Modeling the Growing Plant: The Arabidopsis Shoot Apical Meristem

Bruce E. ShapiroBiological Network Modeling Center

The Beckman Institute at Caltech

bshapiro@caltech.edu

www.computableplant.org

• Some Background Information• Fluorescent Probe Confocal Microscopy• Arabidopsis• Connectivity & Cell Walls form Delaunay and

Voronoi• Cell Division and Plant Growth• Phyllotaxis• Cell Differentiation

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

• "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]

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.

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

lifesci.ucsb.edu/~biolum

www.reefs.org

Luminescent Jellyfish Aequoria victoria

Luminescent Jellyfish Aequoria victoria

Marc Zimmer (Photo: Osamu Shimomura)http://www.conncoll.edu/ccacad/zimmer/GFP-ww/GFP2.htm

Marc Zimmer

GFP: Green Fluorescent Protein

GFP: Green Fluorescent ProteinCommercial Markerswww.anticancer.com

Transgenic ArtEduardo Kac

Neurons J. Lichtman,Science (2003)

Nikon’s Microscopyu.com

Fluorescence Microscopy

Ground State

Higher Energy State

Internal Energy Loss

Photon EmittedSample absorbs high energy photon from laser

Intermediate State

Venu ReddyMarcus Heisler

Laser Scanning Confocal MicroscopeZeiss LSM-510

• Fluorescent Probe Confocal Microscopy• Arabidopsis• Connectivity & Cell Walls form

Delaunay and Voronoi• Cell Division and Plant Growth• Phyllotaxis• Cell Differentiation

Shoot Apical Meristem

Geographical distribution of Arabidopsis thaliana.Koornneff, Ann. Rev. Plant Biol. 2004

Cell 88:299-308 (1997)

LiveImaging

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

Cell 88:299-308 (1997)

Tracing CellLineages

Development 131:4225 (2004) Reddy et al

Venu Reddy, Caltech

Cell centers: Gradient Descent

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Tracking cell motion

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Thin Plate SplinesSoftassign

Stress Tensor

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WallsExtracted by Watershed/Voronoi Model

PIN1

Auxin Derived from PIN1

pH=5.0

pH=5.5pH=4.5

• Fluorescent Probe Confocal Microscopy• Arabidopsis• Connectivity & Cell Walls form

Delaunay and Voronoi• Cell Division and Plant Growth• Phyllotaxis• Cell Differentiation

Cell Walls: Voronoi Model

Cell Connectivity: Delaunay

Raw Data - (x, y, z) cell “centers”

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3D modified Voronoi Cross-section

Slabs Flattened to 2D, modified Voronoi

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DiscreteMath`ComputationalGeometry`DelaunayTriangulation

qdelaunay

regtet

• Fluorescent Probe Confocal Microscopy• Arabidopsis• Connectivity & Cell Walls form

Delaunay and Voronoi• Cell Division and Plant Growth• Phyllotaxis• Cell Differentiation

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

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

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)

Meristem Maintenance and Growth

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Mjolsness, Shapiro, Jönnson & Meyerowitz in BGRS, Kluwer (2002); also EMBS (2002)

• Fluorescent Probe Confocal Microscopy• Arabidopsis• Connectivity & Cell Walls form

Delaunay and Voronoi• Cell Division and Plant Growth• Phyllotaxis• Cell Differentiation

Phyllotaxis

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?

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

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

Cell Division and Differentiation

Activator Model Simulation in Cellerator

270 cells6402 reactions1080 ODEs

Jönsson, Heisler, Reddy, Agrawal, Gor, Shapiro, Mjolsness, Meyerowitz. Bioinformatics 21(S1): i232-i240; ISMB 2005

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

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

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