Transcript What is Math Bio and How Useful is it -25Sept09

What is Mathematical Biology
and how useful is it?
Avner Friedman
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What is life?
What is mathematical biology?
The role of oxygen in wound healing and
tissue transfer
The immune response to infection in the lung
Cancer virotherapy
Summary
What is life?
Unit of life is a cell. Processes of living.
(according to F. Harold, “The Way of the Cell,” 2001)
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Flux of matter and energy
Chemical activities: absorb nutrients, produce biomass,
eliminate waste products
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Adaptation
Structure and function evolve to promote organism survival
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Organization
A bacterial cell consists of 300 million molecules,
assembled non-randomly
DNA  RNA  Protein is strategically planned and executed
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Self-reproduction
Autonomously, not by external forces
What is Mathematical Biology?
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Talking to biologists and getting familiar with their experiments and
data with respect to a biological process.
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Developing a mathematical model that describes the biological
process (e.g., by differential equations).
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Simulating and comparing the numerical results with experimental
results – and keep revising until the fit is satisfactory.
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Using the model to make new biologically testable hypotheses.
Experiments, data
Simulation
Mathematical model
Parameters estimation
Wound healing as a function of tissue oxygen
tension: A mathematical model
R. Schugart, A. Friedman, R. Zao, C.K. Sen
PNAS (2008)
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Chronic wounds represent a major public
health problem worldwide; affecting 6.5 million
individuals in the U.S., with cost of $5-10 billion
each year.
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Wound healing represents a well-orchestrated reparative response that
occurs after all surgical procedures or traumatic injuries. Angiogenesis
plays a central role in wound healing. In this work the role of oxygen is
investigated, and the use of oxygen intervention (hyperbaric chamber) is
considered.
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Hyperbaric
Chamber
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Topical Oxygen
Treatment
(2.1)
(2.2)
(2.3)
(2.4)
(2.5)
(2.6)
(2.7)
Role of Oxygen
Ga
w
hypoxic
normoxic
hyperoxic
Moderate hypoxia and hyperoxia improve healing.
A Mathematical Model of Ischemic Cutaneous
Wounds
C. Xue, A. Friedman, and C. Sen
PNAS (2009)
Experiment:
A more refined model is needed.
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Separating chemoattractant
between VEGF and PDGF.
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Considering the partially healed
tissue as viscoelastic material.
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Modeling ischemia in a circular
geometry.
Experimental and Simulation Results
C. Xue, A. Friedman, and C. Sen (2009)
Modeling Oxygen Transport in Surgical Tissue
Transfer
A. Matzavinos, C.Y. Kao, J.E.F. Green, A. Sutradhar, M. Miller,
and A. Friedman PNAS (2009)
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During surgery, a plastic surgeon must decide how large a flap
(with one artery) can be lifted and transferred to another location,
without developing fat necrosis.
arterial pressure
venous pressure
oxygen diffusion
and transport (tissue)
oxygen diffusion
and transport (artery)
oxygen diffusion
and transport (vein)
Future Work
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The model represents initial step. Subsequent work
will proceed jointly with animal experiments, in
order to refine the model by including heterogeneity
of the vasculature.
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The model will be coupled to that of ischemic
cutaneous wounds.
A model on the influence of age on immunity to
infection with Mycobacterium tuberculosis
A. Friedman, J. Turner, B. Szomolay
Experimental Gerontology
Increasing susceptibility to many infectious diseases is highly
associated with the loss or delay in the generation of antigen specific
CD4+ T cells mediated immunity. For tuberculosis, where antigen
specific CD4+ T cell derived IFN-g is essential, such a loss is
associated with aging, and it can lead to a significant failure to control
infection.
Macrophages
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Infected macrophages: infected by ~10
bacteria in the absence of IFN-γ; cannot
control bacterial growth; they burst releasing
many bacteria.
Activated macrophages: infected by ~5
bacteria in the presence of IFN-γ; they present
antigen to T cells.
Resting macrophages – do not contain
bacteria.
The Model Variables
Modeling the Immune Rheostat of Macrophages in
the Lung in Response to Infection
J. Day, A. Friedman, and L. Schlesinger
(PNAS, 2009)
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Alveolar macrophages are also called Alternatively Activated
Macrophages (AAM). AAM form the first line of cellular defense.
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The macrophages in the lymph nodes are called Classically Activated
Macrophages (CAM).
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CAM are more effective than AAM in combating infection.
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When infection in the lung occurs, there is time delay until CAM arrive
and become more dominant than AAM: “switching time.”
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Using IFN-γ as drug: It decreases the
switching time, the maximum bacterial load,
and the residual bacteria.
Virotherapy in Glioblastoma
A. Friedman, J.J. Tian, G. Fulci, E.A. Chiocca, and J. Wang
Cancer Research, 2006
Glioblastoma is a brain tumor, very invasive,
life expectancy 1 year
glioblastoma
virus
cell
When the cell dies, a swarm of virus particles burst out
b = burst size = replication number
Idea: Use virus to destroy tumor cells
Oncolytic virus: Genetically altered virus which is
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Replication – competent
Infects tumor cells and reproduces in them
Does not harm normal healthy cells
Virotherapy: Actively tested in clinical trials on various types of
cancer
Two important factors:
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Safety
Efficacy
Factors to be considered:
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The immune system: cells which detect virus and
virus-infected cells, and destroy them
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Cyclophasphamide (CPA) suppresses the innate
immune response
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During infection, the population of immune cells
increases dramatically. When the infection is gone,
the population of immune cells returns to its normal
size (quadratic clearance).
Model Equations
uninfected
cell
infected
cell
necrotic
cells
immune
cells
virus
particles
radial
velocity
Tumor Radius
b large
infected
immune
(uninfected )
and kills infected cells and virus
- then: immune cells kill themselves
immune
In the meantime uninfected cells
Remaining virus renew attack
infected
Conclusions
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OV hrR3 cannot eradicate glioma.
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If however b can be increased to ≥ 150 then the radius will
shrink and become very small (even without CPA).
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CPA primary effect is in decreasing the density of uninfected
tumor cells – thus reducing the risk of secondary tumor.
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Protocols of CPA treatment (weekly, or double-dose
biweekly) do not make a significant difference.
Summary
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Mathematical models should relate to experiments.
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In PDE or ODE models the choice of parameters is crucial –
use experimental results as much as possible.
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Use sensitivity analysis.
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Simulations of the model must fit with experimental results.
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The model should then be used to suggest new hypotheses
that are biologically testable.