Model Mathematics

F_vol = \frac{1 e 12}{1} \frac{1}{1000} F C_vol

H_0 = \{\begin{matrix} 0 if time < t_0 \\ 1 otherwise \end{matrix} H_1 = \{\begin{matrix} 0 if time < t_1 \\ 1 otherwise \end{matrix} O_stim = od (H_0 - H_1)

\frac{d}{d time} (bLR) = k_1 O_stim (R_tot - bLR) - (r_1 bLR)

\frac{d}{d time} (aG) = k_G (G_tot - aG) - r_G

k_G = k_2 bLR

r_G = r_2 aG

\frac{d}{d time} (cAMP) = synth - degrad

synth = \frac{aG smax}{1 + {(\frac{aCaMK}{kinh})}^{ninh}}

degrad = pd cAMP

\frac{d}{d time} (Ca) = \frac{1000}{1} \inf I_CNG - J_NCX - (cc_1 - (cc_2 CaCaM))

cc_1 = cc1lin Ca

\frac{d}{d time} (CaCaM) = cc_1 - (cc_2 CaCaM)

\frac{d}{d time} (aCaMK) = ck_1 - (ck_2 aCaMK)

ck_1 = ck1lin CaCaM

\frac{d}{d time} (V) = \frac{1000}{1} \frac{1}{cap} (I_CNG + I_ClCa + I_NCX + I_other)

I_CNG = \frac{cnmax {cAMP}^{n_1}}{{cAMP}^{n_1} + {(inhcng hmc_1)}^{n_1}} \frac{1}{1000} (V_cng - V)

inhcng = 1 + \frac{(inhmax - 1) {CaCaM}^{ninhcng}}{{CaCaM}^{ninhcng} + {kinhcng}^{ninhcng}}

I_ClCa = \frac{clmax {Ca}^{n_2}}{{Ca}^{n_2} + {hmc_2}^{n_2}} \frac{1}{1000} (V_Cl - V)

I_NCX = \frac{1}{1000} F_vol J_NCX

J_NCX = ef Ca

I_other = gl \frac{1}{1000} (V_l - V)