Methods and Software

Stochastic biochemical reactions

Intracellular reactions are modelled as stochastic biochemical reactions. Each reaction \(i\) has an exponential waiting time and changes the number of molecules \(X_j\) by the stoichiometric amount \(S_{j,i}\) with the propensity \(w_i(X)\), where \(X\) is the vector of copy number for all modelled species.

Biochemical reactions were simulated using Gillespie's next reaction method. To correctly model the multicellular nature of the system, well-mixed assumptions are only applied at the individual cell level. In other words, each cell was treated separately in evaluating propensities and executing reactions.

Signalling pathways

Hydrodynamics

2D diffusion with active degradation

The simulator STEW

A simulator engine was developed to Emulate the multicellular Signal Transmission World (STEW). The simulator STEW integrates intracellular stochastic biochemical reactions with extracellular diffusion and cell movement including cell-cell interactions. Hence, STEW captures stochastic, continuous, discrete, and spatial phenomena. This was not an easy task as the numerical stability of each simulator component involves requirements on spatial and temporal granularity. In addition to the methods described above, the following open source modelling libraries were implemented and integrated with the inhouse utilities.

• cell dynamics including collision and movement due to hydrodynamic forces were simulated using ***.
• visualisation of the simulator was pefored using the *** offering shape smoothing and ***