Hyperbolic responses

Figure 13.10 shows the calibration curve of the LED-based optical oxygen sensor compared with the calibration curve of a commercially available Clark-type sensor (Ingold Electrodes, Wilmington, Massachusetts). While the Clark-type shows a linear calibration, the optical sensor allows a hyperbolic response as predicted by the Stem-Volmer-type equation 72 ... 

Hyperbolic response The relationship between the rate of glucose transport and glucose concentration is hyperbolic that is, the transporter has a limited number of glucose-binding sites and there is Vmax for transport. The concentration of glucose at half the V ax is known as the Kni (Figure 5.6). This is exactly the same as an enzyme (Chapter 3). 

An attempt was made recently to find out how sensitively the regulatory system that controls the cell cycle and cell proliferation responds to signal input. Ferrell et found that, in intact oocytes, the response is ultrasensitive , a kinetic characterization introduced by Daniel E. Koshland Jr.26 (Ultrasensitivity has been defined as the response of an enzyme that is more sensitive to changes in the concentration of the substrate than an enzyme with a normal hyperbolic response, according to the Michaelis-Menten equation. One can also use the Hill coefficient (wh) to indicate hyperbolic (Michaelis-Menten) sensitivity ( h = 1-0), ultrasensitivity ( h > l)j and subsensitivity ( h <... 

Assuming that Eg responds to both X and S by a simple two-substrate hyperbolic response the rate equation for Eg is... 

The erythrocyte PRPP synthetase in these patients exhibit in hemolysate, at saturating concentration of ribose-5-phosphate and ATP, a hyperbolic response to increasing inorganic phosphate concentration, as contrasted to the sigmoidal response of the enzyme of of normal control subjects (13,14) (Fig. l). 

DPG. In order to elucidate whether the hyperbolic response of the mutant PRPP synthetase to increasing phosphate concentration in hemolysate reflects an abnormal response to inhibitors, a system devoid of inhibitors was employed. Using stroma-free charcoal-adsorbed hemolysate treated with DEAE-cellulose, the difference in reaction to increasing inorganic phosphate concentration between the mutant enzyme and the normal enzyme disappeared both exhibiting a hyperbolic response (Fig. 2). It was furthermore found that the mutant enzyme had a decreased sensitivity to inhibition by GDP, ADP,... 

An allosteric situation where is constant but the apparent changes in response to effectors is termed a V system. In a V system, all v versus S plots are hyperbolic rather than sigmoid (Figure 15.12). The positive heterotropic effector A activates by raising whereas 1, the negative heterotropic effec-... 

FIGURE 2.16 Effects of successive rectangular hyperbolae on receptor stimulus, (a) Stimulus to three agonists, (b) Three rectangular hyperbolic stimulus-response functions in series. Function 1 ((3 = 0.1) feeds function 2 ((3 = 0.03), which in turn feeds function 3 ((3 = 0.1). (c) Output from function 1. (d) Output from function 2 (functions 1 and 2 in series), (e) Final response output from function 3 (all three functions in series). Note how all three are full agonists when observed as final response. 

While individual stimulus-response pathways are extremely complicated, they all can be mathematically described with hyperbolic functions. 

The function f is usually hyperbolic, which introduces the nonlinearity between receptor occupancy and response. A common experimentally observed relationship between receptor stimulus and response is a rectangular hyperbola (see Chapter 2). Thus, response can be thought of as a hyperbolic function of stimulus ... 

Black and Leff [11] presented a model, termed the operational model, that avoids the inclusion of ad hoc terms for efficacy. This model is based on the experimental observation that the relationship between agonist concentration and tissue response is most often hyperbolic. This allows for response to be expressed in terms of... 

FIGURE 3.6 Classical model of agonism. Ordinates response as a fraction of the system maximal response. Abscissae logarithms of molar concentrations of agonist, (a) Effect of changing efficacy as defined by Stephenson [24], Stimulus-response coupling defined by hyperbolic function Response = stimulus/(stimulus-F 0.1). (b) Dose-response curves for agonist of e = 1 and various values for Ka. 

The operational model, as presented, shows dose-response curves with slopes of unity. This pertains specifically only to stimulus-response cascades where there is no cooperativity and the relationship between stimulus ([AR] complex) and overall response is controlled by a hyperbolic function with slope = 1. In practice, it is known that there are experimental dose-response curves with slopes that are not equal to unity and there is no a priori reason for there not to be cooperativity in the stimulus-response process. To accommodate the fitting of real data (with slopes not equal to unity) and the occurrence of stimulus-response cooperativity, a form of the operational model equation can be used with a variable slope (see Section 3.13.4) ... 

The basis of this model is the experimental fact that most agonist dose-response curves are hyperbolic in nature. The reasoning for making this assumption is as follows. If agonist binding is governed by mass action, then the relationship between the agonist-receptor complex and response must either be linear or hyperbolic as well. Response is thus defined as... 

It can be seen that if KA< v then negative and/or infinite values for response are allowed. No physiological counterpart to such behavior exists. This leaves a linear relationship between agonist concentration and response (where Ka = v) or a hyperbolic one (KA>v). There are few if any cases of truly linear relationships between agonist concentration and tissue response. Therefore, the default for the relationship is a hyperbolic one. 

Assuming a hyperbolic relationship between response and the amount of agonist-receptor complex, response is defined as... 

The transducer function defines the efficiency of the system to translate receptor stimulus into response and defines the efficacy of the agonist. Specifically, it is the fitting parameter of the hyperbolic function linking receptor... 

In terms of classical receptor theory—where response is a hyperbolic function of stimulus (Response = Stimulus/ (Stimulus 4- [3), [3 is a transducer function reflecting the efficiency of the stimulus-response mechanism of the system), and stimulus is given by Stimulus = [A] e/([A] + KA) (e is the efficacy of the agonist)— Response is given by... 

General Procedure Dose-response curves are obtained for an agonist in the absence and presence of a range of concentrations of the antagonist. The dextral displacement of these curves (ECSo values) are fit to a hyperbolic equation to yield the potency of the antagonist and the maximal value for the cooperativity constant (a) for the antagonist. 

Hyperbola (hyperbolic), a set of functions defining nonlinear relationships between abscissae and ordinates. This term is used loosely to describe nonlinear relationships between the initial interaction of molecules and receptors and the observed response (i.e., stimulus-response cascades of cells). 

Mendeleev had personal reasons for indulging in hyperbole, of course, but the general response of the chemical community does indeed seem to have been that this accommodation of argon within Mendeleev s scheme was a major feather in its cap—no less major than any other empirical success, whether predictive in the temporally novel sense or not. 

The cytochrome P-450-dependent metabolism of trichloroethylene was studied in hepatic microsomal fractions from 23 different humans (Lipscomb et al. 1997). CYP2E1 was the predominant form of P-450 responsible for the metabolism of trichloroethylene in humans. Incubations of trichloroethylene with the microsomal preparations resulted in hyperbolic plots consistent with Michaelis-Menton kinetics. The values ranged from 12 to 55.7 pM, and were not normally distributed, and the values range from 490 to 3,455 pmol/min/mg protein and were normally distributed. The study authors concluded that the human variability in metabolism of trichloroethylene via P-450-dependent pathways was within a 10-fold range. 

Though this looks complicated, it still predicts a simple hyperbolic relationship (as with the Hill-Langmuir equation see Figure 1.1 and the accompanying text) between agonist concentration and the proportion of receptors in the state (AR G ) that leads to a response. If a very large concentration of A is applied, so that all the receptors are occupied, the value of pAR.G. asymptotes to ... 

Claims of perpetual motion create moments of mirth and consternation for those knowledgeable in the laws of thermodynamics. Yet, is it only hyperbole when a responsible journal such as the European Plastics News [1] proclaims that depolymerization of polyethylene terephthalate (PET) can be repeated indefinitely The second law of thermodynamics brings us back to reality. The depolymerization of PET does not operate at 100% yields, but does offer the opportunity for near-stoichiometric recovery of the monomers used to make the polyester. With high yields of potentially valuable monomers, the commercial potential for polyester depolymerization to regain feedstocks must be considered. 

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