High Substrate Concentration Limit Saturated Kinetics

High Substrate Concentration Limit Saturated Kinetics 

The situation at high substrate concentrations, when a 1 or s°° Km, where the catalyst is saturated by substrate. This saturation condition results in zero-order kinetics. When a 1, then 1 + an au, and the master equation reduces to 

This expression can readily be integrated with respect to x to obtain 

Introducing the definition of from Eqn. 103, we obtain the following expression for the steady-state current response  

Thus under conditions of reactant saturation, the current response is independent of substrate concentration, but it is first-order with respect to layer thickness and catalyst loading. The rate-determining step involves a breakdown of the catalyst/substrate complex, and it is quantified by the rate constant kc. 

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High Substrate Concentration Limit Saturated Kinetics... 

At a hypothetical infinitely high substrate concentration, all of the enzyme molecules contain bound substrate, and the reaction rate is at V ax The approach to the finite limit of V iax is called saturation kinetics because velocity cannot increase any further once the enzyme is saturated with substrate. Saturation kinetics is a characteristic property of all rate processes dependent on the binding of a compound to a protein. 

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. 

Different from conventional chemical kinetics, the rates in biochemical reactions networks are usually saturable hyperbolic functions. For an increasing substrate concentration, the rate increases only up to a maximal rate Vm, determined by the turnover number fccat = k2 and the total amount of enzyme Ej. The turnover number ca( measures the number of catalytic events per seconds per enzyme, which can be more than 1000 substrate molecules per second for a large number of enzymes. The constant Km is a measure of the affinity of the enzyme for the substrate, and corresponds to the concentration of S at which the reaction rate equals half the maximal rate. For S most active sites are not occupied. For S >> Km, there is an excess of substrate, that is, the active sites of the enzymes are saturated with substrate. The ratio kc.AJ Km is a measure for the efficiency of an enzyme. In the extreme case, almost every collision between substrate and enzyme leads to product formation (low Km, high fccat). In this case the enzyme is limited by diffusion only, with an upper limit of cat /Km 108 — 109M. v 1. The ratio kc.MJKm can be used to test the rapid... 

In zone a of Figure 2.5, the kinetics are first order with respect to [S], that is to say that the rate is limited by the availability (concentration) of substrate so if [S] doubles the rate of reaction doubles. In zone c however, we see zero order kinetics with respect to [S], that is the increasing substrate concentration no longer has an effect as the enzyme is saturated zone b is a transition zone. In practice it is difficult to demonstrate the plateau in zone c unless very high concentrations of substrate are used in the experiment. Figure 2.5 is the basis of the Michaelis-Menten graph (Figure 2.6) from which two important kinetic parameters can be approximated ... 

It is found experimentally in most cases that v is directly proportional to the concentration of enzyme, [E]0. However, v generally follows saturation kinetics with respect to the concentration of substrate, [S], in the following way (Figure 3.1). At sufficiently low [S], v increases linearly with [S]. But as [S] is increased, this relationship begins to break down and v increases less rapidly than [S] until, at sufficiently high or saturating [S], v tends toward a limiting value termed Vmax. This is expressed quantitatively in the Michaelis-Menten equation, the basic equation of enzyme kinetics ... 

Widdas s quantitative model of the simple carrier was able to explain a number of earlier observations and to make predictions about what would be observed in more complex experiments on membrane transport. Thus it was a highly productive scientific insight. One of the earlier, apparently anomalous, results that the theory explained was the dramatic fall of membrane permeability found for solutes which were rapidly transported as solute concentration was increased. For example, in the human red blood cell, Wilbrandt and colleagues had previously measured a permeability constant for glucose which was 1000 times higher in dilute solutions of glucose than it was in a concentrated solution. This phenomenon, subsequently called saturation kinetics, is formally equivalent to the fall, as substrate concentration increases, in the proportion of substrate converted to product by a limited amount of an enzyme. 

This implies that the initial velocity (v) is directly proportional to the enzyme concentration [E], and that v follows saturation kinetics with respect to the substrate concentration [S]. This is shown graphically in Figure 17.2 and explained as follows at very low substrate concentrations v increases in a linear fashion, so that v = V iSyK. As the substrate concentration increases, the observed increase in v is less than the increase in [S]. This trend continues until, at high (saturating) substrate concentrations, v becomes effectively independent of tS] and tends toward the limiting value... 

The effects of this concentration gradient are most significant at low bulk concentrations of the substrate, since substrate is converted to product as soon as it reaches the surface of the particle, so that the surface concentration of substrate is zero. At very high bulk substrate concentrations, the enzymatic reaction rate is limited by enzyme kinetics rather than mass transport, so that surface concentrations do not differ significantly from those in the bulk. Because of the concentration gradient, however, enzyme saturation with substrate occurs at much higher bulk substrate concentrations than required to saturate the soluble enzyme. Apparent Km values (K m) for immobilized enzymes are larger than Km values obtained for the native soluble enzymes. 

Fig. 1. Saturation kinetics for an enzymatic reaction. At low substrate concentrations, [A], the rate of reaction is almost proportional to [A], but an upper limit is approached with high concentrations. The points plotted here are obtained by substituting in Eqn. 4 K ,a, = 10 and = 4. Notice how in looking at such a direct plot of v against [A] the eye tends to underestimate the value of...

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