Explain Michalis-Meten Kinetics?

Question

Based on Biomolecules

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).

Enzyme Kinetic Properties :
* Most enzymes follow Michalis - Menten kinetics (>95%)

(FOR MORE INFORMATION PLEASE VISIT:
http://en.wikipedia.org/wiki/Michaelis-Menten_kinetics)

If the [S] is small then the velocity of the reaction is dependent on the [S]
If the [S] is large then the velocity of the reaction is independent of the [S]

Km = Michalis Menten constant
Km is a measure of the affinity that an enzyme has for a given substrate
A high Km = a low affinity
A low Km = a high affinity
Km = [S] at 1/2 Vmax
V = (Vmax)([S]/[S] + Km)

Answer 2

this is a simple meaning

Michalis–Menten Mechanism

*
Enzyme kinetics mechanism

*
Postulates a reversible reaction of the enzyme binding a substrate to form an enzyme substrate complex

*
A substrate is the substance undergoing the reaction

*
Some of the enzyme substrate complex reacts to form products and the enzyme

this is with good examples for your help
Enzyme Kinetics
Enzymes (which are large protein molecules) are nature's catalysts. The vast majority of chemical reactions that keep living things alive are much too slow (without a catalyst) to sustain life. (This is so even though some of the reactions are highly thermodynamically favored.) An example of this is the oxidation of a sugar - say glucose - to give water, carbon dioxide and energy. You can leave glucose open to the air for years without any appreciable oxidation, yet this is one of the reactions that provides the energy to walk and run in daily life. There are diseases caused by the failure of the body to produce a specific enzyme. (For example, phenylketonuria is a disease which arises from the absence of a single enzyme, phenylalanine hydroxylase.)

The Michaelis-Menten mechanism for the catalysis of biological chemical reactions is one of the most important chemical reaction mechanisms in biochemistry. (Maud Menten graduated from the University of Toronto, but she was unable to obtain a university position in Canada because of the exclusion of women from Canadian universities at that time. As a consequence she did her work the United States.)

The Michaelis-Menten mechanism for enzyme kinetics is:

. (1)

E is the enzyme, S is the "substrate" (the molecule on which the enzyme does its work), and ES is an enzyme-substrate complex. (It is presumed that the substrate must somehow bind to the enzyme before the enzyme can do its work.)

We analyze this mechanism as usual. First, we define the reaction rate as the rate of formation of product and write the kinetic equation implied by this mechanism,

. (2)

The enzyme-substrate complex, ES, is a transient species so we set up an equation for its rate of change and apply the steady state approximation,

. (3)

Solve for [ES],

, (4)

and substitute it into the equation for the rate,

. (5)

We might think that we are finished, but there is a complication and some new notation to introduce. First we introduce the Michaelis-Menten constant, KM,

, (6)

so that the rate becomes,

. (7)

Now we must deal with the difficulty that [E] is the concentration of free (uncomplexed) enzyme and this is usually not known. What is known is the total enzyme concentration, [E]o, but

(8)

from which we obtain,

. (9)

The rate becomes, then,

(10).


Define the reaction velocity as v = Rate. So,

. (11)

Note that the reaction velocity, v, is zero when [S] is zero and that the reaction velocity increases as we increase [S]. The reaction velocity reaches a maximum when [S] becomes very large. Define the maximum velocity, vmax, as,

, (12)

then

. (13)

Note that the kinetics of the reaction are characterized by two parameters, vmax and KM. These are the parameters that are usually given in the literature in studies of the kinetics of biochemical reactions.

In order to deal with experimental data we write,

(14)

In an experiment one measures v as a function of [S]. If we plot 1/v against 1/[S] we should get a straight line with slope, KM/vmax and intercept 1/vmax. This gives us both parameters,

. (15)

Enzyme With Inhibitor

Recall the basic Michaelis-Menten mechanism,

. (1)

There are several possibilities for an inhibitor, I, to interfere with this reaction:

. (16)

In words, the inhibitor binds with the enzyme to the exclusion of the substrate.

. (17)

In words, the inhibitor binds to the enzyme-substrate complex and alters the action of the enzyme on the substrate. You can have 1) or 2) or both. We will only work out the first case. The procedure is the same as for the uninhibited Michaelis-Menten mechanism except for an additional term in the expression for the total enzyme concentration and a new transient, EI. The rate is still

, (18)

and we apply the steady state approximation to ES, which leads to

, (19)

and the same rate expression

. (20)

Use the same definition of KM,

, (21)

which leads to,

. (22)

But the enzyme-inhibitor complex is also a transient,

. (23)

giving

. (24)

Now the total enzyme concentration has an extra term

(25a, b)

leading to

(26)

and the rate is

. (27)

vmax is still

(28)

so the reaction velocity becomes

(29)

and then

. (30)

We still plot 1/v against 1/[S] and the intercept is 1/vmax, but the slope is

, (31)

and

. (32)

We must do several different experiments at different [I] to get KM and k'1/k'-1. Note that you can only get the ratio k'1/k'-1 and not the individual k's.

Answer 3

Kinetics capacity flow. i think you're questioning on the subject of the capacity of kinetics. A shifting merchandise has a undeniable quantity of capacity based on the mass of the article blended with the fee the article is vacationing. the quantity of enrgy is caled kinetic capacity and is realeased while the article collides with yet another merchandise. the comparable could be pronounced for a container sitting precariously on a severe shelf. The container has saved or capacity kinetic capacity in it using fact it has the aptitude to fall, while it does fall, it has kinetic capacity that advance on the fee of the mass situations the acceleration of gravity. it incredibly is early, i ought to in all probability clarify extra helpful after a pair coffees.

Answer 4

you mean how to derive it or how it actually works. if your text can't explain it to you enough go talk to your teacher, TA, or get another book

Answer 5

ENZYMES: concepts and kinetics

Enzymes are the catalysts that drive all biochemical reactions:
Enzymes are one of the fundamental factors that elevate life above just a bag of organic chemical reactions. Remember back in organic chemistry where the mere mixing of two reactants did not guarantee that a single reaction would occur. Many times unwanted side reactions took place and the yield of the final desired product was low. In nature this way of doing chemistry is wasteful and inefficient. Enzymes help keep reactions from deviating from the desired path of reactants (r) products and maintain high conversion rates.

These reactions also greatly enhance the rate at which reactions occur and provide the specificity and regulation that is required to keep the various pathways running efficiently. There is no sense in producing a compound that will just accumulate for no apparent reason.

Enzymes can increase the rate of a reaction by more than a million over the spontaneous rate. As seen before, the enzyme carbonic anhydrase can hydrate 105 molecules of CO2 per sec. Compared to the spontaneous rate the enhancement seen in the presence of enzyme ranges from 103--1017 times faster. http://www.worthington-biochem.com/manual/C/CA.html

The six general classes of enzymes.
Most enzymes contain the suffix –ase to identify them as such and are generally named for the substrate they act on, product the produce, or reaction that they catalyze. There are also a few that have historic names that bear no relation to the reaction that they catalyze. Examples of this are plasmin, trypsin, thrombin and others. The enzyme urease acts on the compound urea with the enzyme DNA polymerase I suggests that this protein is involved in the replication of DNA.

There are six types of reactions that have been identified.

1. Oxidoreductases
a. dehydrogenases
b. oxidases
c. peroxidases,
d. oxygenases
e. reductases See Figure 5-1

2. Transferases
a. methyl transeferases
b. kinases

3. Hydrolases (water transferases) See Figure 5-2

4. Lyases See Figure 5-3.
a. synthases

5. Isomerases

6. Ligases
a. synthetases

Specificity enzyme are specific in the reaction that they catalyze as well as in the reactants that they act upon. These reactants are referred to as substrates. Side reactions that lead to the wasteful loss of substrates rarely occurs. This property is said to be reaction specificity.

In the case of proteolytic enzymes, proteases hydrolyze (or break) specific peptide bonds. The amide bond is broken through the addition of water. These enzymes can also hydrolyze esters which is a different yet similar reaction that also requires the addition of water. Depending on the protease selected there are a range of specificities. Those involved in the general breakdown of proteins (such as that which occurs during digestion) there is relatively little specificity. Two digestive proteases, chymotrypsin and trypsin recognize classes of amino acids and then clip the bond on the carboxyl or right side of the preferred amino acid. Other proteases that have very specific functions such as factor Xa or thrombin (both found in the blood coagulation pathway) recognize a sequence of amino acids. Most proteases cleave in the middle of protein sequences and are referred to as endoproteases. There is a much smaller class of proteases that only cleave at the residues at the end of proteins and those few are referred to as exoproteases.

Trypsin K, R or H
Chymotrypsin F, W or Y
Protease V8 E or D
Subtilisin none

Enzyme Kinetics
The substrate is the term used for a chemical reactant that is acted upon by a specific enzyme. It generally remains in solution until it encounters the enzyme that acts upon it. If the enzyme is in an active state the substrate binds to a particular region of the enzyme usually termed the active site. This binding is promoted by specific interactions between certain reactive groups on the substrate and amino acids contained in the binding or active site. The types of interactions usually involve ionic, van der Waals and hydrogen binding. Once the substrate has bound to the enzyme, the two together are referred to as the ENZYME-SUBSTRATE COMPLEX.

in shorthand form: E + S <----> ES

The existence of this intermediate has been documented in a number of ways:

With the concentration of the enzyme held constant, increases in the substrate concentration lead to an increase in velocity only up to a finite point beyond that all of the enzyme sites are saturated and no more ES complex can form.
Spectroscopic analyses have revealed the existence of altered spectra only upon the mixing of the substrate with enzyme
X-Ray and electron micrograph analyses have seen the complex.
Active sites have common features:

the active site takes up a relatively small part of the total volume on an enzyme.
the active site is a three dimensional entity
substrates are bound by multiple weak attractions
active sites are often in clefts or crevices
some substrates bind to a preformed binding site "lock and key" while other trigger a conformational change that generates the binding site--"induced fit"
Kinetics-- Is the monitoring of the conversion of substrate to product with time.

In non-enzymatic or simple chemical kinetics the rate of product production is directly related to substrate concentration.
Since many reactions are reversible an equilibrium will be reached in which the rate of the forward reaction will equal the reverse reaction.
Velocity of product formation:

(v) = dP/dt = k [S]

where [S]= substrate concentration.

This above equation defines a first order reaction the velocity requires only a single reactant such as seen in an isomerase reaction or in the case where on reactant is present in such excess that its concentration does not change significantly. This occurs quite often in biochemistry where water is the second reactant. These occur in many hydrolysis reactions. Under these special cases the reaction is said to be pseudo-first order.

In many other reactions the rate will depend on the concentration all reactants such that one with two substrates going to two products will be called a second order reaction Some examples include:

2A --> P or A + B --> C + D.

For the first case

(v) = dP/dt = k [A]2 .

An enzymatic reaction:

(the following derivation of the Michaelis-Menton eq. borrows generously from the following MIT website : http://esg-www.mit.edu:8001/esgbio/eb/kinetics/MandM.html

With enzyme kinetics one of the big difference between enzyme kinetic and chemical kinetics is that the enzyme forms a reversible complex with the substrate such that

k1 k2
E + S Û ES Û E + P
k-1 k-2

The symbols represent (in our example):

E = enzyme (concentration added)
S = substrate concentration (M)
ES = enzyme-substrate complex
P = product concentration
First consider the initial velocity of the reaction. In this case, there will be a negligibly small amount of product present. ( [P]<5% of [S] is considered negligible). Under these conditions, the back reaction is negligible, that is, k-2[P]= 0 (approximately). The initial velocity is simply:

vo = k2[ES](eq 5-1)

under these conditions which are routinely used by researchers studying enzymes

(using k2 = kcat,which your text prefers, eq 5-1 is:)

vo = kcat[ES] (eq 5-1)

The problem with this equation is that the quantity [ES] cannot be measured. However, [S] (the initial concentration of substrate) is known, [P] (product produced) can be measured, and [E]total (the amount of enzyme added to the reaction) is known.

Now what we can do is use the rate equations plus a few other assumptions to derive an expression for [ES] (which we cannot measure) in terms of quantities which we can measure ([S], [P], and [E]T for total enzyme concentration).

For the purposes of our analysis we will assume "steady state kinetic conditions". That is, [S] and [P] are changing, but [ES] does not change (a constant flux of S "through" the enzyme). Mathematically, this can be written as: d[ES]/dt = 0

Also (from conservation of matter):

[E]tot = [E]free + [ES] eq. 5-2

(the total enzyme is either bound to substrate or free)

Divide vo = kcat[ES] (eq 1) by [E]total to obtain:

Equation 5-3:

Now, since d[ES]/dt = 0, we know that the rate (velocity) of formation of [ES] must equal the rate of breakdown of [ES].

Vformation = k1 [E]free[S] (2nd order rate equation)

Vbreakdown = kcat [ES] + k-1 [ES] = (kcat + k-1) [ES] (Two 1st order rate equations)

k1 [E]free[S] = (kcat + k-1) [ES] (Rates must be equal)

Rearranging, and solving for [ES]:

Equation 5-4:

A new term, called the Michalis constant (Km) is now defined as:

Equation 5-5:

By substituting equation 5-5 back into equation 5-4 we now have:

Equation 5-6:

Now, let us rearrange equation 5-2 to [E]free = [E]total - [ES] and the substitute into equation 5-4, giving:

Equation 5-7:

Then, solving for [ES] gives:

Km[ES] = [E]total [S] - [ES] [S]

(Km + [S])[ES] = [E]total[S]

Equation 5-7a:

And now, substituting in eq. 2

Equation 5-7b:

And now with the introduction of a final definition- which says that if all of the enzyme is saturated with substrate, a maximal velocity (Vmax) will be achieved.

kcat [E]total = Vmax

making a final substitution we arrive at the Michaelis-Menton EQ. 5-8.

Equation 5-8:


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Consider the effect of varying [S] on the rate of reaction of an enzyme.

At low [S], reaction velocity V is proportional to [S], and rate is first order with respect to substrate. However, as [S] increased reaction rate falls off and is no longer proportional to [S], and rate is mixed order. On further increase in [S] the rate becomes constant and independent of [S]. In this range the reaction is zero order, and the enzyme is saturated with substrate. All enzymes show this saturation effect, but they vary widely with respect to the [S] required to produce saturation.

This saturation effect led Michaelis and Menten in 1913 to formulate a theory about the kinetics of enzyme reactions,which accounts for the kinetic properties of very many, but not all enzymes. The critical feature of the M-M model is that a specific ES complex is a necessary intermediate in catalysis. This is the Michaelis equation and Km is the Michaelis constant. Vmax and Km are both constants, which define the

quantitative relationship between initial velocity and [S] for a simple enzyme catalysed reaction. Km is numerically equal to the [substrate] that provides half maximum rate i.e. half Vmax.

--Taken from http://www-biol.paisley.ac.uk/courses/stfunmac/glossary/Michaelis.html

Km values vary widely for enzymes 10-1--10-7 M . See Table 5-1. Remember the Michaelis constant is the concentration of [S] in which half of the active sites are filled. See Figure 5-4. Once this number has been determined the fractional saturation of the enzyme at any concentration can be determined. Km is also related to the rate constants for the individual steps of the reaction. For the reaction shown in equation 5-5 above {Km = (kcat + k-1)/k1}. Under certain conditions these equations become simplified. Take the case where k-1 >> kcat. This means that the breakdown of ES to E + S is very rapid compared to that of the breakdown of ES to E + P. Under these conditions the equation simplifies to:

Km = k-1/k1 = ([E] [S])/[ES]

Under these conditions, Km = the dissociation constant (Kd) for the ES complex. Under these conditions a high Km (0.1 M) signifies a weak binding interaction and a low Km (10-6 M), a tight binding interaction.

The turnover number -- is the number of conversions of a substrate to product per unit time. This is usually express as molecules/sec. This number is kcat. One usually solves for kcat using the following relationship:

Vmax = kcat [ET] or kcat = Vmax/ [ET]

where Et is the total concentration of enzyme active sites. This value is often used to evaluate the rate enhancement of the catalyzed reaction over that of the non-catalyzed reaction. See Table 5-2 Also not all enzymes have the came catalytic ability. Turnover values are a good way to compare different enzymes (see Table 5-3.

Kcat/Km Criterion
When [S] >> Km the rate of catalysis is equal to kcat . However under most biological conditions such saturating levels of substrate are not the normal condition. More often [S] is between 0.01Km and 1 Km. Under the condition where [S] << Km the enzymatic rate is less than kcat because only a small fraction of the active sites are filled. See Figure 5-5

Now by combining the previously derived equations

V0 = kcat [ES] and [ES] = [E] [S]/Km

we get V0 = [E] [S] x kcat /Km

One can simplify the eq farther when[S] << Km and replace [E] with [ET] because essentially all of the enzyme is free. So under these conditions velocity is dependent on kcat/Km and [S].

Another thing to remember is that the rate of reaction can not exceed the rate of diffusion, which is the rate at which the substrates move within the cell. This number turns out to be 108--109 M-1sec-1 and represents the theoretical limit for kcat/Km. . It has been shown for some enzymes (carbonic anhydrase, acetylcholine esterase and triosephosphate isomerase)that kcat/Km = 108--109 indicating that they have reached the highest level of catalytic evolution. The process in these enzymes is now said to be maximized because of the limitation imposed by the rate of diffusion.

How to experimentally determine the different kinetic parameters:

Equation.5-8

If you were to use equation 5-8 directly and plot velocity verses substrate concentration for a given substrate concentration you would get a curve similar to that shown in Figure 5-4. It is extremely difficult to determine the instantaneous velocity at a given concentration of substrate from this type of continuous curve. The Michaelis-Menton Eq. can be rewritten such that a linear plot (y = mx + b) can be derived. The most famous for of this eq is known as the Lineweaver-Burk plot. Taking the inverse of each side one obtains:

Equation 5-9

Then separating terms you expand the equation to :

Equation 5-10

And then simplifying the equation you obtain the Lineweaver-burk plot equation.

Equation 5-11
Equation for line y = m x + b

Setting 1/v0 = y and 1/[S] = x you get a line with a slope = Km/Vmax, a y-intercept = 1/ Vmax and an X-intercept = -1/Km. see Figure 5-6.

Other forms of this equations have been developed and are also used for determining the various kinetic parameters.

Woolf Plot eq



Eadie-Hofstee eq

These last two plots have advantages over the Lineweaver-Burk equation in the way that the data is weighted. These last two plots give better and more reliable values for the values of Km and Vmax.



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Multi-substrate Reactions:

Up until now we have been discussing simple single substrate reactions. Here a single substrate is acted upon (such as in an isomerase reaction) or the second substrate has been water (e.g. hydrolases), where at a concentration of 55 M, it can be ignored because it is always saturating the enzyme active site. Much more common are reactions in which multiple substrates are brought together and combined.

There are two basic types of multisubstrate kinetic mechanisms:

Sequential (with two subtypes)

Ordered

Random

Here all of the substrates have to bind before products are generated.

2. Ping Pong

Here products can be released before all substrates have been bound.
See Figure 5-7 for examples of these mechanisms.


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Enzyme inhibition

As we have seen above enzymes work rather inefficiently when substrate concentrations are low. This prevents enzymes from depleting substrate stores to zero. This is important because some of these molecules are required in other pathways.

A second method of shutting down enzymes is through the use of inhibitors. If the inhibitor is so strong we term it a poison because it essentially blocks an entire pathway and this can have devastating consequences. There are two classes of inhibitors reversible and irreversible. The irreversible ones generally bind so tightly to the enzyme that they never dissociate. Some irreversible inhibitors can even form stable covalent bonds that block various sites on the enzyme.

An example using diisopropylphosphofluoridate (DIFP) binding to the active site serine in the enzyme acetylcholinesterase. This poison binds irreversible and completely inhibits an enzyme that is essential for neural transmissions. This poison in fact binds irreversible to any hydrolytic enzyme that contains an active site serine (ie trypsin, plasmin, elastase ....)

Reversible inhibitors come in three types: competitive, non-competitive and mixed. All of these inhibitors associate and dissociate from the enzyme in response to their cellular concentration. At high inhibitor concentration the enzyme is usually shut down but as the concentration of the inhibitor decreases the enzyme regains activity as the inhibitor diffuses away from the enzyme.

In competitive inhibition-- the enzyme can bind either substrate or inhibitor but not both so either ES or EI will form but not ESI. Competitve inhibitors tend to be substrate analogs that bind directly to the active site and prevent the binding of substrate. Here the effect of the inhibitor can be overcome by increasing the substrate concentration.

In non-competitive inhibition-- the inhibitor and the enzyme can bind simultaneously due to the fact that the inhibitor and substrate bind at different sites. This inhibitor acts by decreasing the number of turnovers. In this case increasing concentrations of the substrate have no affect on the inhibition

See Figure 5-8 for a cartoon showing how competitive and non-competitive inhibitors might interact with an enzyme.

Mixed inhibition is rather complex and has components that are a consequence of both competitive and non-competitive inhibition

The three forms of inhibition can be determined experimentally by plotting 1/V versus 1/[S] in the presence and absence of inhibitor. For competitve inhibition the two lines (plus and minus inhibitor) intersect on the Y axis. Remember that these are inverse plots and the highest concentrations have the lowest values. This curve confirms that for

competitive inhibition at the highest substrate concentration the inhibitor has little or no effect and hence Vmax remains the same.

The equation used to calculate the binding affinity for a competitive inhibitor is:

1/V = 1/Vmax + Km/Vmax x (1 + [I]/Ki) (1/[S])

remembering that E + I <---> EI

so that Ki = [E][I]/[EI]

Under these conditions the slope of the line increases b y the factor (1 + [I]/Ki) (see Figure 5-9)

In non-competitive inhibition Km is unchanged and Vmax decreases to a new value VImax. The maximal velocity attained under these condition is given by:

VImax = Vmax/1 + [I]/Ki

Under these conditions no increase in substrate concentration will alter the inhibition of the enzyme. See Figure 5-10.
See table 5-4 for a summary of inhibition effects on enzymes.



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Enzyme regulation:

One of the truly marvelous properties of cells is their ability to tightly control many of the enzymatic pathways. Since most biochemical syntheses require multiple steps with multiple enzymes, not all of the enzymes need to be regulated. Blocking production of the substrate for the subsequent step in the path is a most efficient method of blocking a pathway. As mentioned before substrate concentrations in cells are generally well below Km. The key steps that are usually blocked are the first enzymes or enzymes found at branch points in pathways See diagram below.





The cell approaches this problem from two sides. 1) It can make or destroy an enzyme, which in many ways is a slow process—possibly requiring RNA and/or peptide synthesis. Or 2) the enzyme activity can be modulated by one or more cofactors, substrates or products. These enzymes have so-called regulatory sites on them to allow for this much more rapid and energy efficient method of regulation.

Your text describes how the bacterial form of the enzyme phosphofructo-kinase-1, (PFK-1). This enzyme is one of the key regulatory enzymes in the glycolytic pathway.(see Chapter 12) This is a multi-subunit enzyme (tetrameric—see text figure 5-21b) that exhibits allosteric inhibition or activation. This type of regulation is very similar to the cooperativity seen upon the binding of oxygen to hemoglobin (which was covered in chapter 4). It does not follow classical Michaelis- Menton kinetics.

This is a key enzyme in the break down of the six carbon sugar, glucose, which ultimately leads to the production of energy. The cells main source of energy is ATP, which will be discussed in detail in Chapter 7. The basic energy cycle that influences this pathway is shown below.






When energy reserves are low ADP levels are elevated. At high concentration of ADP, ADP binds to the regulatory site of PFK-1 and activates the enzyme by lowering the Km for the substrate Fructose 6- phosphate. Therefore ADP is a positive allosteric effector. See Figure 5-11.

A metabolic generated down stream from PFK-1, is the three carbon compound called phosphoenolpyruvate (PEP) (see text, page 138, for illustration). High concentrations of this compound, signify that the pathway is saturated and needs to slow down. This compound acts as a negative allosteric effector. Together ADP and PEP modulate how much glucose is allowed to enter into the glycolytic pathway. See Figure 5-12 for how these allosteric effectors alter enzyme activity.