Abstract, Background, Introduction

 

                Enzymes are catalyst proteins that allow many biological reactions to occur. A living cell constantly has many reactions occurring simultaneously. Each reaction corresponds to a particular cellular function. Many of these reactions could not occur without an enzyme catalyst because if a catalyst was not present the thermodynamical circumstances (pressure and temperature) of a cell would not be sufficient to allow many reactions to occur. Therefore, without the presence of enzymes many biological functions would be impossible.

 

                The scientist Kϋhn created the term enzyme in 1878. Enzyme was created from the Greek words meaning “in yeast”’ due to the popularity of yeast research at the time. The majority of enzymes have the suffix “-ase” and a prefix that usually corresponds to the type of reaction it catalyzes. A catalyst serves the function of lowering the activation energy (Ea) of a reaction. The activation energy is the energy that is required to transform reactant into products.

 

 

            This lowering of activation energy is achieved because the enzyme forms a complex with the reactants. Enzymes are simply catalysts of biological chemical reactions. In general, enzyme catalysts are significantly more efficient than chemical catalysts, and can perform with in a limited range of temperatures and 

atmosphere of pressure.

 

                The following equations are basic representations of the chemical

 reactions of an enzyme and base on the formulation of L. Michaelis and M.L.

 Menten in 1913.

 

The reactant is referred to as a substrate (S). The enzyme (E) complexes with

 the substrate to form an enzyme-substrate complex (ES) at the active site and

 this action catalyzes the substrate’s transformation into the product (P) which is

 then release from the active site. The rate of the formation (ν) of product is equal to:

 

 

To obtain the desired equation the steady state approximation must be assumed

 for the intermediate complex.

 

 

In the above equations KM is the Michelis constant. For most enzyme calculations

 [S]0>>[E]0, so for initial rates the initial substrate concentration can be assumed to be constant. Furthermore, [E]0=[E]+[ES] so that:

 

 

Through the use of substitution the following equation can be obtained:

 

 

In a situation when [S]0<< KM:

 

 

Also if [S]0>> KM the rate is at its highest and does not depend on the

 concentration of the substrate.

 

 

In the combination of two of the past equations the following equation results:

 

 

It can them be converted into:

 

 

This equation reveals that a Lineweaver-Burk plot can be created to obtain the Michelis constant KM and turnover frequency kcat if the initial concentration of the enzyme is known.  The turnover frequency corresponds to the effectiveness on an enzyme, and is the frequency at which the active site of the enzyme makes a product molecule and is equal to kb:

 

 

The effectiveness of an enzyme can also be characterized by the catalytic efficiency ε.

 

For this particular experiment Trypsin-catalyzed hydrolysis of DL-arginine p-nitroanilide hydrochloride (D,L-BAPA):

 

 

By monitoring this reaction by following the production of p-nitro-aniline at 410 nm using a spectrophotometer much information about the reaction can be

obtained. Knowing that the molar absorption coefficient of p-nitro-aniline is 8,800

(1/Mcm) the concentration of the p-nitro-aniline corresponding to each

absorbance can be determined using beer’s law. The concentration of p-nitro-

aniline is proportional to the concentration of the product created. The initial

rates for each run can then be calculated and a plot showing the concentration

of the product as a function of time can be made. A Lineweaver-Burk plot can

also be made to then calculate the  KM and kcat of the reaction.