Solving dynamical inverse problems by means of Metabolic P systems

MP (Metabolic P) systems are a class of P systems introduced for modelling metabolic processes. We refer to the dynamical inverse problem as the problem of identifying (discrete) mathematical models exhibiting an observed dynamics. In this paper, we complete the definition of the algorithm LGSS (Log-gain Stoichiometric Stepwise regression) introduced in Manca and Marchetti (2011) for solving a general class of dynamical inverse problems. To this aim, we develop a reformulation of the classical stepwise regression in the context of MP systems. We conclude with a short review of two applications of LGSS for discovering the internal regulation logic of two phenomena relevant in systems biology.

[1]  Vincenzo Manca,et al.  A Methodology Based on MP Theory for Gene Expression Analysis , 2011, Int. Conf. on Membrane Computing.

[2]  Andrea De Gaetano,et al.  Modeling the intra-venous glucose tolerance test: A global study for a single-distributed-delay model , 2004 .

[3]  H. Kitano.  Systems Biology: A Brief Overview , 2002, Science.

[4]  Ovide Arino,et al.  Mathematical modelling of the intravenous glucose tolerance test , 2000, Journal of mathematical biology.

[5]  Vincenzo Manca,et al.  Log-gain Principles for Metabolic P Systems , 2009, Algorithmic Bioprocesses.

[6]  ALBERT GOLDBETER Facultd.  A minimal cascade model for the mitotic oscillator involving cyclin and cdc 2 kinase ( cell cycle / maturation-promoting factor / phosphorylation cascade / thresholds / biochemical oscillations ) , .

[7]  R. R. Hocking.  The analysis and selection of variables in linear regression , 1976 .

[8]  P. Brazhnik,et al.  Gene networks: how to put the function in genomics. , 2002, Trends in biotechnology.

[9]  Pasquale Palumbo,et al.  Theoretical Biology and Medical Modelling Open Access a Discrete Single Delay Model for the Intra-venous Glucose Tolerance Test , 2022 .

[10]  Vincenzo Manca,et al.  Biological networks in metabolic P systems , 2008, Biosyst..

[11]  Amir D. Aczel.  Complete Business Statistics , 1992 .

[12]  Jens Timmer,et al.  Dynamical modeling and multi-experiment fitting with PottersWheel , 2008, Bioinform..

[13]  Gheorghe Paun,et al.  Membrane Computing , 2002, Natural Computing Series.

[14]  Vincenzo Manca,et al.  Metabolic approximation of real periodical functions , 2010, J. Log. Algebraic Methods Program..

[15]  Vincenzo Manca,et al.  The metabolic algorithm for P systems: Principles and applications , 2008, Theor. Comput. Sci..

[16]  John W. Sutherland,et al.  General Systems Theory: Foundations, Developments, Applications , 1974 .

[17]  Tilo Strutz,et al.  Data Fitting and Uncertainty: A practical introduction to weighted least squares and beyond , 2010 .

[18]  K. Pearson.  NOTES ON THE HISTORY OF CORRELATION , 1920 .

[19]  Vincenzo Manca,et al.  Evolutions and Oscillations of P Systems: Theorethical Considerations and Applications to Biochemical Phenomena , 2006 .

[20]  Vincenzo Manca,et al.  MP Modelling of Glucose-Insulin Interactions in the Intravenous Glucose Tolerance Test , 2011, Int. J. Nat. Comput. Res..

[21]  T. Ideker,et al.  A new approach to decoding life: systems biology. , 2001, Annual review of genomics and human genetics.

[22]  Vincenzo Manca,et al.  Log-Gain stoichiometric Stepwise Regression for MP Systems , 2011, Int. J. Found. Comput. Sci..

[23]  Vincenzo Manca,et al.  Goldbeter's Mitotic Oscillator Entirely Modeled by MP Systems , 2010, Int. Conf. on Membrane Computing.

[24]  Takeaki Kariya,et al.  Generalized Least Squares , 2004 .

[25]  Mudita Singhal,et al.  COPASI - a COmplex PAthway SImulator , 2006, Bioinform..

[26]  Vincenzo Manca.  Fundamentals of metabolic P systems , 2009 .

[27]  D. Luenberger.  Optimization by Vector Space Methods , 1968 .

[28]  J E Bailey,et al.  Mathematical Modeling and Analysis in Biochemical Engineering: Past Accomplishments and Future Opportunities , 1998, Biotechnology progress.

[29]  S. C. Johnson.  Hierarchical clustering schemes , 1967, Psychometrika.