new jersey city university benjamin griffel freda wasserstein-robbins st. john’s university...
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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