# Table 2 Updating rules for all states in the lattice

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