Michaelis-Menten expression

This is the Michaelis-Menten expression (which dates back to 1913) for the rate of an enzymatic reaction. 

Compare the Michaelis-Menten expression for the rate of an enzyme-catalyzed reaction with the Langmuir-Hinshelwood expression for the same reaction on a metal surface. Are the two expressions equivalent ... 

Confirming that curved lines are the nemesis of the biochemist, at least three or more different transformations of the Michaelis-Menten equation have been invented (actually four)—each one of which took two people to accomplish (Fig. 8-5). The purpose of these plots is to allow you to determine the values of Km and VmaK with nothing but a ruler and a piece of paper and to allow professors to take a straightforward question about the Michaelis-Menten expression and turn it upside down (and/or backward). You might think that turning a backward quantity like Km upside down would make everything simpler—somehow it doesn t work that way. 

Sometimes, however, initial velocities are needed. If measurements of the rate u, are made at the time t, simple division of Michaelis-Menten expressions yields for the initial velocity Oo... 

Thus we expect the rate to be given by a power dependence on the concentrations and an exponential dependence on temperature k[ (T) = kfoe. This form of the rate expression is not always accurate, especially for catalytic and enzyme reactions for which Langmuir-Hinshelwood and Michaelis-Menten expressions are required to fit experimental data. 

Once the methanotroph-containing CSR has been established, we expect it can cometabolically oxidize some of the TCE incidental to the use of the primary substrate, methane. The rate of TCE biotransformation is dictated by the effectiveness of the methane mono-oxygenase for interacting with TCE rather than methane. This enzymatic processing of TCE can be described using a Michaelis-Menten expression ... 

All parameters (J, kp, kT) shall be positive. p(C,) describes an autocatalytic production function which is first-order at small C, and zeroth order at large C,. Formally, it looks like the Michaelis-Menten expression (Eq. 12-32), although it does not have the same mechanistic basis. 

Steady-state approximation is based on the concept that the formation of [ES] complex by binding of substrate to free enzyme and breakdown of [ES] to form product plus free enzyme occur at equal rates. A graphical representation of the relative concentrations of free enzyme, substrate, enzyme-substrate complex, and product is shown in figure 7.8 in the text. Derivation of the Michaelis-Menten expression is based on the steady-state assumption. Steady-state approximation may be assumed until the substrate concentration is depleted, with a concomitant decrease in the concentration of [ES]. 

The phosphorylation rate (v) of the isolated glucokinase enzyme is given by the Michaelis-Menten expression [27] ... 

When n = 1, Eq. 9.45) yields a rectangular hyperbola. Recall that the Michaelis-Menten expression is written with Km being equivalent to (and having the units of) a dissociation constant, whereas binding equations, such as the Hill equation, are usually written with association constants (their numerical values being the reciprocal of the corresponding dissociation constants). 

The final expression is that of a hyperbola it is evident that it is equivalent to the Michaelis-Menten expression when it is recalled that Xi is an association constant. 

How does varying the substrate concentration relative to the enzyme concentration affect the validity of the steady-state assumption and the applicability of the Michaelis-Menten expression ... 

To analyze this system, we assume that the enzymes obey the flux expression of Equation (4.10). Using this Michaelis-Menten expression, we replace Equation (5.5) with the following... 

The maximum velocity, Vmax, will be attained when all the enzyme is forced into the ES form by an excess of substrate. The effect of substrate and enzyme concentrations on the observed velocity is given by the Michaelis-Menten expression (6, 7) ... 

With some calculation it can be shown that this scheme predicts a packaging velocity with an [ATP] dependence described by the Michaelis-Menten expression ... 

It appears that (3.30) can be rewritten as the Michaelis-Menten expression used in biocatalysis ... 

The form of the resulting expression differs from the gas-phase reaction rate expressions due to the presence of a denominator representing the reduction in rate due to adsorption phenomena. The individual terms of this denominator respresent the distribution of the active sites among the possible surface complexes and vacancies. Expressions of this type are termed the Langmuir-Hinshel-wood-Hougen-Watson (LHHW) rate expressions in heterogeneous catalysis and Michaelis-Menten expressions in biocatalysis. 

In the Michaelis-Menten expression, [Ex] represents the total concentration (in moles per liter) of enzyme, equal to [E] -t- [ES]. Therefore, the concentration of free enzyme [E] is equal to [Ej] — [ES]. The following assumptions are made ... 

Other forms of composition function h(C/s) are used for different types of homogenous and heterogeneous reactions. A written chemical reaction is merely a reaction pathway presentation of many elementary reaction steps that usually involve unstable intermediate species (e.g., free radicals). Hence, the rate of a chemical reaction depends on the rates of the individual steps and results in different forms. For example, the rate of many biological and enzymatically catalyzed reactions is described by an expression of the form (known as the Michaelis-Menten expression). 

Linear kinetics assumes that the reaction rate per unit time, r, of a chemical reaction is proportional to the concentration C of the substance being acted upon, r=kC whereas nonlinear kinetics is most often described in the form of a Michaelis-Menten expression, r = aC/(b+C), note that for low concentrations,... 

The turnover rate becomes proportional to the surface coverage 0, Equation (1.6) is the Langmuir - Hinshelwood expression and is very similar to the Michaelis - Menten expression used in enzyme catalysis. Consider the following mechanism describing... 

Equation 4-8 is the Michaelis-Menten expression for the rate of an enzymatic reaction. Compared with a gas phase molecule that reacts in a monomolecular reaction on a solid catalyst, the reciprocal of the Michaelis constant takes the place of the equilibrimn constant of adsorption in the Langmuir-Hinshelwood equations. In case of very high substrate concentrations, the rate reaches its maximum (Eq. 4-9). 

When the enzyme is dissolved in the same phase as the substrate and product, the kinetics is governed solely by the chemical reaction kinetics, which, owing to the simple mechanism of irreversible conversion of a given substrate S to a product P, is given by the Michaelis-Menten expression ... 

---