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.