Model Mathematics

\frac{d}{d time} (D) = k_on R_off + f_prime A_1 + g A_2 - ((k_off + f) D) \frac{d}{d time} (A_1) = f D + h_prime A_2 - ((f_prime + h) A_1) \frac{d}{d time} (A_2) = h A_1 - ((h_prime + g) A_2) R_off = R_T - D - A_1 - A_2 \frac{d}{d time} (x_2) = \{\begin{matrix} dSL_dt if A_2 = 0 \\ \frac{(- h) A_1}{A_2} (x_2 - x_0) + dSL_dt otherwise \end{matrix} \frac{d}{d time} (x_1) = \{\begin{matrix} dSL_dt if A_1 = 0 \\ (- (\frac{f D}{A_1} + \frac{h_prime A_2}{A_1})) x_1 + dSL_dt otherwise \end{matrix} lambda_A1 = \frac{A_1}{R_T} lambda_A2 = \frac{A_2}{R_T} F_t = E_1 x_1 + E_2 x_2 E_1 = e_cb A_1 E_2 = e_cb A_2 g = g_0 ⅇ^{sigma {(x_2 - x_0)}^{2}} h = h_0 ⅇ^{sigma {x_1}^{2}} f_prime = f_prime_0 ⅇ^{sigma {x_1}^{2}} h_prime = h_prime_0 ⅇ^{sigma ({x_2}^{2} - ({x_1}^{2}))} sigma = \{\begin{matrix} sigma_plus if x_2 > x_0 \\ sigma_minus if x_2 < x_0 \\ 0 otherwise \end{matrix} f = f_r {(1 + lambda_A1 (ⅇ^{\frac{x_1}{x_0} (nu - 1)} - 1) + lambda_A2 (ⅇ^{\frac{x_2}{x_0} (nu - 1)} - 1))}^{2} dSL_dt = \{\begin{matrix} 21.2 if time > 0.001 \land time < 0.002 \\ 0 otherwise \end{matrix} \frac{d}{d time} (SL) = dSL_dt