Discussion session

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Discussion session

• Philip K. Maini
• Centre for Mathematical Biology
• Mathematical Institute
• Oxford Centre for Integrative Systems Biology,
  Dept of Biochemistry
• Oxford

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Multiscale Modelling

• If we know that a drug affects an ion channel in
  some way, how do we predict the consequences on
  heartbeat?
• If we know that a mutation confers a
  proliferative advantage on a certain cell, what
  is the tissue dynamics of the resultant tumour
• Why is development (embryology) so robust?

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Traditional Mathematical Biology

• Consider the cell as a black box with certain
  chemical/physical properties and use mathematical
  models (continuum mainly) to see what happens at
  the tissue level.

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• Nutrient required
• Hypoxic core TAF (tumour
  angiogenesis factors)
• Avascular tumour Vascular tumour
• Invasion
• Tumour produces proteases digest ECM
• Competition
• Normal environment

Tumour
Normals
Add H
Gatenby Gawlinski Gap
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Acellular gap at the tumor-host interface in head
and neck cancer
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Where J denotes the cell flux. The standard
chemotatic flux expression is
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Figure 2. Numerical simulation of cell streaming
in Dictyostelium discoideum under the influence
of two signalling centres. Upper panel cell
density (upper row) and cAMP concentration (lower
row) for a counter-rotating pair of spiral waves.
Lower panel cell density and cAMP concentration
for a spiral wave and a periodic pacemaker
(period 6 min). Initial conditions for the
spiral waves were appropriately broken plane
wavefronts. Snapshots taken at 10 min, 40 min
and 100 min colour scale ranging from black for
low values to white for high values See T.
Höfer. Modelling Dictyostelium aggregation, D.Ph.
thesis, Oxford University, 1996.
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Different Models

• Common principles (excitable system,
• chemotaxis, adaptation)
• Coarsening suite of models designed to answer
  specific questions (signal transduction pathways
  effects at the tissue level)

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Bioinformatics

• Investigations at the gene/molecular level in an
  attempt to gain more information from genomic
  data.

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How to bridge the GAP?

• The cell is not a black box!
• How can we determine from information at the
  molecular level what are the physical/chemical
  properties of a cell, to insert into our cell
  population level models?

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Mathematicians working on tumour modelling
Priya Kooner (Upregulation of HIF/ glycolytic
pathway)
Natasha Li (Invasion and metastasis)
Kieran Smallbone (Acidity)
Philip Murray (Nutrient consumption, cell cycle
and growth)
Prof David Gavaghan
Dr Tiina Roose (growth and therapy Che mo,
radiation, anti-angio)
Prof Philip Maini
Dr Marcus Tindall (cell cycle, quiescence, cell
movement)
Prof Jon Chapman
Dr Carina Edwards (biomechanics of a colorectal
crypt)
Dr Chris Breward (vascular tumour growth)
Pras Prasmanathan (Tissue dynamics for breast
cancer management)
Alex Fletcher (hypoxia regulation of cell death)
Matt Johnston (population dynamics in crypts)
Becky Carter (Fluid transport)
James Southern (Tissue dynamics for ultrasound
image analysis)
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Sub-cellular scale

• Model the cell cycle of each individual cell and
  examine the effects of changing the sub-cellular
  on the macroscale.

1000 microns
Macro scale

• We want to examine how nutrients get consumed by
  cells and how this effects their cell cycle.

Nutrient diffusion and consumption by cells
1000 microns
Philip Murray, C.Edwards, M.Tindall, P. Maini.
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Plot of grid at t 2950 mins
Cell growth rates
Cells in G1 Cells in S/G2/M
Y-axis
Y-axis
X-axis
X-axis
Number of cells
Number of cells
Time (mins)
Growth rate
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Cell Population model of a colorectal crypt
Supervisors Professor Maini, Professor
Chapman, Dr Edwards and Professor Bodmer.
Johnston et al.

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Johnston et al.

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• Our models can
• Capture the observed cell dynamics in a healthy
  colonic crypt.
• Simulate the effect of genetic mutations in
  specific cell populations in the crypt.
• Future Work
• Look at the effect of mutations on the model.
• Include spatial variation into the model.
• Combine the model with those of the sub-cellular
  Wnt pathway currently being developed by other
  project members.
• Questions we have
• Are these parameter ranges appropriate? Which
  could be obtained from experiments?
• Other parameters required for the model include
  the crypt turnover time, cell cycle times and
  flux of cells out of the crypt.
• What factors do you think will be important?

Johnston et al.

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Biomechanical modelling

• Hyperproliferation leads to (a) elongation, (b)
  deformation, (c) fission.
• Finally hyperproliferation leads to formation of
  a polyp or adenoma.

Carina Edwards and Jon Chapman
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Modelling

• Crypt shape determined by biomechanical forces
  e.g in 1-D
• Creating biomechanical model that inputs cell
  proliferation rates, and cellular adhesion
  properties as functions of distance along crypt
  (from subcellular Wnt model), to determine
  evolution of crypt shape.

Carina Edwards and Jon Chapman
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Questions and Further Work

• Some initial discussion points
• Hyperproliferation? Is the cell cycle time
  shortened as well as the size of the
  proliferative compartment increased?
• How is cell attachment and the properties of the
  tissue altered by the early genetic mutations?
• More generally interested in how forces are
  generated within the tissue, and how this affects
  structure and function both on a tissue level and
  at a subcellular level.
• Future work
• Incorporate with subcellular models for
  proliferation and attachment.

Carina Edwards and Jon Chapman
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AIMS

• To develop mathematical models based on realistic
  biology
• To validate these models with experimental data
• To use the models as hypotheses
  generating/verifying tools
• To use the models to make experimentally testable
  predictions

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Challenges

• How do we integrate across the spatial/temporal
  scales in a sensible and tractable manner?
• For example, given a detailed interaction
  network, how do we incorporate details into a
  cell (Boolean approach network motifs,
  coarsening, statistical analysis).
• How do we decide which of the above approaches is
  appropriate?
• How do we test this?

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• Do we model cell populations as discrete entities
  (computationally intensive) or as continua (not
  applicable at small cell numbers)
• Stochastics versus deterministic?

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Parameters??

• How do we parametrise models? (consistent
  experimental model)
• How do we verify models?
• How do we make sure that experiments are designed
  with theory in mind?

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Robustness

• How do the model results depend on the
  assumptions behind functional forms and parameter
  values?
• A new mathematics?

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Open Question

• Can we use mathematicteal/computational modelling
  to derive an experimentally-tested integrated
  multiscale model that can be used to make
  predictions??