Stoichiometric Tumor Model: Phosphorus Flow and Metabolic Pathways

1. Stoichiometric Tumor Model:Phosphorus Flow By: Bo Deng, Vladimir Ufimtsev and Melissa Wilson Funded By NSF/REU Grant to University of Nebraska-Lincoln

2. Stoichiometry- The quantitative relationship between elements in a system. • Mass Balance: The concept that matter is conserved. Whatever is put into a system either remains in the system or is excreted from it. On each side of the equation there are: 2-Oxygens 4-Hydrogens

3. PHOSPHORUS!! • Metabolic Pathways • ATP – Adenosine Tri-Phosphate • DNA/RNA Replication http://www.blc.arizona.edu/Molecular_Graphics/DNA_Structure/DNA_Tutorial.HTML#Components

4. http://www.accessexcellence.org/AB/GG/dna_replicating.html

5. Measuring Phosphorus Phosphorus makes up: 1% of Healthy Cells 2% of Tumor Cells Using a healthy person of average mass,70kg, excluding bone mass, 8.9kg, with no tumor, her mass becomes: Kuang et al. 2004, Williams 2002 61.1 kg of Healthy Cells * (1 kg of Phos/100 kg of Healthy Cells) =.611 kg of Phos * (1000 g/kg) = 611 g of Phos

6. Holling’s uptaking/capturing functional form (1959) P P P P P P P P P P P P Total area = , Area of 1 P = Number of discs = P (remains constant) Machine will tap at the board at a rate of: k taps per unit of time. How many units of prey (discs) will the machine tap, in a given search time; ?

7. P P P P P P P P P P P P Total area = Area of 1 P = Handling time for each disc = How many units of prey (discs) will the machine capture, in a given time; ? The total time spent searching becomes:

9. Total number of P captured by Y many machines or cells in a unit time is Also known as the Monod-Jacob form (1961) or the Michaelis-Menten form (1913)

10. http://www4.tpgi.com.au/users/amcgann/body/circulatory.html

11. IMPORTANT: The amounts of all quantities in the system are specified by the amount of Phosphorus that each quantity possesses. Quantities H = Amount of Healthy cells that compose the body (without the organ). O = Amount of Healthy cells that compose the organ. P = Amount of Phosphorus in the blood stream.

12. IMPORTANT: The amounts of all quantities in the system are specified by the amount of Phosphorus that each quantity possesses. Quantities H = Amount of Healthy cells that compose the body (without the organ). O = Amount of Healthy cells that compose the organ. P = Amount of Phosphorus in the blood stream.

13. Organ and Tumor Liver Cancer Angiogenesis http://www.maths.dundee.ac.uk/~sanderso/tumour.htm http://www.robertsreview.com/cancer_pictures.html

14. QuantitiesH = Amount of Healthy Cells that compose the body (without the organ)O = Amount of Healthy Cells that compose the organT = Amount of Cancerous Cell that compose the tumor V = Amount of cells that compose the vessels in the tumorP = Amount of Phosphorus in the blood stream

15. QuantitiesH = Amount of Healthy Cells that compose the body (without the organ)O = Amount of Healthy Cells that compose the organT = Amount of Cancerous Cell that compose the tumor V = Amount of cells that compose the vessels in the tumorP = Amount of Phosphorus in the blood stream

16. The term for Tumor growth: The term is used to explain the distribution of Phosphorus throughout the circulatory system.

17. Immune Response • Effector Cells • NK Cells(NaturalKillers) • Attack likeT-Cells

18. Natural Killer Cells Natural Killer Cell (NK Cell) cell destroying a targeted tumor cell. NK Cell Tumor cell http://www.cancerfoundation.com/NKcells.html, 2004

20. Antigenicity

21. Antigenicity

25. Days until tumor detected

26. Tumor Dynamics without Therapy

27. Chemotherapy and Tumor Death