| Citation |
|---|
| DeYoung GW,Keizer J (1992) A single pool IP3- receptor based model for agonist simulated Ca2+ oscillations,PNAS89:9895-9899. http://www.pnas.org/cgi/content/abstract/89/20/ 9895 |
| Description |
|---|
| This model describes the IP3- sensitive Calcium channel. The receptor has three binding sites, denoted by three indices S[i,j,k],where i,j, k are 0 or 1. A 0 indicates the binding site is empty;a 1 indicates the binding site is occupied. The first site ( index i) binds IP3 (Inositol 1,4,5-Trisphosphate) ; the second site (j) binds Calcium and activates the channel; the third site (k) binds Calcium and inactivates the channel. The open channel probability can be computed as ( S[1,1,0]/(Sum of all S[i,j,k]))^ 3 as described in the reference. The differential equations shown below treate C and P as dynamic variables. To reproduce the results in the original paper both C and P should be treated as constants and not as dynamic variables. |
| Rate constant | Reaction |
|---|---|
| k1 = 400 | P + S[0, 0, 0] -> S[1, 0, 0] |
| k1 = 400 | P + S[0, 1, 0] -> S[1, 1, 0] |
| k2 = 0.2 | C + S[1, 0, 0] -> S[1, 0, 1] |
| k2 = 0.2 | C + S[1, 1, 0] -> S[1, 1, 1] |
| k3 = 400 | P + S[0, 0, 1] -> S[1, 0, 1] |
| k3 = 400 | P + S[0, 1, 1] -> S[1, 1, 1] |
| k4 = 0.2 | C + S[0, 0, 0] -> S[0, 0, 1] |
| k4 = 0.2 | C + S[0, 1, 0] -> S[0, 1, 1] |
| k5 = 20 | C + S[0, 0, 0] -> S[0, 1, 0] |
| k5 = 20 | C + S[0, 0, 1] -> S[0, 1, 1] |
| k5 = 20 | C + S[1, 0, 0] -> S[1, 1, 0] |
| k5 = 20 | C + S[1, 0, 1] -> S[1, 1, 1] |
| km1 = 52 | S[1, 0, 0] -> P + S[0, 0, 0] |
| km1 = 52 | S[1, 1, 0] -> P + S[0, 1, 0] |
| km2 = 0.21 | S[1, 0, 1] -> C + S[1, 0, 0] |
| km2 = 0.21 | S[1, 1, 1] -> C + S[1, 1, 0] |
| km3 = 377.2 | S[1, 0, 1] -> P + S[0, 0, 1] |
| km3 = 377.2 | S[1, 1, 1] -> P + S[0, 1, 1] |
| km4 = 0.029 | S[0, 0, 1] -> C + S[0, 0, 0] |
| km4 = 0.029 | S[0, 1, 1] -> C + S[0, 1, 0] |
| km5 = 1.64 | S[0, 1, 0] -> C + S[0, 0, 0] |
| km5 = 1.64 | S[0, 1, 1] -> C + S[0, 0, 1] |
| km5 = 1.64 | S[1, 1, 0] -> C + S[1, 0, 0] |
| km5 = 1.64 | S[1, 1, 1] -> C + S[1, 0, 1] |
| Variable | IC | ODE |
|---|---|---|
| C | 0.1 | C'[t] == -(k4*C[t]*S[0, 0, 0][t]) - k5*C[t]*S[ 0, 0, 0][t] + km4*S[0, 0, 1][t] - k5*C[ t]*S[0, 0, 1][t] + km5*S[0, 1, 0][t] - k4*C[t]*S[0, 1, 0][t] + km4*S[0, 1, 1][t] + km5*S[0, 1, 1][t] - k2*C[t]*S[1, 0, 0][t] - k5*C[t]*S[1, 0, 0][t] + km2*S[1, 0, 1][t] - k5*C[t]*S[1, 0, 1][t] + km5* S[1, 1, 0][t] - k2*C[t]*S[1, 1, 0][t] + km2*S[1, 1, 1][t] + km5*S[1, 1, 1][t] |
| P | 1 | P'[t] == -(k1*P[t]*S[0, 0, 0][t]) - k3*P[t]*S[ 0, 0, 1][t] - k1*P[t]*S[0, 1, 0][t] - k3*P[t]*S[0, 1, 1][t] + km1*S[1, 0, 0][t] + km3*S[1, 0, 1][t] + km1*S[1, 1, 0][t] + km3*S[1, 1, 1][t] |
| S[0, 0, 0] | 1 | (S[0, 0, 0])'[t] == -(k4*C[t]*S[0, 0, 0][t]) - k5*C[t]*S[0, 0, 0][t] - k1*P[t]*S[0, 0, 0][t] + km4*S[0, 0, 1][t] + km5*S[0, 1, 0][t] + km1*S[1, 0, 0][t] |
| S[0, 0, 1] | 0 | (S[0, 0, 1])'[t] == k4*C[t]*S[0, 0, 0][t] - km4*S[0, 0, 1][t] - k5*C[t]*S[0, 0, 1][t] - k3*P[t]*S[0, 0, 1][t] + km5*S[0, 1, 1][t] + km3*S[1, 0, 1][t] |
| S[0, 1, 0] | 0 | (S[0, 1, 0])'[t] == k5*C[t]*S[0, 0, 0][t] - km5*S[0, 1, 0][t] - k4*C[t]*S[0, 1, 0][t] - k1*P[t]*S[0, 1, 0][t] + km4*S[0, 1, 1][t] + km1*S[1, 1, 0][t] |
| S[0, 1, 1] | 0 | (S[0, 1, 1])'[t] == k5*C[t]*S[0, 0, 1][t] + k4*C[t]*S[0, 1, 0][t] - km4*S[0, 1, 1][t] - km5*S[0, 1, 1][t] - k3*P[t]*S[0, 1, 1][t] + km3*S[1, 1, 1][t] |
| S[1, 0, 0] | 0 | (S[1, 0, 0])'[t] == k1*P[t]*S[0, 0, 0][t] - km1*S[1, 0, 0][t] - k2*C[t]*S[1, 0, 0][t] - k5*C[t]*S[1, 0, 0][t] + km2*S[1, 0, 1][t] + km5*S[1, 1, 0][t] |
| S[1, 0, 1] | 0 | (S[1, 0, 1])'[t] == k3*P[t]*S[0, 0, 1][t] + k2*C[t]*S[1, 0, 0][t] - km2*S[1, 0, 1][t] - km3*S[1, 0, 1][t] - k5*C[t]*S[1, 0, 1][t] + km5*S[1, 1, 1][t] |
| S[1, 1, 0] | 0 | (S[1, 1, 0])'[t] == k1*P[t]*S[0, 1, 0][t] + k5*C[t]*S[1, 0, 0][t] - km1*S[1, 1, 0][t] - km5*S[1, 1, 0][t] - k2*C[t]*S[1, 1, 0][t] + km2*S[1, 1, 1][t] |
| S[1, 1, 1] | 0 | (S[1, 1, 1])'[t] == k3*P[t]*S[0, 1, 1][t] + k5*C[t]*S[1, 0, 1][t] + k2*C[t]*S[1, 1, 0][t] - km2*S[1, 1, 1][t] - km3*S[1, 1, 1][t] - km5*S[1, 1, 1][t] |