New Jersey City University Benjamin Griffel

Freda Wasserstein-Robbins  

St. John’s University Xingguo Cheng

Diane Hardej 

Stony Brook University David Green

Benjamin Martin

FacilitatorsPeter Mirabito- University of KentuckyRona Ramos- Yale University

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.

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

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

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

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

We are segmented animals.

Humans: 33 vertebrae

Images from: Thompson J. Anat. Physiol. (1907). Smartimagebase.com: Item 1988.

Somitogenesis

• Formation of the initial segmentation patterns (somites) that ultimately lead to vertebrae.

Mouse: 60 vertebraeZebrafish: 31 vertebraeImage from:

Saga & Takeda Nat. Rev. Genetics (2001).

Clock (her)

• Negative feedback in the clock gene temporal oscillations within each cell

Protein

RNA

DNA

Wavefront (FGF)

• A tail-to-head gradient and “threshold effect” moving front a fixed distance from the tail.

Wavefront

Posterior (Tail)

Anterior (Head)

Oscillations ON

Oscillations OFF

Clock-Wavefront model in action

• http://www.youtube.com/watch?feature=player_detailpage&v=FRuKxR0T5WQ

Click Question #1In the video you just watched, the lower bar

best represents: A. The clockB. The wavefrontC. The anterior-posterior gradientD. Somites

Click Question #1 - AnswerIn the video you just watched, the lower bar

best represents: A. The clockB. The wavefrontC. The anterior-posterior gradientD. Somites

Click Question #2

In the video, the head of the embryo is locatedA. To the leftB. To the rightC. To the topD. To the bottom

Click Question #2 - Answer

In the video, the head of the embryo is locatedA. To the leftB. To the rightC. To the topD. To the bottom

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.

Wildtype BehaviourTime

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

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

Fill in the pattern for the mutantTime

Wildtype Mutant

Wildtype BehaviourTime

Group share!

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

Mutant (a) Wildtype Mutant (b)

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

Mutant (c) Wildtype Mutant (d)

Different lifestyles require different somite numbers

Corn snake: up to 6ft long – 315 vertebrae

Striped dolphin: up to 9ft long – 72 vertebraeImage from: NY Times, Nov. 6 2007

Image from:Gomez et al. Nature 2008

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

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

Segment number and axial identity in a segmentation clock period mutant Schröter C, Oates AC Curr 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 O Cell. 2001 Jul 27;106(2):219-32