Download Mathematical Modeling (PowerPoint) Northeast 2013

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
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
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
OUTCOMES
Students will be able to…



define somitogenesis
understand the three
control elements
understand how
signaling gradients
position somite borders
GOALS
OUTCOMES
Students will understand…
Students will be able to…
 Factors that affect the
 Discuss why mutations and
process of somitogenesis
chemical agents can disrupt
 how mutation and chemical
genes in somitogenesis
agents can disrupt the
process of somitogenesis
 the interrelatedness of
Math and Bio in the process
of somitogenesis
GOALS
OUTCOMES
Students will be able to…
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




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.
Images from:
Thompson J. Anat. Physiol. (1907).
Smartimagebase.com: Item 1988.
Humans: 33 vertebrae
Somitogenesis
• Formation of the initial segmentation patterns
(somites) that ultimately lead to vertebrae.
Image from:
Saga & Takeda Nat. Rev. Genetics (2001).
Mouse: 60 vertebrae
Zebrafish: 31 vertebrae
Clock (her)
• Negative feedback in the clock gene 
temporal oscillations within each cell
DNA
RNA
Protein
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)
Clock-Wavefront model in action
• http://www.youtube.com/watch?feature=play
er_detailpage&v=FRuKxR0T5WQ
Click Question #1
In the video you just watched, the lower bar
best represents:
A.
B.
C.
D.
The clock
The wavefront
The anterior-posterior gradient
Somites
Click Question #1 - Answer
In the video you just watched, the lower bar
best represents:
A.
B.
C.
D.
The clock
The wavefront
The anterior-posterior gradient
Somites
Click Question #2
In the video, the head of the embryo is located
A.
B.
C.
D.
To the left
To the right
To the top
To the bottom
Click Question #2 - Answer
In the video, the head of the embryo is located
A.
B.
C.
D.
To the left
To the right
To the top
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 Behaviour
Time
Mutants (a) and (b) affect the clock.
Mutants (c) and (d) affect the gradient.
Fill in the pattern for the mutant
Time
Wildtype
Mutant
Wildtype Behaviour
Time
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
Image from:
Gomez et al. Nature 2008
Image from:
NY Times, Nov. 6 2007
Corn snake: up to 6ft long – 315 vertebrae
Striped dolphin: up to 9ft long – 72 vertebrae
GOALS
Students will understand…
 the interrelatedness of
Math and Bio in the process
of somitogenesis
OUTCOMES
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):21932