Dynamic Behavior of p53 Driven by Delay and a Microrna-34a-Mediated Feedback Loop

. 2020 Feb 13;21(4):1271. doi: 10.3390/ijms21041271

\frac{d x_{1} (t)}{d t} = k_{s p 53} + k_{d a 1} x_{7} (t) \frac{x_{2} (t)}{x_{2} (t) + k_{0}} - k_{d p 531} x_{1} (t) + k_{r p} x_{2} (t) - k_{d p 532} x_{3} (t) \frac{x_{1} (t)}{x_{1} (t) + k_{d 1}} - k_{f p} A \frac{x_{1} (t)}{x_{1} (t) + k_{p}},

\frac{d x_{2} (t)}{d t} = k_{f p} A \frac{x_{1} (t)}{x_{1} (t) + k_{p}} - k_{r p} x_{2} (t) - k_{d p 53 s} x_{3} (t) \frac{x_{2} (t)}{x_{2} (t) + k_{d 2}} - k_{d a 1} x_{7} (t) \frac{x_{2} (t)}{x_{2} (t) + k_{0}},

\frac{d x_{3} (t)}{d t} = k_{s m d 1} + k_{s m d 2} \frac{x_{2} {(t - τ)}^{4}}{x_{2} {(t - τ)}^{4} + k^{4}} - k_{d m d m 20} x_{3} (t) - k_{d m d m 21} \frac{A}{A + j_{a t m}} x_{3} (t),

\frac{d x_{4} (t)}{d t} = k_{s m i 1} + k_{s m i 2} \frac{x_{2} {(t)}^{4}}{x_{2} {(t)}^{4} + j_{1}^{4}} - k_{d m 1} x_{4} (t) - k_{o n 2} x_{6} (t) x_{4} (t) + k_{o f f 2} x_{5} (t),

\frac{d x_{5} (t)}{d t} = k_{o n 2} x_{6} (t) x_{4} (t) - k_{o f f 2} x_{5} (t) - k_{s m i r} x_{5} (t),

\frac{d x_{6} (t)}{d t} = k_{s s} - k_{s s i} x_{6} (t) - k_{o n 2} x_{6} (t) x_{4} (t) + k_{o f f 2} x_{5} (t),

\frac{d x_{7} (t)}{d t} = r_{s i r t 1} x_{6} (t) - k_{s i r t 1} x_{7} (t) .