Statistical analysis and comparative visualization of cellular particle-based simulations

Abstract

The present work integrates a set of functions, properties and views to the CellVis framework developed by Martin Falk in order to lay the foundations for a statistical analysis and comparative analysis/visualization module. The CellVis framework employes a stochastic simulation to model and analyze cellular signal transduction. The cell is represented as sphere consisting of a nucleus, proteins, obstacles and cytoskeleton filaments. The particles can move inside the cell by diffusion or by direct transportation along the cytoskeleton filaments The statistical analysis is performed by estimating the first four statistical moments of the sample spatial distribution of the molecules involved in the analyzed simulation. These moments can be visualized in a tree-like view and also with help of a set of time series plots, that illustrate the evolution of these moments through the lifetime of the simulation. The spatial distribution of the concerned particles is separated on the three spatial dimensions. This is possible due to the fact that the motions of one particle on each axis is independent with respect to the other ones. A histogram is also calculated and graphically represented in a 2D plot in order to facilitate understanding the meaning of the estimated sample moments values. To justify the use of moments describing the spatial distribution, an external tool is used to estimate a probability density function that fits the simulated spatial distribution with respect to the estimated sample moments. The results are satisfactory with respect to the matching of the calculated histogram and the histogram of the fitted probability density function. So we could conclude that for typical types of distributions the use of moments can help in finding a suitable probability density function that can be used later on for predicting the spatial distribution for certain types of particles in other simulations. For a more particular type of analysis of the signal transduction process, the trajectory and reaction history of an individual particle are calculated and determined. To visualize them, 2D graphs are employed and integrated in the framework. The trajectory of a particle is plotted as the distance to the nucleus over time. The reactions and interactions are indicated with markers on the same graph. The comparative visualization is performed by employing difference plots and difference volume. For this, the framework is extended with the loading of a second data set. The difference graphs are used to show differences in the statistical sample moments, in the concentrations and in the histograms of the two loaded data sets. The difference volume is performed with respect to the differences of concentrations in the considered data sets. The view of the difference volume can be enabled by the user. However the option of viewing both data sets at the same time remains as a possibility of future work.