Biological stoichiometry of tumor dynamics

Mathematical models and analysis

Yang Kuang, John D. Nagy, James Elser

Research output: Contribution to journalArticle

41 Citations (Scopus)

Abstract

Many lines of evidence lead to the conclusion that ribosomes, and therefore phosphorus, are potentially important commodities in cancer cells. Also, the population of cancer cells within a given tumor tends to be highly genetically and physiologically varied. Our objective here is to integrate these elements, namely natural selection driven by competition for resources, especially phosphorus, into mathematical models consisting of delay differential equations. These models track mass of healthy cells within a host organ, mass of parenchyma (cancer) cells of various types and the number of blood vessels within the tumor. In some of these models, we allow possible mechanisms that may reduce tumor phosphorous uptake or allow the total phosphorus in the organ to vary. Mathematical and numerical analyses of these models show that tumor population growth and ultimate size are more sensitive to total phosphorus amount than their growth rates are. In particular, our simulation results show that if an artificial mechanism (treatment) can cut the phosphorus uptake of tumor cells in half, then it may lead to a three quarter reduction in ultimate tumor size, indicating an excellent potential of such a treatment. Also, in general we find that tumors with a relatively high cell death rate are more susceptible to treatments that block phosphorus uptake by tumor cells. Similarly, tumors with a large phosphorus requirement and (or) low cell reproductive rates are also strongly affected by phosphorus limitation.

Original languageEnglish (US)
Pages (from-to)221-240
Number of pages20
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume4
Issue number1
StatePublished - Feb 2004

Fingerprint

Stoichiometry
Phosphorus
Mathematical Analysis
Dynamic Analysis
Tumors
Tumor
Dynamic Model
Mathematical Model
Mathematical models
Cell
Cells
Cancer
Natural Selection
Tumor Growth
Population Growth
Blood Vessels
Delay Differential Equations
Blood vessels
Cell death
Integrate

Keywords

  • Biological stoichiometry
  • Delay differential equations
  • Qualitative analysis
  • Tumor model

ASJC Scopus subject areas

  • Mathematics(all)
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

Biological stoichiometry of tumor dynamics : Mathematical models and analysis. / Kuang, Yang; Nagy, John D.; Elser, James.

In: Discrete and Continuous Dynamical Systems - Series B, Vol. 4, No. 1, 02.2004, p. 221-240.

Research output: Contribution to journalArticle

@article{0eaffc590f154ead9ab8d38901651f71,
title = "Biological stoichiometry of tumor dynamics: Mathematical models and analysis",
abstract = "Many lines of evidence lead to the conclusion that ribosomes, and therefore phosphorus, are potentially important commodities in cancer cells. Also, the population of cancer cells within a given tumor tends to be highly genetically and physiologically varied. Our objective here is to integrate these elements, namely natural selection driven by competition for resources, especially phosphorus, into mathematical models consisting of delay differential equations. These models track mass of healthy cells within a host organ, mass of parenchyma (cancer) cells of various types and the number of blood vessels within the tumor. In some of these models, we allow possible mechanisms that may reduce tumor phosphorous uptake or allow the total phosphorus in the organ to vary. Mathematical and numerical analyses of these models show that tumor population growth and ultimate size are more sensitive to total phosphorus amount than their growth rates are. In particular, our simulation results show that if an artificial mechanism (treatment) can cut the phosphorus uptake of tumor cells in half, then it may lead to a three quarter reduction in ultimate tumor size, indicating an excellent potential of such a treatment. Also, in general we find that tumors with a relatively high cell death rate are more susceptible to treatments that block phosphorus uptake by tumor cells. Similarly, tumors with a large phosphorus requirement and (or) low cell reproductive rates are also strongly affected by phosphorus limitation.",
keywords = "Biological stoichiometry, Delay differential equations, Qualitative analysis, Tumor model",
author = "Yang Kuang and Nagy, {John D.} and James Elser",
year = "2004",
month = "2",
language = "English (US)",
volume = "4",
pages = "221--240",
journal = "Discrete and Continuous Dynamical Systems - Series B",
issn = "1531-3492",
publisher = "Southwest Missouri State University",
number = "1",

}

TY - JOUR

T1 - Biological stoichiometry of tumor dynamics

T2 - Mathematical models and analysis

AU - Kuang, Yang

AU - Nagy, John D.

AU - Elser, James

PY - 2004/2

Y1 - 2004/2

N2 - Many lines of evidence lead to the conclusion that ribosomes, and therefore phosphorus, are potentially important commodities in cancer cells. Also, the population of cancer cells within a given tumor tends to be highly genetically and physiologically varied. Our objective here is to integrate these elements, namely natural selection driven by competition for resources, especially phosphorus, into mathematical models consisting of delay differential equations. These models track mass of healthy cells within a host organ, mass of parenchyma (cancer) cells of various types and the number of blood vessels within the tumor. In some of these models, we allow possible mechanisms that may reduce tumor phosphorous uptake or allow the total phosphorus in the organ to vary. Mathematical and numerical analyses of these models show that tumor population growth and ultimate size are more sensitive to total phosphorus amount than their growth rates are. In particular, our simulation results show that if an artificial mechanism (treatment) can cut the phosphorus uptake of tumor cells in half, then it may lead to a three quarter reduction in ultimate tumor size, indicating an excellent potential of such a treatment. Also, in general we find that tumors with a relatively high cell death rate are more susceptible to treatments that block phosphorus uptake by tumor cells. Similarly, tumors with a large phosphorus requirement and (or) low cell reproductive rates are also strongly affected by phosphorus limitation.

AB - Many lines of evidence lead to the conclusion that ribosomes, and therefore phosphorus, are potentially important commodities in cancer cells. Also, the population of cancer cells within a given tumor tends to be highly genetically and physiologically varied. Our objective here is to integrate these elements, namely natural selection driven by competition for resources, especially phosphorus, into mathematical models consisting of delay differential equations. These models track mass of healthy cells within a host organ, mass of parenchyma (cancer) cells of various types and the number of blood vessels within the tumor. In some of these models, we allow possible mechanisms that may reduce tumor phosphorous uptake or allow the total phosphorus in the organ to vary. Mathematical and numerical analyses of these models show that tumor population growth and ultimate size are more sensitive to total phosphorus amount than their growth rates are. In particular, our simulation results show that if an artificial mechanism (treatment) can cut the phosphorus uptake of tumor cells in half, then it may lead to a three quarter reduction in ultimate tumor size, indicating an excellent potential of such a treatment. Also, in general we find that tumors with a relatively high cell death rate are more susceptible to treatments that block phosphorus uptake by tumor cells. Similarly, tumors with a large phosphorus requirement and (or) low cell reproductive rates are also strongly affected by phosphorus limitation.

KW - Biological stoichiometry

KW - Delay differential equations

KW - Qualitative analysis

KW - Tumor model

UR - http://www.scopus.com/inward/record.url?scp=0345706907&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0345706907&partnerID=8YFLogxK

M3 - Article

VL - 4

SP - 221

EP - 240

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

SN - 1531-3492

IS - 1

ER -