Substrate concentration relationship

Ward, B. B. (1985). Light and substrate concentration relationships with marine ammonium assimilation and oxidation rates. Mar. Chem. 16, 301—316. 

The electrode has not been used as much as the ultraviolet spectro-photometric method for routine catalase assays, and does not cover a sufficiently wide range of peroxide concentration to be suitable for studying the activity-substrate concentration relationship. The technique is suitable for simultaneous measurements of catalase activity and the catalase complex as described below. 

Monod kinetics Kinetics of microbial cell growth as a function of substrate concentration proposed by Jacques Monod and widely used to understand growth-substrate relationships. 

Viewed in this way, the best definition of rate enhancement depends upon the relationship between enzyme and substrate concentrations and the enzyme s kinetic parameters. 

Give example of an enzyme electrode based on an ion-selective electrode transducer. What is the relationship between the substrate concentration and the potential response ... 

From the Michaelis-Menten model, there is a relationship between 1/Fo and the initial substrate concentration, expressed as the reciprocal, 1/[Bq]. To develop this relationship we shall repeat Example 9.1 using varying concentrations of B cells. Be sure to subtract the number of Bq cells in each study from the total number of water, D, cells in the setup. 

The Michaelis-Menten equation (29) illustrates in mathematical terms the relationship between initial reaction velocity V and substrate concentration [S], shown graphically in Figure 8-3. 

These relationships are identical to Haldane relationships, but unlike the latter, their validity does not derive from a proposed reaction scheme, but merely from the observed hyperbolic dependence of transport rates upon substrate concentration. Krupka showed that these relationships were not obeyed by the set of data previously used by Lieb [64] to reject the simple asymmetric carrier model for glucose transport. Such data therefore cannot be used either to confirm or refute the model. 

When microorganisms use an organic compound as a sole carbon source, their specific growth rate is a function of chemical concentration and can be described by the Monod kinetic equation. This equation includes a number of empirical constants that depend on the characteristics of the microbes, pH, temperature, and nutrients.54 Depending on the relationship between substrate concentration and rate of bacterial growth, the Monod equation can be reduced to forms in which the rate of degradation is zero order with substrate concentration and first order with cell concentration, or second order with concentration and cell concentration.144... 

Today, it is accepted that Langley and Ehrlich deserve comparable recognition for the introduction of the receptor concept. In the same years, biochemists studying the relationship between substrate concentration and enzyme velocity had also come to think that enzyme molecules must possess an active site that discriminates among various substrates and inhibitors. As often happens, different strands of evidence had converged to point to a single conclusion. 

From scheme I, together with the experimentally observed first-order dependence on the total ester concentration, the rate relationship illustrated in Eq. (1) may be derived. In applying this equation, the cycloamylose concentration must be at least tenfold greater than the initial substrate concentration to ensure first-order conditions. Equation (1) may be rearranged in two ways to yield linear forms which permit graphical evaluation of fa, the maximal rate constant for release of phenol from the fully com-plexed ester and Kd, the cycloamylose-substrate dissociation constant (defined in Scheme I as A i/fa). These two methods are illustrated in Eqs. (2) and (3) and may be attributed to Lineweaver and Burk (1934) and to Eadie (1942), respectively. Although in theory both methods should give... 

A plot of the initial reaction rate, v, as a function of the substrate concentration [S], shows a hyperbolic relationship (Figure 4). As the [S] becomes very large and the enzyme is saturated with the substrate, the reaction rate will not increase indefinitely but, for a fixed amount of [E], it reaches a plateau at a limiting value named the maximal velocity (vmax). This behavior can be explained using the equilibrium model of Michaelis-Menten (1913) or the steady-state model of Briggs and Haldane (1926). The first one is based on the assumption that the rate of breakdown of the ES complex to yield the product is much slower that the dissociation of ES. This means that k2 tj. 

The relationship between CL intensity and time is expressed by a kinetic equation including the reaction rate constants and the substrate concentration. Such is the case with the specific equation for the CL of the luminol reaction, which is one of the most widely studied in this context ... 

Figure 3. Schematic view of the substrate uptake rate versus concentration relationship as described by the whole-cell Michaelis-Menten kinetics. Q is the substrate uptake rate, <2max the biologically determined maximum uptake rate per biomass, c the substrate concentration, and Kj the whole-cell Michaelis constant, i.e. the concentration resulting in 2max/2 (mass of substrate per volume). At c

Because of its prominent appearance in the whole cell Michaelis-Menten equation, Kt is frequently mistaken as a measure of the substrate affinity. However, from equations (2) and (4), it becomes obvious that the activity versus concentration relationship is characterised by the two independent parameters, 2max, as a descriptor of the zero-order part at high substrate concentration, and a°A, as a descriptor of the slope of the first-order part of the curve. In his much-cited review paper, Button [9] has listed the specific affinities of various organisms for a range of carbon sources and other elements. Reported variations for the same substrates extend over up to four orders of magnitude. Table 1 updates... 

This equation defines the quantitative relationship between the substrate concentration and enzyme reaction rate when the constants, Vmax and Km, are known. An interesting and important relationship emerges when v is equal to 1/2Vmax. Under these conditions, [S] is equal to KM. 

Depending upon the system and conditions, the relationship between the overall activation energy of a catalyzed reaction and activation energies of the individual steps may be considered. For an Arrhenius complex, which is at equilibrium with reactants, at low substrate concentrations the rate of reaction is equal to 2 [S] [Catalyst] (K = /c, lk ), the overall activation energy is given by... 

The Michaelis equation describes the relationship between substrate concentration and the rate of an enzymt-catalysed reaction. 

The relationship between substrate concentration ([S]) and reaction velocity (v, equivalent to the degree of binding of substrate to the active site) is, in the absence of cooperativity, usually hyperbolic in nature, with binding behavior complying with the law of mass action. However, the equation describing the hyperbolic relationship between v and [S] can be simple or complex, depending on the enzyme, the identity of the substrate, and the reaction conditions. Quantitative analyses of these v versus [S] relationships are referred to as enzyme kinetics. 

O Figure 4-5 illustrates the relationship between [S] and v when substrate concentrations are chosen based on the data shown in O Table 4-2. 

The activity of an enzyme (v) varies according to the substrate concentration [S]. In most cases, the relationship is hyperbolic, that is ... 

Practical Considerations. Typical absorption assay methods utilize ultraviolet (UV) or visible (vis) wavelengths. With most spectrophotometers, the measured absorbance should be less than 1.2 to obtain a strictly linear relationship (/.c., to obey the Beer-Lambert Law). Nonlinear A versus c plots can result from micelle formation, sample turbidity, the presence of stray light (see below), bubble formation, stacking of aromatic chromophores, and even the presence of fine cotton strands from tissue used to clean the faces of cuvettes. One is well advised to confirm the linearity of absorbance with respect to product (or substrate) concentration under the exact assay conditions to be employed in... 

The relationship between reaction velocity and enzyme concentration (in the absence of self-association of the enzyme) should also be adjusted such that reaction rate is linearly related to catalyst concentration, [Etotai]- Initial rates typically fail to obtain if [Etotai] = 0-01 [Ajmitiai where [Ajinitiai is the initial substrate concentration. As a general rule, the substrate concentration will not have changed more than 5-10% of its value over the initial rate phase of the reaction. This rule-of-thumb applies only to thermodynamically favorable reactions, and investigators are well advised to limit substrate consumption to well below 5%. 

See Double-Reciprocal Plot Hanes Plot Direct Linear Plot Dixon Plot Dixon-Webb Plot Eadie-Hofstee Plot Substrate Concentration Range Frieden Protocol Fromm Protocol Point-of-Convergence Method Dal-ziel Phi Relationships Scatchard Plots Hill Plots... 

Kinetic Haldane relations use a ratio of apparent rate constants in the forward and reverse directions, if the substrate concentrations are very low. For an ordered Bi Bi reaction, the apparent rate constant for the second step is Emax,f/ b (where K, is the Michaelis constant for B) and, in the reverse reaction, V ax,v/Kp. Each of these is multiplied by the reciprocal of the dissociation constant of A and Q, respectively. The forward product is then divided by the reverse product. Hence, the kinetic Haldane relationship for the ordered Bi Bi reaction is Keq = KiO V eJKp)l Kiq V eJKp) = y ,ax.f pKiq/ (yranx,rKmKif). For Completely random mechanisms, thermodynamic and kinetic Haldane relationships are equivalent. 

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. 

Two characteristics, the Michaelis constant KM and the maximal velocity V are the most important numeric data. The well-known Michaelis-Menten equation describes the relationship between the initial reaction rate and the substrate concentration with these two constants. The actual form of the rate equation of an enzymic process depends on the chemical mechanism of the enzymic transformation of the substrate to product (Table 8.1). 

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