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What is Mathematical Biology and how useful is it?
Avner Friedman
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)
Flux of matter and energyChemical activities: absorb nutrients, produce biomass, eliminate waste products
AdaptationStructure and function evolve to promote organism survival
OrganizationA bacterial cell consists of 300 million molecules, assembled non-randomlyDNA RNA Protein is strategically planned and executed
Self-reproductionAutonomously, not by external forces
What is Mathematical Biology?
Talking to biologists and getting familiar with their experiments and data with respect to a biological process.
Developing a mathematical model that describes the biological process (e.g., by differential equations).
Simulating and comparing the numerical results with experimental results – and keep revising until the fit is satisfactory.
Using the model to make a new hypothesis and suggest new experiments.
Mathematical model
Parameters estimation
Simulation
Experiments, data
Wound healing as a function of tissue oxygen tension: A mathematical model
R. Schugart, A. Friedman, R. Zao, C.K. Sen PNAS
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.
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.
(2.1)
(2.3)
(2.4)
(2.2)
(2.5)
(2.6)
(2.7)
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 GerontologyIncreasing 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- 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
cell
virus
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
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:
Safety Efficacy
Factors to be considered: The immune system: cells which detect virus and
virus-infected cells, and destroy them
Cyclophasphamide (CPA) suppresses the innate immune response
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).
uninfectedcell
infectedcell
necroticcells
immunecells
(1)
(2)
(3)
(4)
virusparticles
radialvelocity
(5)
(6)
(7)
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 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.