Inhibition linear

A simple mathematical model is used for quantitative description of the process and consists of a set of equations relating inputs, outputs, and key parameters of the system. The model for an alcoholic fermentation fed-batch process developed by Mayer (10) and adapted with the Ghose and Tyagi (11) linear inhibition term by the product was used as the starting point for the development of a model-based substrate sensor with product (ethanol) and biomass on-line measurements. 

Reversible inhibition that produces complete loss of catalytic activity is referred to as linear inhibition because the plots of K IV or 1/y versus [I] are straight lines. When some catalytic activity remains, even at saturating amounts of inhibitor, it is referred to as hyperbohc inhibition because these plots are nonlinear (this case will not be considered here). Both of these types of reversible inhibition are further classified according to the various apparent Michaelis-Menten parameters that are affected by the inhibitor. The two limiting cases are competitive inhibition and uncompetitive inhibition a third type is mixed inhibition, which includes as a special case noncompetitive inhibition. 

The double reciprocal plots are linear (linear inhibition) only when the inhibitor forms the completely inactive complex with one enzyme species (the inhibitor complex formation... 

Further division of reversible inhibitors is made according to their influence on the form of rate equations thus, we can make a difference between the linear and a nonlinear inhibition. In Chapter 5, we shall describe the linear inhibition and in Chapter 6 the main forms of the nonlinear inhibitioa Thus, we could distinguish tfie various types of inhibition stiU further by referring to competitive inhibition as linear, hyperbolic, or paraboUc inhibition. Fven more complex forms are possible (Cleland, 1970). 

AH types of inhibition that have been described in preceding sections are examples of linear inhibition, because for aH of them (i/Vj" and display a simple linear dependence on the inhibitor concentration. Linear inhibition is also a complete inhibition, because the velocity approaches zero if the inhibitor concentration is high enough. 

Eiquation (6.2) is quite general, and it describes a number of different inhibition mechanisms, including the simple linear inhibition mechanisms desaibed in Chapter 5. Thus, a = i and fi = o describe a simple linear noncompetitive inhibition (Section 5.3), and when a = > we have a simple linear competitive inhibition (Section 5.2). 

In the simple linear inhibition, i/F pp (intercept) and (JCa/V,) (slope) functions display a simple linear dependence on the inhibitor concentration (Section 5.7). However, if both a and p are different from unity, as in the general Eq. (6.2), the slopes or intercepts become complex functions of 7 ... 

In Fig. 2, the limiting value of slopes at infinite I is otK/ / Vi (4.0) and for intercepts this value is i// V, (2.0). In contrast to the simple linear inhibition, the replots of slopes and intercepts are hyperbolas therefore, this type of inhibition is usually called a hyperbolic or partial inhibition. Thus, we could distinguish the various types of inhibition stiU further by referring to noncompetitive inhibition as linear or hyperbolic. 

In the linear inhibition, the family of straight lines in the double reciprocal plot of i/uo versus fA (at different fixed concentrations of I) will always have a common intersection point. In the hnear inhibition, the replot of Slopei/A and InterceptyFA from the double reciprocal plot, versus /, is a straight line this type of inhibition was described in Chapter 5. 

Linear Inhibition (Chapters). In linear inhibition, it is particularly important to distinguish between competitive and noncompetitive types of inhibition, that is, to decide between Eqs. (18.55) and (18.56) ... 

CO2 hydration at high pH. Combined with the fact that anionic inhibition is rapidly established (see Section 3), and that under all conditions anionic inhibition is explicable in terms of simple linear inhibition mechanisms, it seems appropriate to propose a scheme... 

---