An expectation–maximisation algorithm for the deconvolution of the intrinsic distribution of single molecule's parameters

Abstract

Values obtained from single molecule techniques exhibit distinct distributions comprising an uncertainty due to random noise convoluted with the intrinsic distribution of the molecule's properties. In the fields of single molecule light microscopy and spectroscopy, force microscopy and spectroscopy as well as other techniques like electrophysiology, sophisticated data analysis algorithms are available which extract the interesting parameters and their uncertainties from the noisy data set. The intrinsic distributions of these parameters contain valuable information about the molecules’ physical and chemical properties, that need to be deconvoluted from the data. Here, we present an expectation–maximisation (EM-) algorithm that estimates the intrinsic distribution in single molecule experiments. The performance is tested by using computer simulations and the application of the method is demonstrated for data from single molecule force spectroscopy.