Maximum-likelihood estimation applied to electron microscopic autoradiography

A new method for analysis of electron microscope autoradiographs is described which is based on the maximum-likelihood method of statistics for estimating the intensities of radioactivity in organelle structures. We adopted a Poisson statistical model to describe the autoradiographic grain distributions that we prove results from the underlying Poisson nature of the radioactive decays as well as the additive errors introduced during the formation of grains. Within the model, an interative procedure derived from the expectation-maximization algorithm of mathematical statistics is used to generate the maximum-likelihood estimates. The algorithm has the properties that at every stage of the iteration process the likelihood of the data increases; and for all initial nonzero starting points the algorithm converges to the maximum-likelihood estimates of the organelle intensities. The maximum-likelihood approach differs from the mask-analysis method, and other published quantitative algorithms in the following ways: (1) In deriving estimates of the radioactivity intensities the maximum-likelihood algorithm requires that we obtain the actual locations of the grains as well as the micrograph geometries; each micrograph is digitized so that both the grain locations as well as the geometries of the organelle structures can be used. (2) The maximum-likelihood algorithm iteratively computes the minimum-meansquared-error estimate of the underlying emission locations that resulted in the observed grain distributions, from which intensity estimates are generated; this algorithm does not minimize a chi-squared error statistic. (3) The maximum-likelihood approach is based on a Poisson model and is therefore valid for low-count experiments; there are no minimum constraints on data collection for any single organelle compartment. (4) The maximum-likelihood algorithm requires the form of the point-spread function describing the emission spread; a probability matrix based on the use of overlay masks is not required. (5) The maximum-likelihood algorithm does not change for different organelle geometries; arbitrary geometries are incorporated by maximizing the likelihood-function subject to the geometry constraints. We have performed a preliminary evaluation of the quantitative accuracy of the maximum-likelihood and mask-analysis algorithms. Based on two different phantoms in which we compared the squared error resulting from the two algorithms, we find that the new maximum-likelihood approach provides substantially improved estimates of the radioactivity intensities of the phantoms.