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ON SIMULATING THE GENERATION OF MOSAICISM DURING MAMMALIAN CEREBRAL CORTICAL DEVELOPMENT

MICHAEL A. CASE

Department of Mathematical Sciences, Clemson University, Box 340975, Clemson, SC, 29634-0975, USA

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and

HUGH R. MACMILLAN

Department of Mathematical Sciences, Clemson University, Box 340975, Clemson, SC, 29634-0975, USA

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https://doi.org/10.1142/S0218339009002740Cited by:1 (Source: Crossref)

Abstract

Renewed calls for a systems biology reflect the hope hat enduring biological questions at single-cell and cell-population scales will be resolved as modern molecular biology, with its reductionist program, approaches a nearly-complete characterization of the molecular mechanisms of specific cellular processes. Due to the confounding complexity of biological organization across these scales, computational science is sought to complement the intuition of experimentalists. However, with respect to the molecular basis of cellular processes during development and disease, a gulf between feasible simulations and realistic biology persists. Formidable are the mathematical and computational challenges to conducting and validating cell population-scale simulations, drawn from single-cell level and molecular level details. Nonetheless, in some biological contexts, a focus on core processes crafted by evolution can yield coarse-grained mathematical models that retain explanatory potential despite drastic simplification of known biochemical kinetics.

In this article, we bring this modeling philosophy to bear on the nature of neural progenitor cell decision making during mammalian cerebral cortical development. Specifically, we present the computational component to a research program addressing developmental links between (i) the cellular response to endogenous DNA damage, (ii) primary mechanisms of neuronal genetic heterogeneity, or mosaicism, and (iii) the cell fate decision making that defines the population kinetics of neurogenesis.

Keywords:

References

A. R. Muotri and F. H. Gage, Nature 441(7097), 1087 (2006), DOI: 10.1038/nature04959. Web of Science, Google Scholar
R. Pamphlett, Med. Hypotheses 62, 679 (2004), DOI: 10.1016/j.mehy.2003.11.023. Web of Science, Google Scholar
B. Ames and M. Shigenaga, Proc. Natl. Acad. Sci. 90, 7915 (1993), DOI: 10.1073/pnas.90.17.7915. Web of Science, Google Scholar
P. Burcham, Mutat. Res.-Gen. Tox. En. 443(1–2), 11 (1999), DOI: 10.1016/S1383-5742(99)00008-3. Web of Science, Google Scholar
J. Chun and D. G. Schatz, Neuron 22, 7 (1999), DOI: 10.1016/S0896-6273(00)80671-6. Web of Science, Google Scholar
B. Deanset al., The EMBO Journal 19(24), 6675 (2000), DOI: 10.1093/emboj/19.24.6675. Web of Science, Google Scholar
A. R. Muotriet al., Hum. Mol. Genet. 16(2), 159 (2007), DOI: 10.1093/hmg/ddm196. Web of Science, Google Scholar
A. R. Muotriet al., Nature 435, 903 (2005), DOI: 10.1038/nature03663. Web of Science, Google Scholar
E. A. Farkash and E. T. Luning–Prak, J. Biomed. Biotechnol. 2006, 1 (2006), DOI: 10.1155/JBB/2006/37285. Google Scholar
A. J. Blaschke, K. Staley and J. Chun, Development 122, 1165 (1996). Web of Science, Google Scholar
S. K. Rehenet al., Proc. Natl. Acad. Sci. 98(23), 13361 (2001), DOI: 10.1073/pnas.231487398. Web of Science, Google Scholar
C. V. Rao, D. M. Wolf and A. P. Arkin, Nature 420(6912), 231 (2002), DOI: 10.1038/nature01258. Web of Science, Google Scholar
R. Laubenbacher and P. Mendes, Computational Systems Biology (Elsevier Academic Press, 2006) pp. 229–247. Google Scholar
L. A. Segel, Proc. Natl. Acad. Sci. 98(7), 3639 (2001), DOI: 10.1073/pnas.081081998. Web of Science, Google Scholar
P. K. Maini, 'In Silico' Simulation of Biological Processes 247 (Novartis Symposium, 2002) pp. 53–59. Google Scholar
M. A. Savageau, Nature 229, 542 (1971), DOI: 10.1038/229542a0. Web of Science, Google Scholar
L. H. Hartwellet al., Nature 402, c48 (1999), DOI: 10.1038/35011540. Google Scholar
H. Kitano, Nat. Rev. Gen. 5, 826 (2004), DOI: 10.1038/nrg1471. Web of Science, Google Scholar
G. von Dassow and G. M. Odell, J. Exp. Zool. 294, 179 (2002), DOI: 10.1002/jez.10144. Google Scholar
G. von Dassow, M. E. M. Meir and G. M. Odell, Nature 406, 188 (2000), DOI: 10.1038/35018085. Web of Science, Google Scholar
A. Eldaret al., Nature 419(6904), 304 (2002), DOI: 10.1038/nature01061. Web of Science, Google Scholar
K. Amonlirdvimanet al., Science 307(5708), 423 (2005), DOI: 10.1126/science.1105471. Web of Science, Google Scholar
M. Morohashiet al., J. Theor. Biol. 216, 19 (2002), DOI: 10.1006/jtbi.2002.2537. Web of Science, Google Scholar
M. Kaernet al., Nat. Rev. Genet. 6(6), 451 (2005), DOI: 10.1038/nrg1615. Web of Science, Google Scholar
M. Kerszberg, Curr. Opin. Gen. Dev. 14, 440 (2004), DOI: 10.1016/j.gde.2004.06.001. Web of Science, Google Scholar
B. J. Molyneauxet al., Nat. Rev. Neurosci. 8(6), 427 (2007), DOI: 10.1038/nrn2151. Web of Science, Google Scholar
G. Kempermann , Adult Neurogenesis ( Oxford University Press , 2006 ) . Google Scholar
M. Gotz and W. B. Huttner, Nat. Rev. Mol. Cell Bio. 6(10), 777 (2005), DOI: 10.1038/nrm1739. Web of Science, Google Scholar
A. Alvarez–Buylla, J. Garcia–Verdugo and A. Tramontin, Nat. Rev. Neurosci. 4, 287 (2001). Google Scholar
S. C. Noctoret al., J. Neurosci. 22(8), 3161 (2002). Web of Science, Google Scholar
D. C. Lieet al., Annu. Rev. Pharmacol. 44(1), 399 (2004). Google Scholar
J. S. Galet al., J. Neurosci. 26(3), 1045 (2006), DOI: 10.1523/JNEUROSCI.4499-05.2006. Web of Science, Google Scholar
S. K. McConnell and C. E. Kaznowski, Science 254, 282 (1991), DOI: 10.1126/science.1925583. Web of Science, Google Scholar
T. Takahashi, R. S. Nowakowski and V. S. Caviness Jr., J. Neurosci. 15(9), 6046 (1995). Web of Science, Google Scholar
T. Takahashi, R. S. Nowakowski and V. S. Caviness Jr., J. Neurosci. 16(19), 6183 (1996). Web of Science, Google Scholar
D. Thomaidouet al., J. Neurosci. 17(3), 1075 (1997). Web of Science, Google Scholar
L. Caiet al., J. Neurosci. Res. 69, 731 (2002), DOI: 10.1002/jnr.10398. Web of Science, Google Scholar
J. Gohlke, W. Griffith and E. Faustman, Dev. Brain Res. 151, 43 (2004), DOI: 10.1016/j.devbrainres.2004.03.020. Google Scholar
McConnell M. J., MacMillan H., Chun J., Mathematical modeling of extensive neural progenitor cell (NPC) death during cerebral cortical development, Cerebral Cortex, Submitted . Google Scholar
F. Calegariet al., J. Neurosci. 25(28), 6533 (2005), DOI: 10.1523/JNEUROSCI.0778-05.2005. Web of Science, Google Scholar
U. Corteset al., Mol. Carcinogen. 27, 57 (2000). Web of Science, Google Scholar
S. L. Harris and A. J. Levine, Oncogene 24, 2899 (2005), DOI: 10.1038/sj.onc.1208615. Web of Science, Google Scholar
B. Vogelstein, D. Lane and A. J. Levine, Nature 408, 307 (2000), DOI: 10.1038/35042675. Web of Science, Google Scholar
A. H. Yanget al., J. Neurosci. Res. 23(32), 10454 (2003). Google Scholar
M. J. McConnellet al., J. Neurosci. 24(37), 8090 (2004), DOI: 10.1523/JNEUROSCI.2263-04.2004. Web of Science, Google Scholar
D. Kaushalet al., J. Neurosci. 23(13), 5599 (2003). Web of Science, Google Scholar
A. F. Smit, Curr. Opin. Gen. Dev. 9, 657 (1999), DOI: 10.1016/S0959-437X(99)00031-3. Web of Science, Google Scholar
S. Gasioret al., J. Mol. Biol. 357, 1383 (2006), DOI: 10.1016/j.jmb.2006.01.089. Web of Science, Google Scholar
W. Weiet al., Mol. Cell Biol. 21(4), 1429 (2001), DOI: 10.1128/MCB.21.4.1429-1439.2001. Web of Science, Google Scholar
R. Oppenheim, Annu. Rev. Neurosci. 14, 453 (1991), DOI: 10.1146/annurev.ne.14.030191.002321. Web of Science, Google Scholar
Muotri A. R., Personal communication, unpublished data, 2008 . Google Scholar
R. M. Merks and J. A. Glazier, Physica A 352(1), 113 (2005), DOI: 10.1016/j.physa.2004.12.028. Web of Science, Google Scholar
A. D. Lander, Cell 128, 245 (2007), DOI: 10.1016/j.cell.2007.01.004. Web of Science, Google Scholar
V. Dubreuilet al., Cell Signaling and Growth Factors in Development 1, eds. K. Unsicker and K. Krieglstein (Wile-VCH, 2006) pp. 229–286. Google Scholar
U. S. Bhalla, P. T. Ram and R. Iyengar, Science 297(5583), 1018 (2002), DOI: 10.1126/science.1068873. Web of Science, Google Scholar
A. K. Howe, A. E. Aplin and R. L. Juliano, Curr. Opin. Gen. Dev. 12, 30 (2002), DOI: 10.1016/S0959-437X(01)00260-X. Web of Science, Google Scholar
B. N. Kholodenko, Nat. Rev. Mol. Cell Biol. 7(3), 165 (2006), DOI: 10.1038/nrm1838. Web of Science, Google Scholar
R. Chignolaet al., B. Math. Biol. 68, 1661 (2006), DOI: 10.1007/s11538-006-9078-8. Web of Science, Google Scholar
M. V. Blagosklonny, Semin. Cancer Biol. 13, 97 (2003), DOI: 10.1016/S1044-579X(02)00127-X. Web of Science, Google Scholar
K. Hardy and J. Stark, Apoptosis 7, 373 (2002), DOI: 10.1023/A:1016183731694. Web of Science, Google Scholar
E. Friedberg, Nature 421, 436 (2003), DOI: 10.1038/nature01408. Web of Science, Google Scholar
Y. Shiloh, Nat. Rev. Cancer 397, 155 (2003). Google Scholar
K. Nyberget al., Annu. Rev. Genet. 36(1), 617 (2002), DOI: 10.1146/annurev.genet.36.060402.113540. Web of Science, Google Scholar
G. Wilson, Cancer Metast. Rev. 23, 209 (2004), DOI: 10.1023/B:CANC.0000031762.91306.b4. Web of Science, Google Scholar
L. Chakalovaet al., Nat. Rev. Gen. 6(9), 669 (2005), DOI: 10.1038/nrg1673. Web of Science, Google Scholar
H. Hermeking, Cancer Cell 12(5), 414 (2007), DOI: 10.1016/j.ccr.2007.10.028. Web of Science, Google Scholar
N. Geva–Zatorskyet al., Mol. Sys. Bio. 2, E1 (2006). Google Scholar
E. Batcheloret al., Mol. Cell 30(3), 277 (2008), DOI: 10.1016/j.molcel.2008.03.016. Web of Science, Google Scholar
B. Novak and J. J. Tyson, J. Theor. Biol. 230(4), 563 (2004), DOI: 10.1016/j.jtbi.2004.04.039. Web of Science, Google Scholar
M. Fussenegger, J. E. Bailey and J. Varner, Nat. Biotechnol. 18, 768 (2000), DOI: 10.1038/81208. Web of Science, Google Scholar
F. Calegari and W. B. Huttner, J. Cell Sci. 116(24), 4947 (2003), DOI: 10.1242/jcs.00825. Web of Science, Google Scholar
S. Ohnuma, A. Philpott and W. A. Harris, Curr. Opin. Neurobiol. 11, 66 (2001), DOI: 10.1016/S0959-4388(00)00175-6. Web of Science, Google Scholar
S. Ohnuma and W. A. Harris, Neuron 40(2), 199 (2003), DOI: 10.1016/S0896-6273(03)00632-9. Web of Science, Google Scholar
B. Bernstein, A. Meissner and E. S. Lander, Cell 128, 669 (2007), DOI: 10.1016/j.cell.2007.01.033. Web of Science, Google Scholar
B. Chau and J. Y. Wang, Nat. Rev. Cancer 3, 130 (2003), DOI: 10.1038/nrc993. Web of Science, Google Scholar
C. Attwooll, E. L. Denchi and K. Helin, The EMBO J. 23, 4709 (2004), DOI: 10.1038/sj.emboj.7600481. Web of Science, Google Scholar
T. E. Harris , The Theory of Branching Processes ( Springer-Verlag , 1963 ) . Google Scholar
B. Weaver and D. Cleveland, Cancer Res. 67, 10103 (2007), DOI: 10.1158/0008-5472.CAN-07-2266. Web of Science, Google Scholar
J. J. Tyson, K. C. Chen and B. Novak, Curr. Opin. Cell Biol. 15, 221 (2003), DOI: 10.1016/S0955-0674(03)00017-6. Web of Science, Google Scholar
R. J. Ellis, Trends Biochem. Sci. 26, 597 (2001), DOI: 10.1016/S0968-0004(01)01938-7. Web of Science, Google Scholar
M. A. Savageau, Biosystems 47(1–2), 9 (1998), DOI: 10.1016/S0303-2647(98)00020-3. Web of Science, Google Scholar
S. Schnell and T. E. Turner, Prog. Biophy. Mol. Biol. 28(3), 235 (2004). Google Scholar
S. Schnell and P. K. Maini, Comment Theor. Biol. 83, 169 (2003). Google Scholar
H. H. McAdams and A. Arkin, Proc. Natl. Acad. Sci. 94, 814 (1997), DOI: 10.1073/pnas.94.3.814. Web of Science, Google Scholar
H. DeJong, J. Comput. Biol. 96(1), 67 (2002). Web of Science, Google Scholar
C. J. Firth and D. Bray , Stochastic Simulation of Cell Signaling Pathways ( The MIT Press , 2000 ) . Google Scholar
T. Kepler and T. Elston, Biophys. J. 81, 3116 (2001), DOI: 10.1016/S0006-3495(01)75949-8. Web of Science, Google Scholar
T. E. Turner, S. Schnell and K. Burrage, Comput. Biol. Chem. 28, 165 (2004), DOI: 10.1016/j.compbiolchem.2004.05.001. Web of Science, Google Scholar
A. Ma'ayan, R. D. Blitzer and R. Iyengar, Annu. Rev. Bioph. Biom. 34, 319 (2005), DOI: 10.1146/annurev.biophys.34.040204.144415. Web of Science, Google Scholar
M. B. Elowitzet al., Science 297, 1183 (2002), DOI: 10.1126/science.1070919. Web of Science, Google Scholar
P. S. Swain, M. B. Elowitz and E. D. Siggia, Proc. Natl. Acad. Sci. 99(22), 12795 (2002), DOI: 10.1073/pnas.162041399. Web of Science, Google Scholar
B. B. Aldridgeet al., Nat. Cell Biol. 8(11), 1195 (2006), DOI: 10.1038/ncb1497. Web of Science, Google Scholar
A. Novick and M. Weiner, Proc. Natl. Acad. Sci. 43, 553 (1957), DOI: 10.1073/pnas.43.7.553. Web of Science, Google Scholar
B. A. Ogunnaike, J. Roy Soc. Interface 3(6), 175 (2006), DOI: 10.1098/rsif.2005.0077. Web of Science, Google Scholar
R. Oren, Cell Death Diff. 10, 431 (2003), DOI: 10.1038/sj.cdd.4401183. Web of Science, Google Scholar
G. von Dassow and E. Meir, Modularity in Development and Evolution (The University of Chicago Press, 2004) pp. 244–288. Google Scholar
N. A. W. van Riel, Brief Bioinform 7(4), 364 (2006), DOI: 10.1093/bib/bbl040. Web of Science, Google Scholar
F. C. Boogerdet al., Synthese 145(1), 131 (2005), DOI: 10.1007/s11229-004-4421-9. Web of Science, Google Scholar
M. Kirschner, Cell 121(4), 503 (2005), DOI: 10.1016/j.cell.2005.05.005. Web of Science, Google Scholar
W. Bechtel and R. C. Richardson , Discovering Complexity: Decomposition and Localization as Strategies in Scientific Research ( Princeton Univ. Press , 1993 ) . Google Scholar
L. von Bertalanffy , General Systems Theory: Foundations, Development, Applications ( George Braziller, Inc. , 1968 ) . Google Scholar
Webster C., Sparse grid stochastic collocation techniques for the numerical solution of partial differential equations with random input data, PhD thesis, Florida State University, Tallahassee, FL, 2007 . Google Scholar
H. J. Bungartz and M. Griebel, Acta Numerica 1 (2004). Google Scholar
S. A. Smolyak, Sov. Math. 4, 240 (1963). Web of Science, Google Scholar
D. Xiu and G. E. Karniadakis, SIAM J. Sci. Comput. 24(2), 619 (2002), DOI: 10.1137/S1064827501387826. Web of Science, Google Scholar
Burkardt J., Webster C., Reduced order modeling of some nonlinear stochastic partial differential equations, Int J Num Anal Mod, to appear . Google Scholar
A. Murray and T. Hunt , The Cell Cycle: An Introduction ( Oxford University Press , 1993 ) . Google Scholar
A. B. Pardeee, Proc. Natl. Acad. Sci. 71(4), 1286 (1974), DOI: 10.1073/pnas.71.4.1286. Web of Science, Google Scholar
J. A. Diehlet al., Gene. Dev. 12(22), 3499 (1998), DOI: 10.1101/gad.12.22.3499. Web of Science, Google Scholar
R. Weinberg, Cell 81, 323 (1995), DOI: 10.1016/0092-8674(95)90385-2. Web of Science, Google Scholar
J. Falcket al., Nature 410, 842 (2001), DOI: 10.1038/35071124. Web of Science, Google Scholar
C. Stewart, A. Soria and P. Hamel, J. Neuro.-Oncol. 51, 183 (2001), DOI: 10.1023/A:1010615822317. Web of Science, Google Scholar
J. Y. J. Wang and S. K. Cho, Adv. Protein Chem. 69, 101 (2004), DOI: 10.1016/S0065-3233(04)69004-8. Web of Science, Google Scholar
J. Shahet al., Curr. Biol. 14, 942 (2004). Web of Science, Google Scholar