Pharmacokinetic-Pharmacodynamic Modeling of Reversible Drug Effects
Hartmut Derendorf, Günther Hochhaus in Handbook of Pharmacokinetic/Pharmacodynamic Correlation, 2019
For example, a vasoconstrictor agent may shorten the length of a series of cells in the arterial muscular layer, thereby reducing the vessel diameter and increasing the resistance of the local vascular bed; this may lead to a change in perfusion pattern and increase in systemic vascular resistance; however, the observed PD response is probably an elevation in arterial blood pressure. The shape of the E-c relationship for the change in length of the individual cells, the decrease in local vessel diameter, and the observed increase in arterial blood pressure will obviously be very different. This complicates the mechanistic interpretation of the Hill coefficient, n, as a cooperativity factor. In most cases, n is only a descriptive parameter to characterize the steepness of the E-c profile for the observed effect; its magnitude depends largely on how close the measured effect is to the primary effect.
Enzyme Kinetics
Clive R. Bagshaw in Biomolecular Kinetics, 2017
for which the Hill coefficient, n, would equal 4. The fact that n is less than 4 suggests that intermediate degrees of saturation exist containing one, two, or three oxygen molecules. Hemoglobin is often described as an “honorary enzyme” because the mechanism of communication between subunits is well understood at the structural level and has inspired the analysis of many cooperative enzymes. In the latter case, the velocity of the reaction is controlled by the fractional saturation of the substrate, which in turn is controlled by homotropic or heterotropic effects. That is, cooperativity is commonly expressed through changes in the apparent Km rather than Vmax and hence involves effects on k+1 and k−1 rather than k+2.
Identification Of Receptors In Vitro
William C. Eckelman, Lelio G. Colombetti in Receptor-Binding Radiotracers, 2019
If log{(Bo − B)/B} is plotted against log[I], a straight line results with slope of 1.0. A straight line on a Hill plot is therefore consistent with simple competitive inhibition. The presence of negative cooperativity (for the inhibitor) or of two sites with different affinity (for the inhibitor) results in a Hill plot with slope less than 1.0. Positive cooperativity or irreversible binding of the inhibitor gives a Hill plot with a slope greater than 1.0. The slope of a Hill plot is called the Hill coefficient. For several neurotransmitter receptors, agonists show Hill coefficients between 0.5 and 1.0, when competed against labeled antagonists. This appears to be due to the existence of two classes of site for agonists.
A molecular perspective on identifying TRPV1 thermosensitive regions and disentangling polymodal activation
Published in Temperature, 2023
Dustin D. Luu, Aerial M. Owens, Mubark D. Mebrat, Wade D. Van Horn
In the concatemer and other studies, a Hill model of cooperativity can be used to assess the allosteric implications between multiple ligand-binding sites [189]. A Hill coefficient (Kd) for additional oxygen-binding molecules [190]. Highly positive cooperative events, like found in hemoglobin, will generally have minimal intermediate bound states with an “all or nothing” binding process. In the context of hemoglobin, which is exceptionally cooperative, it is typically found in either an unbound or fully bound state [191]. Conversely, negative cooperativity functions to decrease the affinity of ligand binding as more ligands bind the substrate. The outcomes of negative cooperativity are more populated and longer-lasting intermediate bound states [191]. A noncooperative process effectively has independent binding sites [191]. Analysis of the rTRPV1–CAP concatemer study identifies a Hill coefficient near unity, indicating that CAP activation is noncooperative. This appears to agree with the conclusion that CAP binding to a single subunit can fully open rTRPV1 [180]. In contrast, rTRPV1 concatemer proton activation exhibits positive cooperativity (4,180]. The reported differences in cooperativity between CAP and protons shines a light on mechanistically distinct TRPV1 activation modes and provide a vignette into the complexity of deciphering the polymodal crosstalk between activation modes.
Compound Danshen Dripping Pill inhibits high altitude-induced hypoxic damage by suppressing oxidative stress and inflammatory responses
Published in Pharmaceutical Biology, 2021
Yunhui Hu, Jia Sun, Tongxing Wang, Hairong Wang, Chunlai Zhao, Wenjia Wang, Kaijing Yan, Xijun Yan, He Sun
Rat arterial blood (1 mL) was used for blood-gas analyses. The partial pressure of oxygen (PO2), SO2, and pH were detected at 37 °C by microelectrodes in a blood gas analyzer (iSTAT-300; Abbott Laboratories, Chicago, IL, USA). The oxygen-dissociation curve and the pressure of oxygen when SO2 level reaches 50% (P50) was calculated according to the Hill equation (Balaban et al. 2013): Equation (a), K is the oxygen dissociation constant, and n is the Hill coefficient. We converted Equation (a) into Equation (b) mathematically. After taking the logarithm on both sides of Equation (b), we obtained Equation (c) for a linear equation in the form of Y = aX + b. When we made Y = log10 SO2/(100 – SO2) and Y = log10 PO2, the slope ‘a’ became the ‘n’ value of the Hill equation, and b the logarithmic value of k. We calculated n and K values using the data for PO2 and SO2 of each group. After the regression, and making PO2 range from 0 to 100, the oxygen-dissociation curve was fitted and P50 was calculated.
Mathematical analysis of oxygen and carbon dioxide exchange in the human capillary and tissue system
Published in Computer Methods in Biomechanics and Biomedical Engineering, 2023
Ahsan Ul Haq Lone, M. A. Khanday
In this section, we derive facilitated diffusion due to haemoglobin is enhanced by a factor known as enhanced-factor. For facilitated diffusion due to haemoglobin, it is important to have accurate analytic expression for fractional saturation of haemoglobin SO2 as a function of oxygen tension PO2 and other parameters. An important curve known as oxyhaemoglobin dissociation curve that can be derived from kinetic model of haemoglobin-oxygen reaction: k1 and k2 are the association and dissociation rate coefficients, respectively. In equilibrium: O2] is the concentration of free oxygen in haemoglobin solution. We can rewrite Equation (31) by Henrys law in the form: PO2 at which the haemoglobin is 50% saturated. This Equation is called the Hill equation, and n the Hill parameter; because of its simplicity, Equation (32) has been most commonly used in physiological and clinical applications. Hill parameter n is a measure of the steepness of the binding curve saturation from hyperbolic to sigmoidal shown in Figure 8. An important parameter that appears in mathematical models is the slope of the oxyhaemoglobin dissociation curve. Therefore, for the Hill equation, we have
Related Knowledge Centers
- Biochemistry
- Cooperativity
- Dissociation Constant
- Ligand
- Macromolecule
- Hemoglobin
- Receptor
- Pharmacology
- Cooperative Binding
- Dose–Response Relationship