Introduction

Chemical reactions occur in all living organisms and are responsible for the proper maintenance and function of such organisms. Chemical reactions provide energy and nutrients and perform essential roles in the growth and survival of living systems. However, without any external forces, many of these necessary reactions that occur within cells and tissues would be highly inefficient and would not begin spontaneously. The presence of organic catalysts, known as enzymes, initiate, facilitate, and regulate the vast majority of the fundamental chemical reactions that propel metabolic processes. Most enzymes are proteins and operate by providing an alternate reaction path with a lower activation energy. As a catalyst, though, the enzyme is independent of the reaction that it catalyzes; the enzyme itself does not appear as a substrate or product of the reaction on which it operates. Thus, one can mathematically model enzymatic activity through the observation of substrate and product concentrations.

Invertase (sucrase) is an enzyme vital to the digestion of carbohydrates and can be found in the small intestine and the kidneys. Invertase is classified as a disaccharidase because it hydrolyzes the disaccharide sugar sucrose into the simple sugars glucose and fructose. The following experiment was designed for an introductory biology class to observe and study the time dependent enzymatic action of invertase on sucrose. Measurements of the conversion of the substrate sucrose to the products glucose and fructose provide data to determine characteristics of the enzyme mechanism such as reaction rate and equilibrium constants within the reactionary process.

Procedure

Initially, a sucrose and acetate buffer solution was made, and, to this solution, the enzyme invertase was added. The introduction of the enzyme begins the process of hydrolysis upon the sucrose, and the exact time at which the invertase was added was recorded. Following this recording, the enzyme-substrate solution was agitated to insure uniformity within the solution. Two minutes after the invertase was added, a sample of the enzyme-substrate solution was placed into the presence of a dinitrosalicyclic acid (DNS) reagent. In the presence of a simple sugar such as glucose or fructose, DNS will convert to ANS (3-amino-5 nitrosalicyclic acid), and the reagent causes a ph change that halts the enzymatic reaction. A spectrometer measured the amount of ANS produced, and this measurement is analogous to the amount of product produced from the enzyme mechanism. This process was repeated at time intervals of five, ten, twenty, and forty minutes after the reagent was initially added to the buffer solution.

Results

The DNS conversion results in a color change, and the intensity of this color change reflects the extent of the DNS conversion. The color change was measured in terms of optical density through a spectrophotometer, and these are the following results from twenty different groups from two separate lab sections:

Here are the results presented in graphical form:

By plotting the optical density of the reagent solution against time, a graph is obtained that can be interpreted as the amount of product formed through the enzyme mechanism. By examination, the product concentration in the reagent solution appears to increase in a linear fashion during the first segment of the experiment, and the rate of product formation decelerates before the final measurement forty minutes after the reaction had been initiated. To investigate the accuracy in this inference requires further analysis of the recorded measurements. In particular, if the reaction proceeds according to a linear model then an equation of the form y(t) = (v * t) + c, where y(t) is product concentration at time t, v is reaction rate, and c is initial product concentration, would be able to describe the enzymatic mechanism. Taking the derivative of the previous equation, we obtain dy/dt = v. To test the linear nature of the enzyme mechanism, an analog of derivation is needed because of the experimental data's discrete nature. The slope between two consecutive measurements serves as this analog, and, within a linear model, this slope should be constant against time. Following are tables of the right differences and the slopes of the sets of experimental data:

Analyzing the data, most of the experimental groups approach a constant slope between consecutive observations, and this provides evidence for the inference that the enzyme reaction and product formation proceed in a linear fashion. However, the product formation rate varies widely from group to group, and no single value for reaction rate is approached by all groups. Assuming that the experiments were conducted in identical circumstances, one would expect a form of conformity in laboratory results, but the empirical data does not reflect this conformity. Despite the variances, one other common trait arises from the data; most of the groups, regardless of previous measurements, experienced a deceleration in product formation in the last measurement. In fact, the slopes between the final two measurements ranged from 0 to 0.0458, with most slopes falling within the range between 0.01 to 0.03. The variance for this final measurement is noticeably smaller than the variance in slopes for the other measurements, and the decelerating trend is reflected in all but two groups (Section 1, Groups 2A and 3A are the only groups whose forty minute slope is greater than the twenty minute calculation). From the calculations above, one can obtain an approximation to the reaction rate for invertase, but kinetic laws state that the rate of a reaction vary according to a variety of factors, such as initial concentration and ph, and these factors are not accounted for within the experimental procedure. Other factors not specified within laboratory procedure may account for experimental differences, but without a procedure to test these other factors, one is unable to hypothesize on these other differences. Further experimentation can also attempt to discover a motivation for the leveling effect within the reaction as it reaches its latter stages.