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Enzyme Catalysis
Published in Harvey W. Blanch, Douglas S. Clark, Biochemical Engineering, 1997
Harvey W. Blanch, Douglas S. Clark
where the second equation is for the case where n ligands are bound. The graph of log (Y‾/(1-Y‾)) versus log[L] is referred to as a Hill plot, and the value of the experimentally determined slope in the region of 50% saturation is the Hill coefficient, h. At very low concentrations of ligand, only one site on the protein will be occupied, and thus the slope of this plot will tend to unity. At high values of [L], very few protein molecules will have more than one binding site available to be filled as most will have all but one site occupied. Thus the slope will again tend to unity. The derivation of the Hill equation assumes that cooperativity is complete, and so the Hill coefficient will assume the value n, the number of binding sites, only as an upper limit. In general, h will be less than n. If h<1, the cooperativity is negative, and for h=1 there is no cooperativity.
An Individualized Automatically Tuned TCI Strategy for Neuromuscular Blockade Control
Published in Cybernetics and Systems, 2022
Jorge Silva, Teresa Mendonça, Paula Rocha
The Hill equation, that relates the effect concentration, and the level of neuromuscular blockade, is given by Silva (2011) and Silva, Wigren and Mendonça (2011): where is the effect (NMB level) at zero drug concentration, that is, is the value of the NMB level when there is no concentration of muscle relaxant in the patient’s body, which according to the literature, assumes the value 100% (corresponding to total muscle activity), is a patient-dependent parameter, and is the drug effect concentration corresponding to half its effect (in this case, the rocuronium effect concentration that corresponds to an NMB level of 50%). Although this latter parameter is patient (and drug) dependent, for rocuronium, in the model proposed in Silva (2011) and Silva, Wigren and Mendonça (2011) it is given a fixed value, namely,
Assessment of flotation kinetics modeling using information criteria; case studies of elevated-pyritic copper sulfide and high-grade carbonaceous sedimentary apatite ores
Published in Journal of Dispersion Science and Technology, 2020
Ahmad Hassanzadeh, Duong Huu Hoang, Mashia Brockmann
The four and five parameter Hill model has been widely used to study sigmoidal dose effect relationships in biochemical and pharmacological contexts. The Hill equation was introduced by Hill[56] to describe the relationship between oxygen tension and the saturation of hemoglobin. In mineral processing context, this model represents comparative binding of the chemical reagents on a particle’s surface. The equation is useful for determining the degree of cooperatively of the ligand(s) binding to the enzyme or receptor. The Hill coefficient provides a way to quantify the degree of interaction between ligand binding sites. It is formally equivalent to the Langmuir isotherm. If k > 1 (positively cooperative binding) and k < 1 (negatively cooperative binding); once one ligand molecule is bound to the enzyme, its affinity for other ligand molecules increases and decreases, respectively. If k = 1 (non-cooperative (completely independent) binding); the affinity of the enzyme for a ligand molecule is not dependent on whether or not other ligand molecules are already bound.
Effect of glutamic acid elimination/substitution on the biological activities of S3 cationic amphiphilic peptides
Published in Preparative Biochemistry & Biotechnology, 2020
Mina Sepahi, Reza Ahangari Cohan, Shahin Hadadian, Dariush Norouzian
Hill equation was used for curve fitting of LPS binding effect, and log was plotted versus log of molar concentration of peptides, where θ was inhibition of LAL activation (%). Linear regression was used to predict Hill equation parameters.[25] where [L] is ligand concentrations here indicating concentrations of peptides. KD is dissociation equilibrium constant, and n is the Hill coefficient (nH). Slope and y-intercept of linear regression of above equation indicate nH and log (1/KD), respectively.