Saturation constants

Half-saturation constant (concentration for 50% saturation of the transport protein). 

The parameters of this model are the maximal rate of the process and the saturation constant The latter can also be defined as the amount of substrate which produces a rate V which is half the maximal rate as can be verified by substituting by X in the above relation. 

Reflux ratio [dm3] Reactor volume [dm3] Ext. volume of product [dm3] Ext. volume of solvent [1/h] Reaction constant [kg/dm3] Inhibition constant [-] Saturation constant [m2/m3min] Transfer coeff. TFIN=50, NOCI=10... 

Let us consider the determination of two parameters, the maximum reaction rate (rITOIX) and the saturation constant (Km) in an enzyme-catalyzed reaction following Michaelis-Menten kinetics. The Michaelis-Menten kinetic rate equation relates the reaction rate (r) to the substrate concentrations (S) by... 

The limiting substrate (glucose) concentration is denoted by S. There are four parameters pmax is the maximum specific growth rate, Ks is the saturation constant for S, kd is the specific death rate and Y is the average yield coefficient (assumed constant). 

They used a value of 4.1 x 10-11 molal s-1 for rmax, the maximum reaction rate, and 1.4 x 10-5 molal for KA, the half saturation constant. We consider application of this kinetic law in detail in Chapter 28. 

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... 

If the concentrations of only the electron donor and acceptor are considered to vary, each mD+ is invariant and the term ] [ n/ 1 in Equation 18.23 reverts to a half-saturation constant K[y Similarly, the corresponding term in Equation 18.24 may be represented by K A. Now, we see the dual Monod equation (Eqn. 18.16) is a specific simplification of the general rate law (Eqn. 18.22). 

Since the enzyme concentration was not observed separately from the rate constant, we carry the product k+ m. in this equation as rmax, the maximum reaction rate. Bekins el al. (1998) fitted their results using values of 1.4 mg kg-1 day-1 (or 1.7 x 10-10 molal s-1) for rmax, and 1.7 mg kg-1 (1.8 x 10-5 molal) for Ka, the half-saturation constant. In a field application lasting many years, of course, the assumption that enzyme concentration remains constant might not be valid,... 

In the calculation results, shown in Figure 28.4, phenol concentration decreases with time at a constant rate for about the first 30 days of reaction. Over this interval, the concentration is greater than the value of K, the half-saturation constant, so the ratio m/(m + K ) in Equation 28.9 remains approximately constant, giving a zero-order reaction rate. Past this point, however, concentration falls below K and the reaction rate becomes first order. Now, phenol concentration does not decrease linearly, but asymptotically approaches zero. 

Following the calculations in Section 18.5, we take a rate constant k+ for sulfate reduction of 10-9 mol mg-1 s-1, a half-saturation constant for acetate of 70 p, molal, and a growth yield of 4300 mg mol-1 from a study of the kinetics of Desulfobacter postgatei by Ingvorsen el al. (1984). We set a value for KA, the half-saturation constant for sulfate, of 200 p molal, as suggested by Ingvorsen el al. (1984) and Pallud and Van Cappellen (2006). 

The relationship between i. and S as depicted in Figure 2.7 is relevant because it quantifies the importance of a substrate in terms of its concentration on the growth rate. As seen from Equation (2.16), X= 1/2 imax for S=Ks. For this reason, Ks is also named the half saturation constant. Equation (2.16) and the corresponding curves shown in Figure 2.7 are called the Monod expression and Monod curve, respectively. 

The biological processes in biofilms are either described by 1-order or 0-order kinetics. However, the 0-order reaction is of specific importance for sewer biofilms as is also the case for treatment processes of wastewater in biofilters. The saturation constant, Ks, is normally insignificant compared with the substrate concentration, and the biofilm kinetics [cf. Equation (2.20)], is therefore 0-order. As shown in Figure 2.8, two different conditions exist the biofilm is either fully penetrated or partly penetrated, corresponding to either a fully effective or a partly effective biofilm. The distinction between these two situations can be expressed by means of a dimensionless constant, P, called the penetration ratio (Harremoes, 1978). For each of these two situations, the flux of substrate across the biofilm surface can neglect the stagnant liquid film being calculated [Equations (2.23) and (2.25)] ... 

XBw = heterotrophic active biomass in the water phase (gCOD m-3) Kx = saturation constant for hydrolysis (-)... 

KXn = saturation constant for hydrolysis, fraction n (gCOD gCOD-1) e = efficiency constant for the biofilm biomass (-)... 

Equation (5.15) may be extended to describe transformations under substrate-limited conditions by including a Monod expression (cf. Section 2.2.1). The information from Section 5.6.1 indicates that the saturation constant for nitrate, KS0, is about 2-3 gN03 nr. ... 

Ksw Saturation constant for readily biodegradable substrate 1.0 gCOD nr3... 

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