Substrate steady-state kinetic

The Henri-Michaelis-Menten Treatment Assumes That the Enzyme-Substrate Complex Is in Equilibrium with Free Enzyme and Substrate Steady-State Kinetic Analysis Assumes That the Concentration of the Enzyme-Substrate Complex Remains Nearly Constant Kinetics of Enzymatic Reactions Involving Two Substrates... 

Kinetic studies involving enzymes can principally be classified into steady and transient state kinetics. In tlie former, tlie enzyme concentration is much lower tlian that of tlie substrate in tlie latter much higher enzyme concentration is used to allow detection of reaction intennediates. In steady state kinetics, the high efficiency of enzymes as a catalyst implies that very low concentrations are adequate to enable reactions to proceed at measurable rates (i.e., reaction times of a few seconds or more). Typical enzyme concentrations are in the range of 10 M to 10 ], while substrate concentrations usually exceed lO M. Consequently, tlie concentrations of enzyme-substrate intermediates are low witli respect to tlie total substrate (reactant) concentrations, even when tlie enzyme is fully saturated. The reaction is considered to be in a steady state after a very short induction period, which greatly simplifies the rate laws. 

Despite these problems, the potential of research with conformationally restricted substrate analogs appears to be great. As yet, the use of these analogs with tools other than steady-state kinetics has been little explored. 

In conclusion, the steady-state kinetics of mannitol phosphorylation catalyzed by II can be explained within the model shown in Fig. 8 which was based upon different types of experiments. Does this mean that the mechanisms of the R. sphaeroides II " and the E. coli II are different Probably not. First of all, kinetically the two models are only different in that the 11 " model is an extreme case of the II model. The reorientation of the binding site upon phosphorylation of the enzyme is infinitely fast and complete in the former model, whereas competition between the rate of reorientation of the site and the rate of substrate binding to the site gives rise to the two pathways in the latter model. The experimental set-up may not have been adequate to detect the second pathway in case of II " . The important differences between the two models are at the level of the molecular mechanisms. In the II " model, the orientation of the binding site is directly linked to the state of phosphorylation of the enzyme, whereas in the II" model, the state of phosphorylation of the enzyme modulates the activation energy of the isomerization of the binding site between the two sides of the membrane. Steady-state kinetics by itself can never exclusively discriminate between these different models at the molecular level since a condition may be proposed where these different models show similar kinetics. The II model is based upon many different types of data discussed in this chapter and the steady-state kinetics is shown to be merely consistent with the model. Therefore, the II model is more likely to be representative for the mechanisms of E-IIs. 

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) ... 

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. 

The determination of bisubstrate reaction mechanism is based on a combination of steady state and, possibly, pre-steady state kinetic studies. This can include determination of apparent substrate cooperativity, as described in Chapter 2, study of product and dead-end inhibiton patterns (Chapter 2), and attempts to identify... 

A steady-state kinetics study for Hod was pursued to establish the substrate binding pattern and product release, using lH-3-hydroxy-4-oxoquinoline as aromatic substrate. The reaction proceeds via a ternary complex, by an ordered-bi-bi-mechanism, in which the first to bind is the aromatic substrate then the 02 molecule, and the first to leave the enzyme-product complex is CO [359], Another related finding concerns that substrate anaerobically bound to the enzyme Qdo can easily be washed off by ultra-filtration [360] and so, the formation of a covalent acyl-enzyme intermediate seems unlikely in the... 

The reduction of 7,8-dihydrofolate (H2F) to 5,6,7,8-tetrahydrofolate (H4F) has been analyzed extensively14 26-30 and a kinetic scheme for E. Coli DHFR was proposed in which the steady-state kinetic parameters as well as the full time course kinetics under a variety of substrate concentrations and pHs were determined. From these studies, the pKa of Asp27 is 6.5 in the ternary complex between the enzyme, the cofactor NADPH and the substrate dihydrofolate. The second observation is that, contrary to earlier results,27 the rate determining step involves dissociation of the product from the enzyme, rather than hydride ion transfer from the cofactor to the substrate. 

Protein concentrations are often reported in terms of mass per unit volume (eg., mg/ml) or in units of activity per volume. Care should be exercised when using these forms of concentrations. To have valid steady-state kinetics, the total enzyme concentration must be much less than the substrate concentration. Hence, one should always be cognizant of the true concentration of active enzyme in terms of molarity. 

In steady-state kinetic studies, the total concentration of the enzyme should be much less than the concentration of the substrate(s), product(s), and effector(s) typically, by at least a thousandfold. When this condition is not true, the steady-state condition will not be valid and other methods, such as global analysis, have to be utilized to analyze the kinetic data. 

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. 

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. 

Reversible Inhibition One common type of reversible inhibition is called competitive (Fig. 6-15a). A competitive inhibitor competes with the substrate for the active site of an enzyme. While the inhibitor (I) occupies the active site it prevents binding of the substrate to the enzyme. Many competitive inhibitors are compounds that resemble the substrate and combine with the enzyme to form an El complex, but without leading to catalysis. Even fleeting combinations of this type will reduce the efficiency of the enzyme. By taking into account the molecular geometry of inhibitors that resemble the substrate, we can reach conclusions about which parts of the normal substrate bind to the enzyme. Competitive inhibition can be analyzed quantitatively by steady-state kinetics. In the presence of a competitive inhibitor, the Michaelis-Menten equation (Eqn 6-9) becomes... 

Steady state kinetics may be used to distinguish between the various mechanisms mentioned above. Under the appropriate conditions, their application can determine the order of addition of substrates and the order of release of products from the enzyme during the reaction. For this reason, the term mechanism when used in steady state kinetics often refers just to the sequence of substrate addition and product release. 

Steady state kinetic measurements on an enzyme usually give only two pieces of kinetic data, the KM value, which may or may not be the dissociation constant of the enzyme-substrate complex, and the kcM value, which may be a microscopic rate constant but may also be a combination of the rate constants for several steps. The kineticist does have a few tricks that may be used on occasion to detect intermediates and even measure individual rate constants, but these are not general and depend on mechanistic interpretations. (Some examples of these methods will be discussed in Chapter 7.) In order to measure the rate constants of the individual steps on the reaction pathway and detect transient intermediates, it is necessary to measure the rate of approach to the steady state. It is during the time period in which the steady state is set up that the individual rate constants may be observed. 

As we discussed in Chapter 3, the KM for an enzymatic reaction is not always equal to the dissociation constant of the enzyme-substrate complex, but may be lower or higher depending on whether or not intermediates accumulate or Briggs-Haldane kinetics hold. Enzyme-substrate dissociation constants cannot be derived from steady state kinetics unless mechanistic assumptions are made or there is corroborative evidence. Pre-steady state kinetics are more powerful, since the chemical steps may often be separated from those for binding. 

The currently accepted mechanism for the hydrolysis of amides and esters catalyzed by the archetypal serine protease chymotrypsin involves the initial formation of a Michaelis complex followed by the acylation of Ser-195 to give an acylenzyme (Chapter 1) (equation 7.1). Much of the kinetic work with the enzyme has been directed toward detecting the acylenzyme. This work can be used to illustrate the available methods that are based on pre-steady state and steady state kinetics. The acylenzyme accumulates in the hydrolysis of activated or specific ester substrates (k2 > k3), so that the detection is relatively straightforward. Accumulation does not occur with the physiologically relevant peptides (k2 < k3), and detection is difficult. 

We have dealt so far with enzymes that react with a single substrate only. The majority of enzymes, however, involve two substrates. The dehydrogenases, for example, bind both NAD+ and the substrate that is to be oxidized. Many of the principles developed for the single-substrate systems may be extended to multisubstrate systems. However, the general solution of the equations for such systems is complicated and well beyond the scope of this book. Many books devoted almost solely to the detailed analysis of the steady state kinetics of multisubstrate systems have been published, and the reader is referred to these for advanced study.11-14 The excellent short accounts by W. W. Cleland15 and K. Dalziel16 are highly recommended. 

The calculation of rate constants from steady state kinetics and the determination of binding stoichiometries requires a knowledge of the concentration of active sites in the enzyme. It is not sufficient to calculate this specific concentration value from the relative molecular mass of the protein and its concentration, since isolated enzymes are not always 100% pure. This problem has been overcome by the introduction of the technique of active-site titration, a combination of steady state and pre-steady state kinetics whereby the concentration of active enzyme is related to an initial burst of product formation. This type of situation occurs when an enzyme-bound intermediate accumulates during the reaction. The first mole of substrate rapidly reacts with the enzyme to form stoichiometric amounts of the enzyme-bound intermediate and product, but then the subsequent reaction is slow since it depends on the slow breakdown of the intermediate to release free enzyme. 

The strategy is to measure the rate constants k2 and k3 of the acylenzyme mechanism (equation 7.1) and to show that each of these is either greater than or equal to the value of kCM for the overall reaction in the steady state (i.e., apply rules 2 and 3 of section Al). This requires (1) choosing a substrate (e.g., an ester of phenylalanine, tyrosine, or tryptophan) that leads to accumulation of the acylenzyme, (2) choosing reaction conditions under which the acylation and deacylation steps may be studied separately, and (3) finding an assay that is convenient for use in pre-steady state kinetics. The experiments chosen here illustrate stopped-flow spectrophotometry and chromopboric procedures. 

Examples of such kinetic treatments were provided by work on chiral 1,1,2,2-tetramethylcyclopropane-d630 and rran -l-ethyl-2-methylcyclopropane146 148. At 350.2 °C, the first substrate approached cis, trans equilibrium with rate constant, and suffered loss of optical activity with a rate constant k The /c, /c, ratio was 1.7 130. The second substituted cyclopropane, at 377.2 °C, exhibited kinetic behavior dictated by kf.ka = 2.0 1. Using steady-state kinetic treatments and the most-substituted-bond hypothesis, these rate constant ratios were calculationally transformed into (cyclization) (rotation) ratios of 11 1 and 0.29 1, ratios different by a factor of 38. 

Since the reaction catalyzed by glutamine synthetase has three substrates (L-glutamate, NH3, and metal-ATP) and three products (L-glutamine, P , and metal-ADP), the kinetic mechanism as deduced by steady-state kinetics... 

The steady-state kinetics of a simple single-substrate, single-binding site, single-intermediate-enzyme catalysed reaction in the presence of competitive inhibitor are shown in Scheme A5.5.1. 

Steady-State Kinetic Analysis Assumes That the Concentration of the Enzyme-Substrate Complex Remains Nearly Constant... 

---