Title: MultiCell Modeling of Biological Development Using the GGH Model and CompuCell3D
1Multi-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
these projects, please visit http//www.biocomplex
ity.indiana.edu
2Bloomington Indiana and Indiana University
Population (excluding students) 55,000, 30 of
whom have PhDs About 35 work at Indiana
University, 40,000 students, 25
international Famous for Sex Research (Kinsey
Institute), Music (Biggest Conservatory in USA),
Central Asian Studies (Biggest Program in
Mongolian Studies in World).
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3Mathematical 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
4Orientation 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.
5Applications 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.
6Development
- What is Development?
- Biological Process by Which a
- Fertilized Egg ? Organism
-
-
- Physical Process Which Translates
- Genetic Information (Genotype)
- ?
- Structure and Behavior (Phenotype)
7The 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)
8Development 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.
9Feedback 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.
10Cell-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?
11Why 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.
12Look at Development Asking What Phenomenological
Behaviors Need to be Included in Models of Tissue
Development
13Main Processes in Development
- Cell Differentiation
- Cell Polarization
- Cell Movement
- Cell Proliferation and Death
- Cellular Secretion and Absorption
14Key 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?
15Cell 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
16Adhesion 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.
17Cells 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.
18Key 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?
19 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.
20Key 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?
21Secretion 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)?
22Cell 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)
23Translation into Model
- Objects/Representations
- Object Properties/Interactions
- Dynamics
- Tweaks
- Initial and Boundary Conditions
24Objects/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.
25Object 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.
26Energy 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,
27Adhesion Energy Examples
Note Maximum Energy is 24J and Minimum -24J
for nearest neighbor 3 x 3 Lattice (Absorbing
Boundaries), all cells same type.
28Interaction 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.
29Chemotaxis/Haptotaxis
- If
- Saturation
- Modify the Effective Energy using the Extension
Direction to bias filopodium extensions
according to chemical gradient (Savill et al.
1997).
30Additional Interactions
- Gravity
- Explicit Forces
- Contact Guidance
- Fluid Flows
-
31Constraints
- 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.
32Volume Constraints
- Most Cells (except Generalized Cells representing
fluid media) have defined volumes. - Provides an easy way to implement Cell growth
- And Cell Death
33Surface 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.
34Additional Constraints
- Cell Elongation/Anisotropy
- Orientational Alignment
- Viscous Forces
- Inertia/Persistent Motion
- Elastic Solids
- Viscoelastic Materials
-
35Typical Interaction Effective Energy
36Dynamics
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.
37Field 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
38Tweaks 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.
39Initial 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).
40Major 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.
41CompuCell3DA 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)
42Building 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
43CC3DML
The most commonly needed functions are predefined
in CC3D and are specified using a specific
eXtended Markup Language (XML).
44Define 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
45Define 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)
46Initializing 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
47Initializing 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.
48Putting 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
49CompuCell3D 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.
50Systems Biology Workbench Subcellular Model
Integration
51Running 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
52Applications
- Now We Can Build Elaborate Models Easily.
- What Type of Questions Can We Answer Using GGH
Modeling?
53Examples
- Engulfment
- Vascular Development
- Biofilms
- Tumor Growth
- Gastrulation
- Somitogenesis
54Cell Sorting/Engulfment
55Cell SortingThe Simplest Model
Three Cell Types More Cohesive, Less Cohesive,
Medium
Random Blob Initial Conditions or Adjacent Domains
Outcome Depends on Js
56Engulfment
57Vascular Development
Courtesy Luigi Preziosi
58Hypothesis 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
59PDE 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
60Contact 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
61Vascular 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
62Sprouting 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?
63Temporal Behavior Agrees with Morphometrics
64Three-Dimensional Angiogenesis
65Results
- 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!
66Biofilms
67Biofilms (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
68Biofilm 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
69Biofilms
- 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).
70Tumors
71Tumor 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.
72MOTIVATION
- 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
73Anderson 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).
74Anderson 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).
75Anderson 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).
76CONSTANT GROWTH RATE ABOVE THRESHOLD
Benign Tumor Sufficient supply of nutrients
77CONSTANT GROWTH RATE ABOVE THRESHOLD
Benign Tumor Sufficient supply of nutrients
78GROWTH RATE PROPORTIONAL TO NUTRIENT
CONCENTRATION ABOVE THRESHOLD
Malignant Tumor Sensitivity of growth to
nutrient supply leads to fingering instabilities
(and possibly metastasis)
79GROWTH RATE PROPORTIONAL TO NUTRIENT
CONCENTRATION ABOVE THRESHOLD
Malignant Tumor Sensitivity of growth to
nutrient supply leads to fingering instabilities
(and possibly metastasis)
80GROWTH RATE PROPORTIONAL TO NUTRIENT
CONCENTRATION WITH SMALLER SLOPE
Benign Tumor Slow nutrient-dependent growth
results in sufficient supply of nutrients
81GROWTH RATE PROPORTIONAL TO NUTRIENT
CONCENTRATION WITH SMALLER SLOPE
Benign Tumor Slow nutrient-dependent growth
results in sufficient supply of nutrients
828
24
16
G
4
12
20
?(m,t)
0
2
4
6
83SUMMARY
- 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).
84Vasculature and Tumors
85Development of Body Plan
- Specification of Body Axes
- Cleavage
- Gastrulation (Formation of Primitive
StreakAnterior-Posterior) - Somitogenesis (Formation of AP compartments)
- Organogenesis
86Gastrulation
87GastrulationFormation of Main Body Axis
88Gastrulation 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
89Various Mechanisms will Produce a Streak
ST secretes chemo-repellant for AO
ST secretes chemo-attractant for KS
KS secretes chemo-repellant for ST
90Various Mechanisms will Produce a Streak
ST secretes chemo-repellant for AO
ST secretes chemo-attractant for KS
KS secretes chemo-repellant for ST
91Which Chemotactic Mechanism?
92Large-Scale MotionChemotaxis and Adhesion not
enough
93Viscous Drag
94Somitogenesis
95Patterning 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.
96Somitogenesis
Anterior (head)
Somites
Forming somite
Older cells more anterior
Younger cells more posterior
Neural tube
Posterior (tail)
Presomitic mesoderm (PSM)
97Somitogenesis
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.
98Caricature of Somitogenesis
99Eph knockout /Initialization
100PSM-ECM Strong Interaction Parameter Optimized
Adhesion-Repulsion /Control
PSM-ECM Strong Interaction
101N-cadherin knockout
102Compartment Boundary Crossing
- Experimental figure from Kulesa et al.
103Adhesion-based Error Correction
104CompuCell3D 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
- If You Want to Learn More Please Visit Our Web
Location at http//www.compucell3d.org and Try
Downloading it Yourself!