Modeling the Growing Plant: The Arabidopsis Shoot Apical Meristem
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Modeling the Growing Plant: The Arabidopsis Shoot Apical Meristem
Bruce E. ShapiroBiological Network Modeling Center
The Beckman Institute at Caltech
www.computableplant.org
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• Some Background Information• Fluorescent Probe Confocal Microscopy• Arabidopsis• Connectivity & Cell Walls form Delaunay and
Voronoi• Cell Division and Plant Growth• Phyllotaxis• Cell Differentiation
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http://www.computableplant.org
• National Science Foundation (US) Frontiers in Integrative Biological Research (FIBR) Program Grants (First grants: Sept. 2003)– must integrate research tools from across multiple
disciplines: biology, math, physical sciences, information technology
– not limited by organizational boundaries– must answer a fundamental biological question– 5 year duration, renewable, ≈$1,000,000/year– 5± new grants annually
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• "To analyze the charms of flowers is like dissecting music; it is one of those things which it is far better to enjoy than to attempt to understand.” [Henry Tuckerman, 1853]
• “The project will track cell-by-cell changes in the mustard plant's meristem - the tissue in which cells actively divide and then differentiate into specialized cells. With fluorescent proteins marking specific cell types in specially designed transgenic plants, researchers will be able to trace the development of leaves and flowers.” [NSF Press Release, 2003]
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Elliot Meyerowitz Marcus HeislerVenu ReddyAdrienne RoederVikas Agrawal*
Bruce ShapiroVictoria Gor
Henrik Jönsson
Eric Mjolsness (PI)Pierre BaldiAlex SadovskyTigran BacarianAlexi VorbyovAshish BhanFang Fang
Nikolai KolchanovNadya OmelianchukNikolay PodkolodnySergei NikolaevVitali Likhoshvai
US National Science Foundation FIBR Grant 0330786
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... to bring together Caltech biologists, bioengineers, mathematicians, and computer scientists to develop and apply state-of-the-art computational tools for modeling and analyzing complex biological systems.
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Mjolsness E. Stochastic Process Semantics for Dynamical Grammer Syntax: An Overview. 9th International Symposium on Artificial Intelligence and Mathematics, Jan 2006.
Reddy GV, Meyerowitz EM. Stem-Cell Homeostasis Growth Dynamics can be Uncoupled in the Arabidopsis Shoot Apex. Science 310(5748):663-667.
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SystemsBiologyOntology
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• Fluorescent Probe Confocal Microscopy• Arabidopsis• Connectivity & Cell Walls form
Delaunay and Voronoi• Cell Division and Plant Growth• Phyllotaxis• Cell Differentiation
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lifesci.ucsb.edu/~biolum
www.reefs.org
Luminescent Jellyfish Aequoria victoria
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Luminescent Jellyfish Aequoria victoria
Marc Zimmer (Photo: Osamu Shimomura)http://www.conncoll.edu/ccacad/zimmer/GFP-ww/GFP2.htm
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Marc Zimmer
GFP: Green Fluorescent Protein
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GFP: Green Fluorescent ProteinCommercial Markerswww.anticancer.com
Transgenic ArtEduardo Kac
Neurons J. Lichtman,Science (2003)
Nikon’s Microscopyu.com
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Fluorescence Microscopy
Ground State
Higher Energy State
Internal Energy Loss
Photon EmittedSample absorbs high energy photon from laser
Intermediate State
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Venu ReddyMarcus Heisler
Laser Scanning Confocal MicroscopeZeiss LSM-510
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• Fluorescent Probe Confocal Microscopy• Arabidopsis• Connectivity & Cell Walls form
Delaunay and Voronoi• Cell Division and Plant Growth• Phyllotaxis• Cell Differentiation
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Shoot Apical Meristem
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Geographical distribution of Arabidopsis thaliana.Koornneff, Ann. Rev. Plant Biol. 2004
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Cell 88:299-308 (1997)
LiveImaging
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FM4-64 dye
Δz=2.25μ150μ ×150μ
51 image
“z-stack”
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PIN1:GFP (blue), REVOLUTA:YFP (green) and pFIL:dsRED (red)
Marcus Heisler, Caltech
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Cell 88:299-308 (1997)
Tracing CellLineages
Development 131:4225 (2004) Reddy et al
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Venu Reddy, Caltech
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Cell centers: Gradient Descent
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Tracking cell motion
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Thin Plate SplinesSoftassign
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Stress Tensor
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WallsExtracted by Watershed/Voronoi Model
PIN1
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Auxin Derived from PIN1
pH=5.0
pH=5.5pH=4.5
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• Fluorescent Probe Confocal Microscopy• Arabidopsis• Connectivity & Cell Walls form
Delaunay and Voronoi• Cell Division and Plant Growth• Phyllotaxis• Cell Differentiation
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Cell Walls: Voronoi Model
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Cell Connectivity: Delaunay
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Raw Data - (x, y, z) cell “centers”
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3D modified Voronoi Cross-section
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Slabs Flattened to 2D, modified Voronoi
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DiscreteMath`ComputationalGeometry`DelaunayTriangulation
qdelaunay
regtet
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• Fluorescent Probe Confocal Microscopy• Arabidopsis• Connectivity & Cell Walls form
Delaunay and Voronoi• Cell Division and Plant Growth• Phyllotaxis• Cell Differentiation
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Shoot Apical Meristem - tip of plant
Central Zone:Provides new cells
Peripheral Zone:Leaves, FlowerFormation
Rib:Cellsdivide and “push”Meristem up
STEM
Flowerbud
MERISTEM
50μ scale bar
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Internal External Receptor, c - Ligand, b
Mjolsness, Sharp & Reinitz J. Theor. Biol. 152: 429 (1991)Shapiro, Levchenko, Mjolsness, Meyerowitz, Wold, Bioinformatics 19(5):677 (2003)
τ a&va t( ) = g ua + ha( ) − λ ava
ua t( ) = Tabvb t( ) + Λi Tabvbi t( ) +
b∑
i∈Nbrs∑
b∑ Λi %Tac
(1) %Tac(2)vc t( )vb
i t( )c∑
b∑
i∈Nbrs∑
Protein regulation model
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Growth Model
&xi = eijkij xi (t)−xj (t) −dij (t)⎡⎣ ⎤⎦j∈Neigbors(i )
n
∑dij (t) =ri (t) + rj (t)
mi (t) =43πρri
3(t)
• Constant growth rate:
• Cell division on mass threshold
• Viscous spring model:
&mi (t)=μmi (t)
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Meristem Maintenance and Growth
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Mjolsness, Shapiro, Jönnson & Meyerowitz in BGRS, Kluwer (2002); also EMBS (2002)
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• Fluorescent Probe Confocal Microscopy• Arabidopsis• Connectivity & Cell Walls form
Delaunay and Voronoi• Cell Division and Plant Growth• Phyllotaxis• Cell Differentiation
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Phyllotaxis
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daidt
=K p −Kdai
É A1 24 34
−Tai Pijj
Ni
∑ +T ajPjij
Ni
∑Transport
1 24 4 4 34 4 4+ D aj
j
Ni
∑ −Niai
⎛
⎝⎜⎞
⎠⎟
Diffusion1 24 4 34 4
Pif (Aj )⏐ →⏐ ⏐ Pij (Auxin induces PIN1 polarization)
Auxin - A Plant HormoneIndole-3-acetic acidSynthesized from tryptophan?
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Jönsson, Heisler, Shapiro, Meyerowitz, Mjolsness, PNAS, USA, 103(5):1633, 2006
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• Fluorescent Probe Confocal Microscopy• Arabidopsis• Connectivity & Cell Walls form
Delaunay and Voronoi• Cell Division and Plant Growth• Phyllotaxis• Cell Differentiation
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Shoot Apical Meristem - tip of plant
Central Zone:Provides new cells
Peripheral Zone:Leaves, FlowerFormation
Rib:Cellsdivide and “push”Meristem up
STEM
Flowerbud
MERISTEM
50μ scale bar
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Cell Division and Differentiation
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Activator Model Simulation in Cellerator
270 cells6402 reactions1080 ODEs
Jönsson, Heisler, Reddy, Agrawal, Gor, Shapiro, Mjolsness, Meyerowitz. Bioinformatics 21(S1): i232-i240; ISMB 2005
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Activator Model
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Natural Template
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Ablation ExperimentsControlWUS domain
AfterAblation-No WUS
24 hrs laterTwo WusDomains
Side viewof ablated
area
Reinhardt et al. (2003) Development, 130:4073
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Ablated Center
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Ablation, random initial conditions
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Coming ...
• Multiscale models • Weighted & Dynamic Delaunay• Physics-based cell dynamic model• Root & Leaf Models• 3D Simulations on Template• Mesh/Finite element simulations
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Elliot Meyerowitz Marcus HeislerVenu ReddyAdrienne RoederVikas Agrawal*
Bruce ShapiroVictoria Gor
Henrik Jönsson
Eric Mjolsness (PI)Pierre BaldiAlex SadovskyTigran BacarianAlexi VorbyovAshish BhanFang Fang
Nikolai KolchanovNadya OmelianchukNikolay PodkolodnySergei NikolaevVitali Likhoshvai
http://www.computableplant.org