Pre-steady state

One way to examine the validity of the steady-state approximation is to compare concentration—time curves calculated with exact solutions and with steady-state solutions. Figure 3-10 shows such a comparison for Scheme XIV and the parameters, ki = 0.01 s , k i = 1 s , 2 = 2 s . The period during which the concentration of the intermediate builds up from its initial value of zero to the quasi-steady-state when dcfjdt is vei small is called the pre-steady-state or transient stage in Fig. 3-10 this lasts for about 2 s. For the remainder of the reaction (over 500 s) the steady-state and exact solutions are in excellent agreement. Because the concen-... 

The calculated concentrations are depicted in Fig. 5-2. The main plot displays them over the full time course of the reaction, and the inset shows the concentration of the intermediate at very short times, prior to the establishment of the steady state. Inspection of these graphs allows one to appreciate the different changes, including the buildup of the intermediate in the pre-steady-state region. 

Picosecond kinetics, 266 Pre-equilibria, 133-135 Pre-steady-state region, 116 Pressure, effect on rate constants, 166-167... 

The predictions of simple rules such as Kaptein s and Muller s can be distorted by relaxation effects. These are particularly noticeable in photochemical experiments. In the pre-steady state (e.g., immediately after irradiation has begun), when build-up of the polarized signals is occurring, relaxation effects in the final product are relatively unimportant and observed spectra accord with the simple theory. Con-... 

Fig. 9. The MoFe protein cycle of molybdenum nitrogenase. This cycle depicts a plausible sequence of events in the reduction of N2 to 2NH3 + H2. The scheme is based on well-characterized model chemistry (15, 105) and on the pre-steady-state kinetics of product formation by nitrogenase (102). The enzymic process has not been chsiracter-ized beyond M5 because the chemicals used to quench the reactions hydrolyze metal nitrides. As in Fig. 8, M represents an aji half of the MoFe protein. Subscripts 0-7 indicate the number of electrons trsmsferred to M from the Fe protein via the cycle of Fig. 8.

The mechanism of the first half-reaction has been studied by a combination of reductive titrations with CO and sodium dithionite and pre-steady-state kinetic studies by rapid freeze quench EPR spectroscopy (FQ-EPR) and stopped-flow kinetics 159). These combined studies have led to the following mechanism. The resting enzyme is assumed to have a metal-bound hydroxide nucleophile. Evidence for this species is based on the similarities between the pH dependence of the EPR spectrum of Cluster C and the for the for CO, deter-... 

Fig. 8. A model of bases on steady-state and pre-steady-state kinetic data. Ps indicate the two phosphorylation sites. Cl, CII and NIII refer to domains A, B, and C, respectively.

Rate constants governing re-orientation of the glucose transporter, and their activation energies, determined from steady-state and pre-steady-state measurements... 

Steady-state and pre-steady-state values are taken from Lowe and Walmsley [48] and from Appleman and... 

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... 

When an enzyme is mixed with a large excess of substrate (which is generally the case due to the high catalytic efficiency of enzymes), there is an initial period, the pre-steady state period, during which the concentrations of enzyme bound intermediates build up to their steady state levels. Once the intermediates reach their steady state concentrations (and this is generally achieved after milliseconds) the reaction rate changes only slowly with time. 

Happe, R. P., Roseboom, W. and Albracht, S. P. (1999) Pre-steady-state kinetics of the reactions of [NiFe]-hydrogenase from Chromatium vinosum with H2 and CO. Eur. J. Biochem., 259, 602-8. 

EP occurs in the pre-steady-state phase. Then, the total concentration of ES + E + EP remains relatively stable during the steady-state phase, the period over which product formation is relatively constant. As substrate becomes depleted, the driving force for maintaining the concentrations of ES and E weakens, and although not shown here, [EP] becomes the dominant reactant-bound species as product accumulates. 

Yang and Schulz also formulated a treatment of coupled enzyme reaction kinetics that does not assume an irreversible first reaction. The validity of their theory is confirmed by a model system consisting of enoyl-CoA hydratase (EC 4.2.1.17) and 3-hydroxyacyl-CoA dehydrogenase (EC 1.1.1.35) with 2,4-decadienoyl coenzyme A as a substrate. Unlike the conventional theory, their approach was found to be indispensible for coupled enzyme systems characterized by a first reaction with a small equilibrium constant and/or wherein the coupling enzyme concentration is higher than that of the intermediate. Equations based on their theory can allow one to calculate steady-state velocities of coupled enzyme reactions and to predict the time course of coupled enzyme reactions during the pre-steady state. 

Refers to that initial period of nonhnear product formation, commencing with the initiation of the reaction and ending when the system is at steady state. Typically, the pre-steady-state phase lasts from milliseconds to a few seconds after mixing reactants. The time course of pre-steady-state rate processes often can be evaluated using stopped-flow, temperature-jump, and mix-quench methods. 

Johnson and Fierke Hammes have presented detailed accounts of how rapid reaction techniques allow one to analyze enzymic catalysis in terms of pre-steady-state events, single-turnover kinetics, substrate channeling, internal equilibria, and kinetic partitioning. See Chemical Kinetics Stopped-Flow Techniques... 

AUTOCATALYSIS LAG TIME HYSTERESIS PRE-STEADY STATE AUTOCATALYSIS... 

PRESSURE-JUMP METHOD CHEMICAL KINETICS PRE-STEADY STATE PHASE Prigogine,... 

It has been known for some time that two molecules of 6,7-dimethyl-8-D-ribityllumazine dismute to form riboflavin. An intermediate pentacyclic compound has now been detected by pre-steady-state kinetic studies <2003JBC47700>. 

It was early established that at least for PAH, which as isolated contains the catalytic iron in the ferric high-spin (S = 5/2) state, the Fe111 is reduced to Fe11 by BH4. This is termed reductive activation of PAH and in vitro this reduction is an obligate step that occurs in the pre-steady-state period (20). A midpoint potential at pH 7.25 (Em (Fein/Fen)) of +207 10 mV was calculated for the iron in hPAH, which seems to be adequate for a thermodynamically feasible electron transfer from BH4 (Em (q-BH2/ BH4) = +174mV) (40). 

The time-dependent concentration ofpNPOH was analyzed on the basis of Eq. (6), which is the sum of an exponential (pre-steady state) phase, characterized by a first-order rate constant k, and a linear (steady state) phase obtained when the exponential term dies out (kt > 5). The equation reduces to the form of Eq. (7). The intercept ofthe linear portion defines the burst ji of ArOH liberation. ... 

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