Alissa Douglas Terry Lahm Andrea M. Karkowski Capital University

1. Computational Science as an Organizing Principle for Interdisciplinary, Multi-Institutional, and Student-Faculty Collaborations Alissa Douglas Terry Lahm Andrea M. Karkowski Capital University Sheryl Hemkin Kenyon College

2. Overview of Talk • Definitions and Learning Goals • Example from a Faculty Perspective • Example from a Student Perspective • Resources and the Take-Home Message

3. What do we mean by Interdisciplinary? • …a mode of research by teams or individuals that integrates information, data, techniques, tools and perspectives, concepts, and/or theories from two or more disciplines or bodies of specialized knowledge to advance fundamental understanding or to solve problems whose solutions are beyond the scope of a single discipline or area of research practice (www.pkal.org).

4. What is Computational Science? • An interdisciplinary field that integrates computing, mathematical modeling, and visualization to solve problems in the physical, natural, behavioral, and social sciences, as well as finance and engineering. • A method, alongside theory and experimentation, in the investigation of scientific phenomena. • A team sport drawing together people from many disciplines via a common technique, approach and philosophy.

5. Volumetric Reconstruction of MRI of Brain with Source Dipole of Scalp-recorded EEG

6. Computational Science Provides a Context for:

7. Oral and Written Arguments • Why is this important? • How is it achieved? • How is it assessed?

9. Cooperative Learning • What is it? • a relationship in a group of students that requires positive interdependence, individual accountability, interpersonal skills, face-to-face interaction, and processing. (www.co-operation.org) • Why is this important? • How is it achieved? • How is it assessed?

10. Creative Nature of Science(Science gets a bum rep.) • Why is this important? • How is this achieved? • How is it assessed?

11. Creative Nature of Science(Science gets a bum rep.)

12. Creative Nature of Science(… but maybe things are changing…)

13. Creative Nature of Science • Why is this important? • How is this achieved? • How is it assessed?

14. Oral and Written Arguments Collaborative Learning Creative Nature of Science

15. Kinetics of Reaction Systems Sheryl Hemkin Department of Chemistry Kenyon College hemkins@kenyon.edu

16. Aims of Module • Continue to learn • how to form chemical rate equations (ODEs) • how equations can be related to the real chemical process, • i.e., gain insight into the potential chemical mechanism • Use numerical methods to • understand and visualize that rate equations can predict reaction • understand that parameters can reflect physical quantities, • e.g., flow rate through an ion channel • see how changes in parameters (~ physical quantities) affect reaction Empower the student Take ideas and apply to other situations or classes - basic ideas apply to any process that is ODE based e.g., localized biochemical reactions, aspects of currency exchange or stock market, etc.

17. Classroom Environment — multi hour segment to allow for integration of concepts, “logistics” and informal discussion of results Laboratory Integration Software User friendly software allow for integration of ODEs using numerical methods e.g., Berkeley Madonna, Stella, Mathematica, etc. Student Background Basic understanding of intro calculus ideas Basic understanding kinetics & how to build rate equations (Upper level students can review & extend concepts to unique projects)

18. Introduction (Kinetics, Software) Section 1 Equilibrium Section 2 Enzyme Kinetics Section 3 Simulations & Mechanisms Section 4 Oscillations Module Basics Although sections tend to build on one another - they can be used individually Intensity can be adjusted with questions used and avoided

19. Fermentation to Enzyme Kinetics Beer & Wine glucose (sugar)  ethanol(alcohol) catalyzed by zymase, a yeast enzyme sucrose + water  glucose + fructose catalyzed by invertase, a yeast enzyme Brown’s studies (1890’s) indicate- reaction more complex than expected… Birth of Enzyme Kinetics

20. k1 sucrose + enzymesucrose-enzyme complex sucrose-enzyme complexglucose + fructose + enzyme k-1 ES S E k2 E ES P Rate of product formation, P (based on reactions): Problem: ~ Chemists can’t “control” reaction intermediates (ES), only can influence reactants and products (S and P) ~ Must rewrite rate in those terms Mechanism & Rate Equations

21. Long story short… Find Bigger Problem - can’t integrate & solve the equations by hand… To get around the problem Traditional Approach: Use “physiologically relevant” assumptions to simplify equations. Ultimately allows for hand integration. Computational Approach: Use numerical methods to integrateequations directly. No need for simplifying assumptions. (Use algorithms like Euler, Runge-Kutta, Gear) In module - Compare simulation results to theory and experiment, start to realize all goes hand in hand.

22. Approaches k1 S + EES ES E + P k-1 k2 Traditional Approach: Michaelis Menten Equilibrium (1913) - Assume reaction 1 in equilibrium & rxn 2 slow. rate forward rxn1 = rate reverse rxn1 Computational Approach: 2. Briggs Haldane Steady State (1925) - Assume the ES complex consumed as quickly as produced. d[ES] dt = 0

23. Do simulation. Results sensible? k1 S + EES ES E + P k-1 k2 P S concentration ES E 0 time Results qualitatively similar to that of assumptions and analogous experiments. Computational Approach:

24. d[ES] dt P BH assumption valid = 0 [ES] S concentration time ES E 0 time After Simulation - Where is Briggs-Haldane assumption valid? Requires concentration of ES to be constant

25. P S concentration Forward rate MM assumption valid Reverserate rate ES E 0 time time After Simulation - Where is Michaelis-Menten assumption valid? Requires rate Forward reaction 1 = rate Reverse reaction 1

26. After Simulation - Does this make sense ????? P BH assumption valid [ES] S concentration Forward rate MM assumption valid Reverserate rate ES E 0 time time

27. After Simulation - Does this make sense ????? P BH assumption valid [ES] S Living systemsnot encounter“end of reaction” behavior concentration Forward rate MM assumption valid Reverserate rate ES E 0 time time Think about living system -- where is “life” on this timeline?

28. After Simulation - Does this make sense ????? Think about living system -- where is “life” on this timeline? “life” closer to BH assumption P BH assumption valid [ES] S Living systemsnot encounter“end of reaction” behavior concentration Forward rate MM assumption valid Reverserate rate ES E 0 time time

29. Brainstorm Improvements for Living Systems k1 S + EES ES E + P k-1 k2 kout kout Sbody Swaste Pbody Pwaste kin Sstock Sbody Inflow of reactants Outflow Reaction in body ~ inflow of reactants (e.g., food) ~ outflow of products ~ degradation of enzyme ~ etc.

30. Improvements for living (open) systems? k1 S + EES ES E + P Inflow of reactants Outflow Reaction in body k-1 k2 kout kout Sbody Swaste Pbody Pwaste kin Sstock Sbody P “live” zone concentration S ES E 0 time When reactant inflow is sufficiently fast, stay in “live” zone. As seen in real life…

31. Outcomes Reinforce kinetics Connect mathematical form of kinetics to experiment via computation Realize that simulation alone can’t “prove” mechanism - experiment, theory and simulation must work together Realize importance of cross-disciplinary work and collaboration Empowerment - can change and edit reactions to fit real circumstances • Parameters relate to physical properties • Variation in the parameters can relate to experimental changes that can be tested

32. A Student’s Perspective • 2008 Capital graduate • Pursuing Statistics at The Ohio State University • Computational Science Minor • Intro. to Computational Science • Computational Physics • Computational Environmental Science • Research Experience in Computational Science • Computational Biology • Important factor in decision to attend Capital • Developed essential skills: communication, cooperative learning, and creativity

33. Communication: Written • Module Write-ups • Unlike math classes • Background, explanation, conceptual model, methods, implementation, results, analysis, conclusion • Important to understand and analyze outcome of data • Must be readable and understandable by someone not familiar with the topic • Skills essential in graduate school and ‘real world’

34. Communication: Oral • Communicating with Professors • Small class sizes = attention from Professors • Interpersonal communication important in independent studies • Communicating with student peers • Usually worked in small groups • Needed communication for entire module • Work through differences

35. Cooperative Learning • Student Peers • Usually small groups • Differences in approach and implementations • Varied backgrounds: math, cs, science • Experience for work after grad school • Process more important than outcome • Always a learning experience

36. Cooperative Learning • Independent Studies • Developed Student-Teacher relationships • Different from other classes at Capital • Interpersonal communication • Student and faculty learning • Computational Environmental Science • Mono Lake problem • Stella • Model incomplete • Research Capstone • Dynamic Pricing for Residential Electricity • Python • Program incomplete

37. Creative Nature of Science • Explore areas related to math • Not typical applied or pure math problems • Research options • Module options • Class options

38. Personal Gains • Experience, experience, experience • Problem solving • Simplifying assumptions • Adding complexities • Real world applications • Interdisciplinary nature • Entrance to grad school

39. Resources and Take-Home Message

40. On a Module ScaleComputational Science Provides a Context for: • Learning to make oral and written arguments • Engaging in cooperative learning • Discovering the creative nature of science • Student-Faculty Collaboration

41. On a Course and Curriculum ScaleComputational Science Provides a Context for: • Cross-Disciplinary and Interdisciplinary Interaction • Multi-Institutional Interaction

42. Computational Science I Introduction to Computer Science Differential Equations and Dynamical Systems Computational and Numerical Methods Parallel Computing High Performance Computing Scientific Visualization Comp. Biology Comp. Chemistry Comp. Environmental Science Comp. Neuroscience and Psychology Comp. Physics Research Experience in Comp. Science Core (required) Electives (select 2) Capstone (required) Overview of Minor Curriculum

43. Cross-Disciplinary and Interdisciplinary Interactions • CSAC – Computational Science Across the Curriculum (2000) • Nine faculty from Capital University • NSF-Course, Curriculum, and Laboratory Improvement (CCLI) (DUE #9952806 ) • 36 modules created in disciplines of Mathematics, Computer Science, Physics, Chemistry, Biology, Psychology, Environmental Science, Scientific Visualization

44. Keck Undergraduate Computational Science Consortium Harvey Mudd Pomona San Diego Supercomputer San Diego State Holy Cross Skidmore Capital Ohio State Wisconsin – Eau Claire Wittenberg Shodor Found.Christ. Newport Wofford

45. Multi-Institution Interactions • W.M. Keck Undergraduate Computational Science Educational Consortium (2003) • 27 faculty from 13 institutions • 45 modules created in disciplines of Computer Science, Mathematics, Physics, Chemistry, Biology, Geology, Environmental Science, Neuroscience, Psychology, Finance, and Scientific Visualization

46. CU Development and Dissemination of Computational Science Educational Materials and Curricula at the Undergraduate LevelFunded by the National Science Foundation (DUE 0618252) OBERLIN

47. Multi-Institution Interactions • Development and Dissemination of Computational Science Educational Materials and Curricula at the Undergraduate Level (2007) • 35 faculty from 14 institutions in Ohio and California • NSF-Course, Curriculum, and Laboratory Improvement (CCLI) (DUE #0618252) • Plan to create 65 modules created in disciplines of Mathematics, Computer Science, Physics, Chemistry, Biology, Psychology, Environmental Science,

48. Over 90+ Modules • Modeling the Cardiovascular System • Phylogeny Project • Diffusion in Biology • Pharmacokinetics • Tumor Dynamics • Gene Identification • Modeling Populations and Habitats for Kirtland’s Warbler • Modeling Mushroom Fairy Rings • Modeling Malaria • Spread of SARS • Molecular Structure and Interaction • Quantum Chemistry in the Environment • Electric Potential • Enzyme Kinetics • Satellite Surveillance • The 1-D Hydrogen Atom • Heat Flow on the Jovian Satellite Europa • Ablation, Aerobraking and Airbursting of a Hypersonic Projectile in Earth’s Atmosphere • Mandelbrot Set • N-Body Problem • Traveling Salesperson Problem • Global Climate Modeling • Groundwater Flow Modeling • Modeling the Performance of a Solar Heated Sunroom

49. (…but, wait, there’s more…) • A Tale of Two Lakes: Environmental Mass Balance Modeling • Geologic Stresses and Faulting • Landslides and Slope Stability • Evaluating Evidence Using Bayesian Networks • Fourier Transforms • Vector Spaces and Linear Transformations • Image Reconstruction in Emission Tomography • Rescorla Wagner Model of Associative Learning • Modeling Self-Esteem • Sex, Sex Role, and Relationships • Artificial Neural Networks • http://www.capital.edu/68/Arts-and-Sciences/Computational-Studies/7111/

50. Virtual School supported by Ohio Board of Regents, OSC, Ohio Learning Network (OLN), and universities in Ohio • Minor in Computational Science • Certificate Programs