Enzyme zero order reaction

Another special case deserves comment—zero-order reactions. For a reaction that is zero-order with respect to a given substrate, the velocity does not depend on the concentration of substrate. We see zero-order behavior at Vmax the reaction is zero-order in the concentration of substrate. Note that even at Vmax, the reaction is full first order in the concentration of enzyme (the rate increases as the enzyme concentration increases). 

Reactions in which the velocity (v) of the process is independent of the reactant concentration, following the rate law v = k. Thus, the rate constant k has units of M sAn example of a zero-order reaction is a Michaelis-Menten enzyme-catalyzed reaction in which the substrate concentration is much larger than the Michaelis constant. Under these conditions, if the substrate concentration is raised even further, no change in the velocity will be observed (since v = Umax)- Thus, the reaction is zero-order with respect to the substrate. However, the reaction is still first-order with respect to total enzyme concentration. When the substrate concentration is not saturating then the reaction ceases to be zero order with respect to substrate. Reactions that are zero-order in each reactant are exceedingly rare. Thus, zero-order reactions address a fundamental difference between order and molecularity. Reaction order is an empirical relationship. Hence, the term pseudo-zero order is actually redundant. All zero-order reactions cease being so when no single reactant is in excess concentration with respect to other reactants in the system. 

An enzyme which hydrolyzes the cellobiose to glucose, /3-glucosidase is immobilized in a sodium alginate gel sphere (2.5 mm in diameter). Assume that the zero-order reaction occurs at every point within the sphere with k0 = 0.0795 mol/sm3, and cellobiose moves through the sphere by molecular diffusion with Ds = 0.6 x 10 5 cm2 /s (cellobiose in gel). Calculate the effectiveness factor of the immobilized enzyme when the cellobiose concentration in bulk solution is 10 mol/m3. 

Right Profiles of decrease in F(t)/F(0) for intraparticle diffusion-influenced zero-order reaction with spherical immobilized enzyme particles packed in the reactor operated under a constant conversion policy (x = 0.99). Enzyme activity decays as E(t)/E(0) = exp ( kd t). 

The overall mass-transfer rates on both sides of the membrane can only be calculated when we know the convective velocity through the membrane layer. For this, Equation 14.2 should be solved. Its solution for constant parameters and for first-order and zero-order reaction have been given by Nagy [68]. The differential equation 14.26 with the boundary conditions (14.28a) to (14.28c) can only be solved numerically. The boundary condition (14.28c) can cause strong nonlinearity because of the space coordinate and/or concentration-dependent diffusion coefficient [40, 57, 58] and transverse convective velocity [11]. In the case of an enzyme membrane reactor, the radial convective velocity can often be neglected. Qin and Cabral [58] and Nagy and Hadik [57] discussed the concentration distribution in the lumen at different mass-transport parameters and at different Dm(c) functions in the case of nL = 0, that is, without transverse convective velocity (not discussed here in detail). 

Zero-order reactions are most often encountered when a substance such as a metal surface or an enzyme is required for the reaction to occur. For example, the decomposition reaction... 

Keeping the factors such as pH, temperature and enzyme concentration at optimum levels, if the substrate concentration is increased, the velocity of the reaction recorded a rectangular hyperbola. At very low substrate concentration the initial reaction velocity (v) is nearly proportional to the substrate concentration (first order kinetics). However, if the substrate concentration is increased the rate of increase slows down (mixed order kinetics). With a further increase in the subshate concentration the reaction rate approaches a constant (zero order-reaction where velocity is independent of substrate concentration). 

Enzyme-catalyzed reactions are important examples of zero-order reactions that is, the rate of such a reaction is independent of the concentration of the substrate (provided some substrate is present). 

The rate constant expresses the proportionality between the rate of formation of B and the molar concentration of A and is characteristic of a particular reaction. The units of k depend on the order of the reaction. For zero order, they are moles liter" time" (time is frequently given in seconds). For first order, they are time" , and for second order, liters moles" time" , etc. The units of k are whatever is needed for zero order reaction, [B] changes at a constant rate independent of the concentration of reactants, which is especially important in enzyme kinetics. A plot of [B] versus t for such a reaction is a straight line. A somewhat more complicated example is... 

Zero-order reactions can be explained in two ways. In a process that is truly zero order with respect to all reactants (and catalysts, in the case of enzymes), either the activation energy is zero or every molecule has sufficient energy to overcome the activation barrier. This kind of reaction is rare in homogeneous reactions in gases or solutions. 

Interestingly enough, under some conditions, a reaction can be zero order. In these cases, the rate is independent of reactant concentrations. Enzyme-catalyzed reactions can approximate zero-order reactions under some circumstances (p. 219). 

In the measurement of enzyme activity, a high substrate concentration that is greatly in excess of the Km value is always used, and the enzyme sample to be investigated is correspondingly diluted vmder the conditions, the rate of the enzyme-catalyzed reaction depends only on the enzyme concentration, i.e., it is a zero order reaction. Even under conditions of substrate saturation, the measured catalytic activities are influenced by slight differences in reaction conditions, such as the temperature, composition and concentration of the buffer, pH value, nature of the substrate and its concentration, coenzymes, and protein content in the sample. Therefore, the results of measurement of the catalytic activity of an enzyme are in principle method dependent direct comparison of the results between laboratories is made difficult by the use of different methods in different laboratories. 

When all the binding sites on Pt are occupied, the rate becomes constant regardless of the amount of N2O present in the gas phase. As we will see in Section 13.6, another well-studied zero-order reaction occurs in enzyme catalysis. 

A reversible chemical reaction in this context is between an enzyme and a substrate (a molecule of biological importance). It has been observed that at low substrate concentration, the reaction velocity is proportional to the substrate concentration and the reaction is first order with respect to substrate. Increasing the concentration of the substrate causes the reaction rate to diminish, and there is a point where it is no longer proportional to the substrate concentration and, indeed, the rate of the enzyme-catalyzed reaction becomes constant and independent of substrate concentration. Here, the reaction is zero-order a zero-order reaction is independent of the concentration of the reactant, so a higher concentration of reactants will not increase the rate of reaction) with respect to the substrate and the enzyme is said to be saturated with substrate (saturation). This effect is described by a process in which the enzyme (E) reacts with substrate (S) to form a complex ES, which then breaks down to regenerate the enzyme and products (P). Both reactions are reversible, with the rate constants that are indicated kj-k4. This reaction has been analyzed to give the following ... 

As the initial substrate concentration, xo, is increased (kiXt, k ), k will change from a first-order to a zero-order reaction velocity constant and will reach its maximum value A max- = As. This represents the maximum turnover number of the enzyme and is usually given in min. or sec.". ... 

Unidirectional (membrane type) steady-state equations of diffusion-reactions with one Michaelis type enzyme. Fundamental case no regulatory effects zero order reaction, v = Vm, assumption 10 Km or s 10 to 50 in all points of the membrane. 

Perhaps the most important examples of zero-order reactions are found in the action of enzymes. Enzyme-catalyzed reactions are discussed in Section 20-11. 

Interestingly, at very low concentrations of micellised Qi(DS)2, the rate of the reaction of 5.1a with 5.2 was observed to be zero-order in 5.1 a and only depending on the concentration of Cu(DS)2 and 5.2. This is akin to the turn-over and saturation kinetics exhibited by enzymes. The acceleration relative to the reaction in organic media in the absence of catalyst, also approaches enzyme-like magnitudes compared to the process in acetonitrile (Chapter 2), Cu(DS)2 micelles accelerate the Diels-Alder reaction between 5.1a and 5.2 by a factor of 1.8710 . This extremely high catalytic efficiency shows how a combination of a beneficial aqueous solvent effect, Lewis-acid catalysis and micellar catalysis can lead to tremendous accelerations. 

Saturation kinetics are also called zero-order kinetics or Michaelis-Menten kinetics. The Michaelis-Menten equation is mainly used to characterize the interactions of enzymes and substrates, but it is also widely applied to characterize the elimination of chemical compounds from the body. The substrate concentration that produces half-maximal velocity of an enzymatic reaction, termed value or Michaelis constant, can be determined experimentally by graphing r/, as a function of substrate concentration, [S]. 

FIGURE 14.7 Substrate saturation curve for au euzyme-catalyzed reaction. The amount of enzyme is constant, and the velocity of the reaction is determined at various substrate concentrations. The reaction rate, v, as a function of [S] is described by a rectangular hyperbola. At very high [S], v= Fnax- That is, the velocity is limited only by conditions (temperature, pH, ionic strength) and by the amount of enzyme present becomes independent of [S]. Such a condition is termed zero-order kinetics. Under zero-order conditions, velocity is directly dependent on [enzyme]. The H9O molecule provides a rough guide to scale. The substrate is bound at the active site of the enzyme. 

On the other hand, for an enzyme that obeys Michaelis-Menten kinetics, the reaction is viewed as being first-order in S at low S and zero-order in S at high S. (See Chapter 14, where this distinction is discussed.)... 

Pyruvic acid is an intermediate in the fermentation of grains. During fermentation the enzyme pyruvate carboxylase causes the pyruvate ion to release carbon dioxide. In one experiment a 200.-mL aqueous solution of the pyruvate in a sealed, rigid 500.-mL flask at 293 K had an initial concentration of 3.23 mmol-L -l. Because the concentration of the enzyme was kept constant, the reaction was pseudo-first order in pyruvate ion. The elimination of CU2 by the reaction was monitored by measuring the partial pressure of the C02 gas. The pressure of the gas was found to rise from zero to 100. Pa in 522 s. What is the rate constant of the pseudo-first order reaction ... 

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