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Stein, P. D’Eustach, Reactome knowledgebase of human biological pathways and processes. Nucleic Acids Res. 37, D619–D622 (2009) 25. H. Mi, S. Dong, A. Muruganujan, P. Gaudet, S. D. Thomas, PANTHER version 7: improved phylogenetic trees, orthologs, and collaboration with the gene ontology consortium. Nucleic Acids Res. 38, D240–D244 (2010) 26. L. L. Menten, Die kinetik der invertinwirkung. Biochemische Zeitschrift 49, 333–369 (1913) 27. D. Nishimura, A view from the web: biocarta. Biotech Softw.

For this reason, only the open-loop system dynamics are considered here and the pulse modulation functions are not explicitly identified from data. 11), as will be shown further, can be readily obtained from the estimates of the weights k and the firing times tk of the GnRH pulses. 9), it is of interest to estimate the GnRH impulse times and weights from measured LH data. The half-life times b1 and b2 of GnRH and LH, respectively, are also considered to be unknown here, so these parameters have to be estimated in some way.

6 presents a simulation example with the same parameters as in Fig. 4, except that the amplitude modulation functions is multiplied by a sinusoid function with a period of 24 h. Conclusions and Future Work An extension of a hybrid mathematical model of testosterone regulation is suggested, together with an algorithm for estimating the firing times of GnRH impulses from time series of measured LH concentrations. (continued) 38 P. Mattsson and A. Medvedev Tests on hormone data collected in healthy human males indicate that the model explains the experimental LH concentration profile very well with a sparse set of GnRH impulses.

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