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ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

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Furthermore, the values are spread out within this interval, thus indicating that there is<br />

no sharp distinction between ‘important’ and ‘unimportant’ parameter combinations and<br />

confirming the sloppy nature of the model under investigation [5]. The results presented<br />

in [5] suggest that sloppy sensitivity spectra, as observed by the sustantial variation in<br />

eigenvalue magnitudes in the model presented here, are universal in systems biology<br />

models. This prevalence of sloppiness highlights the power of collective fits and<br />

suggests that the focus of modelling efforts should be on predictions rather than on<br />

parameters.<br />

In summary, we have shown how a relatively simple system of differential equations<br />

can accurately model the biological process of subventricular neurogenesis and that the<br />

individual parameter values of this system are of equal importance in determining the<br />

properties of its solutions. We have found a particular parameter space (which is likely<br />

not to be unique) that is stable to perturbation and that yields results which match others<br />

in the literature. We compared different mechanisms of migration and found that<br />

chemoattraction is required to obtain physiologically relevant migration into the OB and<br />

that chemorepulsion can fortify this migration pattern. We believe that this model could<br />

be extended and reapplied once more accurate information on the various parameters is<br />

available in order to make quantitative predictions of neurogenic behaviour.<br />

Furthermore, the agreement between this model and the BLI data implies that at least<br />

one chemoattractant factor is secreted in an endocrine/paracrine manner and is<br />

responsible for directing migration, as it is produced by all types of neural stem cells<br />

present. Whether this is physiologically the case remains to be confirmed<br />

experimentally.<br />

5. ACKNOWLEDGEMENTS<br />

The authors would like to thank the Nuffield Foundation for the award of an<br />

Undergraduate Research Bursary (Grant Refs: URB/ 39423, URB/37878) which<br />

supported this research.<br />

6. REFERENCES<br />

1. Ghashghaei, H.T., Lai, C., Anton, E.S., Neuronal migration in the adult brain: are<br />

we there yet? Nat Rev Neuroscience, 2007, Vol 8, 149141-151.<br />

2. Reumers, V., Deroose, C. M., Krylyshkina, O., Nuyts, J., Geraerts, M., Mortelmans,<br />

L., Gijsbers, R., Haute, C. V. D., Debyser, Z., and Baekelandt, V., Noninvasive and<br />

quantitative monitoring of adult neuronal stem cell migration in mouse brain using<br />

bioluminescence imaging. Stem Cells, 2008, Vol. 26(9), 2382-2390.<br />

3. Gerisch, A. and Chaplain, M., Robust numerical methods for taxis-diffusionreaction<br />

systems, Applications to biomedical problems. Math Comp Mod, 2006,<br />

Vol. 43(1-2), 49-75.<br />

4. Ashbourn, J.M.A., Miller, J.J., Reumers, V., Baekelandt, V., Geris, L.,<br />

Mathematical Model of Adult Subventricular Neurogenesis. J Royal Soc Interface,<br />

revised version submitted, <strong>2012</strong>.<br />

5. Gutenkunst, R., Waterfall, J., Casey, F., Brown, K., Myers, C., and Sethna, J.,<br />

Universally sloppy parameter sensitivities in systems biology models. PLoS<br />

Comput Biol, 2007, Vol. 3(10), 1871-1878.

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