单分子阶梯事件分析

Single-molecule detection (SMD) and tracking in living cells is becoming a powerful method for the study of protein local environments, the time course of the enzymatic reaction, and the structure fluctuations of macromolecules, etc. Many single molecule studies have offered new insights into their localization, assembly and activation. Perhaps the dominant advantage of single-molecule fluorescence detection is that it can provide information on the spatial and temporal heterogeneity of molecule that underlies the ensemble average in conventional biochemical experiments. These spatial and temporal heterogeneities often appear as step events, for example, the discrete steps of photobleaching of single fluorescent molecules response to the number of subunits in membrane proteins. Hence，the step events analysis is becoming an important method of stochiometry study.

However, SMD is also a difficult task. The most experiments of single-molecule fluorescence detection are approaching the limits of optical detection, and that the raw experimental data are inundated with all kinds of noise, especially, the Poisson distributed photon shot noise. These steps are so dim that it is very difficult to distinguish them.  To leach out the useful information from these noisy raw data is still a challenging task.

Perhaps the simplest and most commonly used method for the analysis of step events of single molecule inundated in these noisy data is the thresholding method. When a single-molecule trajectory has sufficient contrast between states, thresholds can be applied to distinguish the states of the molecule. These thresholds are typically chosen manually and introduce subjectivity into the analysis inevitablly.  Before thresholding, binning of the data is also required, and this limits the temporal resolution of the measurement to be 1 or 2 orders of magnitude lower than the photon count rate to overcome the effects of shot noise. To mitigate the effects of shot noise, some investigators have applied filters to the data prior to applying a threshold. This can substantially improve the time resolution of the experiment by mitigating some of the effects of shot noise, but there is still the difficulty associated with choosing a threshold.

Recently, many methods, such as hidden Markov models, applications of information theory, photon statistics in the context of two colors, maximum likelihood and Bayesian inferential estimation of change points using Poisson statistics, wavelet correlation, and wavelet shrinkage have been developed and applied to single molecule data as a means of extracting more accurate information about the system under observation.

Although direct, model-independent information theoretical approaches may also work well, especially when a kinetic model is inapplicable. HMM, which uses all the information from the data prior and posterior, has enjoyed wide applicability and success. However, this method needs a long sequence to train the HMM for the parameter extraction.  Many important experimental data sets are far too short to satisfy this requirement, so that the algorithm will converge to a local maximum depending on the initialization of the emission probability distribution.  Another problem of HMMs is the necessary prior knowledge of the number of the states.