Transient enzyme kinetics

The quasi-steady approximation, which was introduced in Section 3.1.3.2 and justified on the basis of rapid cycle kinetics in Section 4.1.1, forms the basis of the study of enzyme mechanisms, a field with deep historical roots in the subject of biochemistry. In later chapters of this book, our studies make use of this approximation in building models of biochemical systems. Yet there remains something unsatisfying about the approximation. We have seen in Section 3.1.3.2 that the approximation is not perfect. Particularly during short-time transients, the quasisteady approximation deviates significantly from the full kinetics of the Michaelis-Menten system described by Equations (3.25)-(3.27). Here we mathematically analyze the short timescale kinetics of the Michaelis-Menten system and reveal that a different quasi-steady approximation can be used to simplify the short-time kinetics. 

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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. 

Biochemistry 8. Fierke, C. A., and Hammes, G. G. (1996) Transient Kinetic Approaches to Fnzyme Mechanisms, in Contemporary Enzyme Kinetics and Mechanisms (Purich, D., Ed.) 2nd ed., pp. 1-35, Academic Press, New York. 

This scheme accounts for the steady-state and transient-state kinetics of the enzyme under normal conditions.1343,1371,1442... 

In disagreement with the above indications was the finding of Aldridge et al. (146) that for enzyme which was phosphorylated at pH 5.5 with inorganic phosphate and rapidly mixed with buffer at pH 8.4, the rate of dephosphorylation was twice as fast as the turnover of the enzyme at pH 8.0. Also, transient state kinetic studies by Femley and Walker (99, 110) showed a rapid release (burst) of phenol followed by a steady state release of phenol, only at pH < 7. Thus, these data would seem to indicate that at pH >7 the rate determining step is phosphorylation. 

The initial rate enzyme kinetics uses very low enzyme concentrations (e.g., 0.1 juM to 0.1 pM) to investigate the steady-state region of enzyme-catalyzed reactions. To investigate an enzymatic reaction before the steady state (i.e., transient state), special techniques known as transient kinetics (Eigen and Hammes, 1963) are employed. The student should consult chapters of kinetic texts (Hammes, 1982 Robert, 1977) on the topics. KinTekSim (http //www.kintek-corp.com/kintek-sim.htm) is the Windows version of KINSIM/FITSIM (Frieden, 1993) which analyzes and simulate enzyme-catalyzed reactions. 

Fierke, C.A. and Hammes, G.G. (1955) Transient kinetic approaches to enzyme mechanism, in Purich, D. L. (eds.), Methods in Enzymology 249, Enzyme Kinetics and Mechanism, Part D, Academic Press, San Diego, pp. 37-6. 

There is almost no biochemical reaction in a cell that is not catalyzed by an enzyme. (An enzyme is a specialized protein that increases the flux of a biochemical reaction by facilitating a mechanism [or mechanisms] for the reaction to proceed more rapidly than it would without the enzyme.) While the concept of an enzyme-mediated kinetic mechanism for a biochemical reaction was introduced in the previous chapter, this chapter explores the action of enzymes in greater detail than we have seen so far. Specifically, catalytic cycles associated with enzyme mechanisms are examined non-equilibrium steady state and transient kinetics of enzyme-mediated reactions are studied an asymptotic analysis of the fast and slow timescales of the Michaelis-Menten mechanism is presented and the concepts of cooperativity and hysteresis in enzyme kinetics are introduced. 

Fortunately, the characteristic absorbance of certain stable and transient enzyme species and, in some instances, of products, together with the fact that the two half-reactions can be studied separately, permits informative rapid kinetic measurements of the overall and partial reactions of flavoprotein oxidases. Stopped-flow spectrophotometric methods (26) have been particularly useful (the irreversibility of the partial and overall reactions rules out relaxation methods) because the measured rate constants often correspond in part or whole to the reciprocals of the steady state coefficients. This is the major reason for using the formulation... 

NAD(P) Dependent Dehydrogenases Oxygen-Activating Enzymes, Chemistry of Transient State Enzyme Kinetics... 

EPSP synthase catalyzes the synthesis of EPSP by an addition-elimination reaction through the tetrahedral intermediate shown in Fig. 2a. This enzyme is on the shikimate pathway for synthesis of aromatic amino acids and is the target for the important herbicide, glyphosate, which is the active ingredient in Roundup (The Scotts Company EEC, Marysville, OH). Transient-state kinetic studies led to proof of this reaction mechanism by the observation and isolation of the tetrahedral intermediate. Moreover, quantification of the rates of formation and decay of the tetrahedral intermediate established that it was tmly an intermediate species on the pathway between the substrates (S3P and PEP) and products (EPSP and Pi) of the reaction. The chemistry of this reaction is interesting in that the enzyme must first catalyze the formation of the intermediate and then catalyze its breakdown, apparently with different requirements for catalysis. Quantification of the rates of each step of this reaction in the forward and reverse directions has afforded a complete description of the free-energy profile for the reaction and allows... 

Johnson KA. Transient-state kinetic analysis of enzyme reaction pathways. The Enzymes. 1992 XX 1-61. 

Cytochrome P450 Monooxygenases, Chemistry of Enzyme Catalysis, Roles of Structural Dynamics in Enzyme Catalysis, Chemical Strategies for NAD+ Dependent Enzymes, Chemistry of Oxygen-Activating Enzymes, Chemistry of Transient State Enzyme Kinetics Flavoenzymes, Chemistry of... 

Carboxypeptidase A is one of the most intensely investigated zinc metalloenzymes. The enzyme as isolated contains 1 g-atom of zinc per protein molecular weight of 34,600. Removal of the metal atom either by dialysis at low pH or by treatment with chelating agents gives a totally inactive apoenzyme (46). Activity can be restored by readdition of zinc or one of a number of other di-valent metal ions (47). Through a combined use of chemical modification and transient state kinetic studies, it has been possible to determine the role of zinc in the catalysis of ester and peptide hydrolysis by this enzyme. 

Owing to differences in the Kyi values and the layer thickness, the transient from kinetic to diffusion control of different enzyme electrodes takes place at rather different enzyme activities. Gelatin-entrapped enzymes exhibit transient values of 0.17 U/cm2 (uricase,iifM= 17 pmol/1), 16 U/cm2 (urease, Kyi = 2 mmol/1) and 1.0 U/cm2 (lactate monooxygenase, Km = 7.2 mmol/1). 

The preceding derivation allows us to highlight a few important points regarding enzyme kinetics. The most fundamental of these is that Michaelis-Menten kinetics are applicable only at steady state. On introduction of a substrate into a cell culture or a natural sample, for example, the initial rate of transformation is zero and increases to its steady-state value over a time whose duration is given by the characteristic t = (k ET + kb + kt) l. This transient time may not be very short and may confound the results of short-term tracer experiments. 

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