Michaelis pH function

In such a case, a Michaelis pH function becomes useful in describing the pH profile for inactivation. Starting with the conservation of enzyme equation ... 

Michaelis pH function, pH EFFECTS ON ENZYMIC CATALYSIS MICRO-... 

For Eq. 3-4, A = H A, A2 = H , A, etc. and Yv F2, etc. are the Michaelis pH functions,2 3 which were proposed by L. Michaelis in 1914. For the case represented by Eq. 3-3 there are four ionic species and therefore four Michaelis pH functions which have the following form (Eq. 3-6). Here, Kv Klf etc. are the usual consecutive acid dissociation constants. 

If there are only three ionic forms the first three of these equations will apply if the final term is dropped from each. The student should be able to verify these equations and to write the appropriate pH functions for other cases. Since these relationships are met so often in biochemistry it is worthwhile to program a computer to evaluate the Michaelis pH functions and to apply them as needed. From Eq. 3-4 it can be seen that the reciprocal of the Michaelis pH function for a given ionic form represents the fraction of the total compound in that form and that the sum of these reciprocals for all the ionic forms is equal to one. Examples of the use of the Michaelis pH functions in this book are given in Eq. 6-50, which relates the Gibbs energy of hydrolysis of ATP to the pH, and in Eqs. 9-55 to 9-57, which de-... 

In this equation KHadp2-/ etc., are consecutive dissociation constants as given in Table 6-4. The expressions in parentheses are the Michaelis pH functions, which were considered in Chapter 3 (Eqs. 3-4 to 3-6). hi Eq. 6-50 they relate the total concentration of each component to hie concentration of the most highly dissociated form. Thus, for the pH range 2-10... 

The denominators (which are the Michaelis pH functions given by the first three terms of Eq. 3-6) represent the fraction of enzyme or of ES complex in the monoprotonated state. The pH dependence of enzymatic action is often more complex than that shown in Fig. 9-8 and given by the foregoing equations. However, it is easy to write Michaelis pH functions (see Chapter 3) for enzymes with any number of dissociable groups in both E and ES and to write appropriate equations of the type of... 

Eqs. 9-55 to 9-57. Bear in mind that if the free substrate contains groups dissociating in the pH range of interest, a Michaelis pH function for the free substrates will also appear in the numerator of Eq. 9-56. If the pH dependence of the enyzme is regulated by a conformational change in the protein, there may be a cooperative gain or loss of more than one proton and the Michaelis pH function must reflect this fact. This can sometimes be accomplished by addition of a term related to Eq. 7-45. For more information see Dixon and Webb,64 Cleland,65/66 or Kyte.67... 

Comparing with Eq. 6-64 and using the Michaelis pH functions (first two terms of Eq. 7-13) for HOx+ and HRed, it is easy to show that the value of E° (E1/2) at which equal amounts of oxidized protein (HOx+ + Ox) and reduced protein (HRed + Red-) are present is given by Eq. 16-19, in which Kox and KTed are the Ka values for dissociation of the protonated oxidized and reduced forms, respectively. 

The expressions containing the concentration of protons are abbreviated by 0, and are called the Michaelis pH functions (Michaelis, 1922). The Michaelis pH functions show directly the relative concentration of each acidic group in the mixture, since ... 

In order to introduce the terms for a dead-end inhibitor into the velocity equation, each enzyme distribution equation is multiplied by an appropriate Michaelis pH function. In order to do so, the corresponding distribution equations for the Ordered Bi Bi mechanism, found in Chapter 9 (Eq. (9.13)), were divided by Va, followed by a partial elimination ofiTeq- The entire procedure is shown in Table 2. 

The Michaelis constants and inhibition constants are now rather complex relationships ofMichaehs pH functions. However, the relationships expressed by Eqs. (14.42)-(14.45) are each a function of a single Michaelis pH function (Laidler, 1955 Schulz, 1994). Thus, in this particular mechanism, by a pmdent choice of parameters, one can calculate the pXa values of all forms of the enzyme in reaction (14.34). For example, Eq. (14.42) can be expanded to obtain... 

Figure 8. CSiange of the Michaelis functions with pH for an amino acid with pXa = 2 for a caibmgdic group, and p a == 9 for the ot-ainino group.

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...

The effect of non-participating ligands on the copper catalyzed autoxidation of cysteine was studied in the presence of glycylglycine-phosphate and catecholamines, (2-R-)H2C, (epinephrine, R = CH(OH)-CH2-NHCH3 norepinephrine, R = CH(OH)-CH2-NH2 dopamine, R = CH2-CH2-NH2 dopa, R = CH2-CH(COOH)-NH2) by Hanaki and co-workers (68,69). Typically, these reactions followed Michaelis-Menten kinetics and the autoxidation rate displayed a bell-shaped curve as a function of pH. The catecholamines had no kinetic effects under anaerobic conditions, but catalyzed the autoxidation of cysteine in the following order of efficiency epinephrine = norepinephrine > dopamine > dopa. The concentration and pH dependencies of the reaction rate were interpreted by assuming that the redox active species is the [L Cun(RS-)] ternary complex which is formed in a very fast reaction between CunL and cysteine. Thus, the autoxidation occurs at maximum rate when the conditions are optimal for the formation of this species. At relatively low pH, the ternary complex does not form in sufficient concentration. 

Menten soon received international recognition for her study of enzymes. From 1912 to 1913, she worked at Leonor Michaelis lab at the University of Berlin. While conducting experiments on the breakdown of sucrose by the enzyme called invertase, Menten and Michaelis were able to refine the work of Victor Henri to explain how enzymes function. A few years earlier, Henri had proposed that enzymes bind directly to their substrates. Michaelis and Menten obtained the precise measurements that were needed to support Henri s hypothesis. Using the recently developed concept of pH, they were able to buffer their chemical reactions and thereby control the conditions of their experiments more... 

Determination of the Michaelis constant for the cofactor NAD (A m.NAo) was carried out by measuring the initial rate of the reduction of NAD as a function of its concentration, at a constant concentration of glucose. All solutions were prepared in 0.1 M phosphate buffer pH 7.55. 

MW 27,500) with no cofactors or metal ions reqnirement for its function, it displays Michaelis-Menten kinetics and it is secreted in large amounts by a wide variety of Bacillus species. Subtilisin is also among the most important industrial enzymes due to its use in laundry detergents. Protein engineering strategies for subtilisin have focused on a number of aspects, namely catalysis, substrate specificity, thermal and oxidative stability and pH profile. We will describe briefly each of these aspects. 

In binding experiments, the affinity of magnesium ADP to native membranes and to the isolated calcium dependent ATPase was found to be considerably lower than that of magnesium ATP173. On the other hand, from the inhibition of the calcium-dependent ATPase or the activation of calcium release and ATP synthesis apparent affinities for ADP are obtained that are very similar to those of ATP (Fig. 12). The affinity of ADP for the enzyme apparently depends on its functional state. The affinity of ADP for the membranes under conditions of calcium release depends markedly on the pH of the medium. When the medium pH is reduced from 7.0 to 6.0, the affinity drops by a factor of 10. At pH 7.0 the affinity of the membrane for ADP corresponds to the affinity for ATP to the high affinity binding sites in the forward running mode of the pump. In contrast to the complex dependence of the forward reaction on the concentration of ATP, the dependence of the reverse reaction on ADP seems to follow simple Michaelis-Menten kinetics. 

The first intensive investigation of the kinetics of step 2 was carried out by Herries et al. (496) in a study of C > p hydrolysis. The data gave linear double reciprocal plots and maximum velocities and Michaelis constants were measured as a function of pH. Similar studies on U > p have been carried out by others (497, 498), but these did not agree well with each other or with the later work of del Rosario and Hammes (499). In one case no indication was given of substrate purity and 1/15 M sulfate was employed (497). In the other product contamination was clearly a problem (498). 

The turnover number (kCM) and the Michaelis constant (Km) as a function of pH for the hydrolysis of /V-acetyl-[ -tryptophanamide by chymotrypsin at 25°C. The decrease in fccat as the pH is lowered between 8 and 6 probably reflects the protonation of His 57. The increase in Km above pH 9 probably reflects the deprotonation of He 16, which results in the rotation of Gly 193 out of the substratebinding site. 

Here k is the rate constant for the irreversible reaction, Ceo is the total enzyme concentration, Cs is the substrate concentration, and is the Michaelis-Menton constant. Both k and KM may be functions of pH, temperature, and other properties of the fermentation medium. From this kinetic expression, we see that at high substrate concentrations the rate of product formation is independent of Cs and is approximately equal to kCm-This is due to the presence of a limited amount of enzyme, which is required for the reaction to proceed, and adding more substrate under these conditions will not cause the reaction rate to increase further. At low substrate concentrations, the rate of product formation becomes first-order with respect to Cs- Under these conditions the substrate concentration becomes the determinant for product formation, and increasing Cs produces a proportional increase in rate. The rate is also proportional to the total enzyme concentration under all conditions of substrate concentration. 

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