Michaelis-Menten coefficient

Enzyme kinetics and the mode of inhibition are well described by transformation of the Michaelis-Menten equation. The binding affinity of the inhibitor to the enzyme is defined as the inhibition constant Ki, whereas the affinity, with which the substrate binds, is referred to the Michaelis-Menten coefficient Km. Michaelis-Menten kinetics base on three assumptions ... 

The operational model allows simulation of cellular response from receptor activation. In some cases, there may be cooperative effects in the stimulus-response cascades translating activation of receptor to tissue response. This can cause the resulting concentration-response curve to have a Hill coefficient different from unity. In general, there is a standard method for doing this namely, reexpressing the receptor occupancy and/or activation expression (defined by the particular molecular model of receptor function) in terms of the operational model with Hill coefficient not equal to unity. The operational model utilizes the concentration of response-producing receptor as the substrate for a Michaelis-Menten type of reaction, given as... 

Km Michaelis-Menten constant mass transport coefficient... 

The remarkable inertness of dialkyl ethers to one-equivalent oxidants is good evidence that the readier oxidation of alcohols involves more than simple electron abstraction. Di-isopropyl ether is oxidised by Co(III) in CH3CN-H2O mixtures with complicated kinetics individual runs show first-order decay of Co(III) but the rate coefficients increase with increasing [Co(III)], and the order with respect to substrate is less than one but is neither fractional nor of a Michaelis-Menten type. The main product is acetone and the following reaction sequence is proposed... 

Ks Michaelis-Menten constant, or half velocity coefficient being numerically equal to the... 

Fig. 20.1. Correlation between the air/water partition coefficient, Kaw, determined from measurements of the surface pressure as a function of drug concentration (Gibbs adsorption isotherm) in buffer solution (50 mM Tris/HCI, containing 114 mM NaCI) at pH 8.0 and the inverse of the Michaelis Menten constant, Km obtained from phosphate release...

Similar to Eq. (67), the first reaction (incorporating the enzyme phosphofructo-kinase) exhibits a Hill-type inhibition by its substrate ATP [126]. The overall ATP utilization v3 (ATP) is modeled by a saturable Michaelis Menten function. The system is specified by five kinetic parameters (with Gx lumped into Vm ), the Hill coefficient n, and the total concentration, 4 / = [ATP] + [ADP]. Note that the model is not intended to capture biological realism, rather it serves as a paradigmatic example to identify dynamic behavior in metabolic pathways. 

An advantage of the normalized (or scaled) coefficients is their straightforward interpretability in biochemical terms. For example, consider the scaled elasticity of a simple Michaelis Menten equation ... 

The overall influence of ATP on the rate V (ATP) is measured by a saturation parameter C (—oo, 1]. Note that, when using Eq. (139) as an explicit rate equation, the saturation parameter implicitly specifies a minimal Hill coefficient min > C necessary to allow for the reverse transformation of the parameters. The interval 6 [0,1] corresponds to conventional Michaelis Menten kinetics. For = 0, ATP has no net influence on the reactions, either due to complete saturation of a Michaelis Menten term or, equivalently, due to an exact compensation of the activation by ATP as a substrate by its simultaneous effect as an inhibitor. For < 0, the inhibition by ATP supersedes the activation of the reaction by its substrate ATP. 

For the irreversible reactions, we assume Michaelis Menten kinetics, giving rise to 15 saturation parameters O1. C [0, 1] for substrates and products, respectively. In addition, the triosephospate translocator is modeled with four saturation parameters, corresponding to the model of Petterson and Ryde-Petterson [113]. Furthermore, allosteric regulation gives rise to 10 additional parameters 7 parameters 9" e [0, — n for inhibitory interactions and 3 parameters 0" [0, n] for the activation of starch synthesis by the metabolites PGA, F6P, and FBP. We assume n = 4 as an upper bound for the Hill coefficient. 

Physiological toxicokinetic models have been presented describing the behaviour of inhaled butadiene in the human body. Partition coefficients for tissue air and tissue blood, respectively, had been measured directly using human tissue samples or were calculated based on theoretical considerations. Parameters of butadiene metabolism were obtained from in-vitro studies in human liver and lung cell constituents and by extrapolation of parameters from experiments with rats and mice in vivo (see above). In these models, metabolism of butadiene is assumed to follow Michaelis-Menten kinetics. 

Male Fischer 344/N rats were exposed via the nose only for 6 h to concentrations of vinylidene fluoride ranging from 27 to 16 000 ppm [71-42 000 mg/m. Tidal volume (mean, 1.51 mL/brcath) and respiratory frequency (mean, 132 breaths/min) were not influenced by exposure concentration. Steady-state blood levels of vinylidene fluoride increased linearly with increasing exposure concentration up to 16 000 ppm. Vinylidene fluoride tissue/air partition coefficients were determined experimentally to be 0.07, 0.18, 0.8,10, and 0.29 for water, blood, liver, fat and muscle, respectively. Previously published detenninations (Filser Bolt, 1979) for the maximum velocity of metabolism in mg/li/kg) and Michaelis Menten constant (K in mg/L) are 0.07 and 0.13, respectively. Time to reach steady-state blood levels of vinylidene fluoride was less than 15 min for all concentrations. After cessation of exposure, blood levels of vinylidene fluoride decreased to 10% of steady-state levels within 1 h. Simulation of the metabolism of vinylidene fluoride mdicated that although blood levels of vinylidene fluoride increased linearly with increasing exposure concentration, the amount of vinylidene fluoride metabolized per 6-h exposure period approached a maximum at about 2000 ppm [5240 mg/m vinylidene fluoride (Medinsky et al., 1988). 

FIGURE 15-35 Elasticity coefficient, e, of an enzyme with typical Michaelis-Menten kinetics. At substrate concentrations far below the Km, each increase in [S] produces a correspondingly large increase in the reaction velocity, v. For this region of the curve, the enzyme has an elasticity, e, of about 1.0. At [S] Km, increasing [S] has little effect on v s here is close to 0.0. 

For an enzyme with typical Michaelis-Menten kinetics, the value of e ranges from about 1 at substrate concentrations far below Km to near 0 as Vmax is approached. Allosteric enzymes can have elasticities greater than 1.0, but not larger than their Hill coefficients (p. 167). 

Included in the following table are some data points from a hypothetical enzyme kinetics study. Using a spreadsheet program with graphing abilities (such as Excel), generate a Line-weaver-Burk plot of the data points in the table. Determine the best-fit line for the data along with Vnax, ATm, and r2 (the square of the correlation coefficient of the line). Does this enzyme follow Michaelis-Menten kinetics Why or why not ... 

Figure 22 Examples of enzyme kinetic plots used for determination of Km and Vmax for a normal and an allosteric enzyme Direct plot [(substrate) vs. initial rate of product formation] and various transformations of the direct plot (i.e., Eadie-Hofstee, Lineweaver-Burk, and/or Hill plots) are depicted for an enzyme exhibiting traditional Michaelis-Menten kinetics (coumarin 7-hydroxylation by CYP2A6) and one exhibiting allosteric substrate activation (testosterone 6(3-hydroxylation by CYP3A4/5). The latter exhibits an S-shaped direct plot and a hook -shaped Eadie-Hofstee plot such plots are frequently observed with CYP3A4 substrates. Km and Vmax are Michaelis-Menten kinetic constants for enzymes. K is a constant that incorporates the interaction with the two (or more) binding sites but that is not equal to the substrate concentration that results in half-maximal velocity, and the symbol n (the Hill coefficient) theoretically refers to the number of binding sites. See the sec. III.C.3 for additional details.

The influx (k+) and efflux (ka) coefficients, Michaelis-Menten constants (fCm), and resistance factors (RF) were determined for a series of anthracyclines (4-13) with different pvalues and octanol-water partition coefficients, D, at pH 7.4 [130, 135]. The results are summarized in Table 5.21. Increases in D favorably influenced k+ and unfavorably affected ka and 1/Km k+ became faster, and ka increased, as did 1/fQjj This implies that, in the case of the anthracyclines studied, lipophilicity affects uptake kinetics more than the kinetics of P-gp-mediated efflux. Their RF value therefore decreased with increasing lipophilicity. However, possible differences in the distribution pattern of these molecules as well as the influence of membrane binding on their uptake rates were not considered. 

D, partition coefficient between 1-octanol and buffer at pH 7 or 7.4. k+, mean influx coefficient, ka mean active efflux coefficient 7Cn, Michaelis Menten constant RF, resistance factor. 

Michaelis Menten constant (2) mass transport coefficient Langmuir-Blodgett... 

In this case, it can be demonstrated, if one molecule has a higher diffusion coefficient, that modelisation should be realized as a single molecular reaction with a Michaelis-Menten mechanism ethanol diffusion coefficient is higher than that of myristic acid in solution. 

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