Parameter Estimation for Cell Cycle Ordinary Differential Equation (ODE) Models using a Grid Approach

Cell cycle is one of the biological processes that has been investigated the most in the recent years, this due to its importance in cancer studies and drug discovery. The complexity of this biological process is revealed every time a mathematical simulation of the processes is carried out. We propose an automated approach that mathematically simulates the cell cycle process with the aim to describe the best estimation of the model. We have implemented a system that starting from a cell cycle model is capable of retrieving from a specific database, called Cell Cycle Database, the necessary mathematical information to perform simulation using a grid approach and identify the best model related to a specific dataset of experimental results from the real biological system. Our system allows the visualization of mathematical expressions, such as the kinetic rate law of a reaction, and the direct simulation of the models with the aim to give the user the possibility to interact with the simulation system. The parameter estimation process usually implies time-consuming computations due to algorithms of linear regression and stochastic methods. In particular, in the case of a stochastic approach based on evolutionary algorithms, the iterative selection process implies many different computations. Therefore, a large number of ODE system simulations are required: the grid infrastructure allows to distribute and obtain the best model that fits the experimental data. The computation of many ODE systems can be distributed on different grid nodes so that the execution time for the estimation of the best model is reduced. This system will be useful for the comparison of models with different initial conditions related to normal and deregulated cell cycles.