Toolbox for analyzing finite two-state trajectories

TL;DR

This paper introduces a comprehensive, automated toolbox for constructing reduced-dimensionality canonical forms of kinetic schemes from finite two-state trajectories, enabling more accurate analysis of complex biological data.

Contribution

It provides a self-contained, efficient method to derive canonical RD forms from two-state trajectory data, improving upon previous approaches by combining statistical and numerical techniques.

Findings

The toolbox can analyze a million-cycle trajectory in a few hours.

It accurately constructs RD forms from finite two-state trajectories.

The method is fully automated and freely available for academic use.

Abstract

In many experiments, the aim is to deduce an underlying multi-substate on-off kinetic scheme (KS) from the statistical properties of a two-state trajectory. However, the mapping of a KS into a two-state trajectory leads to the loss of information about the KS, and so, in many cases, more than one KS can be associated with the data. We recently showed that the optimal way to solve this problem is to use canonical forms of reduced dimensions (RD). RD forms are on-off networks with connections only between substates of different states, where the connections can have non-exponential waiting time probability density functions (WT-PDFs). In theory, only a single RD form can be associated with the data. To utilize RD forms in the analysis of the data, a RD form should be associated with the data. Here, we give a toolbox for building a RD form from a finite two-state trajectory. The methods in the toolbox are based on known statistical methods in data analysis, combined with statistical methods and numerical algorithms designed specifically for the current problem. Our toolbox is self-contained - it builds a mechanism based only on the information it extracts from the data, and its implementation on the data is fast (analyzing a 10^6 cycle trajectory from a thirty-parameter mechanism takes a couple of hours on a PC with a 2.66 GHz processor). The toolbox is automated and is freely available for academic research upon electronic request.