Biological cells are able to perform complex signal transduction tasks quickly, energy-efficiently and yet in a robust and noise-tolerant manner. These signal transduction tasks rely on intracellular information processing mechanisms in which chemical signals are sent, transmitted and received and the state of the overall machinery is stored in chemical or conformational switches. The physicochemical principles of information processing in cells is still not well understood, owing to fundamental restrictions in resolution in experiments and in sampling of molecular dynamics simulations. Here, we will develop new simulation methods based on adaptive molecular dynamics and Markov models. These methods, together with new statistical mechanical theories and single-molecule experimental analyses will be employed to investigate the molecular basis of intracellular signal processing mechanisms. Central to our proposal is the hypothesis that intracellular signal processing relies on spatiotemporal order of molecules arising from dynamical sorting. This hypothesis will be tested using examples of protein-ligand and protein-protein sorting in neuronal signalling. The proposed project is highly multidisciplinary, involving physical chemistry, computer science, mathematics and biology.