In this section we describe step-by-step how to build a simple multistate model filling the different tables of MSMB.

As a running example, we use a small model at the core of the budding yeast cell cycle process. The small model presented in this section contains all the main components of a classical multistate problem and it describes the antagonistic relationship between ClbM and Cdh1 proteins (we refer the reader to the original publication [Barik2010] for the complete characterization of the model).

, , ..., .

Some of these forms take part in specific phosphorylation and dephosphorylation reactions as reactant or product: intuitively every form with

To complete the description of this small model we have also to consider the fact that all eleven forms of Cdh1 take part in the degradation of ClbM.

Reaction | Equation | |
---|---|---|

1 | `->` ClbM |
ks |

2 | ClbM `->` |
ClbM ⋅ Xa |

3 | ClbM + Cdh1 `->` ClbM + Cdh1P_{1} |
kp ⋅ ClbM ⋅ Cdh1 |

4 | ClbM + Cdh1P_{1} `->` ClbM + Cdh1P_{2} |
kp ⋅ ClbM ⋅ Cdh1P_{1} |

5 | ClbM + Cdh1P_{2} `->` ClbM + Cdh1P_{3} |
kp ⋅ ClbM ⋅ Cdh1P_{2} |

6 | ClbM + Cdh1P_{3} `->` ClbM + Cdh1P_{4} |
kp ⋅ ClbM ⋅ Cdh1P_{3} |

7 | ClbM + Cdh1P_{4} `->` ClbM + Cdh1P_{5} |
kp ⋅ ClbM ⋅ Cdh1P_{4} |

8 | ClbM + Cdh1P_{5} `->` ClbM + Cdh1P_{6} |
kp ⋅ ClbM ⋅ Cdh1P_{5} |

9 | ClbM + Cdh1P_{6} `->` ClbM + Cdh1P_{7} |
kp ⋅ ClbM ⋅ Cdh1P_{6} |

10 | ClbM + Cdh1P_{7} `->` ClbM + Cdh1P_{8} |
kp ⋅ ClbM ⋅ Cdh1P_{7} |

11 | ClbM + Cdh1P_{8} `->` ClbM + Cdh1P_{9} |
kp ⋅ ClbM ⋅ Cdh1P_{8} |

12 | ClbM + Cdh1P_{9} `->` ClbM + Cdh1P_{10} |
kp ⋅ ClbM ⋅ Cdh1P_{9} |

13 | Cdc14 + Cdh1P_{1} `->` Cdc14 + Cdh1 |
kh ⋅ Cdc14 ⋅ Cdh1P_{1} |

14 | Cdc14 + Cdh1P_{2} `->` Cdc14 + Cdh1P_{1} |
kh ⋅ Cdc14 ⋅ Cdh1P_{2} |

15 | Cdc14 + Cdh1P_{3} `->` Cdc14 + Cdh1P_{2} |
kh ⋅ Cdc14 ⋅ Cdh1P_{3} |

16 | Cdc14 + Cdh1P_{4} `->` Cdc14 + Cdh1P_{3} |
kh ⋅ Cdc14 ⋅ Cdh1P_{4} |

17 | Cdc14 + Cdh1P_{5} `->` Cdc14 + Cdh1P_{4} |
kh ⋅ Cdc14 ⋅ Cdh1P_{5} |

18 | Cdc14 + Cdh1P_{6} `->` Cdc14 + Cdh1P_{5} |
kh ⋅ Cdc14 ⋅ Cdh1P_{6} |

19 | Cdc14 + Cdh1P_{7} `->` Cdc14 + Cdh1P_{6} |
kh ⋅ Cdc14 ⋅ Cdh1P_{7} |

20 | Cdc14 + Cdh1P_{8} `->` Cdc14 + Cdh1P_{7} |
kh ⋅ Cdc14 ⋅ Cdh1P_{8} |

21 | Cdc14 + Cdh1P_{9} `->` Cdc14 + Cdh1P_{8} |
kh ⋅ Cdc14 ⋅ Cdh1P_{9} |

22 | Cdc14 + Cdh1P_{10} `->` Cdc14 + Cdh1P_{9} |
kh ⋅ Cdc14 ⋅ Cdh1P_{10} |

23 | Cdh1 `->` |
kd ⋅ Cdh1 |

24 | Cdh1P_{1} `->` |
kd ⋅ Cdh1P_{1} |

25 | Cdh1P_{2} `->` |
kd ⋅ Cdh1P_{2} |

26 | Cdh1P_{3} `->` |
kd ⋅ Cdh1P_{3} |

27 | Cdh1P_{4} `->` |
kd ⋅ Cdh1P_{4} |

28 | Cdh1P_{5} `->` |
kd ⋅ Cdh1P_{5} |

29 | Cdh1P_{6} `->` |
kd ⋅ Cdh1P_{6} |

30 | Cdh1P_{7} `->` |
kd ⋅ Cdh1P_{7} |

31 | Cdh1P_{8} `->` |
kd ⋅ Cdh1P_{8} |

32 | Cdh1P_{9} `->` |
kd ⋅ Cdh1P_{9} |

33 | Cdh1P_{10} `->` |
kd ⋅ Cdh1P_{10} |

34 | `->` Cdh1 |
ks1 |

As we can see from the table above, most of the reactions has the same general structure (and rate law) so what the modeller would actually want to have is a way to define Cdh1 states with a range of ordered indexes and a way to refer to the successive/preceding state.

In this case, we have the following definition of Cdh1:

Cdh1(p{0:10})

The intuition behind the definition is that the species called

We can use this compact notation, to reduce the number of reactions from the initial 34 down to 5, by expressing the reactants and products as multistate species.

Reaction | Equation | |
---|---|---|

1 | `->` ClbM |
ks |

2 | ClbM `->` |
ClbM ⋅ Xa |

3 | ClbM + Cdh1(p{0:9}) `->` ClbM + Cdh1(succ(p)) |
kp ⋅ ClbM ⋅ Cdh1(p) |

4 | Cdc14 + Cdh1(p{1:10}) `->` Cdc14 + Cdh1(pred(p)) |
kh ⋅ Cdc14 ⋅ Cdh1(p) |

5 | Cdh1(p{0:10}) `->` |
kd ⋅ Cdh1(p) |

6 | `->` Cdh1(p{0}) |
ks1 |

In Reaction 2,

In particular we have that

)

What the user needs is, again, a compact way to represent this sort of expressions taking advantage of the multistate format and a summation operator as follows:

In MSMB it is possible to define the above summation in a compact way as follows:

ka * Cdh1(p{0}) + kin * SUM(Cdh1;p{1:10})

This summation operator make the expression easy to view, manipulate and edit.

As today, there are no tools which support the multistate format directly.

Even SBML does not provide a direct way to express multistate species and reactions.

Therefore MSMB provides support to

The importance of the multistate concept is, however, acknowledged by the SBML community and there is an ongoing effort in defining a