Solving single molecules: filtering noisy discrete data made of photons and other type of observables

TL;DR

This paper introduces a novel statistical filter that accurately removes noise from single-molecule photon trajectory data, enabling reliable model extraction even in highly noisy conditions, and extends previous work on clean two-state data analysis.

Contribution

The authors develop a new likelihood-based filter that effectively denoises discrete photon trajectory data, improving model accuracy in biophysical single-molecule experiments.

Findings

The filter successfully removes noise in photon trajectory data.

Applying the filter prevents erroneous rate estimations.

The method identifies when data is too noisy for reliable analysis.

Abstract

In numerous systems in biophysics and related fields, scientists measure (with very smart methods) individual molecules (e.g. biopolymers (proteins, DNA, RNA, etc), nano - crystals, ion channels), aiming at finding a model from the data. But the noise is not solved accurately in not so few cases and this may lead to misleading models. Here, we solve the noise. We consider two state photon trajectories from any on off kinetic scheme (KS): the process emitting photons with a rate {\gamma}on when it is in the on state, and emitting with a rate {\gamma}off when it is in the off state. We develop a filter that removes the noise resulting in clean data also in cases where binning fails. The filter is a numerical algorithm with various new statistical treatments. It is based on a new general likelihood function developed here, with observable dependent form. The filter can solve the noise, in the detectable region of the rate space: that is, we also find a region where the data is "too" noisy. Consistency tests will find the region's type from the data. If the data is ruled "too noisy", binning obviously fails, and one should apply simpler methods on the raw data and realizing that the extracted information is partial. We show that not applying the filter while cleaning results in erroneous rates. This filter (with minor adjustments) can solve the noise in any discrete state trajectories, yet extensions are needed in "tackling" the noise from other data, e.g. continuous data and FRET data. The filter developed here is complementary with our previous projects in this field, where we have solved clean two state data with the development of reduced dimensions forms (RDFs): only the combined procedures enabling building the most accurate model from noisy trajectories from single molecules