# Model Mathematics

### Component: volume_i

$volume_i=volume_i0$

### Component: volume_er

$volume_er=volume_igamma$

### Component: volumeCa_i

$ddtimevolumeCa_i=Jipt+Jryr+Jer-Jserca+Jin-Jpm$

### Component: Ca_i

$Ca_i=volumeCa_ivolume_i$

### Component: volumeCa_er

$ddtimevolumeCa_er=-Jipt+Jryr+Jer-Jserca$

### Component: Ca_er

$Ca_er=volumeCa_ervolume_er$

### Component: volume_iIP3

$ddtimevolume_iIP3=J_ip3P-J_ip3D⁢volume_i$

### Component: IP3

$IP3=volume_iIP3volume_i$

### Component: PIP2

$ddtimePIP2=J_ip3R⁢IPX-J_ip3PPIP2_Total$

### Component: IPX

$IPX=1-IP3PIP2_Total-PIP2$

### Component: J_ip3R

$J_ip3R=J_ip3R0$

### Component: receptor

$V_mech=V_mech0iftime>10∧time<25∧MechanicalStimulation>00otherwiseV_IP3=C_1⁢ATP_eC_2+ATP_e+C_3⁢ATP_e2C_42+ATP_e2ddtimeATP_e=-V_ATP⁢ATP_eK_ATP+ATP_e$

### Component: J_ip3P

$J_ip3P=V_IP3⁢PIP2$

### Component: J_ip3D

$F_Ca=Ca_iK_rc+Ca_iJ_ip3D=Beta_1+Beta_2⁢F_Ca2⁢IP3K_IP3+IP3$

### Component: Jipt

$Pipt=O4Jipt=Jipt0⁢volume_i0⁢Pipt⁢Ca_er-Ca_i$

### Component: Jryr

$W_inf=1+KaCa_i4+Ca_iKb31+1Kc+Ca_iKb3+KaCa_i4Pryr=W_inf⁢1+KaCa_i4+Ca_iKb31+1Kc+Ca_iKb3+KaCa_i4Jryr=Jryr0⁢volume_i0⁢Ca_er-Ca_i$

### Component: Jer

$Jer=Jer0⁢volume_i0⁢Ca_er-Ca_i$

### Component: Jserca

$Jserca=volume_i0⁢Vserca⁢Ca_i2Kserca2+Ca_i2⁢1Ca_er$

### Component: Jin

$V_Ca=R⁢Tz_Ca⁢F⁢ln⁡Ca_extCa_iIin_1=volume_i0⁢P_pm_1⁢V_Ca-VmIin_2=volume_i0⁢P_pm_2⁢V_mech⁢V_Ca-VmJin_1=Iin_1z_Ca⁢FJin_2=Iin_2z_Ca⁢FJin=Jin_1+Jin_2$

### Component: Jpm

$Jpm=Vpm⁢volume_i0⁢Ca_i2Kpm2+Ca_i2$

### Component: O

$ddtimeO=k1⁢IP3⁢S-k1_⁢O+k2⁢OS=1-O+I1+I2$

### Component: I1

$ddtimeI1=k2⁢O-k3+k4⁢I1$

### Component: I2

$ddtimeI2=k4⁢I1-k5⁢I2$

### Component: constants

$k1=alpha_1⁢Ca_i3beta_13+Ca_i3k4=alpha_4⁢IP3beta_4+IP3$
Source
Derived from workspace Warren, Tawhai, Crampin, 2009 at changeset 7a277ddc5b1a.
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