Modeling the Growing Plant The Arabidopsis Shoot Apical

Modeling the Growing Plant: The Arabidopsis Shoot Apical Meristem Bruce E. Shapiro Biological 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/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 Heisler Venu Reddy Adrienne Roeder Vikas Agrawal* Bruce Shapiro Victoria Gor Henrik Jönsson Eric Mjolsness (PI) Pierre Baldi Alex Sadovsky Tigran Bacarian Alexi Vorbyov Ashish Bhan Fang Nikolai Kolchanov Nadya Omelianchuk Nikolay Podkolodny Sergei Nikolaev Vitali Likhoshvai US National Science Foundation FIBR Grant 0330786

. . . 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. 9 th 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.

Systems Biology Ontology

• Fluorescent Probe Confocal Microscopy • Arabidopsis • Connectivity & Cell Walls form Delaunay and Voronoi • Cell Division and Plant Growth • Phyllotaxis • Cell Differentiation

Luminescent Jellyfish Aequoria victoria lifesci. ucsb. edu/~biolum www. reefs. org

Luminescent Jellyfish Aequoria victoria Marc Zimmer (Photo: Osamu Shimomura) http: //www. conncoll. edu/ccacad/zimmer/GFP-ww/GFP 2. htm

GFP: Green Fluorescent Protein Marc Zimmer

GFP: Green Fluorescent Protein Neurons J. Lichtman, Science (2003) Commercial Markers www. anticancer. com Transgenic Art Eduardo Kac Nikon’s Microscopyu. com

Fluorescence Microscopy Higher Energy State Internal Energy Loss Intermediate State Sample absorbs high energy photon from laser Photon Emitted Ground State

Laser Scanning Confocal Microscope Zeiss LSM-510 Venu Reddy Marcus Heisler

• 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

Live Imaging Cell 88: 299 -308 (1997)

51 image “z-stack”

PIN 1: GFP (blue), REVOLUTA: YFP (green) and p. FIL: ds. RED (red) Marcus Heisler, Caltech

Tracing Cell Lineages Cell 88: 299 -308 (1997) Development 131: 4225 (2004) Reddy et al

Venu Reddy, Caltech

Cell centers: Gradient Descent

Tracking cell motion Thin Plate Splines Softassign

Stress Tensor

Walls. Extracted by Watershed/Voronoi Model PIN 1

Auxin Derived from PIN 1 p. H=5. 0 p. H=4. 5 p. H=5. 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”

3 D modified Voronoi Cross-section

Slabs Flattened to 2 D, modified Voronoi

Discrete. Math`Computati onal. Geometry`Delaunay Triangulation 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 Flower bud MERISTEM 50 scale bar Peripheral Zone: Leaves, Flower Formation Rib: Cells divide and “push” Meristem up

Protein regulation model 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)

Growth Model • Constant growth rate: • Cell division on mass threshold • Viscous spring model:

Meristem Maintenance and Growth 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

Auxin - A Plant Hormone Indole-3 -acetic acid Synthesized from tryptophan?

Jönsson, Heisler, Shapiro, Meyerowitz, Mjolsness, PNAS, USA, 103(5): 1633, 2006

• 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 Flower bud MERISTEM 50 scale bar Peripheral Zone: Leaves, Flower Formation Rib: Cells divide and “push” Meristem up

Cell Division and Differentiation

Activator Model Simulation in Cellerator 270 cells 6402 reactions 1080 ODEs Jönsson, Heisler, Reddy, Agrawal, Gor, Shapiro, Mjolsness, Meyerowitz. Bioinformatics 21(S 1): i 232 -i 240; ISMB 2005

Activator Model

Natural Template

Ablation Experiments Control WUS domain Side view of ablated area After Ablation. No WUS 24 hrs later Two Wus Domains Reinhardt et al. (2003) Development, 130: 4073

Ablated Center

Ablation, random initial conditions

Coming. . . • • • Multiscale models Weighted & Dynamic Delaunay Physics-based cell dynamic model Root & Leaf Models 3 D Simulations on Template Mesh/Finite element simulations

Elliot Meyerowitz Marcus Heisler Venu Reddy Adrienne Roeder Vikas Agrawal* Bruce Shapiro Victoria Gor Henrik Jönsson http: //www. computableplant. org Eric Mjolsness (PI) Pierre Baldi Alex Sadovsky Tigran Bacarian Alexi Vorbyov Ashish Bhan Fang Nikolai Kolchanov Nadya Omelianchuk Nikolay Podkolodny Sergei Nikolaev Vitali Likhoshvai