MultiCell Modeling of Biological Development Using the GGH Model and CompuCell3D

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Multi-Cell Modeling of Biological Development
Using the GGH Model and CompuCell3D

• James A. Glazier
• Biocomplexity Institute
• Indiana University
• Bloomington, IN 47405
• USA

Marrakesh International Conference Workshop on
Mathematical Biology Saturday, November 14, 2009
Collaborators S. Schnell, R. Merks, M. Swat, C.
Little
Support NIH, Indiana University. For papers on
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Mathematical Biology/Biocomplexity at IUB

• About 15 faculty in Departments of Physics,
  Psychology, Biology, Cognitive Science,
  Chemistry, Computer Science, Mathematics, School
  of Informatics (Biocomplexity Institute).
• Focus Areas Networks, Epidemiology,
  Computational Neuroscience, Cell and Tissue
  Modeling, PDEs.
• Special PhDs in Biocomplexity/Biophysics (through
  Physics) and Complexity (through Informatics).
• Poster Available in Computer Room next to
  Registration office (or e-mail bioc_at_indiana.edu
  to request).
• For More Info visit www.biocomplexity.indiana.edu

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Orientation to Talk

• Focus of Talk a Set of TOOLS (CompuCell3D, a
  FREE, Open Source, Modeling Environment) for
  building multiscale models of cells and tissues.
• Goals of Talk Convince People to try CC3D. Find
  new collaborations.
• Will hold 2nd Training Workshop in Summer 2008
  (some funding available to attend).
• Please visit www.compucell3d.org to download
  software, manuals and info or e-mail
  glazier_at_indiana.edu to join our mailing list.

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Applications of Methodology

• Developed to Study Embryonic Development.
• Useful in Cancer/Tumor Modeling.
• Used in Immune System Modeling.
• Modeling of Spatial Interactions of Bacteria,
  Eukaryotes.
• Potential Use in more Ecosystem-oriented models.

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Development

• What is Development?
• Biological Process by Which a
• Fertilized Egg ? Organism
• Physical Process Which Translates
• Genetic Information (Genotype)
• ?
• Structure and Behavior (Phenotype)

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The Classic Problem of Development

• How does gene activity translate into phenotype?
• The classical genomic/analytic approach says x
  happens because gene y is expressed
• But how to go from expression to organism? Why
  are we not just blobs of cells expressing
  different genes?

Image Courtesy of Prof. Sima Setayeshgar (Indiana
University)
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Development as Self-Organization

• Interesting to Mathematicians because largely
  self-organized not prespecified.
• About 5104 genes and 109 cells. Genome does not
  contain enough information to specify each cell.
• Even if it did, development would be fragile if
  completely specified.
• Instead, highly robust at all levels.

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Feedback Loops

• Not Simply Signal?Differentiation?Pattern (Known
  as Prepatterning).
• Cells Create Their Own Environment, by Moving and
  Secreting New Signals, so Signaling Feeds Back on
  Itself.
• Hence Self-Organization and Robustness.

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Cell-Centered Modeling

• Genetics primarily drives the individual cell
• Response to extracellular signals secretion of
  signaling agents and extracellular matrix
  proteins.
• To understand how genetics drive multicellular
  patterning, distinguish two questions
• How does genetics drive cell phenomenology?
• How does cell phenomenology drive multicellular
  patterning?

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Why a Multi-Cell Model?

• Most mammalian cells are fairly limited in their
  behaviors. They can
• Grow,
• Divide,
• Change Shape,
• Move Spontaneously
• Move in Response to External Cues,
• Stick,
• Absorb,
• Secrete,
• Exert Forces
• Change their local surface properties
• (Send Electrical Signals)
• A long list, but not compared to 1010
  gene-product interactions.
• Many cells have relatively simple
  phenomenological behaviors most of the time.

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Look at Development Asking What Phenomenological
Behaviors Need to be Included in Models of Tissue
Development
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Main Processes in Development

• Cell Differentiation
• Cell Polarization
• Cell Movement
• Cell Proliferation and Death
• Cellular Secretion and Absorption

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Key Questions Concerning Differentiation

• What are the types of cells in a given process?
• What signals cause cells to change types?
• Due to diffusible substances?
• Due to Cell-Cell Contacts?
• Due to Cell History?
• Due to Cell-Extracellular Matrix Contact?
• What are the thresholds for these transitions?
• How do these signals interact?
• What are the rates or probabilities of these
  transitions?

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Cell Movement and Adhesion

• Cells Move Long Distances During Development.
• Move by Protruding and Retracting Filopodia or
  Lamellipodia (Leading Edge)
• Shape Changes During Movement May be Random or
  Directed.
• Move By Sticking Selectively to Other Cells
  (Differential Adhesion)
• Move By Sticking to Extracellular Material
  (Haptotaxis)
• Move By Following External Chemical Gradients
  (Chemotaxis)
• Can also have Bulk Movement
• Secretion of ECM
• Differential Cell Division
• Oriented Cell Division

Chemotaxis Play Movies
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Adhesion is Nice for Physicists

• Cell sorting could be explained by real
  minimization of cell-cell contact energies.
• Differences in Energy (potential) produces
  forces.
• If neglect mechanisms of adhesion,
• let Wab Force per unit contact area between
  cells type a b,
• Econtact?surface Wab ds Sum of all surface
  energies.

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Cells Behave Like Fluids

• Cells of a given type have characteristic
  adhesion strengths to cells of the same or
  different types.
• The cells comprising an aggregate are motile.
• The equilibrium configuration of cells minimizes
  their interfacial energy summed over all the
  adhesive contacts in the aggregate.

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Key Questions

• How strongly do cells of one type adhere to cells
  of another type?
• How strongly do cells of a given type adhere to
  ECM?
• How does cell adhesion change in time?

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Cells Send and Respond to SignalsChemotaxis
(Haptotaxis)

• Cell moves up (down) a gradient of a diffusible
  (non-diffusible) chemical.
• Cell senses diffusible chemicals through their
  receptors on surface.
• Intracellular signal transduction and
  cytoskeleton rearrangement.

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Key Questions

• How do cells move in response to chemical signals
  in their environment?
• How do cells change type in response to these
  signals?
• How do cells remodel their environment?

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Secretion and Absorption

• What chemicals do cells secrete and absorb?
• If they diffuse, how rapidly do these chemicals
  diffuse?
• If they do not diffuse, what are their mechanical
  properties, textures,?
• How stable are they (what is their decay rate)?

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Cell Growth and Death

• What signals cause cells to grow?
• What signals cause cells to die?
• (In many cases very little cell growth or death
  during a given developmental phase)

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Translation into Model

• Objects/Representations
• Object Properties/Interactions
• Dynamics
• Tweaks
• Initial and Boundary Conditions

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Objects/Representation

• Fundamental Entities are Cells and Generalized
  Cells (e.g. mesenchymal cells, epithelial cells,
  ECM, medium), represented on the primary Cell
  Lattice (usually a square lattice with third or
  fourth neighbor interactions). We denote lattice
  position by
• Cells have Internal States and Types which
  describe their properties.
• Have External Chemical Fields represented on
  Auxiliary Lattices with same geometry as the Cell
  Lattice.

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Object Properties/Interactions

• Most biological of Cells and their interactions
  with each other and with Fields are Encapsulated
  in the Effective Energy, H.
• H is generally the sum of many separate terms.
• Each term in H encapsulates a single biological
  mechanism.
• Additional Cell Properties described as
  Constraints.

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Energy Terms Adhesion

• Each unit of Cell Boundary (a Link between
  Adjacent Lattice Sites containing different
  Indices) has an associated Adhesion Energy, J,
  which depends on the Types of the Neighboring
  Cells
• The Total Adhesion Energy, Hadhesion is
• Where,

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Adhesion Energy Examples
Note Maximum Energy is 24J and Minimum -24J
for nearest neighbor 3 x 3 Lattice (Absorbing
Boundaries), all cells same type.
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Interaction between Fields and CellsEnergy
Terms Chemotaxis

• If a Cell is attracted or repelled by a chemical,
  the response is represented by a Chemotaxis or
  Haptotaxis Effective Energy, Hchemo
• mgt0?chemorepulsion, mlt0?chemoattraction.
• f is the response function of the cell to the
  chemoattractant.
• There may be many such terms, with different
  responses for each cell type.

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Chemotaxis/Haptotaxis

• If
• Saturation
• Modify the Effective Energy using the Extension
  Direction to bias filopodium extensions
  according to chemical gradient (Savill et al.
  1997).

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Additional Interactions

• Gravity
• Explicit Forces
• Contact Guidance
• Fluid Flows

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Constraints

• A Constraint is a very convenient method for
  implementing behaviors via an Effective Energy.
• In general, an elastic Constraint has the form
• l is the Constraint Strength and f the
  Constraint Function. The bigger l, the smaller
  the deviations of the behavior of the system from
  the target.
• ANY behavior can be implemented this way.

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Volume Constraints

• Most Cells (except Generalized Cells representing
  fluid media) have defined volumes.
• Provides an easy way to implement Cell growth
• And Cell Death

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Surface Constraints

• Many Cells also have defined membrane areas.
• The ratio
  (ddimension)
• controls the Cells general shape
• Small R means the Cell is floppy (underinflated
  basketball)
• Large R means the Cell is spherical and rigid.

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Additional Constraints

• Cell Elongation/Anisotropy
• Orientational Alignment
• Viscous Forces
• Inertia/Persistent Motion
• Elastic Solids
• Viscoelastic Materials

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Typical Interaction Effective Energy
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Dynamics
For a given DH, the Acceptance Probability is
Heterogeneous Nucleation is Forbidden. Y is a
Dissipation Threshold.
Also introduce concept of Copy or Protrusion
Direction , which May Affect the Acceptance
Probability.
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Field Equations

• Most Fields evolve via diffusion, secretion and
  absorption and cells and by decay.
• Sometimes we couple two or more Fields via
  Reaction-Diffusion Equations of Form

Diffusion Decay Secretion
Absorption
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Tweaks Mitosis

• Implement by setting a Threshold Volume for Cell
  Division.
• When reached, divide Cell along either random
  axis (random cell division) or axis with minimal
  moment of inertia (oriented cell division)
• Assign Cell Lattice Sites in one half of Cell to
  a new unique Index. New Cell Inherits other
  properties of Parent.
• Reset VtargetVtarget/2 for both Cells.
• If used, reset Mitotic Clocks for both cells
  and/or increment Mitotic Counts.

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Initial and Boundary Conditions

• Need to Define Initial Configurations for All
  Lattices and Initial Values for all Internal
  Variables and Parameters.
• Need to Define Boundary Conditions of Fields and
  Cell Lattice (Periodic or Fixed, Absorbing or
  Reflecting, Excluded Volumes/No Excluded
  Volumes).

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Major Simplifications

• No Membrane Curvature Energy (Hard to Implement
  on Lattice). Can do it with Subcells.
• Single Temperature with Boltzmann Spectrum
  Representing Highly Variable Cell Motilities.
• Need to Investigate Alternative Acceptance
  Functions.

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CompuCell3DA Fast Way to Build GGH Models

• An Open Source, Free Program available for
  Download from www.compucell3d.org
• Runs on Windows, Linux and Mac OSX.
• Specify Models using a Simple XML (CC3DML) and
  Python.
• Run Models and store and process output either
  on-screen or in background.
• Allows interfacing with your own code using
  Python or with standard Subcellular models (like
  SBW)

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Building A Model

• Define Objects (Cells, Cell Types and Fields).
• Define Energy Terms.
• Define Initial Conditions.
• Pick Parameter Values (Hard, but some rules of
  thumb).
• Run

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CC3DML
The most commonly needed functions are predefined
in CC3D and are specified using a specific
eXtended Markup Language (XML).
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Define Cell Types Used in the Simulation
Each CC3DML file must list all Cell Types that
will used in the simulation
ltPlugin Name"CellType"gt ltCellType
TypeName"Medium" TypeId"0"/gt ltCellType
TypeNameLight" TypeId"1"/gt ltCellType
TypeNameDark" "2"/gt lt/Plugingt
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Define Energy Terms of the Effective Energy and
their Parameters
Volume volume volumeEnergy(cell)
ltPlugin Name"Volume"gt ltTargetVolumegt25lt/Targ
etVolumegt ltLambdaVolumegt1.0lt/LambdaVolumegt lt/Plugi
ngt
ltPlugin Name"Surface"gt ltTargetSurfacegt21lt/Targ
etSurfacegt ltLambdaSurfacegt0.5lt/LambdaSurfacegt
lt/Plugingt
Surface area surfaceEnergy(cell)
ltPlugin Name"Contact"gt ltEnergy
Type1"Medium" Type2"Medium"gt0 lt/Energygt
ltEnergy Type1"Light" Type2"Medium"gt0
lt/Energygt ltEnergy Type1"Dark"
Type2"Medium"gt0.1 lt/Energygt ltEnergy
Type1"Light" Type2"Light"gt0.5 lt/Energygt
ltEnergy Type1"Dark" Type2"Dark"gt3.0
lt/Energygt ltEnergy Type1"Light"
Type2"Dark"gt0.5 lt/Energygt lt/Plugingt
Contact contactEnergy( cell1, cell2)
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Initializing the Cell Lattice Configuration
BlobInitializer fills a circular (or spherical)
volume and UniformInitializer a specified box
with rectangular cells (with side length given by
width parameter). By default, Cells will be
randomly assigned to have Types 1 or 2 but you
can specify ordered arrangements or additional
cell types. You may repeat commands to specify
multiple regions of cells. ltSteppable
Type"BlobInitializer"gt ltGapgt0lt/Gapgt
ltWidthgt5lt/Widthgt ltCellSortInitgtyeslt/CellSortIni
tgt ltRadiusgt40lt/Radiusgt lt/Steppablegt ltSteppa
ble TypeUniformInitializer"gt ltRegiongt
ltBoxMin x20 y20 z0/gt ltBoxMax
x100 y100 z1/gt ltTypesgt1,2lt/Typesgt
ltGapgt0lt/Gapgt ltWidthgt5lt/Widthgt
lt/Regiongt
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Initializing the Cell Lattice Configuration
You can also read in a PIF File to initialize the
Cell Lattice, using the syntax ltSteppable
Type"PIFInitializer"gt ltPIFNamegtfoaminit2D.piflt
/PIFNamegt lt/Steppablegt Use PIFInitializer to
create sophisticated initial conditions. PIF
files compose cells from single pixels or from
larger rectangular blocks The PIF file syntax
is Cell_id Cell_type x_low x_high y_low y_high
z_low z_high Example 1 amoeba 10 15 10 15 0 0
Creates a rectangular cell with x-coordinates
ranging from 10 to 15 (inclusive), y coordinates
ranging from 10 to 15 (inclusive) and z
coordinates ranging from 0 to 0 inclusive. To add
an extra pixel to the cell you would include the
following (note that cell_id is the same) 1
amoeba 16 16 10 10 0 0 Adding another cell is
also easy 2 bacterium 25 30 25 30 0 0 Later
lines in the PIF File overwrite earlier
assignments at the same Cell Lattice Site.
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Putting it all together - cellsort_2D.xml
ltCompuCell3Dgt ltPottsgt ltDimensions x"100"
y"100" z"1"/gt ltStepsgt10lt/Stepsgt
ltTemperaturegt2lt/Temperaturegt
ltFlip2DimRatiogt1lt/Flip2DimRatiogt lt/Pottsgt
ltPlugin Name"CellType"gt ltCellType
TypeName"Medium" TypeId"0"/gt ltCellType
TypeNameLight" TypeId"1"/gt ltCellType
TypeNameDark" "2"/gt lt/Plugingt ltPlugin
Name"Volume"gt ltTargetVolumegt25lt/TargetVolumegt
ltLambdaVolumegt1.0lt/LambdaVolumegt lt/Plugingt ltPl
ugin Name"Surface"gt ltTargetSurfacegt21lt/TargetSu
rfacegt ltLambdaSurfacegt0.5lt/LambdaSurfacegt
lt/Plugingt
ltPlugin Name"Contact"gt ltEnergy
Type1"Medium" Type2"Medium"gt0 lt/Energygt
ltEnergy Type1"Light" Type2"Medium"gt0
lt/Energygt ltEnergy Type1"Dark"
Type2"Medium"gt0.1 lt/Energygt ltEnergy
Type1"Light" Type2"Light"gt0.5 lt/Energygt
ltEnergy Type1"Dark" Type2"Dark"gt3.0
lt/Energygt ltEnergy Type1"Light"
Type2"Dark"gt0.5 lt/Energygt lt/Plugingt
ltSteppable Type"BlobInitializer"gt
ltGapgt0lt/Gapgt ltWidthgt5lt/Widthgt
ltCellSortInitgtyeslt/CellSortInitgt
ltRadiusgt40lt/Radiusgt lt/Steppablegt lt/CompuCell3Dgt
Coding the same simulation in C/C/Java/Fortran
would take you at least 1000 lines of code
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CompuCell3D Python Extensions
To combine the simplicity of predefined
structures with the flexibility of user-written
code, we allow the user to control any object
properties using the widely-used programming
language Python (quite similar to MatLab) but
Open Source. Python also allows steering from the
terminal.
An increase of the target volume of a cell could
be a complicated function of external chemical
concentrations or be determined by a complex
sub-cellular model. Python allows a simple way to
implement such functions def step(self,mcs)
iterate over all cells and increase target
volume invItrCompuCellPython.STLPyIteratorC
INV() invItr.initialize(self.inventory.getCo
ntainer()) invItr.setToBegin()
cellinvItr.getCurrentRef() while (1)
if invItr.isEnd() break
cellinvItr.getCurrentRef()
cell.targetVolume IncreaseVolumeSubCellModel(cel
l) increase target volume
invItr.next() Users supplies the
IncreaseVolumeSubCellModel(cell) function which
can be in any programming language.
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Systems Biology Workbench Subcellular Model
Integration
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Running the Simulation
Steering bar allows users to start or pause the
simulation, zoom in , zoom out, to switch between
2D and 3D visualization, change view modes (cell
field, pressure field , chemical concentration
field, velocity field etc..)
Player can output multiple views during single
simulation run Add Screenshot function
Information bar
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Applications

• Now We Can Build Elaborate Models Easily.
• What Type of Questions Can We Answer Using GGH
  Modeling?

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Examples

• Engulfment
• Vascular Development
• Biofilms
• Tumor Growth
• Gastrulation
• Somitogenesis

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Cell Sorting/Engulfment
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Cell SortingThe Simplest Model
Three Cell Types More Cohesive, Less Cohesive,
Medium
Random Blob Initial Conditions or Adjacent Domains
Outcome Depends on Js
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Engulfment
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Vascular Development
Courtesy Luigi Preziosi
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Hypothesis Chemotaxis (Gamba et al. 2003 Serini
et al., 2003)
Chemotaxis cells migrate to higher
concentrations of VEGF-A

• Saturation of VEGF-A gradients inhibits
  directional cell migration
• ECs produce VEGF-A during first hour of vascular
  development
• Lateral Inhibition of Cell movement on Cell-Cell
  contact

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PDE model by Gamba et al. PRL 90 (41) 118101.
Cell density n moves with velocity v, driven by
gradient of chemoattractant excreted by
endothelial cells.
Needs Unbiological Inertial Term. Pattern Forms,
then falls Apart. No Pattern Coarsening.
Ambrosi Gamba, B. Math. Biol. 2004
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Contact Inhibition of Motility

• Context-dependent effect of VEGF-A
  (Vascular-endothelial growth-factor A stimulates
  vasculogenesis)
• VE-Cadherin clusters at adherens junctions
  between endothelial cells
• VE-Cadherin-binding ? dephosporylation of VEGFR-2
• VEGF-A signaling
• in presence of VE-Cadherin AKT/PKB ?
• cell survival
• In absence of VE-Cadherin ERK/MAPK ?
• Actin polymerization cell motility / filopodia
• In model suppress chemotaxis at cell interfaces

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Vascular Development
Two Cell Types Vascular Endothelial Cells (ECs),
Medium One Field Vascular Endothelial Growth
Factor A (VEGF-A)
Surface tension Between Cells set to 0 (No
Adhesion). Cells are floppy. Cells secrete and
chemotax (with Contact Inhibition) to a
diffusible chemical field, which decays in the
external environment (autocrine
signaling) Random blob Initial Conditions or
Random Separated ECs
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Sprouting Angiogenesis

• Reproduces aspects of both capillary formation
  and sprouting
• How can we explain constant width of the cords?
• What are the scaling properties of the vascular
  network?

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Temporal Behavior Agrees with Morphometrics
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Three-Dimensional Angiogenesis
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Results

• Need Contact Inhibition to Generate Patterns.
• Same Mechanisms work for both Angiogenesis and
  Vasculogenesis.
• Can Rule Out VEGF165 as Chemoattractant.
• Including Cell Elongation Reproduces Experimental
  Pattern Structure and Kinetics Quantitatively.
• Not bad for such a simple model!

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Biofilms
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Biofilms (Bacterial Colonies)

• Formation of structures (mushrooms, etc)
• Why do biofilms collapse?
• Differentiation within Biofilm
• Competition, cooperation and patterning within
  multispecies biofilms

• How do biofilms form?
• Cell attachment
• Reorganization inside cell
• Spreading on surfaces
• Cell motility
• Cell division
• Secretion of Extracellular material
• Antimicrobial Resistance
• Mutation and competence

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Biofilm Model
Two Cell Types Bacteria, Medium One Diffusing
Field Nutrient
Bacterial Cells stick strongly to each
other. Nutrient Supplied at top of Lattice,
diffuses in Lattice, Consumed by Bacterial Cells.
Diffusion Decay Secretion
Absorption
Bacteria Grow and Divide randomly in Response to
Nutrient
Bacteria initially Randomly Spread on Bottom of
Cell Lattice
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Biofilms

• The crucial factor is nutrient competition
  between Bacteria, which we can define as the R
  consumption per unit growth of Bacteria /
  Diffusion constant of nutrient.
• If R is small, the bacteria grow as a flat front.
  
• For slightly larger values of R, the front
  becomes wavy.
• For still larger values of R, mushrooms form
  (equivalent to viscous fingering in fluids or
  fingering in directional solidification).
  
• The instability in biofilm growth occurs because
  the any mushrooms which grow faster than the
  others see a higher nutrient concentration and
  grow faster still. Their consumption of nutrient
  creates a surrounding nutrient deficit (a similar
  phenomenon occurs in reaction-diffusion systems
  with an inhibitor and activator and is called
  lateral inhibition).

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Tumors
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Tumor Types

• MALIGNANT
• Cancerous, has the potential to invade and
  destroy neighboring tissues and create metastases
  (spread of cancer to other parts of the body).
• BENIGN
• Compact, may locally grow to great size. Does not
  invade neighboring tissues and does not seed
  metastases. It usually does not return after
  surgical removal.

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MOTIVATION

• What is the physical difference between benign
  and malignant tumors?
• What mechanisms determine whether a tumor is
  benign or malignant?

Clue Biofilms Benign tumors smooth
interface Malignant tumors rough interface
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Anderson Tumor Model
Cell types normal, quiescent, mutated and
necrotic. Fields nutrient, extracellular matrix
(ECM) (non-cellular material supporting cells)
and matrix degradative enzyme (MDE) (degrades ECM
increasing tumor motility).
A. R. A. Anderson, Math. Med. Biol. 22, 163
(2005).
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Anderson Tumor Model
Cell types Normal, Quiescent, Mutated and
Necrotic. Fields nutrient, extracellular matrix
(ECM) (non-cellular material supporting cells)
and matrix degradative enzyme (MDE) (degrades ECM
increasing tumor motility).
Normal Cells Motile, adhere strongly to each
other, chemorepelled by ECM, divide, consume
nutrients and secrete MDE. Grow at a rate which
is 0 below a threshold, then jumps to a non-zero
value and increases linearly thereafter. Divide
randomly when reach threshold volume. At each
cell division, a Normal Cell has a fixed
probability of becoming a Mutated Cell. Normal
Cells experiencing excessive external pressure
(as measured by the difference between their
actual and target volumes) become Quiescent.
A. R. A. Anderson, Math. Med. Biol. 22, 163
(2005).
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Anderson Tumor Model
Mutated Cells have the same properties as normal
Cells except for reduced cell-cell adhesiveness.
Quiescent Cells consume nutrient but do not
divide. If pressure reduced, become Normal. If
pressure increases, become necrotic. Necrotic
Cells do nothing. Reaction-diffusion equations
for the Fields Nutrient concentration change
diffusion production by ECM uptake by tumor
cells decay MDE concentration change
diffusion production by cells decay ECM
concentration change degradation by MDE
A. R. A. Anderson, Math. Med. Biol. 22, 163
(2005).
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CONSTANT GROWTH RATE ABOVE THRESHOLD
Benign Tumor Sufficient supply of nutrients
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CONSTANT GROWTH RATE ABOVE THRESHOLD
Benign Tumor Sufficient supply of nutrients
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GROWTH RATE PROPORTIONAL TO NUTRIENT
CONCENTRATION ABOVE THRESHOLD
Malignant Tumor Sensitivity of growth to
nutrient supply leads to fingering instabilities
(and possibly metastasis)
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GROWTH RATE PROPORTIONAL TO NUTRIENT
CONCENTRATION ABOVE THRESHOLD
Malignant Tumor Sensitivity of growth to
nutrient supply leads to fingering instabilities
(and possibly metastasis)
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GROWTH RATE PROPORTIONAL TO NUTRIENT
CONCENTRATION WITH SMALLER SLOPE
Benign Tumor Slow nutrient-dependent growth
results in sufficient supply of nutrients
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GROWTH RATE PROPORTIONAL TO NUTRIENT
CONCENTRATION WITH SMALLER SLOPE
Benign Tumor Slow nutrient-dependent growth
results in sufficient supply of nutrients
82
8
24
16
G
4
12
20
?(m,t)
0
2
4
6
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SUMMARY

• Competition for nutirents as measured by r, the
  degree to which the growth rate of the cells
  depends on te nutrient concentration controls
  tumor morphology (spherical benign vs. fingering
  malignant).
• Agrees with in vitro experiments as reported in
  P. Macklin, J. Lowengrub, J. Theor. Biol. (2007).

84
Vasculature and Tumors
85
Development of Body Plan

• Specification of Body Axes
• Cleavage
• Gastrulation (Formation of Primitive
  StreakAnterior-Posterior)
• Somitogenesis (Formation of AP compartments)
• Organogenesis

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Gastrulation
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GastrulationFormation of Main Body Axis
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Gastrulation Model

• 4 types of cells Area Pellucida, Area Opaca,
  Kohlers Sickle, Streak Tip
• 5 cell behaviors Adhesion, Volume control,
  Secretion, Chemotaxis, (velocity correlation)
• Auxiliary mechanisms diffusion, decay

89
Various Mechanisms will Produce a Streak
ST secretes chemo-repellant for AO
ST secretes chemo-attractant for KS
KS secretes chemo-repellant for ST
90
Various Mechanisms will Produce a Streak
ST secretes chemo-repellant for AO
ST secretes chemo-attractant for KS
KS secretes chemo-repellant for ST
91
Which Chemotactic Mechanism?
92
Large-Scale MotionChemotaxis and Adhesion not
enough
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Viscous Drag
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Somitogenesis
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Patterning through segmentation
In most animal species, the anteroposterior (AP)
body axis is generated by the formation of
repeated structures segments. The brain, thorax
and limbs are formed through segmentation. In
vertebrates segmentation, mesodermal structures
called somites gives rises to the skeletal
muscles, occipital bone, vertebrae, ribs, some
dermis and vascular endothelium.
96
Somitogenesis
Anterior (head)
Somites
Forming somite
Older cells more anterior
Younger cells more posterior
Neural tube
Posterior (tail)
Presomitic mesoderm (PSM)
97
Somitogenesis
c-hairy-1 oscillations
Somitogenesis is controlled by a clock, whose
gene expression periodicity corresponds to the
formation of one somite. Hairy is a homologue of
a Drosophila segmentation gene.
Signaling and gene pathways involved in
somitogenesis segmentation clock. Dashed lines
indicate interactions with conflicting findings,
double arrow represent interactions with more
protein components than are represented here.
98
Caricature of Somitogenesis
99
Eph knockout /Initialization
100
PSM-ECM Strong Interaction Parameter Optimized
Adhesion-Repulsion /Control
PSM-ECM Strong Interaction
101
N-cadherin knockout
102
Compartment Boundary Crossing

• Experimental figure from Kulesa et al.

103
Adhesion-based Error Correction
104
CompuCell3D Allows You Easily to Reproduce any of
the Cell-Based Models in this Talk, or to Develop
Your OwnWe are always looking for new groups to
work with and can support training at IUB of
people interested in learning to use
CompuCell3DWill have Training Workshop in
Summer 2008

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