Transcript What is Mathematical Biology and How Useful is It?

What is Mathematical Biology
and how useful is it?
Avner Friedman
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What is life?
What is mathematical biology?
Wound healing
Hemodialysis
Tuberculosis (aging)
Glioblastoma
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 a new hypothesis and suggest
new experiments.
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
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Chronic wounds represent a substantial public
health problem; treating these wounds costs an
estimated $5-10 billion each year. Need to
develop tools to study genetic signature of wounds
under various conditions, and develop mathematical models.
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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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A mathematical model of venous neointimal
hyperplasia formation
P. Budu-Grajdeanu, R. Schugart, A. Friedman, C. Valentine, B.H. Rovin
Theoretical Biology & Medical Modeling
In hemodialysis the most common cause of vascular failure is
neointimal hyperplasia of vascular smooth muscle cells at the
venous anastomosis of fistulas or grafts.
Fistula and Graft in Hemodialysis
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.
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).
uninfected
cell
(1)
infected
cell
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necrotic
cells
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immune
cells
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virus
particles
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radial
velocity
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Tumor Radius
b large
infected
(uninfected )
immune
and kills infected 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.
If however b can be increased to ≥ 150 then the radius will
shrink and become very small (even without CPA)
CPA will help a little bit in decreasing the radius, but its
primary effect is decreasing the density of uninfected tumor
cells – thus reducing the risk of secondary tumor.
Protocols of CPA treatment (weekly, or double-dose
biweekly) do not make a significant difference.
Problem
Provide vigorous mathematical proof to the numerical results.