Empirical Bayes method using surrounding pixel information for number and brightness analysis

Number and brightness (N&B) analysis is useful for monitoring the spatial distribution of the concentration and oligomeric state of fluorescently labeled proteins in cells. N&B analysis is based on the statistical analysis of fluorescence images by using the method of moments (MoM). Furthermore, N&B analysis can determine the particle number and particle brightness, which indicate the concentration and oligomeric state, respectively. However, the statistical accuracy and precision are limited in actual experiments with fluorescent proteins, owing to low excitation and the limited number of images. In this study, we applied maximum likelihood (ML) estimation and maximum a posteriori (MAP) estimation coupled with the empirical Bayes (EB) method (referred to as EB-MAP). In EB-MAP, we constructed a simple prior distribution for a pixel to utilize the information of the surrounding pixels. To evaluate the accuracy and precision of our method, we conducted simulations and experiments and compared the results of MoM, ML, and EB-MAP. The results showed that MoM estimated the particle number with many outliers. The outliers hampered the visibility of the spatial distribution and cellular structure. In contrast, EB-MAP suppressed the number of outliers and improved the visibility notably. The precision of EB-MAP was better by an order of magnitude in terms of particle number and 1.5 times better in terms of particle brightness compared with those of MoM. The proposed method (EB-MAP-N&B) is applicable to studies on fluorescence imaging and would aid in accurately recognizing changes in the concentration and oligomeric state in cells. Our results hold significant importance because quantifying the concentration and oligomeric state would contribute to the understanding of dynamic processes in molecular mechanism in cells.