# Model Mathematics

### Component: Ca_i

$ddtimeCa_i=J1-J2 J1 = c1 ⁢ v1 ⁢ P_open + v2 ⁢ Ca_ER - Ca_i J2 = v3 ⁢ Ca_i 2.0 Ca_i 2.0 + k3 2.0$

### Component: Ca_ER

$Ca_ER = c0 - Ca_i c1$

### Component: IP3

$ddtimeIP3= v4 ⁢ Ca_i + 1.0 - alpha ⁢ k4 Ca_i + k4 - Ir ⁢ IP3$

### Component: receptor_dissociation_constants

$d1 = K_d1 - IP3_cold$$d2=b2a2$$d3=K_d2-IP3_cold⁢1+d2-d1⁢d2$$d4=d1⁢d2d3$$d5=b5a5$

### Component: probability_of_an_open_IP3_receptor_channel

$P_open = Ca_i ⁢ IP3 ⁢ d2 Ca_i ⁢ IP3 + IP3 ⁢ d2 + d1 ⁢ d2 + Ca_i ⁢ d3 ⁢ Ca_i + d5 3.0$

### Component: x_000

$ddtimex_000=- V1 - V3$

### Component: x_001

$ddtimex_001= V1 - V4$

### Component: x_010

$ddtimex_010= V3 - V2$

### Component: x_011

$x_011= 1.0 - x_000 + x_001 + x_010$

### Component: fluxes

$V1 = a4 ⁢ Ca_i ⁢ x_000 - d4 ⁢ x_001 V2 = a4 ⁢ Ca_i ⁢ x_010 - d4 ⁢ x_011 V3 = a5 ⁢ Ca_i ⁢ x_000 - d5 ⁢ x_010 V4 = a5 ⁢ Ca_i ⁢ x_001 - d5 ⁢ x_011$

### Component: constants

$b1 = d1 ⁢ a1 b3 = d3 ⁢ a3 b4 = d4 ⁢ a4$
Source
Derived from workspace Deyoung, Keizer, 1992 at changeset 5221e51ca22f.
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