3D visualization of concentrations from stochastic agent-based signal transduction simulations

Cellular signal transduction involves a transport step from the plasma membrane towards the nucleus, during which the signaling molecules are partly deactivated in control loops. This leads to a gradient in the concentration of active signaling molecules. The low number of molecules introduces spatio-temporal fluctuations and the asymmetric cellular architecture further increases the complexity. We propose a technique to represent this pattern in a continuous three-dimensional concentration map. The local concentration is computed and visualized with volume rendering techniques at interactive frame rates and is therefore well-suited for time-dependent data. Our approach allows the transition from the nano-scale of single and discrete signaling proteins to a continuous signal on the cell level. In the application context of this paper, we employ an agent-based Monte Carlo simulation to calculate the actual particle positions depending on reaction and transport parameters in the cell. The applicability of the proposed technique is demonstrated by an investigation of the effects of different transport parameters in Mitogen-activated protein kinase (MAPK) signaling.