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Investigating Continuous Models
of WUSCHEL Expression in the
Shoot Apical Meristem of A.thaliana
Dana Mohamed
Mentor: Bruce Shapiro, Caltech
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?
+
=
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
WUSCHEL expression
Side View
Birds Eye View
Strategy Background
• In paper, model is discrete on extracted
template
• Average WUS intensity for individual cells is
obtained using confocal microscopy
Discrete Version
Determined
[WUS]
Activator Model
[WUS]
Repressor Model
[WUS]
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.
Equations, Repressor Model
Equations, Activator Model
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
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.
Initial, Boundary Conditions
Initial conditionswhere the expression levels start
↓
↑
Boundary conditions-
↑
where the edges of the model (of the
expression levels) are held through time
Basic Line, R-M, Standard Plot
•W[0,x] = Sin[Pi x]
•Plot[W(t,x)] from {t,0,1000}, {x,0,1}:
→
•Video:
Basic Line, R-M, Standard Plot
•W[0,x] = Sin[Pi x](1+Sin[5 Pi x])
•Plot[W(t,x)] from {t,0,1000}, {x,0,1}:
→
•Video:
2D Basic Square, R-M, Standard Plot
• Plot3D[W(t,x,y)]
at {t=0},
from {x,0,1},
{y,0,1}
W[0,x,y] = (1+Cos[Pi 2 x])(Sin[Pi x]Sin[Pi y])
• Plot3D[W(t,x,y)]
at {t=150},
from {x,0,1},
{y,0,1}
2D Basic Square, R-M, Standard Plot
•Plot3D[W(t,x,y)]
at {t=0,150},
from {x,0,1},
{y,0,1}
W[0,x,y] = (1+Cos[Pi 2 x])(Sin[Pi x]Sin[Pi y])
•Plot3D[W(t,x,y)]
at {t=0,150},
from {x,0,1},
{y,0,1}
W[0,x,y] = (1-Cos[Pi/2 x])(Sin[Pi x]Sin[Pi y])
2D Basic Square, A-M, Standard Plot
•Plot3D[W(t,x,y)]
at {t=0,150},
from {x,0,1},
{y,0,1}
W[0,x,y] = (1+Cos[1.5Pi x])(1+Cos[3Pi y])(Sin[Pi x]Sin[Pi y])
•Plot3D[W(t,x,y)]
at {t=0,150},
from {x,0,1},
{y,0,1}
W[0,x,y] = (1-Cos[.5Pi x])(Cos[.5Pi y])(Sin[Pi x]Sin[Pi y])
2D Basic Square, A-M, Time Difference
•Plot3D[W(t,x,y)]
at {t=0,300},
from {x,0,1},
{y,0,1}
W[0,x,y] = (1+Sin[4Pi x])(1+Sin[4Pi y])(Sin[Pi x]Sin[Pi y])
•Plot3D[W(t,x,y)]
at {t=0,250},
from {x,0,1},
{y,0,1}
W[0,x,y] = (1+Sin[6Pi x])(1+Sin[6Pi y])(Sin[Pi x]Sin[Pi y])
Polar Coordinates
•W[0,r,θ] = 0
•Plot[W(t,r,θ)] from {t,0,150}, {θ,0,2Pi}:
R-M Polar
A-M Polar
Polar Coordinates
Top View
Side View
Eric Mjolsness (PI)
Pierre Baldi
Alex Sadovsky
Tigran Bacarian*
Ashish Bhan*
Fang Fang*
Elaine Wong*
James Folsom
Elliot Meyerowitz
Marcus Heisler
Venu Reddy
Vikas Agrawal*
Victoria Gor
Bruce Shapiro
Arabidopsis
thaliana
Huntington
Botanical Gardens
Nikolai Kolchanov, Russian
Henrik Jönsson
Academy of Sciences,
Novosibirsk
Sponsored by the
NSF Frontiers in Integrative Biology Award 0330786
*not shown
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
Basic Line, R-M, Standard Plot
•W[0,x] = Sin[Pi x
•Plot[W(t,x)] from {t,0,1000}, {x,0,1}:
→
Basic Line, R-M, Standard Plot
•W[0,x] = Sin[Pi x](1+Sin[5 Pi x])
•Plot[W(t,x)] from {t,0,1000}, {x,0,1}:
→
2D Basic Square, R-M, Standard Plot
• Plot3D[W(t,x,y)]
at {t=0},
from {x,0,1},
{y,0,1}
W[0,x,y] = (1+Cos[Pi 2 x])(Sin[Pi x]Sin[Pi y])
• Plot3D[W(t,x,y)]
at {t=150},
from {x,0,1},
{y,0,1}
Basic Square, A-M, Standard Plot
• Plot3D[W(t,x,y)]
at {t=0},
from {x,0,1},
{y,0,1}
W[0,x,y] = (1+Sin[6Pi x])(1+Sin[6Pi y])(Sin[Pi x]Sin[Pi y])
• Plot3D[W(t,x,y)]
at {t=150},
from {x,0,1},
{y,0,1}
Polar Coordinates
•W[0,r,θ] = 0
•Plot[W(t,r,θ)] from {t,0,150}, {θ,0,2Pi}:
R-M Polar
A-M Polar
Polar Coordinates
Top View
Side View
Eric Mjolsness (PI)
Pierre Baldi
Alex Sadovsky
Tigran Bacarian*
Ashish Bhan*
Fang Fang*
Elaine Wong*
James Folsom
Elliot Meyerowitz
Marcus Heisler
Venu Reddy
Vikas Agrawal*
Victoria Gor
Bruce Shapiro
Arabidopsis
thaliana
Huntington
Botanical Gardens
Nikolai Kolchanov, Russian
Henrik Jönsson
Academy of Sciences,
Novosibirsk
Sponsored by the
NSF Frontiers in Integrative Biology Award 0330786
*not shown
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