Stoichiometric Tumor Model: Phosphorus Flow

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Stoichiometric Tumor ModelPhosphorus Flow

• By Bo Deng, Vladimir Ufimtsev and Melissa Wilson

Funded By NSF/REU Grant to University of
Nebraska-Lincoln
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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
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PHOSPHORUS!!

• Metabolic Pathways
• ATP Adenosine Tri-Phosphate
• DNA/RNA Replication
• http//www.blc.arizona.edu/Molecular_Graphics/DNA_
  Structure/DNA_Tutorial.HTMLComponents

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http//www.accessexcellence.org/AB/GG/dna_replicat
ing.html
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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
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Hollings 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 ?
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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
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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)
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http//www4.tpgi.com.au/users/amcgann/body/circula
tory.html
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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.
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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.
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Organ and Tumor
Liver Cancer
Angiogenesis
http//www.maths.dundee.ac.uk/sanderso/tumour.htm
http//www.robertsreview.com/cancer_pictures.html
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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
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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
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• The term for Tumor growth
• The term is used to
  explain the
• distribution of Phosphorus throughout the
  circulatory system.

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Immune Response

• Effector Cells
• NK Cells(NaturalKillers)
• Attack likeT-Cells

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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
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Antigenicity
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Antigenicity
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Days until tumor detected
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Tumor Dynamics without Therapy
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Chemotherapy and Tumor Death
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