Spatially mapping the diffusivity of proteins in live cells based on cumulative area analysis

Molecular motion provides a way for biomolecules to mix and interact in living systems.Quantifying their motion is critical to the understanding of how biomolecules perform its function.However,it has been a challenged task to spatially map the fast diffusion of unbound proteins in the heterogenous intracellular environment.Here we reported a new imaging technique named cumulative area based on single-molecule diffusivity mapping(CA-SMdM).The strategy is based on the comparison of singlemolecule images between a shorter and longer exposure time.With longer exposure time,molecules will travel further,thus giving more blurred single-molecule images,hence implying its local diffusion rates.We validated our technique through measuring the fast diffusion rates(10–40μm~2/s)of fluorescent dye in glycerol-water mixture,and found the values fit well with Stokes-Einstein equation.We further showed that the spatially mapping of diffusivity in live cells is plausible through CA-SMdM,and it faithfully reported the local diffusivity heterogeneity in cytosol and nucleus.CA-SMdM provides an efficient way to mapping the local molecular motion,and therefore will have profound applications in probing the biomolecular interactions for living systems.

Fuzzy Diffusion Distance Learning for Cartoon Similarity Estimation

In this paper, a novel method called fuzzy diffusion maps （FDM） is proposed to evaluate cartoon similarity, which is critical to the applications of cartoon recognition, cartoon clustering and cartoon reusing. We find that the features from heterogeneous sources have different influence on cartoon similarity estimation. In order to take all the features into consideration, a fuzzy consistent relation is presented to convert the preference order of the features into preference degree, from which the weights are calculated. Based on the features and weights, the sum of the squared differences （L2） can be calculated between any cartoon data. However, it has been demonstrated in some research work that the cartoon dataset lies in a low-dimensional manifold, in which the L2 distance cannot evaluate the similarity directly. Unlike the global geodesic distance preserved in Isomap, the local neighboring relationship preserved in Locally Linear Embedding, and the local similarities of neighboring points preserved in Laplacian Eigenmaps, the diffusion maps we adopt preserve diffusion distance summing over all paths of length connecting the two data. As a consequence, this diffusion distance is very robust to noise perturbation. Our experiment in cartoon classification using Receiver Operating Curves shows fuzzy consistent relation＇s excellent performance on weights assignment. The FDM＇s performance on cartoon similarity evaluation is tested on the experiments of cartoon recognition and clustering. The results show that FDM can evaluate the cartoon similarity more precisely and stably compared with other methods.