Catalysts in biochemical reactions

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Enzyme is a class of proteins that function as catalysts in biochemical reactions. On their Characteristics is that they increases the rate of reactions by several orders of magnitude A very dramatic example of enzyme kinetics is given by decomposition of hydrogen

Peroxide. Enzymes are usually protein molecules that manipulate other molecules — the enzymes' substrates. These target molecules bind to an enzyme's active site and are transformed into products through a series of steps known as the enzymatic mechanism. These mechanisms can be divided into single-substrate and multiple-substrate mechanisms. Kinetic studies on enzymes that only bind one substrate, such as triosephosphate isomerase's, aim to measure the affinity with which the enzyme binds this substrate and the turnover rate.

When enzymes bind multiple substrates, such as dihydrofolate reductase (shown right), enzyme kinetics can also show the sequence in which these substrates bind and the sequence in which products are released. An example of enzymes that bind a single substrate and release multiple products are proteases, which cleave one protein substrate into two polypeptide products. Others join two substrates together, such as DNA polymerase linking a nucleotide to DNA. Although these mechanisms are often a complex series of steps, there is typically one rate-determining step that determines the

Overall kinetics


Reaction rates increase as substrate concentration increase, but become saturated at very high concentrations of substrate.The reaction catalyzed by an enzyme uses exactly the same reactants and produces exactly the same products as the unanalyzed reaction. Like other catalysts, enzymes do not alter the position of equilibrium between substrates and products. However, unlike uncatalysed chemical reactions, enzyme-catalysed reactions display saturation kinetics. For a given enzyme concentration and for relatively low substrate concentrations, the reaction rate increases linearly with substrate concentration; the enzyme molecules are largely free to catalyze the reaction, and increasing substrate concentration means an increasing rate at which the enzyme and substrate molecules encounter one another. However, at relatively high substrate concentrations, the reaction

rate asymptotically approaches the theoretical maximum; the enzyme active sites are

almost all occupied and the reaction rate is determined by the intrinsic turnover rate of the enzyme. The substrate concentration midway between these two limiting cases is denoted by KM.[2]


  1. Enzyme-catalyzed reactions are characterized by the formation of a complex between the enzyme and its substrate (the ES complex).
  2. Substrate binding occurs in a pocket on the enzyme called the active site. Enzymes accelerate reactions by lowering the free energy of activation G‡.The equilibrium of the reaction remains unaffected by the enzyme do this by binding the transition state of the reaction better than the substrate….[3]


The rate of reaction is estimated to be 1/100000000 /m /s in the absence of a catalyst .this could very well be the upper limit since one can never be certain of avoiding the catalytic action of dust particles. In the presence of catalyses an enzyme found in the never and other organs, the rate of the reaction is 10000000/m/s

Another important characteristic of enzyme kinetics is specifilty.for example, enzyme urease catalysis the decomposition of urea to ammonia and carbon dioxide but it found to been effective in other reaction. Enzyme is a class of reaction, and their name usual reflect this aspect of the chemistry………..

Particular classes of reaction common in biochemistry have the form:


Where a compound s (usually called the substate) is transformed to a product p, under the

Influence of an Enzyme. Since an enzyme is specific to a class of substrates, it is responsible to assume that a complex is formed between the enzyme E and substate: 4)

E+S -------àES (COMPLEX)


In 1913 L.Michalis and M.L.Menten proposed a mechanism of enzyme action that involves equllibirum among the enzyme ,the substate , and the complex ES.G.E .Briggs and J.B.S Haaldane showed that the michaelis -mentaen mechanism with less restrictive steady state hypothesis for ES ,leads to a correct rate law .Consist of an enzyme binding to a substate to form a complex which dissocites to give either the product or the substate:


The kinetics of single-substrate enzyme-catalysis. The interactions between enzymes and substrates are often difficult to understand and the model allows users to visualize the complex reaction.

The standard equation for this reaction is shown below:

Kc Kr
E + S <=======> E-S ------> + P

At the concentration of P is zero ,and thus there is no back reaction.the intial rate of formation of the product is there given by :


vo = ------ = k3 [ES]


According to steay state approximation,

D [ES]

------- = 0 = - (k2+k3)[ES]+k1[E][S]


Michaelis-Menten equation the conc. Of enzyme at a given time is related to this intial conc. [E]o by

[E] = [E] - [ES]

(Free) (Intial) (Bound)

This assumption implies that each enzyme molecule provides one side in binding of the substate ……

[ES] = K1[E]o[S]


K2+ K3+ K1[S]

From steady state conc of ES:

VO = K3K1 [E]o[S]


K2+K3+ K1[S]

For intial rate .this equation is frequently written as :

Vo = k3[E]o[S]


Km+ [S]


Km = k3+ k2



Is called the Michaelis constant.

Let us consider the case of [S]>Km

Vo =k3 [E]o = vm (2)

The intial concetation of enzyme is also its maximum concentration .hence the intial velocity with a large substate conc. must be the max. Velocity Vm.

The reaction is zero order reaction in substreateconc. This property of enzyme was first observed by A.Brown in 1903 , while studying the enzymatic hydrolysis of sucrose. The rate substate molclules converted is called turnover number because it is equal to no of substrates.[4]


The turnover no for catalase, which catalyzes the decomposition of hydrolysis peroxide is 5.. The volume of oxygen generated during 1 s when 0.10g of catalyse is added to excess hydrogen peroxide.the reaction peroxide isothermally at 300K . The molar mass of catalyse is 60,000 Daltons



------- = 0.5 k3[E]o



This corresponds to 100 L of O2 per second![5]

The bombardier bettle uses this reaction effectively dense it carries a 25% solution of

hydrogen peroxide in a sack and when threatened triggers the above reaction …the

Sudden release of oxygen rapidly heats to a high temp ,making it possible for bettle to

Spray the enemy with near boiling water.[6]

At low concentration [S] <Km and we have

Vo = Vm



This indicates that the reaction is first order reaction in substrate show how the velocity

of the reaction changes as a function of substate concentration. The order of the reaction

changes from one to zero as the substrate concentration increases If k3<k2 the Michalies

Binding….the largest Michaels constant, the smaller the velocity constant is measure

The equllibirum constant for enzyme substrate bindings. the large the Michelins constant,. the smaller the velocity…..[7]

Variation in the intial rate of enzyme kinetics reaction as a function substrate concentration:

Significance of KM

When [S] = KM, then V=Vmax/2. Hence KM is equal to the substrate concentration at which the reaction rate is half its maximum value. In other words, if an enzyme has a small value of KM, it achieves its maximum catalytic efficiency at low substrate concentrations. Hence, the smaller the value of KM, the more efficient is the catalyst. The value of KM for an enzyme depends on the particular substrate. It also depends on the pH of the solution and the temperature at which the reaction is carried out. For most enzymes KM lies between 10-1 and 10-7 M.[7]

Determining KM and Vmax experimentally

To characterize an enzyme-catalyzed reaction KM and Vmax need to be determined. The way this is done experimentally is to measure the rate of catalysis (reaction velocity) for different substrate concentrations. In other words, determine V at different values of [S]. Then plotting 1/V vs. 1/[S] we should obtain a straight line described by equation (18). From the y-intercept and the slope, the values of KM and Vmax can be determined. For example, use EXCEL to plot the data shown below. Fit the data to a straight line, and from the equation of the straight line determine the values of KM and Vmax.[8]


The ES Complex break then to release the product and free enzyme:

E+ S………K1……>ES…K3……>.P+E

The rate is given by:

D[ES]/dt = k1([E]-[ES])[S]

-d[ES]/dt = k2[ES] + K3[ES]

At equallibrum two rates rep by th above equation

K1([E] - [ES] = K2 [ES] + K3[ES]

Rearrange the equation:

[S][E] -[ES] K2+K3

……………. = ……….. = Km

[ES] K1

Km is called Michaelis constant.

[ES] == [E][S]


Km + S

Since intial rate v of enzyme is proposal to ES

V == k3[ES]

Vmax == k3 [E]

We can written also:

V = k3 = [E][S]


KM + [S]

IN this reaction to use the final reaction is:

V = Vmax [S]

……….. [9]

Km + [S]



Ternary-complex mechanisms:

Random-order ternary-complex mechanism for an enzyme reaction. The reaction path is shown as a line and enzyme intermediates containing substrates A and B or products P and Q are written below the line.

In these enzymes, both substrates bind to the enzyme at the same time to produce an EAB ternary complex. The order of binding can either be random (in a random mechanism) or substrates have to bind in a particular sequence (in an ordered mechanism). When a set of v by [S] curves (fixed A, varying B) from an enzyme with a ternary-complex mechanism are plotted in a Line weaver-Burk plot the set of lines produced will intersect.

Enzymes with ternary-complex mechanisms include glutathione S-transfer dihydrofolate reductase and DNA polymerase The following links show short animations of the ternary-complex mechanisms of the enzymes dihydrofolate reductase and DNA polymerase.

2) Ping-pong mechanisms

Ping-pong mechanism for an enzyme reaction. Intermediates contain substrates A and B or products P and Q.

As shown on the right, enzymes with a ping-pong mechanism can exist in two states, E and a chemically modified form of the enzyme E*; this modified enzyme is known as an intermediate.. In such mechanisms, substrate A binds, changes the enzyme to E* by, for example, transferring a chemical group to the active site, and is then released. Only after the first substrate is released can substrate B bind and react with the modified enzyme, regenerating the unmodified E form. When a set of v by [S] curves (fixed A, varying B) from an enzyme with a ping-pong mechanism are plotted in a Lineweaver-Burk plot, a set of parallel lines will be produced.[13]

Enzymes with ping-pong mechanisms include some oxidoreductases such as thioredoxin peroxides, transferases such as acylneuraminate cytydilyltransferase and serine proteases such as trypsin and chymotrypsin Serine proteases are a very common and diverse family of enzymes, including digestive enzymes (trypsin, chymotrypsin, and elastase), several enzymes of the blood clotting cascade and many others. In these serine proteases, the E* intermediate is an acyl-enzyme species formed by the attack of an active site serine residue on a peptide bond in a protein substrate.[14]

3) RNA as an Enzyme:

Although enzymes are considered to be proteins, enzyme activity has recently been found in ribonucleic acid (RNA) in certain organisms. These "ribozymes" may yield clues to the origins of life on Earth. DNA needs enzymes to replicate, whereas enzymes need the instructions of DNA. This represents a "chicken-and-egg" question that has stumped researchers. Early life may have used RNA that was able to catalyze its own replication.


Since enzymatic reactions are so important to biological chemical reactions, it is of great interest to be able to model them. By use of the study of chemical kinetics, it is possible derive rate equations for the steps involved in an enzymatic reaction. These rate equations are differential equations and can be used to model the concentrations of each compound in the system. However, this system of differential equations is hard to determine experimentally because of the difficulty of determining the rate constants. By use of the Quasi-Steady-State Assumption, we can turn our system of differential equations into the Michaelis-Menten enzyme equation. Many benefits stem from this transition. One benefit is the fact that it is now easy to determine the constants related to the enzyme equations. However, how do we know the Quasi-Steady-State Assumption is valid? It seems reasonable from a physical argument. By use of dimensional analysis, we can give a more rigorous mathematical argument for the Quasi-Steady- State Assumption. The Michaelis-Menten enzyme equation is very important in the study of cellular