Transcript Slide 1

Toward An Integrative Theory Of Within-host Disease Dynamics
Using Principles of Biological Stoichiometry to Understand the Pathobiology of Cancer and Infectious Disease:
A Collaboration of Empirical and Theoretical Biology, Theoretical Physics and Mathematics
Yang
1Department
1
Kuang
(Project Director), Jim
2
Elser ,
Timothy
3
Newman ,
John
4,2
Nagy ,
Val
5
Smith
and Marilyn
6
Smith
of Mathematics and Statistics, Arizona State University; 2School of Life Sciences, Arizona State University; 3Department of Physics and Astronomy, Arizona State University; 4Department of Life Sciences, Scottsdale Community College; 5Department of Ecology and Evolutionary Biology, University of Kansas; 6Department of Microbiology, Molecular Genetics and Immunology, University of Kansas Medical Center
Abstract: This multi-campus,
interdisciplinary team is studying
processes within a single biological host
that can be described by models inspired
by ecological stoichiometry, the study of
the balance of energy and multiple
chemical resources (usually elements) in
ecological interactions. This work weaves
together threads of theoretical and
experimental research. Our primary aim is
to construct predictive and verifiable
theoretical models that can begin to
explicitly deal with the effects of
stoichiometric interactions in within-host
disease dynamics.
Fig. 1. Squamous cell cancer of the lung, H&E stain.
Necrotic areas are marked ‘N’. Our early work seeks to
understand the ecological collapse leading to necrosis.
From Nagy (2005).
Yang Kuang
Tim Newman
Fig. 2. Dynamics of a tumor growing in a healthy organ.
Tumor growth is limited by phosphorus well below its
“carrying capacity” for the given blood supply. In
general, this model showed that tumors are very sensitive
to changes in phosphorus supply.
Fig. 3. Local acidosis in a mathematical model of
malignant neoplasia. Supply of glucose and nutrient (P)
are adequate (left panels), although lactic acid builds up in
the cells and interstitium (lower left, top right), which cell
metabolism reaches an equilibrium with no cell growth
(lower right).
Val Smith
Jim Elser
Fig. 4. Phase portrait from a mathematical model of
cancer with two competing parenchyma (cancer) cell
types, immature vascular cells (w) and mature blood
vessel density (v). Variable u1 represents the proportion
of the parenchyma of cell type 1. (a) Dynamics on the
boundary. (b) Dynamics in the interior.
Fig. 5. Hypertumor dynamics. Resident cancer cells with
growth and death rates shown in blue (upper left panel)
are invaded by a fast-growing, cell line unable to secrete
tumor angiogenesis factors. The fast growing cell line
invades the tumor, causing it to become hypoxic (lower
left), resulting in cessation of tumor growth (upper right)
and eventual tumor destruction (lower right).
John Nagy
Marilyn Smith
Acknowledgements: We gratefully acknowledge the
support of the National Science Foundation and National
Institutes of Health through grant number DMS/NIGMS
0342388.
Fig. 6. Survivorship of larval mosquitoes given food of various quality. Mosquitoes infected with the fungus Beauvaria
bassiana (right panel) survived equally well compared to uninfected larvae (left panel) when given high-quality food (blue
triangles). However, infected larvae suffer much higher mortality than uninfected when food quality is low (green circles).
Synthesis: This research program takes a step toward new ways to understand pathology, aiming to develop robust and
experimentally calibrated mathematical theories of disease-host interactions that can be applied to a wide variety of diseases.
We firmly believe that such theories have a central role to play in present and future research.
Synopsis: Necrosis (Fig. 1), a common feature of cancer, represents a profound ecological collapse within a tumor, the cause
of which remains unclear. Elser et al. (2003), applying the concept of biological stoichiometry, suggest that cancer cells
should generally require more phosphorus than normal cells do, a prediction that we have subsequently confirmed
(unpublished data), and shown with modeling to be have potentially significant influences on tumor growth dynamics (Fig.
2). In particular, an unfavorable C:P ratio may be a cause of necrosis—cells lacking P relative to C may “burn off” excess C
through futile metabolic cycles, which produce lactic acid. A model of tumor metabolism supports the viability of this
hypothesis for realistic parameter values (Fig. 3). This local acidosis may be the immediate cause of necrosis. Alternatively,
necrosis may be caused by competition among tumor cells for a single nutrient. A variation of this hypothesis was proposed
by Nagy (2004), in which necrosis arose when natural selection favored cells that traded off the ability to produced tumor
angiogenesis factors for growth potential, producing a “hypertumor,” or a tumor growing parasitically on an established tumor
(Figs. 4 and 5).
Elser, J.J., J.D. Nagy and Y. Kuang 2003. Biological stoichiometry: an ecological perspective on tumor dynamics. Bioscience
53: 1112-1120.
Biological stoichiometry also suggests that pathogen growth potential should respond to changes in the ratios of carbon to
various nutrients, including P, N and Fe. Indeed, larval mosquitoes infected with Beauvaria bassiana suffer a much higher
mortality if given low-quality food (Fig. 6).
Nagy, J.D. 2004. Competition and natural selection in a mathematical model of cancer. Bulletin of Mathematical Biology.
66: 663-687.
References
Kuang, Y., J.D. Nagy and J.J. Elser 2004. Biological stoichiometry of tumor dynamics: mathematical models and analysis.
Discrete and Continuous Dynamical Systems B 4: 221-240.
Nagy, J.D. 2005. The ecology and evolutionary biology of cancer: a review of mathematical models of necrosis and tumor
cell diversity. Mathematical Biosciences and Engineering 2: 281-418.
Smith, V.H., T.P. Jones and M.S. Smith. 2005. Host nutrition and infectious disease: an ecological view. Frontiers in
Ecology and the Environment. 3: 268-274.