Diffusion in crowded biological environments: applications of Brownian dynamics

Intracellular organelles are packed with small solutes, macromolecules, membranes and skeletal proteins. Such crowding is characteristic not only of the cell's interior but also for extracellular tissues [1]. The kinetics and thermodynamics of macromolecular processes and biochemical reactions taking place in vivo are known to be affected by complex, volume-occupied environments [2-5].More and more experimental methods have become available to investigate macromolecules under in vivo conditions. These include nuclear magnetic resonance [6-8] and fluorescence spectroscopies [9]. Techniques such as SPT (single-particle tracking) [10,11], FRAP (fluorescence recovery after photobleaching) [12,13], FCS (fluorescence correlation spectroscopy) [14] have been applied to measure diffusion constants of macromolecules in the cytoplasm and membranes. All experiments show that diffusion of proteins in vivo is significantly reduced compared to dilute conditions. In the cytoplasm of eukaryotic cells, diffusion of both large and small molecules is slowed down three to four times [1]. FRAP measurements of the diffusion coefficient of GFP in the Escherichia coli (E. coli) cytoplasm [15,16] yield about 10 times smaller values than at infinite dilution in water.Theories of diffusion for colloidal soft matter are well established. Within their framework, the behavior of colloidal systems (both dilute and concentrated), consisting of mesoscopically large colloidal particles dispersed in low-molecular-weight solvent, can be simulated, reproduced, and more importantly predicted [17-21]. In cell biology, however, an appropriate theory of diffusion phenomena is still lacking. Complications arise due to the cellular heterogeneity. Moreover, there are different cell types whose compositions vary over space and time on the scales associated with diffusive motion and the knowledge of the surroundings of diffusing species is essential for successful applications of theoretical approaches. Unfortu