Links between biology and math at Haverford College

Phil Meneely (Biology)

Rob Manning (Math)

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

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

Collaborative Research: from Anal. Bioch.(2005) 346:189-200

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”

Milo et al. 2004, Science 303: 1538-1542

Does the frequency of “motifs” characterize a network?

A Journal Club Talk from the Summer of 2005

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)

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)

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.

Faculty Development Statistics Group

Curriculum: Math in BiologyChallenges

• 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

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

Computational Genomics SyllabusSpring 2007

Week Dates Lecture

1 March 20 Genome projects Demo: accessing databases

March 22 Workshop: organism databases, NCBI

2 March 27 Reports; Alignment basics Demo: BLAST

March 29 Alignments. Workshop: dot plots, BLAST

3 April 3 Reports; Scoring Matrices, statistics

April 5 Workshop: other BLAST tools, PSI-BLAST

4 April 10 Multiple alignments Demo: CLUSTALW

April 12 Workshop: Multiple Alignments

5 April 17 presentations on multiple alignments

April 19 Gene finding Demo: EST assembly

6 April 24 Comparative genomics Workshop: comparative genomics

April 26 Comparative genomics and predicting regulatory regions

7 May 1 Presentations

May 3 Presentations

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

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?

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

Curriculum: Biology in CS/Math

• CS 185: Computing Across the SciencesCo-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

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

Curriculum: Biology in CS/Math• Math 222: Introduction to Scientific

Computing– Some examples

Genetic algorithm solvinga knapsack problem

Persistence length via simulated random polymers

Best-fit drug decay curves:exponential, bi-exponential

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

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