WHAT IS THE Michaelis-Menten equation?

Question

Also could you explain how you could use it?

Answer 1

Michaelis-Menten kinetics describes the kinetics of many enzymes. It is named for Leonor Michaelis and Maud Menten. This kinetic model is valid only when the concentration of enzyme is much less than the concentration of substrate (i.e., enzyme concentration is the limiting factor), and when the enzyme is not allosteric.

if u dunno allosteric:

allosteric regulation is the regulation of an enzyme or protein by binding an effector molecule at the protein's allosteric site (that is, a site other than the protein's active site.

Answer 2

Michaelis Menten

Answer 3

Michaelis-Menten kinetics describes the kinetics of many enzymes. It is named for Leonor Michaelis and Maud Menten. This kinetic model is valid only when the concentration of enzyme is much less than the concentration of substrate (i.e., enzyme concentration is the limiting factor), and when the enzyme is not allosteric.

Contents [hide]
1 History
2 Determination of constants
3 Reaction rate/velocity V
4 Michaelis constant 'KM'
5 Equation
6 References
7 Further reading



[edit] History
The modern relationship between substrate and enzyme concentration was proposed in 1903 by Victor Henri. [1]. A microsco[ic interpretation was therafter in 1913 by Leonor Michaelis and Maud Menten, following earlier work by Archibald Vivian Hill.[2]. It postulated that enzyme (catalyst) and substrate (reactant) are in fast equilibrium with their complex, which then dissociates to yield product and free enzyme.

The current derivation, based on the quasi steady state approximation, that is the concentration(s) of intermediate complex(es) do(es) not change has been proposed by Briggs and Haldane.[3]


[edit] Determination of constants

Diagram of reaction speed and Michaelis-Menten constant.To determine the maximum rate of an enzyme mediated reaction, the substrate concentration ([S]) is increased until a constant rate of product formation is achieved. This is the maximum velocity (Vmax) of the enzyme. In this state enzyme active sites are saturated with substrate. Note that at the maximum velocity, the other factors that affect the rate of reaction (ie. pH, temperature, etc) are at optimal values.


[edit] Reaction rate/velocity V
The speed V means the number of reactions per second that are catalyzed by an enzyme. With increasing substrate concentration [S], the enzyme is asymptotically approaching its maximum speed Vmax, but never actually reaching it. Because of that, no [S] for Vmax can be given. Instead, the characteristic value for the enzyme is defined by the substrate concentration at its half-maximum speed (Vmax/2). This KM value is also called Michaelis-Menten constant.


[edit] Michaelis constant 'KM'
Since Vmax cannot be reached at any substrate concentration (because of its asymptotic behaviour, V keeps growing at any [S], albeit ever more slowly), enzymes are usually characterized by the substrate concentration at which the rate of reaction is half its maximum. This substrate concentration is called the Michaelis-Menten constant (KM) a.k.a. Michaelis constant. This represents (for enzyme reactions exhibiting simple Michaelis-Menten kinetics) the dissociation constant (affinity for substrate) of the enzyme-substrate (ES) complex. Low values indicate that the ES complex is held together very tightly and rarely dissociates without the substrate first reacting to form product.

It is worth noting that KM can only be used to describe an enzyme's affinity for substrate when product formation is rate-limiting, i.e., when k2 << k-1 and KM becomes k-1/k1. Often, k2 >> k-1, or k2 and k-1 are comparable.[4]


[edit] Equation
This derivation of "Michaelis-Menten" was actually described by Briggs and Haldane. It is obtained as follows:

The enzymatic reaction is supposed to be irreversible, and the product does not rebind the enzyme.



Because we follow the steady state approximation, the concentrations of the intermediates are assumed to not change, i.e. their time derivatives are zero:





Let's define the Michaelis constant:



This simplifies the form of the equation:

(1)

The total (added) concentration of enzyme is a sum of that which is free in the solution and that which is bound to the substrate, and the free enzyme concentration is derived from this:

[E0] = [E] + [ES]

[E] = [E0] − [ES] (2)

Using this concentration (2), the bound enzyme concentration (1) can now be written:



Rearranging gives:





(3)

The rate (or velocity) of the reaction is:

(4)

Substituting (3) in (4) and multiplying numerator and denominator by [S]:



This equation may be analyzed experimentally with a Lineweaver-Burk diagram.

E0 is the total or starting amount of enzyme. It is not practical to measure the amount of the enzyme substrate complex during the reaction, so the reaction must be written in terms of the total (starting) amount of enzyme, a known quantity.
d[P]/dt a.k.a. V0 a.k.a. reaction velocity a.k.a. reaction rate is the rate of production of the product. Note that the term reaction velocity is misleading and reaction rate is preferred.
k2[E0] a.k.a. Vmax is the maximum velocity or maximum rate. k2 is often called kcat.

Notice that if [S] is large compared to Km, [S]/(Km + [S]) approaches 1. Therefore, the rate of product formation is equal to k2[E0] in this case.

When [S] equals Km, [S]/(Km + [S]) equals 0.5. In this case, the rate of product formation is half of the maximum rate (1/2 Vmax). By plotting V0 against [S], one can easily determine Vmax and Km. Note that this requires a series of experiments at constant E0 and different substrate concentration [S].


[edit] References
^ Victor Henri. Lois Générales de l'Action des Diastases. Paris, Hermann, 1903.
^ Leonor Michaelis, Maud Menten (1913). Die Kinetik der Invertinwirkung, Biochem. Z. 49:333-369.
^ G. E. Briggs and J. B. S. Haldane (1925) A note on the kinetics of enzyme action, Biochem. J., 19, 339-339.
^ Nelson, DL., Cox, MM. (2000) Lehninger Principles of Biochemistry, 3rd Ed., Worth Publishers, USA

[edit] Further reading
Catalysis chapter from the Biochemistry textbook released under the GFDL
Retrieved from "http://en.wikipedia.org/wiki/michaelis-m...
Categories: Enzyme kinetics | Chemical kinetics | Ordinary differential equations

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Answer 4

K2 is the cost of reaction from complicated to product and Vmax is the utmost value that the enzyme will convert to product so as that they are genuinely an identical. K2 is comparable to Kcat.

Answer 5

Michaelis-Menten kinetics describes the kinetics of many enzymes. It is named for Leonor Michaelis and Maud Menten. This kinetic model is valid only when the concentration of enzyme is much less than the concentration of substrate (i.e., enzyme concentration is the limiting factor), and when the enzyme is not allosteric.

Contents [hide]
1 History
2 Determination of constants
3 Reaction rate/velocity V
4 Michaelis constant 'KM'
5 Equation
6 References
7 Further reading



[edit] History
The modern relationship between substrate and enzyme concentration was proposed in 1903 by Victor Henri. [1]. A microsco[ic interpretation was therafter in 1913 by Leonor Michaelis and Maud Menten, following earlier work by Archibald Vivian Hill.[2]. It postulated that enzyme (catalyst) and substrate (reactant) are in fast equilibrium with their complex, which then dissociates to yield product and free enzyme.

The current derivation, based on the quasi steady state approximation, that is the concentration(s) of intermediate complex(es) do(es) not change has been proposed by Briggs and Haldane.[3]


[edit] Determination of constants

Diagram of reaction speed and Michaelis-Menten constant.To determine the maximum rate of an enzyme mediated reaction, the substrate concentration ([S]) is increased until a constant rate of product formation is achieved. This is the maximum velocity (Vmax) of the enzyme. In this state enzyme active sites are saturated with substrate. Note that at the maximum velocity, the other factors that affect the rate of reaction (ie. pH, temperature, etc) are at optimal values.


[edit] Reaction rate/velocity V
The speed V means the number of reactions per second that are catalyzed by an enzyme. With increasing substrate concentration [S], the enzyme is asymptotically approaching its maximum speed Vmax, but never actually reaching it. Because of that, no [S] for Vmax can be given. Instead, the characteristic value for the enzyme is defined by the substrate concentration at its half-maximum speed (Vmax/2). This KM value is also called Michaelis-Menten constant.


[edit] Michaelis constant 'KM'
Since Vmax cannot be reached at any substrate concentration (because of its asymptotic behaviour, V keeps growing at any [S], albeit ever more slowly), enzymes are usually characterized by the substrate concentration at which the rate of reaction is half its maximum. This substrate concentration is called the Michaelis-Menten constant (KM) a.k.a. Michaelis constant. This represents (for enzyme reactions exhibiting simple Michaelis-Menten kinetics) the dissociation constant (affinity for substrate) of the enzyme-substrate (ES) complex. Low values indicate that the ES complex is held together very tightly and rarely dissociates without the substrate first reacting to form product.

It is worth noting that KM can only be used to describe an enzyme's affinity for substrate when product formation is rate-limiting, i.e., when k2 << k-1 and KM becomes k-1/k1. Often, k2 >> k-1, or k2 and k-1 are comparable.[4]


[edit] Equation
This derivation of "Michaelis-Menten" was actually described by Briggs and Haldane. It is obtained as follows:

The enzymatic reaction is supposed to be irreversible, and the product does not rebind the enzyme.



Because we follow the steady state approximation, the concentrations of the intermediates are assumed to not change, i.e. their time derivatives are zero:





Let's define the Michaelis constant:



This simplifies the form of the equation:

(1)

The total (added) concentration of enzyme is a sum of that which is free in the solution and that which is bound to the substrate, and the free enzyme concentration is derived from this:

[E0] = [E] + [ES]

[E] = [E0] − [ES] (2)

Using this concentration (2), the bound enzyme concentration (1) can now be written:



Rearranging gives:





(3)

The rate (or velocity) of the reaction is:

(4)

Substituting (3) in (4) and multiplying numerator and denominator by [S]:



This equation may be analyzed experimentally with a Lineweaver-Burk diagram.

E0 is the total or starting amount of enzyme. It is not practical to measure the amount of the enzyme substrate complex during the reaction, so the reaction must be written in terms of the total (starting) amount of enzyme, a known quantity.
d[P]/dt a.k.a. V0 a.k.a. reaction velocity a.k.a. reaction rate is the rate of production of the product. Note that the term reaction velocity is misleading and reaction rate is preferred.
k2[E0] a.k.a. Vmax is the maximum velocity or maximum rate. k2 is often called kcat.

Notice that if [S] is large compared to Km, [S]/(Km + [S]) approaches 1. Therefore, the rate of product formation is equal to k2[E0] in this case.

When [S] equals Km, [S]/(Km + [S]) equals 0.5. In this case, the rate of product formation is half of the maximum rate (1/2 Vmax). By plotting V0 against [S], one can easily determine Vmax and Km. Note that this requires a series of experiments at constant E0 and different substrate concentration [S].


[edit] References
^ Victor Henri. Lois Générales de l'Action des Diastases. Paris, Hermann, 1903.
^ Leonor Michaelis, Maud Menten (1913). Die Kinetik der Invertinwirkung, Biochem. Z. 49:333-369.
^ G. E. Briggs and J. B. S. Haldane (1925) A note on the kinetics of enzyme action, Biochem. J., 19, 339-339.
^ Nelson, DL., Cox, MM. (2000) Lehninger Principles of Biochemistry, 3rd Ed., Worth Publishers, USA

[edit] Further reading
Catalysis chapter from the Biochemistry textbook released under the GFDL
Retrieved from "http://en.wikipedia.org/wiki/Michaelis-Menten_kinetics"
Categories: Enzyme kinetics | Chemical kinetics | Ordinary differential equations

ViewsArticle Discussion Edit this page History Personal toolsSign in / create account Navigation
Main page
Community portal
Featured content
Current events
Recent changes
Random article
Help
Contact Wikipedia
Donations
Search
Toolbox
What links here
Related changes
Upload file
Special pages
Printable version
Permanent link
Cite this article
In other languages
Català
Deutsch
Español
Français
עברית
Italiano
日本語
Nederlands
Русский
Slovenčina
Српски / Srpski
中文