On multiscale approaches to threedimensional modeling of morphogenesis

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On multiscale approaches to three-dimensional
modeling of morphogenesis

• Mark S. AlberDepartment of Mathematics and
  Interdisciplinary Center for the Study of
  Biocomplexity
• http//www.nd.edu/icsb/
• University of Notre Dame, Notre Dame, IN 46556
• July 18, 2005
• Acknowledgements
• NSF Biocomplexity Grant No. IBN-0083653

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Skeletal Pattern Formation stages in a chicken
limb bud
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Mathematical model (PDE)
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(No Transcript)
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Morphogen dynamics
ds - diffusion coefficients, cs -
concentrations. a - activator, i inhibitor, s-
stable-state values, R0 - the density of mobile
cells. Mobile cell density changes slowly
compared with the rate of cell differentiation.
Alber, M., Glimm, T., Hentschel, H. G. E.,
Kazmierczak, B., Newman, S. A. 2005, Stability of
n-dimensional patterns in a generalized Turing
system implications for biological pattern
formation, Nonlinearity 18 125-138 (2005).
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Cellular Dynamics CPM

• Energy minimization formalism
• extended by Graner and Glazier, 1992
• DAH Contact energy depending on cell types
  (differentiated cells)
• Extensions
• J_cell_cell is type dependent
• Other terms Cell volume, Chemotaxis/Haptotaxis
• Metropolis algorithm probability of
  configuration change

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A typical two-dimensional (2D) CPM configuration.
The numerals indicate indices at lattice sites.
The colors indicate cell type. A cell is a
collection of connected lattice sites with same
index. The number of lattice sites in a cell is
its volume and its number of links with other
indices is its surface area. We represent ECM as
a generalized cell with index 1.
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• Gastrulation-like mechanism
• Clonal selection of b-cells in the germinal
  center through competition for contact with a
  (large) antigen-presenting cell
• Tumor invasion
• Notch-Delta-mediated stem-cell cluster-size
  control in the human interfollicular epidermis
• Mesenchymal condensation through cellECM
  interactions
• Convergent extension
• Endothelial cells, secreting VEGF-A,
  chemotactically aggregate to form a vascular
  network
• Limb bud outgrowth
• Formation of a fruiting body in Dictyostelium
  discoideum

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Composite Limb bud results
Simulation
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• Cell condensation into humerus, ulna and radius,
  and digits after 1040 Monte Carlo steps.
• Chaturvedi, R., C. Huang, J. A. Izaguirre, S. A.
  Newman, J. A. Glazier, M. Alber,
• On Multiscale Approaches to 3-Dimensional
  Modeling of Morphogenesis,
• Journal of the Royal Society Interface 2, 3
  237-253.

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a)
b)
Fussing Digits (a) Fibronectin distribution and
(b) cell condensation, after 940 Monte Carlo
steps
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Acknowledgements

• J.A. Glazier1, S.A. Newman 2, M. G. Hentschel
  3, G. Forgacs 4,
• J. Izaguirre 5, R. Chatuverdi 5, M.
  Kiskowski 6
• 1 Departments of Physics and Biology and
  Biocomplexity Institute, Indiana University,
  Bloomington, IN 47405
• 2 Department of Cell Biology and Anatomy, Basic
  Science Building, New York Medical College,
  Valhalla, NY 10595
• 3 Department of Physics, Emory University,
  Atlanta, GA 30332
• 4 Department of Physics and Biology, University
  of Missouri, Columbia, MO 65211
• 5 Department of Computer Science and
  Engineering, University of Notre Dame, Notre
  Dame, IN 46556
• 6 Department of Mathematics, Vanderbilt
  University,1326 Stevenson Center, Nashville, TN
  37240-0001

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Applications of Methods of Stochastic Systems and
Statistical Physics in Biology University of
Notre Dame October 28-30, 2005
http//www.nd.edu/icsb/wrkshp2005.html ICSB at
Notre Dame, BI at IU Bloomington, LANL,
SIAM Public Lecture Alan Perelson, Los Alamos
National laboratory Keynote Address Dennis Bray,
Cambridge University Miller Lecture in
Biophysics Albert Libchaber, The Rockefeller
University The objectives of the Workshop are
to 1. Discuss new methods stochastic analysis
and statistical physics of importance
in biomedical modeling and suggest new problems
for modeling and experiment 2. Explore
similarities and differences between complex
biological phenomena due to noise 3. Promote
interactions between biologists, chemists,
physicists, mathematicians, and engineers with
interests in modeling stochastic behavior in
biology 4. Provide a forum for junior faculty and
graduate students to interact with a wide range
of experts and attract new researchers to the
field of biological modeling.