Abstract
Retinitis pigmentosa (RP) is an inherited disease affecting approximately 1: 4000 individuals in North America. It is characterized clinically by the gradual apoptotic death of photoreceptor cells that occurs nonuniformly across the surface of the retina. Recently, it has been demonstrated that the time of death of many individual photoreceptors is random, a fact that must be reconciled with the spatiotemporal patterns of photoreceptor degeneration that are observed in patients with RP. One possible explanation is that a diffusible toxic factor is released by dying photoreceptors and induces adjacent cells to likewise undergo apoptosis. To determine if such a mechanism can result in patchy distributions of photoreceptor death, as frequently observed in RP patients, we studied cell attrition produced by a bistable biochemical switch in an idealized one-dimensional retina. We found that with a reasonable choice of parameter values, our model was able to produce patterns of cell death resembling those observed in RP. In the context of this model, patches on the order of histologically observable size could develop from a single release event, but their rates of formation were independent of the concentration of toxic factor released. Instead, factor concentration affected the overall rate of cell death, the number of degenerating patches, and their distribution across the retina.
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References
Berson, E. L. (1993). Retinitis pigmentosa. Invest. Ophthalmol. Vis. Sci. 34, 1659–1676.
Burns, J. (2000). A mathematical study of retinal cell death. MSc Qualifying Research Report. C. J. Lumsden, supervisor. Department of Mathematics, University of Toronto.
Campochiaro, P. A., M. Chang, M. Ohsato, S. A. Vinores, Z. Nie, L. Hjelmeland, A. Mansukhani, C. Basilico and D. J. Zack (1996). Retinal degeneration in transgenic mice with photoreceptor-specific expression of a dominant-negative fibroblast growth factor receptor. J. Neurosci. 16, 1679–1688.
Cideciyan, A. V., D. C. Hood, Y. Huang, E. Banin, Z. Y. Li, E. M. Stone, A. H. Milam and S. G. Jacobson (1998). Disease sequence from mutant rhodopsin allele to rod and cone photoreceptor degeneration in man. Proc. Natl. Acad. Sci. USA 95, 7103–7108.
Clarke, G., R. A. Collins, B. R. Leavitt, D. F. Andrews, M. R. Haydon, C. J. Lumsden and R. R. McInnes (2000). A one-hit model of cell death in inherited neuronal degenerations. Nature 406, 195–199.
Clarke, G., C. J. Lumsden and R. R. McInnes (2001). Inherited neurodegenerative diseases: The one-hit model of neurodegeneration. Hum. Mol. Gen. 10, 2269–2275.
Creagh, E. M. and S. J. Martin (2001). Caspases: cellular demolition experts. Biochem. Soc. Trans. 29, 696–702.
Curcio, C. A., K. R. Sloan, R. E. Kalina and A. E. Hendrickson (1990). Human photoreceptor topography. J. Comp. Neurol. 292, 497–523.
Daiger, S. P., L. S. Sullivan and B. J. F. Rossiter (2002). RetNetM: retinal information network: cloned and/or mapped human genes causing retinal degeneration or related diseases. http://www.sph.uth.tmc.edu/Retnet/home.htm.
Eastman, A. (1995). Assays for DNA fragmentation, endonucleases, and intracellular pH and Ca2+ associated with apoptosis. Methods Cell Biol. 46, 41–55.
Evans, L. C. (1998). Partial Differential Equations, Graduate Studies in Mathematics, Vol. 19, Providence, RI: American Mathematical Society.
Fain, G. L. and J. E. Lisman (1999). Light, Ca2+, and photoreceptor death, new evidence for the equivalent-light hypothesis from arrestin knockout mice. Invest. Ophthalmol. Vis. Sci. 40, 2770–2772.
Faktorovich, E. G., R. H. Steinberg, D. Yasumura, M. T. Matthes and M. M. LaVail (1990). Photoreceptor degeneration in inherited retinal dystrophy delayed by basic fibroblast growth factor. Nature 347, 83–86.
Ferrell, J. E. and W. Xiong (2001). Bistability in cell signaling: how to make a continuous process discontinuous, and reversible processes irreversible. Chaos 11, 227–236.
Fontaine, V., N. Kinkl, J. Sahel, H. Dreyfus and D. Hicks (1998). Survival of purified rat photoreceptors in vitro is stimulated directly by fibroblast growth factor-2. J. Neurosci. 18, 9662–9672.
Fussenegger, M., J. E. Bailey and J. Varner (2000). A mathematical model of caspase function in apoptosis. Nat. Biotech. 18, 768–774.
Gao, H. and J. G. Hollyfield (1995). Basic fibroblast growth factor in retinal development: differential levels of bFGF expression and content in normal and retinal degeneration (rd) mutant mice. Dev. Biol. 169, 168–184.
Gillespie, D. T. (1976). A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys. 22, 413–424.
Gillespie, D. T. (1977). Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81, 2340–2361.
Hicks, D. (1996). Characterization and possible roles of fibroblast growth factors in retinal photoreceptor cells. Keio J. Med. 45, 140–154.
Huang, P. C., A. E. Gaitin, Y. Hao, R. M. Petters and F. Wong (1993). Cellular interactions implicated in the mechanism of widespread photoreceptor degeneration in transgenic mice expressing a mutant rhodopsin gene. Proc. Natl. Acad. Sci. USA 90, 8484–8488.
Jacobson, M. D., M. Weil and M. C. Raff (1997). Programmed cell death in animal development. Cell 88, 347–354.
Kaufmann, S. H. and M. O. Hengartner (2001). Programmed cell death: alive and well in the new millennium. Trends Cell Biol. 11, 526–534.
Kerr, J. F. R., A. H. Wyllie and A. R. Currie (1972). Apoptosis: a basic biological phenomenon with wide-ranging implications in tissue kinetics. Br. J. Cancer 26, 239–255.
Krewson, C. E., M. L. Klarman and M. W. Saltzman (1995). Distribution of nerve growth factor following direct delivery to brain interstitium. Brain Res. 680, 196–206.
Leutjens, C., D. Kögel, C. Reimertz, H. Düßmann, A. Renz, K. Schulze-Osthoff, A.-L. Nieminen, M. Poppe and J. Prehn (2001). Multiple kinetics of mitochondrial cytochrome c release in drug-induced apoptosis. Mol. Pharmacol. 60, 1008–1019.
Lewis, J., J. M. W. Slack and L. Wolpert (1977). Thresholds in development. J. Theor. Biol. 65, 579–590.
Li, T., W. K. Snyder, J. E. Olsson and T. P. Dryja (1996). Transgenic mice carrying the dominant rhodopsin mutation P347S: evidence for defective vectorial transport of rhodopsin to the outer segments. Proc. Natl. Acad. Sci. USA 93, 14176–14181.
Ma, C., D. Papermaster and C. L. Cepko (1998). A unique pattern of photoreceptor degeneration in cyclin D1 mutant mice. Proc. Natl. Acad. Sci. USA 95, 9938–9943.
Maruyama, R. et al. (2001). Dynamic process of apoptosis in adult rat cardiomyocytes analyzed using 48-hour videomicroscopy and electron microscopy. Am. J. Pathol. 159, 683–691.
Milam, A., Z. Li and R. Fariss (1998). Histopathology of the human retina in retinitis pigmentosa. Prog. Ret. Eye Res. 17, 175–205.
Mills, J., S. Wang, M. Erecinska and R. Pittman (1995). Use of cultured neurons and neuronal cell lines to study morphological, biochemical, and molecular changes occurring in cell death. Methods Cell Biol. 46, 218–242.
Mohand-Said, S., A. Deudon-Combe, D. Hicks, M. Simonutti, V. Forster, A. C. Fintz, T. Leveillard, H. Dreyfus and J. A. Sahel (1998). Normal retina releases a diffusible factor stimulating cone survival in the retinal degeneration mouse. Proc. Natl. Acad. Sci. USA 95, 8357–8362.
Morimoto, A., S. Matsuda, K. Uryu, H. Fujita, N. Okumura and M. Sakanaka (1993). Light-and electron-microscopic localization of basic fibroblast growth factor in adult retina. Okajimas Folia Anat. Jpn. 70, 7–12.
Murray, J. D. (1981). On pattern formation mechanisms for lepidopteran wing patterns and mammalian coat markings. Phil. Trans. R. Soc. Lond. B 295, 473–496.
Murray, J. D. (1989). Mathematical Biology, New York: Springer.
Pagon, R. A. (1988). Retinitis pigmentosa. Surv. Opthalmol. 33, 137–177.
Remé, C. E., C. Grimm, F. Hafezi, A. Marti and A. Wenzel (1998). Apoptotic cell death in retinal degenerations. Prog. Ret. Eye Res. 17, 443–464.
Schmitt, E., A. Steyaert, G. Cimoli and R. Bertrand (1998). Bax-alpha promotes apoptosis induced by cancer chemotherapy and accelerates the activation of caspase 3-like cysteine proteases in p53 double mutant B lymphoma Namalwa cells. Cell Death Diff. 5, 506–516.
Seigel, G. M. and L. Liu (1997). Inducible apoptosis-promoting activity in retinal cell-conditioned medium. Mol. Vision 3, 14–14. http://www.molvis.org/molvis/
Stennicke, H. R., C. A. Ryan and G. S. Salvesen (2002). Reprival from execution: the molecular basis of caspase inhibition. Trends Biochem. Sci. 27, 94–101.
Travis, G. H. (1998). Mechanisms of cell death in the inherited retinal degenerations. Am. J. Hum. Genet. 62, 503–508.
Yuan, J. and B. A. Yankne (2000). Apoptosis in the nervous system. Nature 407, 802–809.
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Burns, J., Clarke, G. & Lumsden, C.J. Photoreceptor death: Spatiotemporal patterns arising from one-hit death kinetics and a diffusible cell death factor. Bull. Math. Biol. 64, 1117–1145 (2002). https://doi.org/10.1006/bulm.2002.0320
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DOI: https://doi.org/10.1006/bulm.2002.0320