. 2018 Jan 2;17(1):73–79. doi: 10.1080/15384101.2017.1403681

Table 1.

Hybrid Model I: the numerical model of p53 response when single-stranded breaks and double-stranded breaks exist simultaneously; Hybrid Model II: the numerical model of DNA damage repair when single-stranded breaks and double-stranded breaks exist simultaneously.

{\begin{cases} \frac{d [A T M]}{d t} = β_{1} * [I R] + β_{11} * {[A T M]}^{n_{1}} / ({[A T M]}^{n_{1}} + T_{1}^{n_{1}}) - α_{15} * [W i p 1] * [A T M] \\ \frac{d [A T R]}{d t} = β_{2} * [U V] - α_{2} * [A T R] \\ \frac{d [p 53]}{d t} = β_{3} * \frac{{[A T M]}^{n_{2}}}{({[A T M]}^{n_{2}} + T_{2}^{n_{2}})} + β 31 * \frac{{[A T R]}^{n_{3}}}{({[A T R]}^{n_{3}} + T_{3}^{n_{3}})} - α_{34} * [M d m 2] * [p 53] - α_{35} * [W i p 1] * [p 53] \\ \frac{d [M d m 2]}{d t} = β_{4} * [p 53 (t - τ_{1})] - α_{41} * [A T M] * [M d m 2] - α_{42} * [A T R] * [M d m 2] - α_{4} * [M d m 2] \\ \frac{d [W i p 1]}{d t} = β_{5} * [p 53 (t - τ_{2})] - α_{5} * [W i p 1] \\ I R = r e c t p u l s (t - t_{1}, d_{1}) \\ U V = r e c t p u l s (t - t_{2}, d_{2}) \end{cases}

{\begin{cases} \frac{d [{D A M}_{D S B}]}{d t} = - k_{12} * [p 53] * [{D A M}_{D S B}] \\ \frac{d [{D A M}_{S S B}]}{d t} = - k_{22} * [p 53] * [{D A M}_{S S B}] \\ \frac{d [A T M]}{d t} = β_{1} * [{D A M}_{D S B}] + β_{11} * {[A T M]}^{n_{1}} / ({[A T M]}^{n_{1}} + T_{1}^{n_{1}}) - α_{15} * [W i p 1] * [A T M] \\ \frac{d [A T R]}{d t} = β_{2} * [{D A M}_{S S B}] - α_{2} * [A T R] \\ \frac{d [p 53]}{d t} = β_{3} * \frac{{[A T M]}^{n_{2}}}{({[A T M]}^{n_{2}} + T_{2}^{n_{2}})} + β_{31} * \frac{{[A T R]}^{n_{3}}}{({[A T R]}^{n_{3}} + T_{3}^{n_{3}})} - α_{34} * [M d m 2] * [p 53] - α_{35} * [W i p 1] * [p 53] \\ \frac{d [M d m 2]}{d t} = β_{4} * [p 53 (t - τ_{1})] - α_{41} * [A T M] * [M d m 2] - α_{42} * [A T R] * [M d m 2] - α_{4} * [M d m 2] \\ \frac{d [W i p 1]}{d t} = β_{5} * [p 53 (t - τ_{2})] - α_{5} * [W i p 1] \\ k_{12} + k_{22} = C \end{cases}