Michaelis-Menten half-saturation constant

This relation is the broadly known Michaelis-Menten equation. The effect of substrate concentration ni on the rate predicted by this equation follows a characteristic pattern. Where substrate concentration is considerably smaller than the half saturation constant (ni <reactive intermediate EA depends on the availability of the substrate A. In this case, (mA + K A ) and reaction rate r+ given by 17.18 is proportional to mA. For the opposite case, (mA K ), little free enzyme E is available to complex with A. Now, (mA + mA and reaction... 

Satisfaction of kinetic order. Carriers follow Michaelis-Menten-type saturation kinetics or first-order kinetics. Ion channels follow the type of respective structure—unimolecular transmembrane channels and bimolecular half-channels follow first- and second-order kinetics, respectively. The kinetic order of supramolecular channels depends on the assembly number. However, this principle can be applied only when the association constants are small. If the association becomes strong, the kinetic order decreases down to zero. Then the validity becomes dubious in view of the absolute criterion of the mechanism. Decreased activation energy compared to the carrier transport mechanism and competitive inhibition by added other cations stand as criteria. 

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. 

FIGURE 2-26 Microbial uptake rate of a chemical, according to Michaelis-Menten kinetics [see Eq. [2-71a]]. The rate cannot exceed Vmax no matter how high the chemical concentration becomes. Ks, the half-saturation constant, is the chemical concentration at which uptake equals half of Vmax. At low concentrations, uptake is nearly proportional to concentration and may be approximated as a first-order process. 

Methane oxidation kinetics was assessed as follows. In these experiments, cells were inoculated into medium containing different initial amounts of copper sulfate and grown to an optical density at 600 nm of 0.5-0.7. Aliquots were then placed in closed vials at different initial dissolved methane concentrations. These aliquots were incubated under optimal conditions, and head-space samples were taken at four different time points (1-4 h) for determination of methane concentrations by gas chromatography. From these data, initial methane consumption rates determined for different methane concentrations were used to obtain the Michaelis-Menten parameters Ks (half-saturation constant) and Vmax (rate at substrate saturation). Under these conditions sMMO was not expressed, as described previously (9). 

The distinction between the two kinds of direct coupling between transport and chemical reaction does not apply to secondary active transport, as the coupled processes are both vectorial. This transport is assumed to involve a ternary complex, i.e. between the translocator (carrier), the transportable solute and the co-ion. The latter is assumed to influence the translocation of the solute in two ways [25] (1) it may favor the formation of the ternary complex, in that its binding to the translocator increases the affinity of the latter to the transportable solute and vice versa (affinity effect) or, (2) it may increase the velocity at which the solute is translocated through the barrier, e.g. in that the ternary complex moves faster across the barrier than do the two binary complexes (velocity effect). In natural systems both effects appear to occur, separately as well as mixed. A crude distinction is often attempted on the basis of the two Michaelis-Menten parameters the maximum velocity V ) and the half saturation constant (A ) in the assumption that the former is altered in the velocity effect (V-type) and the latter, in the affinity effect (K-type). The relationship is often more complicated especially if electric potentials are involved [26]. 

The data in Table 22.5 present the Michaelis-Menten kinetic data from Suarez and Rifai (1999). Half-saturation constants varied from 0.6 mg/L to 29.5 mg/L for TCE and from 0.17 mg/L to 28 mg/L for DCE. Maximum specific degradation rates were within the ranges 0.038-478,59 for TCE, and 0-11,115 mg,o jpou d/mgp t,i -... 

Saturation kinetics are also called zero-order kinetics or Michaelis-Menten kinetics. The Michaelis-Menten equation is mainly used to characterize the interactions of enzymes and substrates, but it is also widely applied to characterize the elimination of chemical compounds from the body. The substrate concentration that produces half-maximal velocity of an enzymatic reaction, termed value or Michaelis constant, can be determined experimentally by graphing r/, as a function of substrate concentration, [S]. 

The question arises as to whether comparisons with protein enzymes are justified. In other words, what can ribozymes really do An important parameter for measuring the efficiency of enzymes is the value of kc-JK. This quotient is derived from the values of two important kinetic parameters kc-Al is a rate constant, also called turnover number, and measures the number of substrate molecules which are converted by one enzyme molecule per unit time (at substrate saturation of the enzyme). Km is the Michaelis-Menten constant it corresponds to the substrate concentration at which the rate of reaction is half its maximum. 

If we set up the same enzyme assay with a fixed amount of enzyme but vary the substrate concentration we will observe that initial velocity (va) will steadily increase as we increase substrate concentration ([S]) but at very high [S] the va will asymptote towards a maximal value referred to as the Vmax (or maximal velocity). A plot of va versus [S] will yield a hyperbola, that is, v0 will increase until it approaches a maximal value. The initial velocity va is directly proportional to the amount of enzyme—substrate complex (E—S) and accordingly when all the available enzyme (total enzyme or E j) has substrate bound (i.e. E—S = E i -S and the enzyme is completely saturated ) we will observe a maximal initial velocity (Pmax)- The substrate concentration for half-maximal velocity (i.e. the [S] when v0 = Vmax/2) is termed the Km (or the Michaelis—Menten constant). However because va merely asymptotes towards fT ax as we increase [S] it is difficult to accurately determine Vmax or Am by this graphical method. However such accurate determinations can be made based on the Michaelis-Menten equation that describes the relationship between v() and [S],... 

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.)... 

Fig. 9.1. Relation of reaction speed (v) to substrate concentration ([S]) in the absence (A, B, C) and presence of enzyme (D, E). The Michaelis constant, K , is the substrate concentration at which half the maximum reaction speed is obtained. To saturate the enzyme completely with substrate, close to lOOxAmis required (D). When the dependence of the rate of enzyme-catalyzed reaction on the substrate concentration can be described by a rectangular hyperbola (E), the reaction is said to obey classical or Michaelis-Menten kinetics.

The substrate concentration at which an enzyme reaches one-half of its maximal catalytic activity is often used as a measure of the sensitivity of an enzyme to substrate saturation. This particular substrate concentration usually has about the same numerical value as Km, sometimes known as the Michaelis-Menten constant for the enzyme. The maximum rate of reaction per mole of enzyme is often given the symbol cat. and the maximum rate of reaction for a given enzyme concentration is often symbolized as Vmax- Often, the kinetics of more complex enzyme-catalyzed reactions can be placed in this form under some restricted range of conditions [1]. 

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