Mathematical Models of Tumor-Immune System Dynamics by Amina Eladdadi Peter Kim & Dann Mallet

Author:Amina Eladdadi, Peter Kim & Dann Mallet
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

Based on the signaling network shown in Fig. 3b, we write the phenomenological equations for the rate change of those key molecules (m, a) as follows:

(1)

(2)

where g represents the signaling pathways from glucose to miR-451, s represents the signaling pathways to AMPK, Λ 1 and Λ 3 are the autocatalytic enhancement parameters for miR-451 and AMPK complex, respectively, Λ 2 and Λ 4 are the Hill-type inhibition saturation parameters from the counterpart of miR-451 and AMPK complex, respectively, Λ 5 is the inhibition strength of miR-451 by the AMPK complex, Λ 6 is the inhibition strength of the AMPK complex by miR-451, μ 1 and μ 2 are microRNA/protein degradation rates of miR451 and AMPK complex, respectively. The glucose signal g increases the rate of miR-451 levels through a function f(g), while the AMPK signal s increases the AMPK activity through another function h(s). A requirement on these functions is

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