrease in the intracellular Na+ activity developed during exposure of intact papillary muscles to hyposmolar solutions, and a sustained increase developed during exposure to hyperosmolar solutions. We conclude that osmotic myocyte swelling stimulates the sarcolemmal Na(+)-K+ pump at near-physiological levels of intracellular Na+, whereas shrinkage inhibits the pump. These changes are due to increases and decreases, respectively, in the apparent affinity of the pump for Na+.

Download Full-text

Perspective on the relationship between GABAA receptor activity and the apparent potency of an inhibitor

Current Neuropharmacology ◽

10.2174/1570159x19666211104142433 ◽

2021 ◽

Vol 19 ◽

Author(s):

Allison L. Germann ◽

Spencer R. Pierce ◽

Alex S. Evers ◽

Joe Henry Steinbach ◽

Gustav Akk

Keyword(s):

Gabaa Receptor ◽

Hill Equation ◽

Response Relationship ◽

Inhibition Concentration ◽

Level Of Activity ◽

Control Response ◽

The Hill ◽

The Relationship ◽

Inhibition Curve ◽

Receptor Channel

Background : In electrophysiological experiments inhibition of a receptor-channel, such as the GABAA receptor, is measured by co-applying an agonist producing a predefined control response with an inhibitor to calculate the fraction of the control response remaining in the presence of the inhibitor. The properties of the inhibitor are determined by fitting the inhibition concentration-response relationship to the Hill equation to estimate the midpoint (IC50) of the inhibition curve. Objective: We sought to estimate here the sensitivity of the fitted IC50 to the level of activity of the control response. Methods: The inhibition concentration-response relationships were calculated for models with distinct mechanisms of inhibition. In Model I, the inhibitor acts allosterically to stabilize the resting state of the receptor. In Model II, the inhibitor competes with the agonist for a shared binding site. In Model III, the inhibitor stabilizes the desensitized state. Results: The simulations indicate that the fitted IC50 of the inhibition curve is sensitive to the degree of activity of the control response. In Models I and II, the IC50 of inhibition was increased as the probability of being in the active state (PA) of the control response increased. In Model III, the IC50 of inhibition was reduced at higher PA. Conclusions: We infer that the apparent potency of an inhibitor depends on the PA of the control response. While the calculations were carried out using the activation and inhibition properties that are representative of the GABAA receptor, the principles and conclusions apply to a wide variety of receptor-channels.

Download Full-text

Time- or Space-Dependent Coefficient Recovery in Parabolic Partial Differential Equation for Sensor Array in the Biological Computing

Mathematical Problems in Engineering ◽

10.1155/2015/573932 ◽

2015 ◽

Vol 2015 ◽

pp. 1-9 ◽

Cited By ~ 1

Author(s):

Guanglu Zhou ◽

Boying Wu ◽

Wen Ji ◽

Seungmin Rho

Keyword(s):

Differential Equation ◽

Partial Differential Equation ◽

Inverse Problem ◽

Iteration Method ◽

Numerical Experiments ◽

Sensor Array ◽

Variational Iteration Method ◽

Parabolic Partial Differential Equation ◽

Partial Differential ◽

Variational Iteration

This study presents numerical schemes for solving a parabolic partial differential equation with a time- or space-dependent coefficient subject to an extra measurement. Through the extra measurement, the inverse problem is transformed into an equivalent nonlinear equation which is much simpler to handle. By the variational iteration method, we obtain the exact solution and the unknown coefficients. The results of numerical experiments and stable experiments imply that the variational iteration method is very suitable to solve these inverse problems.

Download Full-text

Kinetic studies on two isoforms of acetyl-CoA carboxylase from maize leaves

Biochemical Journal ◽

10.1042/bj3180997 ◽

1996 ◽

Vol 318 (3) ◽

pp. 997-1006 ◽

Cited By ~ 36

Author(s):

Derek HERBERT ◽

Lindsey J PRICE ◽

Claude ALBAN ◽

Laure DEHAYE ◽

Dominique JOB ◽

...

Keyword(s):

Kinetic Studies ◽

Product Inhibition ◽

Hill Equation ◽

Acetyl Coa Carboxylase ◽

Acetyl Coa ◽

Maize Leaves ◽

Ic50 Values ◽

A Minor ◽

The Hill

The steady-state kinetics of two multifunctional isoforms of acetyl-CoA carboxylase (ACCase) from maize leaves (a major isoform, ACCase1 and a minor isoform, ACCase2) have been investigated with respect to reaction mechanism, inhibition by two graminicides of the aryloxyphenoxypropionate class (quizalofop and fluazifop) and some cellular metabolites. Substrate interaction and product inhibition patterns indicated that ADP and Pi products from the first partial reaction were not released before acetyl-CoA bound to the enzymes. Product inhibition patterns did not match exactly those predicted for an ordered Ter Ter or a random Ter Ter mechanism, but were close to those postulated for an ordered mechanism. ACCase2 was about 1/2000 as sensitive as ACCase1 to quizalofop but only about 1/150 as sensitive to fluazifop. Fitting inhibition data to the Hill equation indicated that binding of quizalofop or fluazifop to ACCase1 was non-cooperative, as shown by the Hill constant (napp) values of 0.86 and 1.16 for quizalofop and fluazifop respectively. Apparent inhibition constant values (K´ from the Hill equation) for ACCase1 were 0.054 µM for quizalofop and 21.8 µM for fluazifop. On the other hand, binding of quizalofop or fluazifop to ACCase2 exhibited positive co-operativity, as shown by the napp values of 1.85 and 1.59 for quizalofop and fluazifop respectively. K´ values for ACCase2 were 1.7 mM for quizalofop and 140 mM for fluazifop. Kinetic parameters for the co-operative binding of quizalofop to maize ACCase2 were close to those of another multifunctional ACCase of limited sensitivity to graminicide, ACC220 from pea. Inhibition of ACCase1 by quizalofop was mixed-type with respect to acetyl-CoA or ATP, but the concentration of acetyl-CoA had the greater effect on the level of inhibition. Neither ACCase1 nor ACCase2 was appreciably sensitive to CoA esters of palmitic acid (16:0) or oleic acid (18:1). Approximate IC50 values were 10 µM (ACCase2) and 50 µM (ACCase1) for both CoA esters. Citrate concentrations up to 1 mM had no effect on ACCase1 activity. Above this concentration, citrate was inhibitory. ACCase2 activity was slightly stimulated by citrate over a broad concentration range (0.25–10 mM). The significance of possible effects of acyl-CoAs or citrate in vivo is discussed.

Download Full-text

An approach based on diffusion to study ligand-macromolecule interaction.

Acta Biochimica Polonica ◽

10.18388/abp.2002_3779 ◽

2002 ◽

Vol 49 (3) ◽

pp. 703-707 ◽

Cited By ~ 3

Author(s):

Mohammad R Housaindokht ◽

Mahmood Bahrololoom ◽

Shirin Tarighatpoor ◽

Ali A Mossavi-Movahedi

Keyword(s):

Methyl Orange ◽

Diffusion Process ◽

Binding Constant ◽

Phosphate Buffer ◽

Binding Capacity ◽

Free Ligand ◽

Hill Equation ◽

New Approach ◽

Binding Isotherm ◽

The Hill

A new approach has been developed to study binding of a ligand to a macromolecule based on the diffusion process. In terms of the Fick's first law, the concentration of free ligand in the presence of a protein can be determined by the measurement of those ligands which are diffused out. This method is applied to the study of binding of methyl-orange to lysozyme in phosphate buffer of pH 6.2, at 30 degrees C. The binding isotherm was determined initially, followed by application of the Hill equation to the data obtained, then binding constant and binding capacity were estimated.

Download Full-text

Regularization by Denoising for simultaneous source separation

Geophysics ◽

10.1190/geo2021-0068.1 ◽

2021 ◽

pp. 1-56

Author(s):

Breno Bahia ◽

Rongzhi Lin ◽

Mauricio Sacchi

Keyword(s):

Inverse Problem ◽

Inverse Problems ◽

Data Processing ◽

Spectrum Analysis ◽

Numerical Experiments ◽

Source Separation ◽

Singular Spectrum Analysis ◽

Source Data ◽

Blended Data ◽

Simultaneous Source

Denoisers can help solve inverse problems via a recently proposed framework known as regularization by denoising (RED). The RED approach defines the regularization term of the inverse problem via explicit denoising engines. Simultaneous source separation techniques, being themselves a combination of inversion and denoising methods, provide a formidable field to explore RED. We investigate the applicability of RED to simultaneous-source data processing and introduce a deblending algorithm named REDeblending (RDB). The formulation permits developing deblending algorithms where the user can select any denoising engine that satisfies RED conditions. Two popular denoisers are tested, but the method is not limited to them: frequency-wavenumber thresholding and singular spectrum analysis. We offer numerical blended data examples to showcase the performance of RDB via numerical experiments.

Download Full-text

Myoglobin oxygen dissociation by multiwavelength spectroscopy

Journal of Applied Physiology ◽

10.1152/jappl.1997.82.1.86 ◽

1997 ◽

Vol 82 (1) ◽

pp. 86-92 ◽

Cited By ~ 106

Author(s):

Kenneth A. Schenkman ◽

David R. Marble ◽

David H. Burns ◽

Eric O. Feigl

Keyword(s):

Least Squares ◽

Hill Equation ◽

Oxygen Binding ◽

Dissociation Curve ◽

Nitrogen Gas ◽

Binding Characteristics ◽

Oxygen Fraction ◽

Oxygen Dissociation ◽

Dissociation Curves ◽

The Hill

Schenkman, Kenneth A., David R. Marble, David H. Burns, and Eric O. Feigl. Myoglobin oxygen dissociation by multiwavelength spectroscopy. J. Appl. Physiol. 82(1): 86–92, 1997.—Multiwavelength optical spectroscopy was used to determine the oxygen-binding characteristics for equine myoglobin. Oxygen-binding relationships as a function of oxygen tension were determined for temperatures of 10, 25, 35, 37, and 40°C, at pH 7.0. In addition, dissociation curves were determined at 37°C for pH 6.5, 7.0, and 7.5. Equilibration was achieved with a myoglobin solution, at the desired temperature and pH, and 16 oxygen-nitrogen gas mixtures of known oxygen fraction. Correction for the inevitable presence of metmyoglobin was made by using a three-component least squares analysis and by correcting the end point oxymyoglobin spectra for the presence of metmyoglobin. The[Formula: see text] at which myoglobin is half-saturated with O2(P50) was determined to be 2.39 Torr at pH 7.0 and 37°C. The myoglobin dissociation curve was well fit by the Hill equation [saturation =[Formula: see text]/([Formula: see text]+ P50)].

Download Full-text

On the gaps in the spectrum of the Hill equation

Quarterly of Applied Mathematics ◽

10.1090/qam/59430 ◽

1954 ◽

Vol 11 (4) ◽

pp. 496-498 ◽

Cited By ~ 2

Author(s):

C. R. Putnam

Keyword(s):

Hill Equation ◽

The Hill

Download Full-text

Beyond non-integer Hill coefficients: A novel approach to analyzing binding data, applied to Na+-driven transporters

The Journal of General Physiology ◽

10.1085/jgp.201511365 ◽

2015 ◽

Vol 145 (6) ◽

pp. 555-563 ◽

Cited By ~ 9

Author(s):

Silvia Ravera ◽

Matthias Quick ◽

Juan P. Nicola ◽

Nancy Carrasco ◽

L. Mario Amzel

Keyword(s):

Hill Equation ◽

Integer Coefficient ◽

Novel Approach ◽

Binding Data ◽

Na Ions ◽

Hill Coefficients ◽

Integer Exponent ◽

The Individual ◽

The Hill ◽

Analyze Data

Prokaryotic and eukaryotic Na+-driven transporters couple the movement of one or more Na+ ions down their electrochemical gradient to the active transport of a variety of solutes. When more than one Na+ is involved, Na+-binding data are usually analyzed using the Hill equation with a non-integer exponent n. The results of this analysis are an overall Kd-like constant equal to the concentration of ligand that produces half saturation and n, a measure of cooperativity. This information is usually insufficient to provide the basis for mechanistic models. In the case of transport using two Na+ ions, an n < 2 indicates that molecules with only one of the two sites occupied are present at low saturation. Here, we propose a new way of analyzing Na+-binding data for the case of two Na+ ions that, by taking into account binding to individual sites, provides far more information than can be obtained by using the Hill equation with a non-integer coefficient: it yields pairs of possible values for the Na+ affinities of the individual sites that can only vary within narrowly bounded ranges. To illustrate the advantages of the method, we present experimental scintillation proximity assay (SPA) data on binding of Na+ to the Na+/I− symporter (NIS). SPA is a method widely used to study the binding of Na+ to Na+-driven transporters. NIS is the key plasma membrane protein that mediates active I− transport in the thyroid gland, the first step in the biosynthesis of the thyroid hormones, of which iodine is an essential constituent. NIS activity is electrogenic, with a 2:1 Na+/I− transport stoichiometry. The formalism proposed here is general and can be used to analyze data on other proteins with two binding sites for the same substrate.

Download Full-text