Abstract
MP systems are a class of P systems introduced for modeling metabolic processes. Here we apply an algorithm, we call Log-Gain Stoichiometric Stepwise Regression (LGSS), to Golbeter’s oscillator. In general, LGSS derives MP models from the time series of observed dynamics. In the case of Golbeter’s oscillator, we found that by considering different values of the resolution time τ, different analytical forms of regulation maps were appropriate. By means of a suitable MATLAB implementation of LGSS, we automatically generated 700 MP models (τ varying from 10− 3 min to 700 ·10− 3 min with increments of 10− 3 min). Many of these models exhibit a good approximation, and have second degree polynomials as regulation maps. These results provide an experimental evidence of LGSS adequacy.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
von Bertalanffy, L.: General Systems Theory: Foundations, Developments, Applications. George Braziller Inc., New York (1967)
Draper, N., Smith, H.: Applied Regression Analysis, 2nd edn. John Wiley & Sons, New York (1981)
Goldbeter, A.: A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase. PNAS 88(20), 9107–9111 (1991)
Goldbeter, A.: Biochemical Oscillations and Cellular Rhythms: The molecular bases of periodic and chaotic behaviour. Cambridge University Press, Cambridge (1996)
Goldbeter, A.: Computational approaches to cellular rhythms. Nature 420, 238–245 (2002)
Hocking, R.R.: The Analysis and Selection of Variables in Linear Regression. Biometrics, 32 (1976)
Luenberger, D.G.: Optimization by Vector Space Methods. John Wiley & Sons, Chichester (1969)
Manca, V.: Log-Gain Principles for Metabolic P Systems. In: Condon, A., et al. (eds.) Algorithmic Bioprocesses. Natural Computing Series, ch. 28, pp. 585–605. Springer, Heidelberg (2009)
Manca, V.: Fundamentals of Metabolic P Systems. In: [15], ch. 19.Oxford University Press, Oxford (2010)
Manca, V.: Metabolic P systems. Scholarpedia 5(3), 9273 (2010)
Manca, V., Bianco, L., Fontana, F.: Evolutions and Oscillations of P systems: Theoretical Considerations and Application to biological phenomena. In: Mauri, G., Păun, G., Jesús Pérez-Jímenez, M., Rozenberg, G., Salomaa, A. (eds.) WMC 2004. LNCS, vol. 3365, pp. 63–84. Springer, Heidelberg (2005)
Manca, V., Marchetti, L.: Metabolic approximation of real periodical functions. Journal of Logic and Algebraic Programming (2010), doi:10.1016/j.jlap.2010.03.005
Manca, V., Marchetti, L.: Log-Gain Stoichiometic Stepwise regression for MP systems. IJFCS (to appear, 2010)
Păun, G.: Membrane Computing. An Introduction. Springer, Heidelberg (2002)
Păun, G., Rozenberg, G., Salomaa, A. (eds.): Oxford Handbook of Membrane Computing. Oxford University Press, Oxford (2010)
Pearson, K.: Notes on the History of Correlation. Biometrika 13(1), 25–45 (1920)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Manca, V., Marchetti, L. (2010). Goldbeter’s Mitotic Oscillator Entirely Modeled by MP Systems. In: Gheorghe, M., Hinze, T., Păun, G., Rozenberg, G., Salomaa, A. (eds) Membrane Computing. CMC 2010. Lecture Notes in Computer Science, vol 6501. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18123-8_22
Download citation
DOI: https://doi.org/10.1007/978-3-642-18123-8_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-18122-1
Online ISBN: 978-3-642-18123-8
eBook Packages: Computer ScienceComputer Science (R0)