Steady state kinetic constants

Factors Affecting the Steady State Kinetic Constants... 

Figure 2.8 Relationship between steady state kinetic constants and specific portions of the enzyme reaction pathway.

For our purposes the most important factor that can impact the individual steady state kinetic constants is the presence of an inhibitor. We will see in Chapter 3 how specific modes of inhibitor interactions with target enzymes can be diagnosed by the effects that the inhibitors have on the three steady state kinetic constants. 

An inhibitor that binds exclusively to the free enzyme (i.e., for which a = °°) is said to be competitive because the binding of the inhibitor and the substrate to the enzyme are mutually exclusive hence these inhibitors compete with the substrate for the pool of free enzyme molecules. Referring back to the relationships between the steady state kinetic constants and the steps in catalysis (Figure 2.8), one would expect inhibitors that conform to this mechanism to affect the apparent value of KM (which relates to formation of the enzyme-substrate complex) and VmJKM, but not the value of Vmax (which relates to the chemical steps subsequent to ES complex formation). The presence of a competitive inhibitor thus influences the steady state velocity equation as described by Equation (3.1) ... 

Table 3.3 Effects of inhibitors of different modalities on the apparent values of steady state kinetic constants and on specific steps in catalysis... 

Table 3. Steady-state kinetic constants of wild type and mutants a-fucosidases...

The goal of a complete kinetic analysis is to define the rate and free energy change of each step in the reaction. Because the rates of each reaction in an enzymic pathway are comparable, the measurable events are kinetically linked and sometimes difficult to separate. Therefore, solution of an enzyme mechanism must include a fitting of all experiments to the complete model, including all steps in the pathway. Ideally one should measure each reaction in a sequence and then provide one additional measurement as a check for internal consistency. The two important checks on an enzyme reaction sequence are (1) measurement of the overall free energy change for the reaction in solution and (2) comparison of the predicted and measured steady-state kinetic constants. 

Table 2 Steady-state kinetic constants of AOP synthase ...

The initial kinetic characterization of a mutant enzyme consists of comparison to wild type with respect to the two fundamental steady-state kinetic constants Itcai, the maximum rate at saturating substrate, and kcJKm, the apparent second-order rate constant for substrate binding, often referred to as the specificity constant. The Michaelis constant, K, as the ratio of the maximum rate divided by the apparent substrate binding rate, should be considered as a derivative of the two fundamental enzymic constants. 

Actually we should not be surprised at the fact that steady-state rate studies are not decisive for determination of the number (or nature) of the intermediates in the mechanism. By the very nature of the steady-state assumption, the intermediates are virtually impossible to detect experimentally. What then is the value of carrying out steady-state rate experiments For one thing, information about the structural specificity of the enzyme can often be obtained by varying the substrate for another, in more complicated mechanisms, possible reaction pathways can be inferred from the form of the rate law. Also of considerable interest to the kineticist is the fact that knowledge of the steady-state kinetic constants allows the determination of a lower bound for all the rate constants in the mechanism. For example, in the case of a reaction mechanism of the type we are considering with n reaction intermediates (where n is an arbitrary number), the following inequalities can be shown to prevail [2] ... 

Michaelis-Menten equations for the monosubstrate reactions (Eqs. (3.9) and (3.27)) in the forward direction (A -> P), have four fundamental kinetic constants or steady-state kinetic constants ... 

TABLE 2.1 Apparent Steady-State Kinetic Constants of T4 RNA Ligase... 

Two steady-state kinetic constants are most useful in evaluating biocatalytic reactions. "k J is often known as the turnover number and higher values indicate more catalytically efficient enzymes. This first-order rate constant describes the speed at which an enzyme converts bound substrates to products and re-forms the free enzyme to prepare for the next round of catalysis. It includes both the "chemical" steps (bond making and bond breaking) as well as the product release step(s). Note that it is not uncommon for product release to be the slowest step. As a practical matter, one normally seeks enzymes with > 1 s under the process conditions to ensure reasonable space-time yields along with acceptable catalyst loading levels. 

Photoinitiation is an excellent method for studying the pre- and posteffects of free radical polymerization, and from the ratio of the specific rate constant (kx) in non-steady-state conditions, together with steady-state kinetics, the absolute values of propagation (kp) and termination (k,) rate constants for radical polymerization can be obtained. 

The reader can show that, with the steady-state approximation for [Tl2+], this scheme agrees with Eq. (6-14), with the constants k = k i and k = k j/k g. Of course, as is usual with steady-state kinetics, only the ratio of the rate constants for the intermediate can be determined. Subsequent to this work, however, Tl2+ has been generated by pulse radiolysis (Chapter 11), and direct determinations of k- and k g have been made.5... 

The Kmax (and K, see below) constants determined from steady-state kinetic measurements are thus seen to be complex constants containing two or more of the individual rate constants illustrated in Fig. 2. 

In this chapter we described the thermodynamics of enzyme-inhibitor interactions and defined three potential modes of reversible binding of inhibitors to enzyme molecules. Competitive inhibitors bind to the free enzyme form in direct competition with substrate molecules. Noncompetitive inhibitors bind to both the free enzyme and to the ES complex or subsequent enzyme forms that are populated during catalysis. Uncompetitive inhibitors bind exclusively to the ES complex or to subsequent enzyme forms. We saw that one can distinguish among these inhibition modes by their effects on the apparent values of the steady state kinetic parameters Umax, Km, and VmdX/KM. We further saw that for bisubstrate reactions, the inhibition modality depends on the reaction mechanism used by the enzyme. Finally, we described how one may use the dissociation constant for inhibition (Kh o.K or both) to best evaluate the relative affinity of different inhibitors for ones target enzyme, and thus drive compound optimization through medicinal chemistry efforts. 

A number of different approaches have been employed in different laboratories to characterize cyt c ccp binding. The earliest estimates of binding constants come from steady state kinetic studies by Yonetani and coworkers [19] (subsequently refined by Erman) [29]. At 50 mM phosphate, pH6, (conditions which favor maximum turnover), an apparent Km value of 3 pM is obtained using yeast isol cyt c as the reaetion partner of ccp. Km is intrinsically a kinetic parameter, which in the complex ccp mechanism may incorporate a number of elementary rate constants unrelated to binding. 

Kinetics of O-Methylaiion. The steady state kinetic analysis of these enzymes (41,42) was consistent with a sequential ordered reaction mechanism, in which 5-adenosyl-L-methionine and 5-adenosyl-L-homocysteine were leading reaction partners and included an abortive EQB complex. Furthermore, all the methyltransferases studied exhibited competitive patterns between 5-adenosyl-L-methionine and its product, whereas the other patterns were either noncompetitive or uncompetitive. Whereas the 6-methylating enzyme was severely inhibited by its respective flavonoid substrate at concentrations close to Km, the other enzymes were less affected. The low inhibition constants of 5-adenosyl-L-homocysteine (Table I) suggests that earlier enzymes of the pathway may regulate the rate of synthesis of the final products. 

DETERMINATION OF ABSOLUTE RATE CONSTANTS 3-8a Non-Steady-State Kinetics... 

When the enzyme is first mixed with a large excess of substrate, there is an initial period, the pre-steady state, during which the concentration of ES builds up. This period is usually too short to be easily observed, lasting just microseconds. The reaction quickly achieves a steady state in which [ES] (and the concentrations of any other intermediates) remains approximately constant over time. The concept of a steady state was introduced by G. E. Briggs and Haldane in 1925. The measured V0 generally reflects the steady state, even though V0 is limited to the early part of the reaction, and analysis of these initial rates is referred to as steady-state kinetics. 

One less kinetic parameter can be obtained from an analysis of the data for a ping-pong mechanism than can be obtained for ordered reactions. Nevertheless, in Eq. 9-47, twelve rate constants are indicated. At least this many steps must be considered to describe the behavior of the enzyme. Not all of these constants can be determined from a study of steady-state kinetics, but they may be obtained in other ways. 

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