In the Classroom
Modeling Chemical and Biological Systems: A Successful Course for Undergraduate Students
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Maria João Ramos,* Pedro Alexandrino Fernandes, and André Melo Requimte, Departamento de Química, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal; *
[email protected] As lecturers on quantum mechanics we find it difficult to motivate many of our chemistry majors to attend courses about quantum mechanics. In the past we have tried sharing our knowledge with the students in the traditional manner: via formal lectures and practical classes in which the students solve several problems associated with the lecture material. In this article we examine an optional course that is part of the third-year curriculum (the degree in chemistry is four years). The fact that “Modeling Chemical and Biological Systems” is an optional course should result in low student attendance. As students found it difficult to attend, follow, and enjoy the lectures of the second-year compulsory course, “Atomic and Molecular Structure”, one can imagine the problems associated with students voluntarily choosing a course connected with quantum mechanics. The Modeling Chemical and Biological Systems course is 68 hours, spread over a semester, and in principle should follow the traditional format of lectures and practical classes. However, rather than following the traditional format, we decided to organize the course into separate practical projects, introducing the theory as it is needed. We chose the projects to be motivating yet, in a way, already familiar to the students. The idea was that even though one has the impression of knowing the material, it is only when one goes as deep as understanding the associated microscopic world that one can fully appreciate the whole picture! The Course The general structure of the course is presented in Table 1. A detailed description of the course is given in the following sections.
Introduction to the Course and the Linux Operating System (4 Hours) During the course introduction we presented a list of reference materials (1–10), the evaluation criteria, and the general structure and ideas behind the course. The general structure includes the fact that theory would be presented during each project and that each student would write a report for each project, which would be completed during the classes. Specific information on the three reports is found in Appendices 1–3 in the Supplemental Material.W In addition to the report, there were two more factors contributing to the final course grade. The first is a presentation made at the end of each project. Even though the course work was individual, we defined four groups of students and each of these groups had to present the work concerning one particular project. Each class had 16 students, which meant that each group had four students. All presentations were done in the class. The total number of hours shown in Table 1 for each project includes the presentation hours. The second factor 72
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contributing to the final grade is a final exam that focused only on the theory introduced during the course and shown in Table 2. The Linux operating system was introduced in this segment of the course as all calculations performed were carried out on Pentium III Personal Computers running under Linux. All programs were written by the authors (difcl, difmg, diffusion, rdf.anion.water, rdf.cation.water, rdf.cation.anion, statistic, average) and have been provided in the Supplemental Material.W
Project 1: Simulations of Aqueous Solutions of the Ionic Salt MgCl2 (30 Hours) This project focused on the simulation of two aqueous solutions of magnesium chloride with different concentrations. With this project, we introduced statistical mechanics and molecular dynamics (MD) (see sections I. C and I. D in Table 2). We used MD, the ensemble isothermal–isobaric (NPT), and the Nosé–Hoover thermostat and barostat to keep both the temperature (300 K) and the pressure (1 bar) constant. Both systems consisted of a box and were treated with periodical boundary conditions in all three directions. Although both boxes had 1221 rigid water molecules, the number of ions was different in each box: 22 chloride ions and 11 magnesium ions (system 1); and 132 chloride ions and 66 magnesium ions (system 2). Both simulations were performed before classes owing to their long execution time. They were run using the software DL_POLY (11) with an integration step of 2 fs. The students were given two files, one for each system containing the trajectories of each particle. They were then asked to analyze the trajectories and perform the necessary calculations to get some system properties, specifically density, ionic diffusion coefficients, and hydration numbers. The students also visualized the animated trajectories and analyzed the hydration shells of each ion. The instructions and report format for project 1 can be found in Appendix 1 in the Supplemental Material.W Project 2: Study of the Mechanism of Destruction of Ozone by a CFC (20 Hours) In this project the mechanism of destruction of ozone by Freon 12 (CF2Cl2) was studied using a quantum method, the semi-empirical method PM3 (12). During this project we spoke generally of computational chemistry and, in particular, of quantum methods, ab initio, and semi-empirical, as well as basis functions. We revisited the chemistry connected with the ozone layer and introduced the mechanism of reaction we wanted to study; finally we followed all the steps of the mechanism, using PM3, by optimizing the reactants, the products, and the transition states, and by visualizing the reactions occurred. The software package used for the quantum calculations was MOPAC6 (13), and the visu-
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In the Classroom Table 1. General Structure of the Modeling Chemical and Biological Systems Course Subject
Total No. Hours
Table 2. Theory Lectured to the Students during the Course Theory
Project
I. Theoretical calculations in chemistry
1
Introduction to the course
2
A. Introduction
1
Linux operating system
2
B. Systems
1
Project 1: Simulation of aqueous solutions of the ionic salt MgCl2
30
Project 2: Study of the mechanism of destruction of ozone by a CFC
20
Project 3: Study of the proteic mutation responsible for sickle cell anemia
12
The Human Genome Project
2
1. Small molecules
1
2. Macromolecules and biological systems
1
C. Introduction to statistical mechanics 1. State functions 2. Macrostate, microstate, and ensemble
1
3. Property values: experimental and calculated
1
4. Ergodicity
1
D. Molecular Dynamics
alization of all geometries, as well as the internal reaction coordinates (IRC), was done with the software MOLDEN (14). Gnuplot (15) was used to plot graphs of the calculated energies versus the reaction coordinates. All theory introduced during this project is listed as I. E and II in Table 2. The instructions and report for project 2 can be found in Appendix 2 in the Supplemental Material.W We also used several Internet sites to help us follow some of the theory. These sites have been specified in Appendix 2. The students were encouraged to examine those sites during the classes and use them to complete their reports.
Project 3: Study of the Proteic Mutation Responsible for Sickle Cell Anemia (12 Hours) In this project the students worked out, in a qualitative and in a quantitative way, the proteic mutation in hemoglobin responsible for sickle cell anemia. We started this project by introducing amino acids, followed by proteins and enzymes. We focused on the databases of molecular structures, in general, and on the Protein Data Bank, in particular, where the 3D structures for both normal human hemoglobin and mutated human hemoglobin, which is directly responsible for the sickle cell anemia, were found. We used the software Swiss-PDB Viewer (16) for the graphics visualization. Finally, we built models of a different number of valines and water molecules, as well as models of glutamates and water molecules, to study the electrostatic interactions between the mutated amino acid (Glu to Val), responsible for sickle cell anemia, and the environment (water). This quantitative study was performed with the software MOPAC6 (13), using the semi-empirical quantum method AM1 (17). The instructions and report for this project can be viewed in Appendix 3 in the Supplemental Material.W The Human Genome Project (2 Hours) The three projects complete 66 hours out of a total of 68 hours. During the introduction to the course we asked the students if there was any subject that they would like to discuss in an informal manner. After some discussion we decided on the Human Genome Project (HGP). Few references (18) were recommended as the students were expected to find their own reference materials. No specific directives were given but the students still had to write reports and one group www.JCE.DivCHED.org
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1 1
1
1. Multibody dynamics
1
2. Numerical integration of Newton‘s equations
1
3. Periodical boundary conditions
1
4. Potentials of interaction
1
5. Methods for the calculation of long range forces
1
6. Some properties obtained by molecular dynamics (density, diffusion coefficients, radial distribution functions, etc.)
1
E. Quantum methods
2
1. Introduction
2
2. The molecular Hamiltonian
2
3. Self-consistent-field method
2
4. Hartree–Fock–Roothaan theory
2
5. Hartree–Fock limit
2
6. Electronic correlation
2
7. Koopmans‘ theorem
2
8. Basis functions
2
II. Depletion of ozone in the strastosphere
2
III. Proteins
3
IV. Sickle cell anemia
3
V. Protein Data Bank
3
VI. Molecular Graphics
3
made a presentation on the subject. One hour was spent listening to the presentation and one hour spent discussing the HGP. The goal of this section was to encourage the students to do research on their own, formulate their own ideas, and present the information in a concise, organized fashion. This section was interesting, even if it was far from a comprehensive study. Results and Discussion The three projects covered the theory that the students were supposed to learn, that is, quantum and classical mechanics in a basic, applied way. In this section we highlight some of the points pertaining to the students. The students tackled the first project with enthusiasm. The effort that we put in to provide the students with the files necessary for the animation of the trajectories of the hydration complexes definitely paid off. A snapshot of the Mg2+
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In the Classroom
and Cl− hydration spheres is shown in Figure 1. As expected Mg2+ interacts with the oxygen atoms from H2O, whereas Cl− is surrounded by hydrogen atoms. Moreover, the bigger charge of Mg2+ imposes a more structured, regular geometry to the hydration complex than the smaller charge of Cl−. In the second project, the students worked towards the visualization of the complete mechanism of destruction of ozone by CF2Cl2. We had them scan the reaction coordinate of each of the reactions. The students were delighted to be able to animate the files with MOLDEN and actually see the reaction occurring. The calculated overall energies for the reaction Cl + O3 → ClO + O2, one reaction of the mechanism, together with the structures of the correspondent reagents, products, and transition states are shown in Figure 2. The third project was a big success, mainly because of the graphical possibilities of the program Swiss-PDB Viewer, which enabled the students to understand the disease and, again, to visualize the results obtained in the calculations. Additionally, this is a most extraordinary example of how such a small mutation (Glu to Val) gives rise to such a terrible disease. Visualization and movement captivated our students. A view of one of the four monomers of hemoglobin is shown in Figure 3. Also shown is the heme and the position of the iron cation, shown as a larger, light gray sphere.
Figure 1. Snapshot of the first hydration shell for ions Mg2+ and Cl− in aqueous solution at 300K.
Further Suggestions We realize that the three projects described in this article might not apply to every quantum and classical mechanics course. However, the type of course structure presented here is successful. Instructors can successfully employ projects in their field of expertise if the projects are relevant to the theory that they would like to deliver during the course. We have new ideas for projects, such as: •
Simulation of the IR spectra of a series of gradually more complex molecules (e.g., N2, HCl, CO2, HCN, H2O, HCOOH, C2H4).
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Quantum mechanical study of the heme in hemoglobin.
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Building a 3D computer model of an enzyme (e.g., β-factor XIIa) by sequence homology.
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Molecular dynamics simulation of a melting piece of ice.
Figure 2. Overall energies for reaction Cl + O3 → ClO + O2, together with the structures of the correspondent reagents (R), products (P), and transition states (T). The light gray circles represent the oxygen atoms and the dark gray circles represent the chlorine atoms.
We think that any of these projects can be easily adapted to a course of the type structured here. Background work needs to be performed for these projects, such as working out the structures and the calculations to ensure that everything can be completed within the timeframe of the classes. Conclusions During the course we have noticed that students reacted very favorably. The students were motivated, their reports were good, and their presentations excellent. They all used PowerPoint and several students made videos to animate the presentations. This course ran for the first time in the second semester of the academic year of 2000–2001 with 16 students (out of an average of 59 students for that academic year). The best way of weighting its success is by considering the fact that during the next academic year, 2001–2002,
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Figure 3. One of the four monomers of hemoglobin (2hbs.pdb).
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In the Classroom
double the number of students chose this course—29 students out of an average of 47 students for that academic year. When asked why they had decided to attend the course, the general reply was that they had heard excellent reports from their colleagues from the previous year. Acknowledgments We thank the 16 students who chose this course in the first academic year 2000–2001. W
Supplemental Material
Specific information on each project and the computer programs are available in this issue of JCE Online. Literature Cited 1. Fernandes, P. A.; Ramos, M. J. Notas em Mecânica Quântica e Dinâmica Molecular; Faculty of Sciences: University of Porto, 2001. 2. Magalhães, A. L. Sistema Operativo LINUX & Linguagem de Programação FORTRAN, Faculty of Sciences: University of Porto, 2000. 3. Feller, D.; Davidson, E. Basis Sets for Ab Initio Molecular Orbital Calculations and Intermolecular Interactions. In Reviews in Computational Chemistry; Lipkowitz, K. B., Boyd, D. B., Eds.; VCH Publishers, Inc.: New York, 1990; Vol. 1, p 1. 4. Stewart, J. J. P. Semiempirical Molecular Orbital Methods. In Reviews in Computational Chemistry; Lipkowitz, K. B., Boyd, D. B., Eds.; VCH Publishers, Inc.: New York, 1990; Vol. 1, p 45. 5. Lybrand, T. P. Computer Simulation of Biomolecular Systems Using Molecular Dynamics and Free Energy Perturbation Methods. In Reviews in Computational Chemistry; Lipkowitz, K. B., Boyd, D. B., Eds.; VCH Publishers, Inc.: New York, 1990; Vol. 1, p 295.
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6. Boyd, D. B. Aspects of Molecular Modeling. In Reviews in Computational Chemistry; Lipkowitz, K. B., Boyd, D. B., Eds.; VCH Publishers, Inc.: New York, 1990; Vol. 1, p 321. 7. Bowen, J. P.; Allinger, N. L. Molecular Mechanics: The Art and Science of Parameterization. In Reviews in Computational Chemistry; Lipkowitz, K. B., Boyd, D. B., Eds.; VCH Publishers, Inc.: New York, 1990; Vol. 1, p 81. 8. Dinur, U.; Hagler, A. T. New Approaches to Empirical Force Fields. In Reviews in Computational Chemistry; Lipkowitz, K. B., Boyd, D. B., Eds.; VCH Publishers, Inc.: New York, 1990; Vol. 1, p 99. 9. McKee, M. L, Computing Reaction Pathways on Molecular Potential Energy Surfaces. In Reviews in Computational Chemistry; Lipkowitz, K. B., Boyd, D. B., Eds.; VCH Publishers, Inc.: New York, 1990; Vol. 1, p 35. 10. Pettersson, I.; Liljefors, T. Molecular Mechanics Calculated Conformational Energies of Organic Molecules: A Comparison of Force Fields. In Reviews in Computational Chemistry; Lipkowitz, K. B., Boyd, D. B., Eds.; VCH Publishers, Inc.: New York, 1990; Vol. 1, p 167. 11. Forrester, T.; Smith, W. DL_POLY (2.1 version); CCLRC: Daresbury Laboratory, Daresbury, United Kingdom, 1995. 12. Stewart, J. J. P. J. Comp. Chem. 1989, 10, 209. 13. Stewart, J. J. P. QCPE Program no. 455, 1983. 14. Schaftenaar, G.; Noordik, J. H. J. Comput.-Aided Mol. Design 2000, 14, 123. 15. Gnuplot Central Home Page. http://www.gnuplot.info/ (accessed Oct 2003). 16. (a) Guex, N.; Peitsch, M. C. Electrophoresis 1997, 18, 2714. (b) DeepView–Swiss PDB Viewer Home Page. http:// us.expasy.org/spdbv/mainpage.htm; http://us.expasy.org/spdbv/text/ getsgi.htm (both accessed Oct 2003). 17. Dewar, M. J. S.; Zoebisch, E. G.; Heale, F.; Stewart, J. J. P. J. Am. Chem. Soc. 1985, 107, 107. 18. Passarge, E. Color Atlas of Genetics, 2nd ed.; Thieme Medical Publishers, Inc.: New York, 2001.
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