Michaelis-Menten constant organization

Table 3. Representative affinity constants for the binding of metal to transport sites or whole cells/organisms. Ionic strengths and pH values are given for the conditional constants. In the column Comments , information on the method of determination (Km = Michaelis-Menten constant WC = whole-cell titrations) the type of constant (CC = conditional constant IC = intrinsic constant) and special conditions (Cl = competitive inhibitors NICA = nonideal competitive adsorption) are given...

The scaled elasticities of a reversible Michaelis Menten equation with respect to its substrate and product thus consist of two additive contributions The first addend depends only on the kinetic propertiesand is confined to an absolute value smaller than unity. The second addend depends on the displacement from equilibrium only and may take an arbitrary value larger than zero. Consequently, for reactions close to thermodynamic equilibrium F Keq, the scaled elasticities become almost independent of the kinetic propertiesof the enzyme [96], In this case, predictions about network behavior can be entirely based on thermodynamic properties, which are not organism specific and often available, in conjunction with measurements of metabolite concentrations (see Section IV) to determine the displacement from equilibrium. Detailed knowledge of Michaelis Menten constants is not necessary. Along these lines, a more stringent framework to utilize constraints on the scaled elasticities (and variants thereof) as a determinant of network behavior is discussed in Section VIII.E. 

To motivate the form of the experiments, note first that two parameters are properties of the organism the m and the a of the chemostat equations. One might postulate that the competitor with the largest m or the one with the smallest a should win the competition. Recall that m is the maximal growth rate and that a (the Michaelis-Menten constant) represents the half-saturation concentration (and so is an indicator of how well an organism thrives at low concentrations). Both of these quantities are obtainable in the laboratory by growing the organism (without a competitor) on the nutrient. (Hansen and Hubbell used a Lineweaver-Burk plot.)... 

The quantities a and have units of concentration, so if all concentrations (nutrients, organisms, and Michaelis-Menten constants) are measured in units of then S may be scaled out of system (2.1). Similarly, the units of m , and D are reciprocal time, so with an appropriate change of time scale D may also be scaled out of the system. Moreover, the conversion factors 7 and 7 can be incorporated into m, and f,. This is essentially the scaling that has been used in all of the previous models. With these changes of scale, the new system takes the form... 

Sato et al. (1991) expanded their earlier PBPK model to account for differences in body weight, body fat content, and sex and applied it to predicting the effect of these factors on trichloroethylene metabolism and excretion. Their model consisted of seven compartments (lung, vessel rich tissue, vessel poor tissue, muscle, fat tissue, gastrointestinal system, and hepatic system) and made various assumptions about the metabolic pathways considered. First-order Michaelis-Menten kinetics were assumed for simplicity, and the first metabolic product was assumed to be chloral hydrate, which was then converted to TCA and trichloroethanol. Further assumptions were that metabolism was limited to the hepatic compartment and that tissue and organ volumes were related to body weight. The metabolic parameters, (the scaling constant for the maximum rate of metabolism) and (the Michaelis constant), were those determined for trichloroethylene in a study by Koizumi (1989) and are presented in Table 2-3. 

Figure 2.4 A typical conceptual representation of a PBTK model for a volatile organic chemical A. Each box represents a tissue compartment and arrows depict arterial and venous blood circulation. RAM refers to the rate of the amount metabolized. Vmax and Km refer to the maximal rate of metabolism and the Michaelis-Menten affinity constant, respectively. C is concentration in blood (V ), fat (FA), richly perfused tissues (RA), poorly perfused tissues (PA), liver (LA), and arterial blood (aA). Ql is the blood flow.

The variables and the units are those which have been used since Chapter 1 S(t) is the nutrient concentration at time t, Xx(t) is the concentration of plasmid-bearing organisms at time t, and X2(0 is the concentration of plasmid-free organisms at time t S is the input concentration of the nutrient, and D is the washout rate of the chemostat. These are the operating parameters. The mj term is the maximal growth rate of x, and a, is the Michaelis-Menten (or half-saturation) constant of x,. These are assumed to be known (measurable) properties of the organism that characterize its growth and reproduction. A plasmid is lost in reproduction with probability q, and y is the yield constant. 

Cationic oxorhenium(V) oxazoline (Figure 3.23) was found to be especially reactive toward perchlorate in acetonitrile water media.73 The reaction is not pH dependent and proceeds smoothly at neutral pH. The perchlorate ion, C1C>4, was reduced all the way to the chloride ion, Cl. The reaction of oxorhenium(V) with perchlorate followed Michaelis-Menten showing saturation in [C10 ]. The apparent second-order rate constant for CIO4 is ca. 0.5L/(mols). The resulting cationic dioxorhenium(VII) species is more reactive toward OAT than MTO and can be turned over with organic sulfides quite readily (Figure 3.27). Therefore, under catalytic... 

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