Quantifying Multistate Cytoplasmic Molecular Diffusion in Bacterial Cells via Inverse Transform of Confined Displacement Distribution

Single-molecule tracking (SMT) of fluorescently tagged cytoplasmic proteins can provide valuable information on the underlying biological processes in living cells via subsequent analysis of the displacement distributions; however, the confinement effect originated from the small size of a bacterial cell skews the protein's displacement distribution and complicates the quantification of the intrinsic diffusive behaviors. Using the inverse transformation method, we convert the skewed displacement distribution (for both 2D and 3D imaging conditions) back to that in free space for systems containing one or multiple (non)interconverting Brownian diffusion states, from which we can reliably extract the number of diffusion states as well as their intrinsic diffusion coefficients and respective fractional populations. We further demonstrate a successful application to experimental SMT data of a transcription factor in living E. coli cells. This work allows a direct quantitative connection between cytoplasmic SMT data with diffusion theory for analyzing molecular diffusive behavior in live bacteria.