CASTANET (Computational package for deriving Analytical STAtionary distribution of biochemical reaction networks with NEtwork Translation)

This is a matlab code to analytically derive stationary distributions for a given stochastic biochemical reaction networks. Detailed step-by-step manual will be uploaded soon.

Code Description

1. CRN_main.m

Main function for this package. Users need to work only with this function. If one specify the source complexes, product complexes, and propensity functions of reactions then the code provides a symbolic expression for a stationary distribution.

Since all the below functions are automatically run by CRN_main.m function, users do not need to run nor edit the below functions separately.

2. CRN_translation.m

This function generates all possible translated networks whose reaction orders are at most 'max_order', which is specified by users.

3. CRN_find_elementary_path.m

This function finds an elementary path. Here, the elementary path means that the sequence of a pair of the source complexes, which form a basis for the lattice.

4. CRN_find_elementary_function.m

This function finds elementary functions corresponding to the elementary basis, identified by the function CRN_find_elementary_path.m. The elementary function is the term to be multiplied when the state moves from n-e_j to n. Here, e_j is the jth element of the elementary basis, which corresponds to the jth elementary function.

5. CRN_solve_sym_linear.m

This functions compute the coordinate of n-n_0 where n_0 is the start point with respect to the elementary basis.

6. CRN_check_factorization_condition.m

This function tests whether the construced candidate theta_c satisfies the factorization condition.

7. CRN_compute_cbe.m

This functions compute a complex balanced equilibrium of the deterministic mass action model for the translated network.

Found Examples

1. In FoundExamples folder, we have stored the data representing biochemical reaction networks whose stationary distributions can be derived with CASTANET. The subfolders 2D and 3D contain the examples with two and three species, respectively. Note that all the rate constants are set to be one for simplicity.

Limitations

1. Solve the system of linear equation with symbolic variables.

• When the CRN_solve_sym_linear.m is performed, the code may not fully use underlying assumptions for the variables. It sometimes leads to failure of the code. For instance, if one sovle the system of linera equations x = 5 - a and y = a - 5 under the assumption x == -y, then the solution is x=5-a itself because the assumption x==-y is consistent to the system of equations. However, the code cannot solve this system. This occurs especially when there is a conservation law in a given biochemical reaction network.