The complexity of biological systems is enormous, even when considering a single cell where a multitude of highly parallel and intertwined processes take place on the molecular level. This paper focuses on the parallel simulation of signal transduction processes within a cell carried out solely on the graphics processing unit (GPU). Each signaling molecule is represented by an agent performing a discretetime continuous-space random walk to model its diffusion through the cell. Since the interactions and reactions between the agents can be competitive and are interdependent, we propose spatial partitioning for the reaction detection to overcome the data dependencies in the parallel execution of reactions. In addition, we present a simple way to simulate the Michaelis-Menten kinetics in our particle-based method using a per-particle delay. We apply this agent-based simulation to model signal transduction in the MAPK (Mitogen-Activated Protein Kinase) cascade both with and without cytoskeletal filaments. Finally, we compare the speed-up of our GPU simulation with a parallelized CPU version resulting in a twelvefold speedup.