Bayesian Inference: The Comprehensive Approach to Analyzing Single-Molecule Experiments

Abstract

Biophysics experiments performed at single-molecule resolution provide exceptional insight into the structural details and dynamic behavior of biological systems. However, extracting this information from the corresponding experimental data unequivocally requires applying a biophysical model. In this review, we discuss how to use probability theory to apply these models to single-molecule data. Many current single-molecule data analysis methods apply parts of probability theory, sometimes unknowingly, and thus miss out on the full set of benefits provided by this self-consistent framework. The full application of probability theory involves a process called Bayesian inference that fully accounts for the uncertainties inherent to single-molecule experiments. Additionally, using Bayesian inference provides a scientifically rigorous method of incorporating information from multiple experiments into a single analysis and finding the best biophysical model for an experiment without the risk of overfitting the data. These benefits make the Bayesian approach ideal for analyzing any type of single-molecule experiment. Expected final online publication date for the Annual Review of Biophysics, Volume 50 is May 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Bayesian machine learning analysis of single-molecule fluorescence colocalization images

“…These priors embed pre-existing knowledge about the CoSMoS experiment, such as the fact that target-specific spots will be close to the target molecule locations. Third, we infer the values of the model parameters, including p (specific), using Bayes’ rule ( Bishop, 2006 ; Kinz-Thompson et al, 2021 ). The Tapqir analysis is “time-independent”, meaning that we ignore the time dimension of the recording – the order of the images does not affect the results.…”

“…Third, we infer the values of the model parameters, including ( ), using Bayes' rule (Bishop, 2006;Kinz-Thompson et al, 2021). The Tapqir analysis is "time-independent", meaning that we ignore the time dimension of the recording -the order of the images does not affect the results.…”

“…Tapqir analyzes two-dimensional image data, not integrated intensities. Unlike prior methods, our approach is based on an explicit, global causal model for CoSMoS image formation and uses Bayesian inference ( Kinz-Thompson et al, 2021 ) to determine the values of model parameters and their associated uncertainties. The physics-informed model includes realistic shot noise in fluorescent spots and background, camera noise, the size and shape of spots, and the presence of both target-specific and nonspecific binder molecules in the images.…”

Elevator mechanism dynamics in a sodium-coupled dicarboxylate transporter

“…Global vbHMMs were estimated in a manner similar to a previously described single trajectory vbHMM implemented in the software package vbFRET (Bronson et al, 2009). vbFRET is a Bayesian inference-based ‘maximum evidence’ method (Kinz-Thompson et al, 2021), which allowed one to determine the simplest HMM that sufficiently accounts for the complexity of the smFRET data (Bronson et al, 2009; van de Meent et al, 2014; Hon and Gonzalez, 2019). In this method, one can find the most parsimonious HMM for smFRET data by estimating several HMMs, each with an increasing number of hidden states, then calculating the ‘evidence’ for each HMM and choosing the one with the maximum evidence value (Bronson et al, 2009).…”

Bayesian machine learning analysis of single-molecule fluorescence colocalization images

“…Tapqir analyzes two-dimensional image data, not integrated intensities. Unlike prior methods, our approach is based on an explicit, global causal model for CoSMoS image formation and uses variational Bayesian inference ( Kinz-Thompson et al, 2021 ; Gelman et al, 2013 ) to determine the values of model parameters and their associated uncertainties. This model, which we call ‘ cosmos’ , implements time-independent analysis of single-channel (i.e., one-binder) data sets.…”