Links between biology and math at Haverford College

1. Links between biology and math at Haverford College Phil Meneely (Biology) Rob Manning (Math)

2. Collaborative Research • We have a relatively large student-faculty research program, especially in biology (typical biology professor runs a lab with 4-8 students during the academic year and summer). • Some projects have linked math & bio, often co-advised, e.g., • Quantitative analysis of AFM images of myosin rod-domain filaments (Rigotti et al, Anal. Biochem. 346 (2005) 189.) • Multiple alignments of chromosomal proteins in C. elegans • Network analysis of the C. elegans germline proteins • Elastic rod models of DNA cyclization experiments • Epidemiological modeling of the effect of various testing procedures on the spread of Ebola • Statistical analysis of flexibility of helix-pairs in the PDB

3. Collaborative Research: from Anal. Bioch.(2005) 346:189-200 Quantitative AFM image analysis of unusual filaments formed by the Acanthamoeba castellanii Myosin II rod domain. Daniel J. Rigotti,* Bashkim Kokona,* Theresa Horne,† Eric K. Acton,§ Carl D. Lederman,†Karl A. Johnson,* Robert S. Manning,§ Suzanne Amador Kane,† Walter F. Smith,† and Robert Fairman*,1 *Department of Biology, †Department of Physics and, §Department of Mathematics, Haverford College, 370 Lancaster Ave, Haverford, PA 19041

4. Summer journal club • Weekly summer journal club for entire science division (for faculty and 50+ summer research students) • Many topics are interdisciplinary, often linking math, CS, & bio, e.g., • “Evidence for dynamically organized modularity in the yeast protein-protein interaction network” • “Superfamilies of evolved and designed networks” • “Coupling between catalytic site and collective dynamics: A Requirement for Mechanochemical Activity of Enzymes”

5. A Journal Club Talk from the Summer of 2005 Does the frequency of “motifs” characterize a network? Milo et al. 2004, Science 303: 1538-1542

6. Faculty Development • Series of HHMI faculty seminars involving 6-12 faculty from multiple science departments (plus some social science and humanities): • Computing Across the Sciences (2000-01) • Bioinformatics (2001-02) • Science and Society (2002-03) • Statistics Across the Curriculum (2003-04) • Imaging (2007-08)

7. Faculty Development (con’t) • Weekly presentations made by groups of 2-3 faculty from different departments, e.g.,: • Computational techniques in genomics (math, biology) • Numerical methods in molecular mechanics (math, chemistry, physics) • Hypothesis testing (biology, economics) • Analysis of Variance (psychology, chemistry, math) • Drug development and public health (chemistry, biology, economics) • What is modeling? (physics, CS, math)

8. Faculty Development (con’t) • Concrete Goals • New course “Computing Across the Sciences”, and production of “course modules” in scientific computation by seminar participants • New course “Computational Genomics” and outside experts for specific technical training in bioinformatics • Intangible Goals • For many, best part of seminar was chance to work with faculty from another department and division • Great way to see firsthand some differences between departments: terminology, level of mathematical formalism, what do students “need to know”, etc.

9. Faculty Development Statistics Group

10. Curriculum: Math in Biology Challenges • A distinctive constraint: our biology department is entirely molecular/cellular, so some familiar applications of mathematical biology such as population dynamics are not in our curriculum (but others, like bioinformatics and network biology, fit naturally). • Due to limited number of courses in liberal arts curriculum (32 in 4 years, including distribution requirements, and several chemistry prereqs for biology major), no math course required for biology major

11. Curriculum: Math in Biology (cont) • Biology 354: Computational Genomics • Junior/senior level course • Mostly biology or biochemistry students, few math students • Lecture and workshop format • Open-ended student projects and presentations

12. Computational Genomics SyllabusSpring 2007

13. Curriculum: Math in Biology (cont) • Lab module on bacterial growth in Bio 200 (Intro Bio) • Basic understanding of dN/dt = kN: sample mathematical derivation of solution; assigned reading: Neidhardt, “Bacterial Growth: Constant Obsession with dN/dt”, J. Bacteriology, 181 (1999) 7405. • Grow E. coli in Luria-Bertani medium • Quantify growth via optical density measurements (serial dilution added for improved accuracy) • Examine effect of antibiotics on growth curves, also situations in which dN/dt = kN model breaks down

14. Curriculum: Math in Biology (cont) • Statistics modules/consulting in Bio 499 (senior seminar) • Statistician made a couple of presentations to biology seniors and faculty on basics of experimental design and data analysis • Throughout the year, served as statistical consultant for students as they developed their senior project • Future development: with a new tenure-line statistician, we’re considering this model as a half-credit “consulting course” – attach statistician and a few students to a different senior seminar each year?

15. Curriculum: Biology in CS/Math Challenges • With small student body and faculty size, unlikely to regularly offer classes dedicated to biology students (though we have offered such a class every few years) • Core of our major is in pure math; applied electives often not taken until junior year or later

16. Curriculum: Biology in CS/Math • CS 185: Computing Across the Sciences • Co-taught by computer science and other faculty members (including biology) • Involves some programming with different scientific questions: the n-body problem, alignments, protein structure • BUT: enrollments have been small

17. Curriculum: Biology in CS/Math • Math 222: Introduction to Scientific Computing • “Look under the hood” at fundamental algorithms: nonlinear equations, optimization, random simulation, discretizations of differential equations • Lab-based (Mathematica): each problem offers students a choice between application in natural or social science • Some biological applications: bioinformatics, molecular mechanics, polymer statistics, reaction-diffusion equations, genetic algorithms

18. Curriculum: Biology in CS/Math • Math 222: Introduction to Scientific Computing • Some examples Genetic algorithm solving a knapsack problem Best-fit drug decay curves: exponential, bi-exponential Persistence length via simulated random polymers

19. Outreach • Haverford Summer Science Institute • For incoming science/premed students from high schools with no AP courses (this audience often struggles in 1st year chemistry and calculus, never making it to biology) • 5-week “boot camp” in chemistry, pre-calculus at a level representative of our intro courses • Weekly labs in each science discipline • Mentoring during the 1st year • Research placement during summer after 1st year • Develops peer group, relationships with science faculty

20. Future goals • Develop core set of mathematical/computational skills in biology students, tailored to some degree to our molecular/cellular specialization • Develop stronger curricular ties between math and biology at upper level • Minor in computational science – more bio majors taking advanced math/CS courses, and vice versa