Integration of Biology and Math Group

1. Integration of Biology and MathGroup New Jersey City University Benjamin Griffel Freda Wasserstein-Robbins St. John’s University Xingguo Cheng Diane Hardej Stony Brook University David Green Benjamin Martin Facilitators Peter Mirabito- University of Kentucky Rona Ramos- Yale University

2. Mathematical Modeling in Somitogenesis A unit in a class on Modeling in Developmental Biology Rationale: • Why was this topic chosen? • Pattern formation in development is a fundamental problem in biology. It is a topic where math has provided deep insight. Extensive modeling has been done in this area.

3. Context • What kind of course is unit designed for? • Undergraduate STEM Juniors and Seniors • How long is unit? • 6 lecture hours  • When will the unit be used in the course? • Last half of the course

4. Goals and Outcomes GOALS OUTCOMES Students will understand… • Factors that affect the process of somitogenesis • how mutation and chemical agents can disrupt the process of somitogenesis • the interrelatedness of Math and Bio in the process of somitogenesis Students will be able to… • define somitogenesis • understand the three control elements • understand how signaling gradients position somite borders

5. Goals and Outcomes GOALS OUTCOMES Students will understand… • Factors that affect the process of somitogenesis • how mutation and chemical agents can disrupt the process of somitogenesis • the interrelatedness of Math and Bio in the process of somitogenesis Students will be able to… • Discuss why mutations and chemical agents can disrupt genes in somitogenesis

6. Goals and Outcomes GOALS OUTCOMES Students will understand… • Factors that affect the process of somitogenesis • how mutation and chemical agents can disrupt the process of somitogenesis • the interrelatedness of Math and Bio in the process of somitogenesis Students will be able to… • use mathematical models to determine oscillations in the genes responsible for somitigenesis • explain how signaling gradients position somite borders • Explain the limitations of the model • Predict changes in phenotype based on quantitative changes in a model

7. We are segmented animals. Images from: Thompson J. Anat. Physiol. (1907). Smartimagebase.com: Item 1988. Humans: 33 vertebrae

8. Somitogenesis • Formation of the initial segmentation patterns (somites) that ultimately lead to vertebrae. Mouse: 60 vertebrae Zebrafish: 31 vertebrae Image from: Saga & Takeda Nat. Rev. Genetics (2001).

9. Clock (her) • Negative feedback in the clock gene  temporal oscillations within each cell DNA RNA Protein

10. Wavefront (FGF) • A tail-to-head gradient and “threshold effect”  moving front a fixed distance from the tail. Posterior (Tail) Oscillations ON Oscillations OFF Wavefront Anterior (Head)

11. Clock-Wavefront model in action • http://www.youtube.com/watch?feature=player_detailpage&v=FRuKxR0T5WQ

12. Click Question #1 In the video you just watched, the lower bar best represents: • The clock • The wavefront • The anterior-posterior gradient • Somites

13. Click Question #1 - Answer In the video you just watched, the lower bar best represents: • The clock • The wavefront • The anterior-posterior gradient • Somites

14. Click Question #2 In the video, the head of the embryo is located • To the left • To the right • To the top • To the bottom

15. Click Question #2 - Answer In the video, the head of the embryo is located • To the left • To the right • To the top • To the bottom

16. Think-Pair-Share, Group Discussion and Class Share • Think and work in pairs for 3 minutes. • As a table, share your results (2 minutes) and come up with a final answer to present to the class. • Consider a mutant organism with a difference in either the dynamics of the clock (“her” expression), or in the gradient that sets the wavefront (“fgf” expression). Predict the pattern of somites that should be observed as the mutant organism develops.

17. Wildtype Behaviour Time

18. Mutants (a) and (b) affect the clock.

19. Mutants (c) and (d) affect the gradient.

20. Fill in the pattern for the mutant Time Wildtype Mutant

21. Wildtype Behaviour Time

22. Group share!

23. Mutants (a) and (b) affect the clock.

24. Mutant (a) Wildtype Mutant (b)

25. Mutants (c) and (d) affect the gradient.

26. Mutant (c) Wildtype Mutant (d)

27. Different lifestyles require different somite numbers Image from: Gomez et al. Nature 2008 Corn snake: up to 6ft long – 315 vertebrae Image from: NY Times, Nov. 6 2007 Striped dolphin: up to 9ft long – 72 vertebrae

28. Tidbit Goals and Outcomes GOALS OUTCOMES Students will understand… • the interrelatedness of Math and Bio in the process of somitogenesis Students are now better able to… • Predict changes in phenotype based on quantitative changes in a model

29. Homework • Predict changes in the clock and wavefront model based on changes of phenotype • Analyze embryos with changes in somite phenotype and draw new clock and wavefront graphs on top of the wild-type graphs

30. Supplemental reading Segment number and axial identity in a segmentation clock period mutant Schröter C, Oates ACCurr Biol. 2010 Jul 27;20(14):1254-8 FGF signaling controls somite boundary position and regulates segmentation clock control of spatiotemporal Hox gene activation Dubrulle J, McGrew MJ, Pourquié OCell. 2001 Jul 27;106(2):219-32