Abstract
The Generalized Method of Moments (GMM) is a statistical method for the analysis of samples from random processes. First developed for the analysis of econometric data, the method is here formulated to extract hidden kinetic parameters from measurements of single molecule dwell times. Our method is based on the analysis of cumulants of the measured dwell times. We develop a general form of an objective function whose minimization can return estimates of decay parameters for any number of intermediates directly from the data. We test the performance of our technique using both simulated and experimental data. We also compare the performance of our method to nonlinear least-squares minimization (NL-LSQM), a commonly-used technique for analysis of single molecule dwell times. Our findings indicate that the GMM performs comparably to NL-LSQM over most of the parameter range we explore. It offers some benefits compared with NL-LSQM in that it does not require binning, exhibits slightly lower bias and variance with small sample sizes (N<20), and is somewhat superior in identifying fast decay times with these same low count data sets. Additionally, a comparison with the Classical Method of Moments (CMM) shows that the CMM can fail in many cases, whereas the GMM always returns estimates. Our results show that the GMM can be a useful tool and complements standard approaches to analysis of single molecule dwell times.
Highlights
A fundamental challenge in analysis of single molecule data is the determination of the correct model to explain observations
By minimizing an objective function composed of moment functions, the Generalized Method of Moments (GMM) provides estimates of parameters which approximately satisfy the condition that all the moment functions have the value zero
We have developed an application of the Generalized Method of Moments (GMM) to the analysis of single molecule dwell times
Summary
A fundamental challenge in analysis of single molecule data is the determination of the correct model to explain observations. Methods that have been developed to address this fundamental problem include Bayesian inference [1], maximum likelihood [2], as well as Hidden Markov Models (HMM) [3]. These methods produce a list of dwell times that estimate the time spent in individual molecular states. We develop and characterize the use of the Generalized Method of Moments for the analysis of dwell times. This method is a statistical estimation method originally developed in econometrics [5]
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