INTERDISCIPLINARY QUANTITATIVE REASONING IN BIOLOGY EDUCATION

26 March 2014 John R. Jungck

BioQUEST Curriculum Consortium Editor, Biology International, International Union of Biological Sciences

Professor of Biological & Mathematical Sciences, University of Delaware, USA Director, Interdisciplinary Sciences Learning Laboratories

jungck@udel.edu <http://bioquest.org>

Examples: Population Size

(Capture-Mark-Recapture) Buffer Preparation

(Henderson-Hasselbach) Serial Dilution

(Enumerating Bacteria) Allele Frequencies (Classroom Data)

Modeling More Mold

Measuring the area covered by mold over intervals of time!

Image J Measurement

“Exponential growth and then levels off” - Microbio Teacher!

Robert Blystone Trinity University

Ka-me: A Voronoi Image Analyzer

Bioinformatics (2012)

Problem  for  today:    How  do  we  understand  biological  tessella7ons  that  are  produced  by  several  rounds  of  successive  cell  division?  

Richard  Jones  

Mito7c  Division  2  

Abstract!

Bibliography!

What happens when?

•  Your ruler doesn’t seem to work right?

•  Your mean and variance don’t agree with another published study?

•  Duplicates of experiments vary widely?

Fractal Measurements • Rulers

•  Box Plots • Concentric Annuli

•  Log-Log Plots

Fractal Dimension Calculator Written by Paul Bourke (February 2003)

• Bacterial colonies exhibit complex growth patterns on starvation conditions (Shane Stafford and Yan Li:):!

• Experimentally:!

• The growth pattern and fractal dimension depend on both the nutrient concentration and roughness of the agar substrate !

• Bacteria perform a random walk like movement on the substrate, within a well-defined envelope (lubrication layer)!

• Under extreme adverse living conditions, patterns become dense again by chemo tactic signaling!

E Ben-Jacob et al, Nature,368, (47)1994,!

Fractal Bacterial Growth

Fractal Dimension of Healthy and Leukemic Cells

Dangers of Linear Transformations:!Michaelis-Menten Enzyme kinetics!

-d[S]/dt = Vmax[S]/KM + [S]!

Computational Complexity

EBI: “Important: We kindly ask all users of EMBL-EBI Web Services to submit tool jobs in batches of up to 25 at a time and to not submit more until the results and processing has completed for these. This enables users as well as the service maintainers to deal more easily with local and remote network outages as well as

scheduled or unscheduled downtime.”

Visualization

 visualization + equations + simulations lead to better understanding

 aesthetic aspects attract attention  examples: WWW, images, toys, gadgets

Barbara Maria Stafford!!!

“What is lacking today, however, is a concomitant !high-level visual education to accompany the!

advances in visualization”!!!!

Artful Science: Enlightenment, Entertainment and the!Eclipse of Visual Education, MIT Press (1994) !

Hans Rosling and Gapminder: provide resources for context

www.gapminder.org  

Gapminder: Goal to make data accessible and understandable

•  What’s here: Gapminder WORLD from UNICEF

Health vs Wealth

Visualizing Data

www.gapminder.org/

Starvation Plot

BIRDD: Species with regard to Wing Length Upper Beak Length and Beak Height

http://people.eku.edu/ritchisong/RITCHISO//DarwinsFinches.jpg

Evolution class yesterday: Jared Wynne, David Meltzer, and Aaron Nesser

Arthur Nature Reviews Genetics; 11 April 2006

Bioorthogonal Transformations!

Scaling and shear

transformations capture beak

shape variation in Darwin’s

finches.

O. Camp , R. Mallarinob, A.

Herrelb, A. Abzhanovb, and M. P. Brennera/

School of Engineering and

Applied Sciences, Harvard

University and Department

of Organismic and Evolutionary Biology, Harvard

University

D’Arcy Wentworth Thompson: Linear

D’Arcy Wentworth Thompson: Affine

D’Arcy Wentworth Thompson: Quadratic

STEM TO STEAM

http://www.steamedu.com/!!

Richard Dawkins & Lalla Ward (“Dr. Who”)

(1994)!

Seeing is:

•  Doing •  Measuring •  Testing hypotheses •  Re-visioning •  Modeling

SequenceIt!

 COMBINATORIAL EXPLOSION  19! = 1.22 * 1017  opportunity for “infinite opportunity” to

do research  heuristics vs. algorithms  realism: run out of material; improperly

designed experiments = poor results

Mastermind Mastermind Mathematics:

Logic, Strategies, and Proofs by Mathew Mitchell.

Key Curriculum Press.

Mathematics teachers have long used the game MASTERMIND to teach logic and deduction. Mathew Mitchell, an associate professor at the University of San Francisco Department of Learning and Instruction, makes the connections between game strategies and mathematics concepts such as problem-solving and proof strategies. As students use this book and play MASTERMIND, apply strategies such as establishing subgoals, making a chart, deductive reasoning, eliminating possibilities, pattern searching, and proof by contradiction.

http://www.maa.org/mathland/mathtrek_10_11_99.html Ivars Peterson’s Math Trek column on math & “Mastermind.”

Done by an undergraduate

Alfred Henry Sturtevant 1891-1970

First Ever Genetic Map - Drosophila X-chromosome !

3!

Linkage Analysis in the

Biological ESTEEM Project Excel Simulations and Tools for

Exploratory, Experiential Mathematics

Benzer 1959, 1961 papers: topology and topography of

genetic fine structure

•  Topography paper: –  map several thousand point mutations using nested set of deletion alleles

–  note difference between spontaneous and induced mutations, first detailed analysis of mutagen specificity

javaBENZER Problem Solving Tools: Solve Problem = rearranges Shkurba (Mut) into Shkurba form

with all Maximal Cliques ordered on main diagonal Applications: Protein and Nucleic Acid Sequencing;

Restriction, Deletion, and Complementation Mapping; Microarray Gene Expression Data; Food Webs

My interactive solution Computer algorithm solution

Lower right to upper left is isomorphic to upper left to lower right

Phylogenetic Trees

Fitch, W.M. and Margoliash, E. 1967. The construction of phylogenetic trees - a generally applicable method utilizing estimates of the mutation distance obtained from cytochrome c sequences. Science 155: 279-284.

Walter M. Fitch Emmanuel Margoliash

4!

4!

Graph Theory: Phylogenetic Trees!4!

An example problem using Phylogenetic Analysis

•  1990: HIV+ dentist in Florida •  several patients also HIV+ •  was the dentist the source? •  some patients with other HIV risk

factors •  virus from dentist, patients, others •  evolutionary relationships of virus gp120

gene → transmission of virus

4!

CDC Conclusion Dentist Patient Patient Patient Other Other Other

Split Decomposition: Evaluate Evidence for Internal Branches

Alpha !AAGAAGCAGGGGCTGGAGATGAAGGCCCATG!Beta !AAGAAGCGGAGGCTGGAGCTGAAGGCCCATG!Gamma !AAGAAGCGGAGGGTGGAGCTGAAGGCCCACG!Delta !GAGAAGAGGAGCCTGGAGCTGAAGGCCCACA!

Three possible unrooted trees:

A

B

G

D

A

G

B

D

A

D

B

G

Alpha !AAGAAGCAGGGGCTGGAGATGAAGGCCCATG!Beta !AAGAAGCGGAGGCTGGAGCTGAAGGCCCATG!Gamma !AAGAAGCGGAGGGTGGAGCTGAAGGCCCACG!Delta !GAGAAGAGGAGCCTGGAGCTGAAGGCCCACA!

A

B

G

D

dAB dGD

dAG

dBD

dcentral =

dcentral

2 ONLY for the correct tree!!!

How can we calculate the length of the central branch?

dAB

dGD

dAG + dBD - ( dAB + dGD )

Split Decomposition

Which tree topology is most consistent with the data?

The Algorithmic Beauty of Sea Shells

Biological Cellular Automata Laboratory (BioCA Lab)

Author(s): John Jungck, University of Delaware Jennifer Spangenberg, Washington State University

Nobel Prize 1969

Salvador Luria Max Delbrück 1924-1998 1919-2004 “Fluctuation Test” Poisson Statistics Mutation Rates!

Darwin vs Lamarck!Considered by many as the finest experiment in 20th Century!

9!

FLUCTUATION TEST

A TEST OF DARWINISM VS LAMARCKISM

Genetics Construction Kit  Gene Interaction

1:2:1:2:4:2:1:2:1 3:6:3:1:2:1 9:3:3:1  Epistasis

9:3:4 9:7 15:1 13:3 12:3:1  Polygenes

1:4:6:4:1  Quasi-quantitative

10:5:1 11:4:1 11:2:2:1

Genetics Construction Kit (the integrated organismal model)

 Linkage (Haldane Function)  Multiple Loci/ Stochasticity 1-10  Multiple Alleles 1-5  Sex-linkage, Sex-limited, Sex-influenced  Gene Interaction/Polygenes/Epistasis  Monoecious/Dioecious  Lethality/Penetrance/Pleiotropy

3!

Beer-Lambert law,

E. O. Wilson

Robert MacArthur

Island Biogeography

Theory

Allometry Species-Area- Distance-Law

8!

Source of most CONSEVATION strategies and policies!

Island Biogeography: Species-Area Law!

“Bacterial genetic diversity in this system increased with increasing island size according to the familiar species-area power law (Fig. 1A). The slope z of the relationship (z = 0.26) is indistinguishable from published values for larger organisms (Fig. 1B). The data show that area size strongly influences the diversity of these microbial communities.” (Bell et al. 2005 Science 308:1884).

Spatial scaling of bacteria in water-filled treeholes

Lee Segel Prize for Best Paper 2010

Brynja R. Kohler, Rebecca J. Swank, James W. Haefner, James A. Powell.

"Leading Students to Investigate Diffusion as a Model

of Brine Shrimp Movement” Bull. Math. Biol. 72: 230-57 (2010).

Society for Mathematical Biology

Invade  the  Biology  Lab!  

SMB Lee Segel Prize