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Table 2 Updating rules for all states in the lattice

From: Modeling calcium signaling by Cellular Automata simulation incorporating endocrine regulation and trafficking in various types of receptors

Cell type Probability Description
Rule 1: \(N_{t}\) \(\rho _{0}=(1-e^{-k_{0}E_{t}})\) (a) \(N_{t}\) could become an activated free receptor if \(\rho_{0}>\rho\)
(b) It remains inactive if \(\rho_{0}\leq\rho\)
(c) It changes into \(H_{t}\) if \(\rho\geq\rho_{0}\rho_{1}\)
(d) It becomes \(F1_{t}\) if \(\rho\geq\rho_{0}\rho_{1}\rho_{2}\)
(e) Else, it becomes \(F2_{t}\)
Rule 2: \(H_{t}\) \(\rho _{3}=e^{-(k_{2}E_{t}+k_{3}I_{t})}\) (a) \(H_{t}\) binds to Ca2+ into \(\mathit{BH}_{t}\) if \(\rho_{3}<\rho\)
(b) If \(\rho_{3}\geq\rho\) and there is one of \(\mathit{BH}_{t}\) or \(B1_{t}\) or \(B2_{t}\) in its neighborhood, \(H_{t}\) may change into \(\mathit{HB}_{t}\) and form a dimer if \(\rho_{3}\geq\rho>\rho_{3}\rho_{4}\)
(c) If \(\rho_{3}\geq\rho\) and there is no \(\mathit{BH}_{t}\) or \(B1_{t}\) or \(B2_{t}\) in its neighborhood, but there is one such receptor in its distant neighborhood, it can move closer to a randomized distant bound receptor, if there are more than one, and change into \(\mathit{BH}_{t}\) if \(\rho _{3}\geq\rho>\rho_{3}\rho_{5}\)
(d) If \(\rho_{3}\geq\rho\) and there is no \(\mathit{BH}_{t}\) or \(B1_{t}\) or \(B2_{t}\) in its neighborhood or distant neighborhood, but there is such a receptor in its far distant neighborhood, it can move closer to a randomized far distant bound receptor; it becomes \(\mathit{BH}_{t}\) if \(\rho _{3}\geq\rho>\rho_{3}\rho_{5}\) and forms a dimer. Else, it does not change
Rule 3: \(F1_{t}\) \(\rho_{6}=r_{1}\rho_{3}\), \(\rho _{\tau}=r_{2}\rho_{4}\) F1 receptor can bind to Ca2+ like \(H_{t}\) but with less binding affinity, with \(\rho_{6}\), \(\rho_{7}\) instead of \(\rho_{3}\), \(\rho_{4}\)
Rule 4: \(F2_{t}\) \(\rho_{8}=r_{3}\rho_{3}\), \(r_{1}< r_{3}<1\), \(\rho_{9}=r_{4}\rho_{4}\), \(r_{4}>r_{2}>1\) F2 receptor can bind to Ca2+ like \(H_{t}\) but with an even less binding affinity \(\rho_{8}\), \(\rho_{9}\) instead of \(\rho_{3}\), \(\rho_{9}\)
Rule 5: \(\mathit{BH}_{t}\) \(\rho _{10}=(1-e^{-k_{-1}})e^{-k_{4}I_{t}}\), \(\rho_{11}=1-e^{-k_{r}}\) (a) If BH’s age is still less than its life span \(\tau_{H}\), it is unchanged
(b) If its age reaches its life span \(\tau_{H}\), then it dissociates at probability \(\rho_{10}\). It dissociates back into \(N_{t}\) at the probability \(\rho_{10}\rho_{11}\). Otherwise, it dissociates into \(H_{t}\)
Rule 6: \(B1_{t}\) \(\rho _{12}=(1-e^{-0.95\triangle t})e^{-k_{5}I_{t}}>\rho_{10}\) (a) If B1’s age is less the life span \(\tau_{F}\), it remains unchanged
(b) If its age reaches \(\tau_{F}\), then it may dissociate at the probability \(\rho_{12}\). It dissociates back into \(N_{t}\) at the probability \(\rho_{11}\rho_{12}\). Else, it dissociates into F1
Rule 7: \(B2_{t}\)   In the next step, immediately after \(B2_{t}\) binds to a receptor, it dissociates