Revisiting the Temperature Dependence of Protein Diffusion inside Bacteria: Validity of the Stokes-Einstein Equation

Although the transport and mixing of proteins and other molecules inside bacteria rely on the diffusion of molecules, many aspects of the molecular diffusion in bacterial cytoplasm remain unclear or controversial, including how the diffusion-temperature relation follows the Stokes-Einstein equation. In this study, we applied single-particle tracking photoactivated localization microscopy to investigate the diffusion of histonelike nucleoid structuring (HNS) proteins and free dyes in bacterial cytoplasm at different temperatures. Although the diffusion of HNS proteins in both live and dead bacteria increased at higher temperatures and appeared to follow the Arrhenius equation, the diffusion of free dyes decreased at higher temperatures, questioning the previously proposed theories based on superthermal fluctuations. To understand the measured diffusion-temperature relations, we developed an alternative model, in which the bacterial cytoplasm is considered as a polymeric network or mesh. In our model, the Stokes-Einstein equation remains valid, while the polymeric network contributes a significant term to the viscosity experienced by the molecules diffusing in bacterial cytoplasm. Our model was successful in predicting the diffusion-temperature relations for both HNS proteins and free dyes in bacteria. In addition, we systematically examined the predicted diffusion-temperature relations with different parameters in the model, and predicted the possible existence of phase transitions.