November 2010, Volume 7, No.11 (Serial No.72) Journal of Communication and Computer, ISSN 1548-7709, USA
Problem Based Learning: Obtaining Enzyme Kinetics Parameters Integrating Linear Algebra, Computer Programming and Biochemistry Curriculum Regalado Alejandro1, Báez Juan2 and Peralta Ever1 1. Environment Engineering, Del Mar University, Oaxaca, Puerto Ángel 70902, México 2. Department of Food, Faculty of Biological Sciences, Nuevo León Autonomous University, Nuevo León 66451, México Received: August 06, 2010 / Accepted: September 30, 2010 / Published: November 25, 2010. Abstract: This work is focused on a project that integrates the curriculum of biochemistry, lineal algebra and computer programming. The purpose is for students to develop a software tool which calculates enzyme kinetic parameters based on proposed data. This program calculates such parameters using a linear regression of one of the linear forms of the Michaelis-Menten equations; moreover it characterizes the confidence of the lineal fit with the correlation coefficient. Once the different proposed steps were accomplished, we concluded that the purpose was satisfactorily reached with an increment in creative ability. The most important fact is that the percentage of failure among students was 57%, 50%, 28% and 18% from 2005 to 2008, respectively. Key words: Enzymatic kinetics parameters, flux diagram, minimum squares, linear regression, problem based learning.
1. Introduction Problem Based Learning (PBL) dates back to the early 1970s. As a new learning paradigm, PBL was first adopted in the McMaster medical school of Canada. With the realization of PBL in the institution, the curriculum shifted from a faculty-centered to student-centered, interdisciplinary teaching model. The PBL approach is thought to be well suited especially to medical schools since the skill of life-long learning is critical in this field [1]. Today the PBL is widely recognized as a strategy for effective learning. In PBL, the learning is triggered by striving to tackle a “problem” which may be presented in many forms such as a description of a design Corresponding author: Regalado Alejandro (1976), M.Sc., professor, research fields: process control. E-mail: alejandro.
[email protected]. Báez Juan (1973), Ph.D., professor, research fields: bioprocess. E-mail:
[email protected]. Peralta Ever (1970), M.Sc., professor, research fields: process modeling. E-mail:
[email protected].
scenario, a curious outcome or an extreme event. Basically students form teams, organize the work, research and negotiate a response to the problem [2-3]. In Mexico, problem based learning (PBL) has not been developed much, contrary to what is found in European countries and The United States. In the last few years, this type of learning has become very popular, allowing the integration of different disciplines into the curriculum. Frequently, students ask themselves about the usefulness of some courses, as they don’t manage to see any concrete application. To ensure that students take a primary part in their own academic formation, the lecturer should assume a facilitator role, and encourage the students to motivate themselves in searching for possible solutions to a given problem, looking at it from a multidisciplinary viewpoint. The role of the lecturer is to act as a facilitator of learning by defining the problem and then guiding the students along the learning curve. The main aim of this PBL based learning is to overcome the shortcomings in
Problem Based Learning: Obtaining Enzyme Kinetics Parameters Integrating Linear Algebra, Computer Programming and Biochemistry Curriculum
the traditional method of “lecture-tutorial” based learning. In the traditional learning method, the knowledge of the lecturer is presented to the students and the learning of the students is tested usually in the form of a final examination with or without laboratory/practical assessment [4-5]. The need for inclusion of Problem-based Learning (PBL) in engineering classes especially have been the result of the numerous feedback and complaints received from stakeholders of higher learning institutions especially the job industry [5-6]. As shown in Fig.1, students from the Universidad del Mar have high failure statistics which leads teachers to seek different pedagogic approaches. A project that allows integrating courses of biochemistry, linear algebra, and programming is proposed herein. It is intended to be used with undergraduate students of the Universidad del Mar, Mexico. Until now, it has been applied to students in the Environmental Engineering program, but it can be expanded to students of Natural Sciences as well. To improve the Teaching-Learning process in Mexico, it is necessary that professors interconnect the knowledge obtained by the program curricula not only in a horizontal way but also vertically, with the objective to improve the cognitive processes of students in the first semesters, in order to form more critical and less procedural students [7].
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The PBL structure was kept similar to the one adopted by Offman and Cadet, 2002, with 3 work sessions of 2-3 hours, the first with an introductory purpose. In these sessions, discussion is encouraged with a minimum involvement of the professor (facilitator) [8-11]. Each session is spaced by three days; in each a written report that answers specific questions is expected. The authors wish to mention that the PBL strategy designed will be followed in accordance to that of the Bolognha Declaration in 1999. In which it shows the need of reorganization of the higher education curricula in Europe according to a three cycle structure, it suggests a reduction of formal lecture hours and stresses the importance of autonomous work [12].
2. Problem Description The PBL problem is: Determine the enzymechymoptrypsin kinetic parameters, developing a software program. The rates of hydrolysis of N-acetyl -phenylalaninamide by-chymoptrypsin at different concentrations are shown in Table 1 [13]. 2.1 Part I (Session 1) The facilitator, in this section, should motivate the students to investigate subjects related with enzyme kinetics. In order to assist, he can propose the following questions: What are enzymes? What are they useful for? How do they work? What is their reaction mechanism? Do models that allow predicting their reaction rate exist? If so, which would be the simplest? 2.2 Part II (Session 2) Once the enzymatic kinetics is understood, the facilitator must introduce the mathematical tool and outline Table 1 Experimental data.
Fig. 1 Number of failed and accredited students each year.
[S]/mM 10.5 15.1 20.0 35.0 93.4
V/mM de Alanine minute-1 3.33×10-2 4.55×10-2 5.56×10-2 7.15×10-2 10.0×10-2
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Problem Based Learning: Obtaining Enzyme Kinetics Parameters Integrating Linear Algebra, Computer Programming and Biochemistry Curriculum
the following questions: What is the mathematical form of the models encountered? How can we turn the simplest model into a linear form? How can we determine the fit parameters, mathematically, in a linear equation?
4. Expected Answers In this section the authors write an example of the expected answers of the problem based learning. It’s divided in three parts as in the problem designed. 4.1 Part I (Session 1)
2.3 Part III (Session 3) In this section we will apply the programming theory, using flux diagrams to facilitate the program design. To develop software that will quickly obtain the kinetic parameters for any case study, using the linear equation of part II, the program must: y Be able to read the data directly from keyboard capture or those present in a file with extension .dat; y Calculate kinetic parameters; y Present them on screen and keep them saved as text extension files; y Characterize the quality of the adjustment realized.
Enzymes are proteins that are highly specialized, due to the fact that they catalyze numerous reactions in biological systems. In general, an enzyme gives the adequate environment for a determined reaction to be, energetically, more favorable. The particularity of an enzymatic catalyzed reaction is that it occurs in a specific place of the enzyme, the active site. The molecule that is fixed on the active site and on the enzyme is called substrate. The enzyme-substrate complex formed is of vital importance in order to define the kinetic behavior of the different catalyzed
3. Student Self-Assessment
reactions. A simple enzymatic reaction can be
In the self-assessment the students are asked to identify their skills and weaknesses in problem solutions. Students answer each of the following questions. When he/she finishes, he/she should grade themselves using a points system between 0 and 10.
represented by the Michaelis-Menten equation.
2 3
4 5 6
If I didn’t understand how to the begin problem. I tried understanding it. I was honest with my self-learning (I didn’t copy; I did my work without help). I was responsible in my self-learning (I searched for information, I always looked) more in-depth, I didn’t stop with the information acquired, (and I didn’t depend on others to do my work). I did all the indicated activities. I actively participated in my team and contributed some individual ideas. I was respectful in team participation (Made decisions, agreements, and etcetera).
I understand all the concepts. Now I could solve the problem by myself. From this example, I understand the importance of teamwork.
enzymatic reactions needs the formation of a complex between the enzyme E and the substrate S. This E and S, or can undergo some reorganization and form
YES NO YES NO
YES NO YES NO YES NO YES NO
3.2 Knowledge 7 8 9
Generally, it is accepted that the catalysis of
enzyme-substrate complex ES, can dissociate to reform
3.1 Attitude 1
4.1.1 Michaelis-Menten Equation
YES NO YES NO YES NO
E and products P. The simplest mechanism of all can be represented as [2]:
⎯⎯ → ES ←⎯ ⎯⎯ →E + P E + S ←⎯ ⎯ ⎯ k1
k3
k2
k4
(1)
When concentration ES is constant, the rate at which it is formed is the same as the rate of its decomposition. Therefore, according to the law of mass, the equilibrium state is: k1 [ E ][ S ] + k 4 [ E ][ P ] = k2 [ ES ] + k3 [ ES ] (2) At the beginning of the reaction we have [P]
