Investigating Continuous Models of WUSCHEL Expression in the Shoot Apical Meristem of A.thaliana

1
Investigating Continuous Models of WUSCHEL
Expression in the Shoot Apical Meristem of
A.thaliana

• Dana Mohamed
• Mentor Bruce Shapiro, Caltech

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Computable Plant

• How do environmental factors and genetic makeup
  interact to shape plant meristem developmental
  processes that lead to plant flowers, leaves,
  shoots and stems?

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Shoot Apical Meristem

• Stem cell equivalent
• Where new cells are
• created for the stem,
• leaves, and flowers
• Controlled by intercellular
• signaling of 2 genes
• WUSCHEL and CLAVATA3

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WUSCHEL expression

• Side View Birds Eye View

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Strategy Background

• In paper, model is discrete on extracted template
  
• Average WUS intensity for individual cells is
  obtained using confocal microscopy

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Discrete Version
Determined WUS
Activator Model WUS
Repressor Model WUS
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Activator Model Vs. Repressor Model

• The activator model assumes
• there is an activator that
• activates WUS, located where
• WUS expression is high.
• The repressor model assumes
• there is always high WUS
• expression except where
• there is an inhibitor.

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Equations, Repressor Model
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Equations, Activator Model
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Goal Rationale

• Goal
• To extend the models of the gene expression to a
  continuous model
• to see if model still holds
• Rationale
• The models of this project were created as a way
  to describe and test several hypotheses
• Further testing the models and extending their
  applicability simply furthers their research

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Strategy

• To use Mathematica to extend the models.
• 1 Dimension, Line - 2 Dimensions,
  Square
• 2 Dimensions, Circle
• To test different initial conditions while
  holding the boundary conditions to 0, as set in
  the original paper.

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Initial, Boundary Conditions

• Initial conditions-
• where the expression levels start
• Boundary conditions-
• where the edges of the model (of the expression
  levels) are held through time

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?
?
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Basic Line, R-M, Standard Plot

• W0,x SinPi x
• PlotW(t,x) from t,0,1000, x,0,1
• Video

?
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Basic Line, R-M, Standard Plot

• W0,x SinPi x(1Sin5 Pi x)
• PlotW(t,x) from t,0,1000, x,0,1
• Video

?
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2D Basic Square, R-M, Standard Plot

• Plot3DW(t,x,y)
• at t0,
• from x,0,1,
• y,0,1
• W0,x,y (1CosPi 2 x)(SinPi xSinPi y)
• Plot3DW(t,x,y)
• at t150,
• from x,0,1,
• y,0,1

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2D Basic Square, R-M, Standard Plot

• Plot3DW(t,x,y)
• at t0,150,
• from x,0,1,
• y,0,1
• W0,x,y (1CosPi 2 x)(SinPi xSinPi y)
• Plot3DW(t,x,y)
• at t0,150,
• from x,0,1,
• y,0,1
• W0,x,y (1-CosPi/2 x)(SinPi xSinPi y)

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2D Basic Square, A-M, Standard Plot

• Plot3DW(t,x,y)
• at t0,150,
• from x,0,1,
• y,0,1
• W0,x,y (1Cos1.5Pi x)(1Cos3Pi
  y)(SinPi xSinPi y)
• Plot3DW(t,x,y)
• at t0,150,
• from x,0,1,
• y,0,1
• W0,x,y (1-Cos.5Pi x)(Cos.5Pi y)(SinPi
  xSinPi y)

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2D Basic Square, A-M, Time Difference

• Plot3DW(t,x,y)
• at t0,300,
• from x,0,1,
• y,0,1
• W0,x,y (1Sin4Pi x)(1Sin4Pi y)(SinPi
  xSinPi y)
• Plot3DW(t,x,y)
• at t0,250,
• from x,0,1,
• y,0,1
• W0,x,y (1Sin6Pi x)(1Sin6Pi y)(SinPi
  xSinPi y)

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Polar Coordinates

• W0,r,? 0
• PlotW(t,r,?) from t,0,150, ?,0,2Pi
• R-M Polar A-M Polar

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Polar Coordinates

• Top View Side View

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References, Acknowledgements

• (2005) Jönsson H, Heisler M, Reddy GV, Agrawal V,
  Gor V, Shapiro BE, Mjolsness E, and Meyerowitz
  E.M., Modeling the organization of the WUSCHEL
  expression domain in the shoot apical meristem.
  Bioinformatics 21(S1) i232-i240.
• Bruce Shapiro, Ph.D
• Computable Plant
• SoCalBSI

23
Basic Line, R-M, Standard Plot

• W0,x SinPi x
• PlotW(t,x) from t,0,1000, x,0,1

?
24
Basic Line, R-M, Standard Plot

• W0,x SinPi x(1Sin5 Pi x)
• PlotW(t,x) from t,0,1000, x,0,1

?
25
2D Basic Square, R-M, Standard Plot

• Plot3DW(t,x,y)
• at t0,
• from x,0,1,
• y,0,1
• W0,x,y (1CosPi 2 x)(SinPi xSinPi y)
• Plot3DW(t,x,y)
• at t150,
• from x,0,1,
• y,0,1

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Basic Square, A-M, Standard Plot

• Plot3DW(t,x,y)
• at t0,
• from x,0,1,
• y,0,1
• W0,x,y (1Sin6Pi x)(1Sin6Pi y)(SinPi
  xSinPi y)
• Plot3DW(t,x,y)
• at t150,
• from x,0,1,
• y,0,1

27
Polar Coordinates

• W0,r,? 0
• PlotW(t,r,?) from t,0,150, ?,0,2Pi
• R-M Polar A-M Polar

28
Polar Coordinates

• Top View Side View

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(No Transcript)
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References, Acknowledgements

• (2005) Jönsson H, Heisler M, Reddy GV, Agrawal V,
  Gor V, Shapiro BE, Mjolsness E, and Meyerowitz
  E.M., Modeling the organization of the WUSCHEL
  expression domain in the shoot apical meristem.
  Bioinformatics 21(S1) i232-i240.
• Bruce Shapiro, Ph.D
• Computable Plant
• SoCalBSI