Investigating Continuous Models of WUSCHEL Expression in the Shoot Apical Meristem of A.thaliana...
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Transcript of Investigating Continuous Models of WUSCHEL Expression in the Shoot Apical Meristem of A.thaliana...
Investigating Continuous Models of WUSCHEL Expression in the
Shoot Apical Meristem of A.thaliana
Dana MohamedMentor: 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 intercellularsignaling of 2 genes
• WUSCHEL and CLAVATA3
Strategy Background
• In paper, model is discrete on extracted template
• Average WUS intensity for individual cells is obtained using confocal microscopy
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.
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 conditions-where 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](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])
Eric Mjolsness (PI)Pierre Baldi
Alex SadovskyTigran Bacarian*
Ashish Bhan*Fang Fang*
Elaine Wong*
Elliot MeyerowitzMarcus Heisler
Venu ReddyVikas Agrawal*
Victoria GorBruce Shapiro
James FolsomHuntington Botanical Gardens
Nikolai Kolchanov, RussianAcademy of Sciences,
Novosibirsk
Henrik Jönsson
Arabidopsis thaliana
*not shown
Sponsored by theNSF Frontiers in Integrative Biology Award 0330786
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](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}
Eric Mjolsness (PI)Pierre Baldi
Alex SadovskyTigran Bacarian*
Ashish Bhan*Fang Fang*
Elaine Wong*
Elliot MeyerowitzMarcus Heisler
Venu ReddyVikas Agrawal*
Victoria GorBruce Shapiro
James FolsomHuntington Botanical Gardens
Nikolai Kolchanov, RussianAcademy of Sciences,
Novosibirsk
Henrik Jönsson
Arabidopsis thaliana
*not shown
Sponsored by theNSF Frontiers in Integrative Biology Award 0330786
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