## INTRODUCTION

The kinetics of an enzyme reaction, which describe the ability of the protein to bind to substrate(s) and catalyze the reaction, are fundamental properties of this type of biomolecule. Enzyme behavior was first described by the separate work of Henri and Michaelis and Menten (1). The latter pair is broadly recognized as mathematically describing enzyme behavior with their eponymous equation (1,2). This early treatment of enzyme kinetics assumed a rapid equilibrium between the enzyme and substrate. Briggs and Haldane then added the steady-state approximation to this Michaelis-Menten equation, which is now widely used to describe enzyme catalysis and how it is altered through mutations or changes in enzyme environment (1). Examples of practical applications of enzyme kinetics are in enzyme evolution to measure the improvement in catalytic efficiency in engineered enzymes and in the pharmaceutical industry to determine the effects of an inhibitor on a potential drug target.

Despite the important role of enzyme kinetics for our understanding of biochemistry and the inclusion of this topic in introductory biochemistry and molecular biology courses, we find that students still struggle with the conceptual basis for V_{max}, K_{M}, and how to determine these values. Previous approaches to address aspects of this issue have used analogies (3), Pop-it beads (4), coins (5), beans (6), marbles (7), and unscrewing bolts-nuts (8) to have students visualize aspects of kinetics. Even further, there are demonstrations using actual enzymatic reactions in the classroom (9). One limitation of some of these demonstrations is the reliance on moving an object from one location to another, which can obscure from the students the chemical transformations that the enzymes perform. In other cases, the absence of using initial rates for enzyme kinetics can lead to a disconnect between using steady-state/initial velocities and the calculation of kinetic parameters. While much of this can be demonstrated in a lab, biochemistry labs are not required in all cases. Thus, there is an opportunity for further development of these early demonstrations to more completely illustrate enzyme kinetics.

The series of lessons described here build on these previous demonstrations through the use of three linked activities to show how the use of initial rates leads to construction of a saturation curve and a quantitative description of enzyme catalysis. In these activities, we teach enzyme kinetics by having students act as enzymes and unwrap candy to visualize enzyme behavior. These activities demonstrate the need to measure initial rates and the effect of candy concentration (substrate) on the rate of unwrapping. Students then learn to estimate kinetic values from their data and then fit the data in Excel/Sheets to calculate better kinetic values.

#### Intended Audience

The primary author (Berndsen) teaches this set of lessons at a mid-sized, public PUI in an introductory biochemistry course, which surveys the discipline in a single semester. The class population ranges from 50 to 110 students with a typical number being 80 students. Entry into the course requires two semesters of general chemistry and one semester of organic chemistry. The student population is typically composed of basic science majors and health science majors.

Early versions of this lesson have also been performed with first-year students in medical school biochemistry at a large public research university and in an introductory biology course with first-year college students at a liberal arts college. While not tested by these authors, the activities and lessons require little prior knowledge of chemistry and kinetics, thus this activity could be performed in a high school setting.

#### Required Learning Time

These lessons are taught over two 75-minute sections with the data fitting activity performed as homework, taking about two hours for most students. It is possible to expand these lessons across three periods or abbreviate them into a single 50 minute period.

#### Prerequisite Student Knowledge

Students should understand that chemical rates are measured using kinetics, that enzymes accelerate reaction rates or kinetics, and how to estimate values from a plot. It is helpful if students are able to plot data and perform calculations within Microsoft Excel with guidance, however this is not required.

#### Prerequisite Teacher Knowledge

The teacher should be familiar with enzyme kinetics and the experimental design used to measure initial rates, V_{max}, and K_{M}, and they should be proficient in Microsoft Excel.

## SCIENTIFIC TEACHING THEMES

#### Active Learning

Students will play the part of enzymes unwrapping candies, physically demonstrating the action of enzymes in two distinct activities. Following the demonstration, students typically work in groups to analyze their data and then discuss their findings as a class. After the second lesson, students work outside of class to fit the saturation curve data to reinforce how kinetic parameters are determined.

#### Assessment

Students were assessed based on the homework assignment showing the data fit and their explanations of those data. Further assessment came via questions from an in-class exam and the cumulative course final exam asking students to analyze kinetics data.

#### Inclusive Teaching

The interactive demonstrations allow students to observe and describe enzyme function in a way that breaks from the traditional lecture or lab didactic style where enzymes are invisible entities. By acting as enzymes, it incorporates a physical connection to the material, which engages students through additional routes. Some of the work is done in small groups with several roles (enzyme, scientist, recorder, etc.), allowing students to participate at their level of comfort or ability. Moreover, in these groups, students can ask questions of each other or the instructor. The whole class works together to determine the candy saturation curve, which again allows students to participate at the level of their comfort and ability. For students who are not mobile, part of the demonstration is measuring the rate of unwrapping in the absence of having to find and bind the candy, thus allowing contributions from those who cannot, or do not want to, run around the class space. The homework data fitting assignment can be completed individually or as a group assignment and outside resources can be consulted if they are appropriately cited and follow the institutional Honor Code.

## LESSON PLAN

#### Initial Rates Activity

##### Pre-class Preparation

The instructor should prepare bowls or containers with 30 candies to be unwrapped. We prefer to use Jolly Rancher candies made by the Hershey Company; however, other wrapped candies can be used. We prepare one bowl per group and provide an additional bowl for the control assay. A video of the time course demonstration and an example data set are provided on the Open Science Framework to help the instructor and/or students see the desired behavior (https://osf.io/58wtn/).

##### In-class

Students are provided Handout 1 (Supporting File S1. Enzyme Kinetics - Time Course Activity Sheet) and are asked to follow the instructions on the handout to measure initial rates of candy unwrapping. After the activity is complete, students can eat the candy if they so choose and should answer questions 1-8 in the handout in anticipation of the class discussion. Groups that quickly complete the activity and the questions are encouraged to discuss and compare answers with other groups that are done. Most groups complete these tasks in ~30 minutes.

Next, we discuss the candy unwrapping data. The discussion can take the form of students presenting their plotted data and findings to the class. Additionally, groups/individuals should describe how the student enzyme unwrapped the candy and how this changed over the course of the experiment. The example plot available on the author's Open Science Framework page may be useful for students to compare their data (Figure 1A). Students are also encouraged to plot the time to unwrap each candy, as this plot can illustrate the trend that later candies take longer to unwrap (Figure 1B). The instructor should then lead students to define and discuss the terms "initial rate/velocity" and "product inhibition." We describe the decrease in the unwrapping rate as due to product inhibition because it is visually easy to see the students trying to move the unwrapped candies and wrappers around to find substrate, however saying the slowdown is due to a lack of substrate is also correct. Ultimately, the students should provide an answer to the question: "Which rate calculated from your data is more likely to be an accurate measure of the enzyme's true ability to catalyze the reaction?"

##### Optional Discussion

In addition to the activity above, we introduce in this session how to describe enzymes using the algebraic notation (E + S ➝ ES ➝ ES* ➝ EP ➝ E + P) and that enzymes increase reaction rates by lowering the activation energy required to reach the transition state. This can be a separate discussion depending on the length of the class.

#### Effect of Substrate Concentration on Enzyme Rates

##### Pre-class Preparation

The instructor should fill five containers with 10, 20, 50, 100, and 200 candies. Additionally, the instructor should create a spreadsheet for recording and plotting the data that is collected during the activity. A model spreadsheet can be found as Supporting File S3. Enzyme Kinetics - Kinetics Data Spreadsheet or at osf.io/58wtn/files/. Arrange the classroom so that students do not hurt themselves while searching for candies to be unwrapped. In our experience, students get competitive by the end of the demonstration as they try to unwrap the candies quickly; this is when you need to take care to ensure that accidents do not occur.

##### In-class

A detailed script for this lesson with question prompts is provided as Support File S2. Enzyme Kinetics - Instructor Guide for Michaelis-Menten Activity or osf.io/58wtn/files/ and summarized below. We start with a brief recap of the previous lesson and the role of enzymes as catalysts. A student, or a small number of students, then measure the minimum time needed to unwrap a candy when the candy is already in their hands and they do not have to search for it. This number will be used as the minimum unwrapping time (which will be linked to V_{max} later). We point out that, in cells, enzymes have to collide with or bind the substrate before reacting and ask how this might change the reaction rate. We then select students to be "enzymes" and "scientists" to observe how adding the collision and binding aspects of the reaction may change the kinetics and how substrate concentration affects the kinetics. In the demonstration, the "scientists" will observe one of the "enzymes" and measure how long it takes that "enzyme" to find the candy and unwrap it. Once roles are assigned and described to the students, the "enzymes" are asked to leave the room and the instructor distributes the 10 candies around the room. The "scientists" begin their timers when the "enzymes" re-enter the classroom as a group and search for a candy to unwrap. When an "enzyme" unwraps a candy, the "scientist" stops the timer for that "enzyme" specifically. The demonstration continues until all "enzymes" unwrap the candy. The "scientists" report the times of each "enzyme" and the instructor (or a student) then records all the times in the spreadsheet and calculates the average unwrap time given the substrate concentration. The class is then asked whether the average value is the same as the minimum time measured earlier, which lacks the searching aspect. The demonstration is repeated, and the data recorded until all five concentrations of candy have been tested. By the end, the average unwrapping time at the highest concentration (200 candies) is usually two times as long as the previously determined minimum time needed to unwrap a candy.

Students are asked to clean up all candies and, while they are probably eating candies, the class converts the searching and unwrapping times to rates by dividing '1' by the unwrapping times at each concentration, respectively. Students then plot the data as directed in Handout 2 (Supporting File S4. Enzyme Kinetics - Michaelis-Menten Activity Sheet). In theory, students can do this independently, but in practice they get stuck and need guidance. We prefer to provide some guidance and proceed as a class through the steps of the calculations and plotting. Example data collected in class are shown in Figure 2. Next, the class estimates the kinetic values from both the Michaelis-Menten and Lineweaver-Burk plots. The V_{max} estimate should be similar to the minimum unwrapping time measured at the beginning of class, which sometimes impresses the students. Additional whole-class discussions focus on what actions dominate at low concentrations of substrate (the time it takes to find/collide with the candy) versus high concentrations (unwrapping). To avoid lecturing, we encourage the students to describe what they observed while watching the enzymes at the different concentrations. Finally, we introduce students to their data fitting homework assignment and the resources they should consult to be successful in fitting those kinetics data.

#### Fitting Kinetic Data to Determine V_{max} and K_{M}

##### Pre-assignment Preparation

The instructor can make data from class available to students, although most students should have recorded the data in their handout. We provide our students with a Nature Protocols manuscript describing fitting enzyme kinetics data in Excel (10). Additionally, students are provided with websites that can walk them through the theory behind data fitting and provide a brief description of how to fit the data in Excel/Sheets (https://protocols.io/view/fitting-enzyme-kinetics-data-with-solver-bik7k...). We distribute this information through the learning management system for the course.

##### Homework

Students work to fit the data using direct fitting and Lineweaver-Burk methods to validate their in-class estimates of the kinetic parameters. We give the students about one week to complete the assignment and try to have that time interval span at least one office hours session for students to come in and ask questions. Students frequently struggle with showing two data sets (raw and fitted) on the same plot and showing the fit appropriately. For a homework grade, we ask students to submit a write up of their fitting procedure and describe their data and results. Additionally, we ask them to compare the calculated kinetic values between the two fitting methods to illustrate the limitations of Lineweaver-Burk fitting (11). Students are also asked to connect the demonstration to enzyme behavior by explaining what V_{max} and K_{M }represent for biological catalysts.

## TEACHING DISCUSSION

#### Student Outcomes

We asked students to rate their confidence in analyzing enzyme kinetics data and calculating enzyme rates or kinetic parameters from data before and after doing this activity. The aggregated data from two semesters is shown in Figure 3 and indicates student confidence increased for the majority of students from feeling that they would need significant guidance to feeling more comfortable in their understanding of enzyme kinetics and the experiments involved. Students were also asked about their confidence in making figures of numerical data and showed increased confidence in this activity as well (Figure 3).

#### Struggles in Fitting Data

A portion of students regularly show issues with showing the fit to the data correctly in Excel. How to show the data is explicitly discussed in the Kemmler and Keller paper (10); however, we typically receive a few homework assignments where the data are fit with a log/polynomial trendline. This line is easy to add using the Add Trendline command in Excel and appears to fit, which we believe confuses students. While it is easy to identify the error in the homework since the log trendline does not pass through the origin, getting students to understand the error is more difficult even when shown a proper fit alongside their fit. We believe this is a data and Excel literacy issue, which we are working to address by introducing small Excel-based assignments earlier in the course.

#### The Activity Overall

Broadly speaking, students are positive about performing these activities in part because they are highly interactive and there is candy provided, but also because they aid in their visualization of a previously unseen phenomenon. By "seeing enzymes" at sub-saturating and saturating concentrations of substrate and in the presence of product, enzyme behavior under these distinct conditions becomes clearer.

#### Extensions and Adaptions

These lessons can be extended to cover other topics including enzyme specificity, active site structure, and enzyme inhibition. We do not use these extensions as frequently because of the content constraints of teaching a one-semester survey course. However, brief outlines of how these variations work in class are described below.

##### Competitive Enzyme Inhibition

After performing the saturation experiment, introduce a second candy type as the inhibitor. We use Tootsie Rolls given their size and shape similarity to Jolly Ranchers. We give student groups both candies, and then have one student, who will be the "enzyme," close their eyes. The other students in the group place several Tootsie Rolls in front of the student and one Jolly Rancher. The student "enzyme" with eyes still closed, then is asked to unwrap the Jolly Rancher. This is repeated at increasing concentrations of Tootsie Rolls and the time to unwrap the Jolly Rancher is recorded. When there are lots of Tootsie Rolls present, it is harder to find the Jolly Rancher and only by increasing the concentration of substrate is inhibition able to be overcome.

##### Enzyme Specificity

Jolly Ranchers are produced in many flavors and students often prefer one flavor over another. While the overall shape of the candy is similar, flavor is a chemical property of the substrate that influences whether a particular student will unwrap and eat the candy. Like students, enzymes prefer specific but sometimes subtle features in their substrates. We then discuss that NADH and NAD^{+} or oxidized and reduced cytochromes or ubiquitin and ubiquitin-like molecules have similar shapes, but that other features can dictate whether an enzyme will act on the molecule.

##### Active Site Structure

Part of enzyme specificity is how well the molecule fits in the active site and aligns with the catalytic features. In groups, a student enzyme should unwrap a number of candies while the rest of the group observes the unwrapping. As a group, the students should describe how the unwrapping occurred and whether the enzyme consistently held the candy the same way while unwrapping. More often than not, students have a consistent method to unwrap the candies much like enzymes bind to substrates and catalyze the reaction the same way each time.

## SUPPORTING MATERIALS

- S1. Enzyme Kinetics - Time Course Activity Sheet. Student activity sheet for Day 1 activity on initial rates
- S2. Enzyme Kinetics - Instructor Guide for Michaelis-Menten Activity. A guide to help instructors prepare and perform the activity including some prompts.
- S3. Enzyme Kinetics - Kinetics Data Spreadsheet. An .xlsx file for collecting data from the Michaelis-Menten kinetics activity.
- S4. Enzyme Kinetics - Michaelis-Menten Activity Sheet. Student activity sheet for Day 2 activity on the effect of substrate concentration on enzyme rate.

## ACKNOWLEDGMENTS

The authors wish to thank the students in CHEM361 for their enthusiasm and participation in these activities. CEB wishes to thank Dr. John M. Denu at the University of Wisconsin-Madison for his initial inspiration of the saturation curve activity on which the authors built the present work. Research and teaching activities by the authors are supported by the Thomas and Kate F. Jeffress Memorial Trust, the National Science Foundation, and the 4-VA organization. The student assessment activities are monitored by IRB protocols 19-0070 and 20-1076.

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