Biochemistry: The Chemical Reactions of Living Cells, Volume 2 - D. Metzler 1980

Enzymes: Protein Catalysts of the Cell
Fundamentals of Enzyme Kinetics
Kinetics of Rapid Reactions

Conventional Methods FOR STUDYING stationary kinetics do not allow the observation of the fastest stages of an enzymatic process—they are applicable only when the half-life of the reaction exceeds 10 s. Therefore, to measure reaction rates with half-lives ranging from 10^-13 to 1 s, a variety of new methods have been developed [10, 28–30]¹⁾.

¹⁾ We can also recommend the collection *Molecular biology, biochemistry and biophysics*, V. 24, *Chemical relaxation in molecular biology*, I. Pecht and R. Rigler (Eds.), Springer-Verlag, Berlin, 1977, as well as the recently published book *Methods for Investigating Fast Reactions*, G. Hammies (Ed.), Moscow: Mir, 1977. — Transl. note.

a. Flow methods

One of the earliest methods for studying The kinetics of fast reactions is based on the rapid mixing of reactants achieved by merging two solution streams in a special mixer. The mixture is then passed through a straight tube at a velocity of several meters per second. If the velocity is 10 m∙с^-1, the stream travels 1 cm in 10^-13 s. The mixture can be observed at a suitable distance from the mixing point (for example, at a distance of 1 cm) and at various flow velocities. Spectrophotometric or other methods are used to record The formation of product or the consumption of substrate. The advantage of this method is that it does not require rapid detection; however, its use involves the consumption of large quantities of scarce Reagents, primarily purified Enzymes.

The widely used stopped-flow method is based on the rapid mixing of two solutions within a time interval of only 1–2 ms (or even less). The stream is created and stopped by means of a plunger that drives two medical syringes. Both solutions enter the mixer and then the cuvette, where, after the flow is stopped, Light absorption, electromotive force, electrical conductivity, etc., are measured. The method requires rapid detection. If, for example, light absorption is measured, a photomultiplier tube connected to an oscilloscope is used. Changes in absorption occurring over fractions of a second are recorded on the oscilloscope screen, and the resulting curve "trace" is photographed. In this way, relaxation times down to a few milliseconds can be measured.

b. Relaxation methods

Kinetic measurements in time intervals of tens of microseconds and less are carried out by means of a short-term perturbation of the system, leading to a small shift in THE POSITION OF reaction equilibrium (or a series of equilibria), followed by observation of the rate at which a new equilibrium is reached (i.e., the relaxation process). The most widely used method is the Temperature-jump technique proposed by Eigen and his coworkers. A potential difference of ~100 kV is generated within ∼10^-6 s between electrodes placed in the solution under study. A rapid electrical discharge from a bank of capacitors passing through the solution (without causing sparking) raises its temperature by 2–10°. The equilibrium of all Chemical Reactions for which ∆Н ≠ 0 is shifted. By measuring any parameter of the system (for example, optical density at a specific wavelength or the electrical conductivity of the solution), one can record very short relaxation times.

Although it may not be obvious, when the Displacement of the equilibrium position is small, the establishment of a new equilibrium state can always be represented as a first-order process [see, for example, equation (6-13)].

If more than one chemical reaction participates in the restoration of equilibrium, each corresponds to its own characteristic relaxation time. When these times are approximately equal, it is quite difficult to determine them individually; however, as a rule, the relaxation times of different chemical reactions differ by an order of magnitude or even more. Thus, for the system under study, it is often possible to measure two or more relaxation times. In individual cases, these times can be directly related to the rate constants of specific stages. For example, Eigen observed The rate of interaction of H⁺ with OH^- by recording The change in electrical conductivity of Water following a temperature jump [10]. At 23 °C, the value of τ was 37∙10^-6 s. The rate constant of the process

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was calculated using the following relation:

Pressure or electric field jumps can be used in a mode that leads to a periodic change in a certain parameter of the system. For example, ultrasonic absorption causes a periodic change in pressure within the system.

c. Flash photolysis

Another widely used method is flash photolysis. A light pulse generated by discharging a flashlamp capacitor is rapidly absorbed by a sample placed in a parallel tube. The pulse duration can vary from 10^-12 to 10^-14 s. Changes in the absorption or fluorescence spectrum of the sample accompanying the flash are recorded using a photomultiplier and an oscilloscope. Currently, lasers emitting an exceptionally high-intensity light pulse over several nanoseconds are used as light sources. Laser techniques make it possible to measure extremely short relaxation times [31].

d. Some results

The methods described above have established that the processes of complex formation between enzymes and substrates proceed exceptionally rapidly [32]—The values of the rate constant k₁ in scheme (6-14) often lie in the range from 10⁶ to 10⁸ M^-1∙s^-1. Nevertheless, the second-order rate constant for the enzyme-substrate interaction is lower than the limiting value corresponding to a diffusion-controlled bimolecular reaction (10⁹–10¹⁰ M^-1∙s^-1). This implies that a substrate molecule requires a certain amount of time to properly orient and bind to the Active Site of the enzyme. Relaxation times for helix-coil transitions in Polypeptides are about 10^-8 s, whereas for the renaturation of previously denatured Proteins they can be much higher. Conformational transformations of cyclohexane derivatives of the "chair"–"boat" type at room temperature occur with a characteristic time τ of approximately 10^-5 s, while rotation around the amide C—N bond occurs with τ ≈ 0.1 s, i.e., much more slowly. For the non-enzymatic Hydration of the aldehyde group of pyridoxal-5'-phosphate (Ch. 8, Sec. D), τ ranges from 0.01 to 0.1 s (depending on pH). This result was obtained using the reliable temperature-jump method [33].