Michaelis Menten equation represents aEnzymatic reactionThe velocity equation of the relationship between the initial velocity and the substrate concentration.[1]
stayEnzymatic reactionMedium, at low concentrationsubstrateIn this case, the reaction isFirst order reaction（first order reaction）；When the substrate concentration is in the middle range, the reaction (relative to the substrate) is mixed order reaction.When the substrate concentration increases, the reaction changes from the first order reaction toZero order reaction(zero order reaction) Transition.
）The unit is usually mol/L, which is only determined by the nature of the enzyme, but not the concentration of the enzyme.available
Value to identify different enzymes.
When the substrate concentration is very high,reaction rate Close to a constant value.In this region of the curve, the enzyme is almostsubstrateSaturation, the reaction is aZero order reaction。That is to say, adding more substrate has no effect on the reaction speed.
The constant value that the reaction speed gradually approaches is called the maximum reaction speed
。For a given amount of enzyme
It can be defined as the initial reaction rate n at the saturated substrate concentration.aboutreaction curveThis fakeFirst order reactionThe velocity equation of the zone can be written in an equivalent form:
N (when saturated)=Vmax=k[E][S]0=k[E]total=kcat[ES]
The velocity constant k is equal toCatalytic constantK cat, k cat is the rate constant of ES conversion to free E and product.When saturated, all E exists as ES.There is another simple relation in equation (3.2): Vmax=kcat[E]total。It can be concluded that: kcat=Vmax/ [E]total。kcatThe unit of is s-1.The catalytic constant can measure the speed of an enzymatic reaction.
Is the substrate concentration when the enzymatic reaction rate n is half of the maximum enzymatic reaction rate value.This can be achieved by substituting [S] for
It is proved that n=V can be obtained through calculationmax/2。
Equation derivation
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Build model
In 1913, Michaelis L. and Menten M. proposed the single substrate enzymatic reaction based on the intermediate complex theoryQuick balancing modelorEquilibrium model(equilibrium state model), also known asMie Mann model（Michaelis-Menten model）：
In the formula, E is an enzyme, S is a substrate, ES is an intermediate complex, and P is a product,
It's ESDissociation constant, that is, the rate constant in the reverse reaction of the first step
And forward rate constant
Ratio
，
Is the catalytic constant, that is, the forward rate constant in the second step
。
Model Assumptions
When building the model and deriving the rate equation of the model, they actually made the following assumptions:
① For simplicity, assume that there is only one intermediate complex in the reaction, the first step of the reaction
It is a reversible reaction and remains constant;
② The second step of the reaction
Is the speed limit step, here is the speed limit step, here
That is to say, the rate of ES decomposition to generate P is not enough to break the fast balance between E and ES;
③ To achieve equilibrium, only the initial substrate concentration [Szero]A small part of, because generally [Szero]>>[Ezero](initial enzyme concentration), so at the initial stage of the reaction, the substrate concentration [S] can be used as [Szero]Replace, or treat [S] as [Szero] ；
④ The enzyme is not consumed in the reaction, but exists in free form E or in combined form ES, so the concentration of free enzyme [E] and the concentration of intermediate complex [ES] are only equal to the initial enzyme concentration [Ezero]Or total enzyme concentration [Et], that is, [E]+[ES]=[Ezero]=[Et], this is the so-calledEnzyme conservation formula（conservation equation of enzyme）；
⑤ This model does not consider
This reverse reaction, but obviously k-2Is a constant that is not equal to zero. To ignore this step, it is necessary to make [P] close to zero, so the Mie Mann equation is only applicable to the initial rate of reaction.
Derivation process
According to the equilibrium state model, the total rate of transformation from S to P should be determined by the rate limiting reaction (the second step in the model), so the product formation rate
The concentration of ES complex [ES] is not easy in experimentdeterminationIt is necessary to find out other parameters that are easy to determine (such as certain constants and known
And so on).Therefore, the dissociation constant of ES to E and S in the first step reaction (fast equilibrium) is used[2]
be
The enzyme conservation formula
Substituting into the above formula
Collated
Substitution
have to
here
It has special significance.When the substrate concentration [S] is high enough to saturate all enzyme molecules
, initial rate of reaction
Will reach the maximum value,
It can be expressed as
therefore
It can also be written as
Model improvement
The first two assumptions in the equilibrium model are not universal, especially there is no reason to think that all enzymatic reactions
Are much smaller than
。Therefore, Briggs G. E. and Haldane J. B. S. proposed amendments to the model in 1925, but still retained the last three points of the Mie Mann hypothesis.They use the steady state model orBriggs Haldane model:
It replaces the equilibrium model.For the observed initial velocity rate (that is, when the product P has not been generated or is rarely generated), it can still be ignored in the formula.The so-called steady state refers to a period of time when the reaction fails (incidentally, within a few milliseconds, the state of this period is calledPrestable state）In the system, [ES] increases from zero to a certain value. In a certain time, although [S] and [P] are constantly changing, and the ES complex is also constantly generating and decomposing, the generation rate of ES
And decomposition rate
Nearly equal, [ES] basically remains unchanged.So the net rate of ES formation under steady state,
because
And
therefore
Tidied up
Here, the rate is the ratio of constants
It is also a constant and is defined asMichaelis constant（Michaelis constant），
：
take
Substitution
, sorted out as:
According to the steady state model, the rate at which S changes to P depends on the steady state concentration [ES] and the rate constant of speed limit
。therefore
take
Substituting the above formula, we get
or
The rate equations derived from the two models are the same in form, but the difference is
than
It has greater universality.In steady state, when
When, then
Therefore, the equilibrium state can be regarded as a special case of steady state.In memory of Michaelis and Menten, the above equations with triangular symbols are calledmichaelis-menten equation （Michaelis-Menten equation）。
Parameter meaning
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① When
When,
。Therefore, Km is equal toSubstrate concentration。
② When
When,
=Ks。Therefore, Km can reflect the affinity between enzyme and substrate, that is
The lower the value, the greater the affinity between the enzyme and the substrate;On the contrary, it is smaller.
③
Can be used for judgmentReaction order: When [S]<0.01Km, ν=(Vmax/Km) [S], the reaction isFirst order reactionThat is, the reaction rate is proportional to the substrate concentration;When [S]>100Km, ν=Vmax, the reaction isZero order reaction, i.ereaction rate It is independent of substrate concentration;When 0.01Km<[S]<100Km, the reaction is between the zero order reaction and the first order reaction, which is a mixed order reaction.
④
Is the characteristic constant of an enzyme: under certain conditions, the Km value of an enzyme is constant, so it can be determined by measuring different enzymes (especially a group ofisozyme）To determine whether it is a different enzyme.
⑤
It can be used to judge the optimal substrate of the enzyme: when the enzyme has several different substrates, the one with the smallest Km value is the enzyme'sOptimum substrate。
⑥
It can be used to determine the substrate concentration required for enzyme activity determination: when [S]=10Km, ν=91% Vmax, which is the most appropriate substrate concentration for enzyme activity determination.
⑦
Available forEnzyme conversion numberCalculation of: When the total concentration and maximum speed of the enzyme are known, the conversion number of the enzyme can be calculated, that is, the number of molecules of each enzyme molecule that catalyzes the conversion of substrate into product in unit time.
Values can be measured in several ways.Fixed reactionEnzyme concentrationAnd then analyze the initial velocity under several different substrate concentrations to obtain
and
Value.But it is directly determined from the graph of initial velocity versus substrate concentration
or
Values are difficult because the curve is close to
Time is a gradual process.So we usually use the transformation form of Michaelis' equation to get
and
Value.The commonly used transformation form of Mie equation isLineweaver Burk equation, also called doubleReciprocal equation。
If 1/v is plotted against 1/[S], a straight line can be obtained.From the intercept between the line and the x-axis, 1 can be obtained/
Absolute value of;1/Vmax is the intercept between the line and the y-axis.Double reciprocal drawingIntuitive and easy to understand, providing easy to recognize graphics for enzyme inhibition research.
Disadvantages: When the substrate concentration is low, the coordinate points are concentrated at the bottom left of the coordinates, which increases the error and often deviates from the straight line,
、
It cannot be precisely determined.
Solution: The substrate concentration is matched to a concentration gradient of 1/[S] instead of a concentration range of [S], so that the distance between the points is averaged, and then the least square method is used for linear regression analysis.
inhibition
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Competitive inhibition
The value increases,
Value unchanged
Non competitive inhibition
The value remains the same,
Value becomes smaller
Anti competitive inhibition
The value becomes smaller,
The value decreases, but
The value does not change.
Other influencing factors
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1. Effect of Substrate Concentration on Enzymatic Reaction Speed
When the substrate concentration is very low, there are redundant enzymes that do not bind to the substrate. With the increase of substrate concentration, the concentration of intermediate complexes increases continuously.
When the substrate concentration is high, all enzymes in the solution combine with the substrate to form intermediates. Although the substrate concentration is increased, no more intermediates will be generated.
2. Effect of temperature on enzyme reaction rate
On the one hand, the temperature increases and the speed of enzymatic reaction accelerates.On the other hand, the higher structure of the enzyme will change or denature with the increase of temperature, leading to the decrease or even loss of enzyme activity.Therefore, most enzymes have an optimal temperature.Under the optimum temperature, the reaction rate is the highest.
3. Effect of pH value on enzyme reaction rate
The speed of enzymatic reaction is affected by the pH of the medium. When measuring the activity of an enzyme in several pH mediums, it can be seen that the enzymatic efficiency is the highest at a certain pH, which is called the optimal pH of the enzyme.The existence of the optimal pH for enzyme action indicates that the ionization state of the active group of the enzyme molecule, the ionization state of the substrate molecule and coenzyme and coenzyme are all related to the catalytic action of the enzyme, but the optimal pH of the enzyme is not the characteristic constant of the enzyme, such as the type and concentration of buffer solution, substrate concentration, etc. can change the optimal pH for enzyme action.
4. Effect of activator on enzyme reaction rate
All substances that can improve enzyme activity are called activators.
(1) Inorganic ion: metal ion (K+、Na+、Mg2+、Zn2+、Fe2+、Ca2+）Anion (Cl-、Br-）, hydrogen ion.
(2) Medium sized organic molecules: some reducing agentsEDTA(EDTA)
5. Effect of inhibitors on enzyme action
A substance that changes the chemical properties of the essential group or group in the active site of an enzyme, thereby reducing the activity of the enzyme or even inactivating the enzyme, is called an inhibitor.
(1) Irreversible inhibition: the combination of inhibitor and enzyme (covalent bond) is an irreversible reaction. After the combination of inhibitor and enzyme, the inhibitor cannot be removed by dialysis and other methods to restore the enzyme activity.asDiisopropyl fluorophosphoric acidyesChymotrypsinOr acetylcholinesterase;Iodine acetic acid, iodoacetamide, paraChloromercuric benzoic acidParathiolase.
(2) Reversible inhibition: the combination of inhibitor and enzyme is a reversible reaction, and the inhibitor can be removed by dialysis and other methods to restore enzyme activity.It can also be divided into competitive inhibition andNoncompetitive inhibition。
Competitive inhibition refers to that some inhibitors are very similar to the substrate in structure and can compete with the substrate to combine with the enzyme. When the inhibitor combines with the enzyme, it will hinder the combination of the substrate and the enzyme, reduce the opportunity of the enzyme, and thus reduce the activity of the enzyme.It is characterized by that when the substrate concentration is increased, the probability of substrate and enzyme binding is increased, and the inhibition will be weakened if the combination of inhibitor and enzyme is reduced.
Non competitive inhibition means that some inhibitors and substrates can bind to different parts of the enzyme at the same time, that is, after the inhibitor binds to the enzyme, it does not prevent it from binding to the substrate, but the formed enzyme substrate inhibitor ternary complex (ESI) cannot react.High concentration of substrate could not reverse the inhibitory effect.[3]
