Rates of substrate binding

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. 

INFLUENCE OF OTHER STEPS ON THE MAGNITUDE OF OBSERVED ISOTOPE EFFECTS. As noted earlier, nonenzymatic reaction mechanisms do not involve those complexities imposed by substrate binding order, rates of substrate binding/release, as well as conformational changes that attend enzyme catalysis. As a result, the opportunity for detecting isotope effects is... 

The rate of substrate binding. At very low substrate concentrations the Michaelis-Menten equation (Eq. 9-15) simplifies as follows ... 

The velocity of this reaction v = d[P]/dt) is a function of the bimolecular rate of substrate binding (ki) and the unimolecular rates of chemistry (k2,fe-2) and substrate and product release (k i,k3). The steady-state velocity expression under initial rate conditions (Eq. (10.2)) demonstrates how each microscopic rate constant contributes to the macroscopic reaction rate and the dependence of the velocity upon substrate concentration. 

One useful limit is the velocity at saturating substrate ([S] oo), which, when normalized for the enzyme concentration, gives the macroscopic rate constant kcat- It can be seen (Eq. (10.3)) that kcat is independent of the rate of substrate binding, a situation that exists for more complex mechanisms as well. Consequently, kcat is a unimolecular rate constant obtained in the limit of infinite substrate concentration that reflects the rate of all steps after the formation of the ES complex. 

Although steady-state kinetic methods cannot establish the complete enzyme reaction mechanism, they do provide the basis for designing the more direct experiments to establish the reaction sequence. The magnitude of kcm will establish the time over which a single enzyme turnover must be examined for example, a reaction occurring at 60 sec will complete a single turnover in approximately 70 msec (six half-lives). The term kcJKm allows calculation of the concentration of substrate (or enzyme if in excess over substrate) that is required to saturate the rate of substrate binding relative to the rate of the chemical reaction or product release. In addition, the steady-state kinetic parameters define the properties of the enzyme under multiple turnovers, and one must make sure that the kinetic properties measured in the first turnover mimic the steady-state kinetic parameters. Thus, steady-state and transient-state kinetic methods complement one another and both need to be applied to solve an enzyme reaction pathway. 

Measure the rates of substrate binding and dissociation by stopped-flow methods or by substrate trapping methods. This is an optional step in that although information on binding rates can be useful, it is not essential for the design of subsequent experiments. 

Because the amplitude of the burst is less than or equal to the concentration of enzyme sites, these experiments must be performed using enzyme concentrations that will produce measurable amounts of product in the first turnover. In order to saturate the rate of substrate binding so that chemistry, not binding, limits the rate of the burst, high concentrations of substrate must be used. The major experimental limitation of the method is due to the problems associated with measurement of less than one product per enzyme site with a background of excess substrate. Depending on the chromatographic resolution of the product from substrate, the ability to observe and measure a burst of product formation may be limited by accessible concentrations of enzyme. 

Even with computer simulation, it is still a concern that the rate of substrate binding must be faster than catalysis if the intent of the experiment is to measure... 

In a single-turnover experiment with enzyme in excess, the kinetics of the reaction are different than with substrate in excess. The rate of substrate binding... 

The Km of an enzyme for a substrate is related to the dissociation constant, K, which is the rate of substrate release divided by the rate of substrate binding. For example, a genetic mutation that decreases the rate of substrate binding to the enzyme decreases the affinity of the enzyme for the substrate and increases the and Km of the enzyme for that substrate. The higher the Km, the higher is the substrate concentration required to reach Vi Vmax-... 

The right hand side of this equation can be rearranged to expose the relation of one or other rate constant to the rest. It is, however, readily ascertained that k jK gives a minimum value for kf2- This has been widely used as an estimate for the rate of substrate binding from steady state kinetic investigations. During the detailed discussion of the rate of collision complex formation (section 7.4), criteria will be discussed which help to decide how close k K is, in different systems, to the true second order rate constant characteristic of the first step of enzyme-substrate complex formation. 

Direct and indirect methods for the determination of rates of substrate binding are discussed extensively in chapters S and 6 and there are special methods for the study of transmitter mediated channel gating (Hille, 1992). As emphasized above, the indirect evaluation of substrate binding to enzymes, in single substrate reactions, relies on the determination of cat/ M- shown in section 5.1, this function, which has the units of a second order reaction, has a minimum value of k 2, the rate constant for the first step of substrate binding. Even so, as seen in table 7.2 it is often near 10 M s. Similar complications for the extraction of k, the rate constant for the first step, arise in the usual two step binding reactions of ligands. 

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