Michaelis-Menten equation assumptions

Equation 11-15 is known as the Michaelis-Menten equation. It represents the kinetics of many simple enzyme-catalyzed reactions, which involve a single substrate. The interpretation of as an equilibrium constant is not universally valid, since the assumption that the reversible reaction as a fast equilibrium process often does not apply. 

This is an assumption used to derive the Michaelis-Menten equation in which the velocity of ES formation is assumed to be equal to the velocity of ES breakdown. 

When these assumptions hold, Thellier et al. [264] and others [267,268] have shown that the Michaelis-Menten equation (equation (35)) can be rigorously derived from the conservation equations for the various forms of the carrier. By... 

The Michaelis-Menten equation can also be derived by applying the steady state assumption to the following scheme ... 

If it is assumed that ES is formed at the same rate at which it breaks down to E + P (a steady-state assumption), and that the concentration of S is much larger than the concentration of E, then the change in reaction velocity, v, relative to changes in [S], is described by the Michaelis-Menten equation ... 

Moreover, the rapid equihbrium assumption used in obtaining the Michaelis-Menten equation requires that... 

UNI UNI ENZYME KINETIC MECHANISM MICHAELIS-MENTEN EQUATION ISO UNI UNI MECHANISM RAPID EQUILIBRIUM ASSUMPTION Unpaired electron,... 

Here we develop the basic logic and the algebraic steps in a modern derivation of the Michaelis-Menten equation, which includes the steady-state assumption introduced by Briggs and Haldane. The derivation starts with the two basic steps of the formation and breakdown of ES (Eqns 6-7 and 6-8). Early in the reaction, the concentration of the product, [P], is negligible, and we make the simplifying assumption that the reverse reaction, P—>S (described by k 2), can be ignored. This assumption is not critical but it simplifies our task. The overall reaction then reduces to... 

Menten assumptions. However, there is an alternative approach for rapidly calculating the ratio of the reaction rates. Substitution of equation 3.24 into the Michaelis-Menten equation (3.1) gives... 

For most enzymes, the rate of reaction can be described by the Michaelis-Menten equation which was originally derived in 1913 by Michaelis and MENTEN 21 . Its derivation can be achieved by making one of two assumptions, one of which is a special case of the more general Briggs-Haldane scheme, whilst the alternative is the rapid-equilibrium method given in Appendix 5.3(2 ). 

Appendix 5.3. Derivation of the Michaelis-Menten Equation using the Rapid Equilibrium Assumption... 

Even this scheme represents a complex situation, for ES can be arrived at by alternative routes, making it impossible for an expression of the same form as the Michaelis-Menten equation to be derived using the general steady-state assumption. However, types of non-competitive inhibition consistent with the Michaelis-Menten type equation and a linear Linweaver-Burk plot can occur if the rapid-equilibrium assumption is valid (Appendix S.A3). In the simplest possible model, involving simple linear non-competitive inhibition, the substrate does not affect the inhibitor binding. Under these conditions, the reactions... 

When the rate of diffusion is very slow relative to the rate of reaction, all substrate will be consumed in the thin layer near the exterior surface of the spherical particle. Derive the equation for the effectiveness of an immobilized enzyme for this diffusion limited case by employing the same assumptions as for the distributed model. The rate of substrate consumption can be expressed by the Michaelis-Menten equation. 

If tj - 1 the reaction is not, or not significantly, influenced by pore diffusion. If tj pore diffusion is the sole dominating rate-limiting step. For the determination of Tj, the combined diffusion and reaction equation has to be solved. With a sequential model of the two rate phenomena, diffusion and reaction, and with the assumption of spherical geometry and validity of the Michaelis-Menten equation for the en2yme kinetics, r = kcat[E] [S]/(JCM + [S]), Eq. (5.58) results. 

If two different substrates bind simultaneously to the active site, then the standard Michaelis-Menten equations and competitive inhibition kinetics do not apply. Instead it is necessary to base the kinetic analyses on a more complex kinetic scheme. The scheme in Figure 6 is a simplified representation of a substrate and an effector binding to an enzyme, with the assumption that product release is fast. In Figure 6, S is the substrate and B is the effector molecule. Product can be formed from both the ES and ESB complexes. If the rates of product formation are slow relative to the binding equilibrium, we can consider each substrate independently (i.e., we do not include the formation of the effector metabolites from EB and ESB in the kinetic derivations). This results in the following relatively simple equation for the velocity ... 

Answer The basic assumptions used to derive the Michaelis-Menten equation still hold. The reaction is at steady state, and the overall rate is determined by... 

Which consideration or assumption does not enter into the derivation of the Michaelis-Menten equation ... 

Enzyme kinetics and the mode of inhibition are well described by transformation of the Michaelis-Menten equation. The binding affinity of the inhibitor to the enzyme is defined as the inhibition constant Ki, whereas the affinity, with which the substrate binds, is referred to the Michaelis-Menten coefficient Km. Michaelis-Menten kinetics base on three assumptions ... 

To determine the Cl-nt of compound X, we are able to use the in vitro half-life method, which is simpler than finding all the component Cl nt values. When the substrate concentration is much smaller than Km, the Michaelis-Menten equation simplifies from velocity (V) = Vmax([S])/(Km + [S]), because [S] (substrate concentration) becomes negligible. Furthermore, under these conditions, the in vitro half-life (7) 2 = 0.693/Xel) can be measured, and this, in turn, is related to the Michaelis-Menten equation through the relationship velocity (V) = volume x Kel (where volume is standardized for the volume containing 1 mg of microsomal protein). When both V and Vmax are known, then Km is also found. Although simpler than finding a complicated Cint, one caveat of the in vitro half-life method is that one assumes that the substrate concentration is much smaller than Km. It may be necessary to repeat the half-life determinations at several substrate concentrations, and even model the asymptote of this relationship, because very low substrate concentrations that are beneath biochemical detection may be needed to fulfill the assumptions needed to simplify the Michaelis-Menten equation. 

The quantitative treatment of kinetic data is based on the pseudophase separation approach, i.e. the assumption that the aggregate constitutes a (pseudo)phase separated from the bulk solution where it is dispersed. Some of the equations below are reminiscent of the well-known Michaelis- Menten equation of enzyme kinetics [101]. This formal similarity has led many authors to draw a parallel between micelle and enzyme catalysis. However, the analogy is limited because most enzymatic reactions are studied with the substrate in a large excess over the enzyme. Even for systems showing a real catalytic behavior of micelles and/or vesicles, the above assumption of the aggregate as a pseudophase does not allow operation with excess substrate. The condition... 

In deriving the rate law for a particular radical mechanism, the steady-state assumption in respect of all species with unpaired electrons, i.e. d[Ra ]/dt = 0, can usually be made, since the absolute concentrations are so low. The assumption parallels that made in steady-state enzyme kinetics (d[ES] / dt = 0), but whereas, in the absence of cooperativity, the steady-state approximation in enzyme kinetics always leads to the Michaelis-Menten equation (whatever the significance of or in terms of individual rate constants), the steady-state assumption in radical kinetics often leads to complex expressions. Dimerisations and dissociations in key steps can lead to fractional... 

The Michaelis-Menten equation can be derived from the chemical kinetics of a very simplified enzyme reaction. The main assumption is that there is only one intermedi-... 

It should also be noted that the Michaelis-Menten equation was derived under the assumption that the substrate concentration is always much higher than the enzyme concentration. This condition may not be met when the substrates involve macromolecules such as proteins. Thus at a low activator or high enzyme concentration some deviation from linearity may be encountered. 

As shown above, the equilibrium assumption leads to a version of the Michaelis-Menten equation in which the Michaelis constant is equivalent to the dissociation constant for the enzyme-substrate complex EA. This unfortunately encourages many biochemists to assume that Michaelis constants can always be so equated. The misleading statement that K, reflects an enzyme s affinity for its substrate is often encountered. Even if we consider only 1-substrate enzymes, the Briggs-Haldane version of will only approximate to k /k if However, if, for instance, /c2 = 10/c, then is 11 times greater than the dissociation constant for EA. If kj k, then = k2/k rather than k /k. ... 

This equation embodies all the features of positive cooperative binding of substrate and the effect of this upon biocatalytic rate. Given the power terms, this equation is decidedly not identical with the Michaelis-Menten equation (8.8) However, an alternative and equally important biocatalytic equation can be derived from Equation (8.30) with a little more work and a few simple assumptions. First, let us assume that cooperative binding is sufficiently positive that terms in [S] are eliminated from Equation (8.30). Second, let us define Vmax according to... 

Reproduce the derivation of the Michaelis-Menten equation in the text. Relate the Michaelis-Menten equation to experimentally derived plots of velocity (V) versus substrate concentration [S]. List the assumptions underlying the derivation. 

In this case, v is the velocity of the reaction, [S] is the substrate concentration, Vmax (also known as V or Vj ) is the maximum velocity of the reaction, and is the Michaelis constant. From this equation quantitative descriptions of enzyme-catalyzed reactions, in terms of rate and concentration, can be made. As can be surmised by the form of the equation, data that is described by the Michaelis-Menten equation takes the shape of a hyperbola when plotted in two-dimensional fashion with velocity as the y-axis and substrate concentration as the x-axis (Fig. 4.1). Use of the Michaelis-Menten equation is based on the assumption that the enzyme reaction is operating under both steady state and rapid equilibrium conditions (i.e., that the concentration of all of the enzyme-substrate intermediates (see Scheme 4.1) become constant soon after initiation of the reaction). The assumption is also made that the active site of the enzyme contains only one binding site at which catalysis occurs and that only one substrate molecule at a time is interacting with the binding site. As will be discussed below, this latter assumption is not always valid when considering the kinetics of drug metabolizing enzymes. 

The studies of the kinetics of bioelectrocatalytic transformations show that in some systems (for instance, adsorbed laccase ) the kinetic parameters correspond to the phenomenology of electrochemical kinetics, while in other systems (for instance, lactate oxidation they fit the phenomenology of enzymatic catalysis. In the latter case, we observe a hyperbolic dependence of anode current on the substrate concentration, as expected from the Michaelis-Menten equation. The absence of a general theory of bioelectrocatalysis does not permit us to examine the kinetics of electrochemical reactions in the presence of enzymes under different conditions. At present we can only try to estimate the scope of possible accelerations of electrochemical reactions by making some simple assumptions. 

Because the busy metabolic traffic of cells produces a steady state more often than an equilibrium, much use has been made of an equation devised by Briggs and Haldane (1925) who showed that it was unnecessary to assume an equilibrium between [E] and [S]. They derived Equation (v), formally similar to the Michaelis—Menten equation but free from this assumption and suitable for steady-state conditions. 

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