Unique mechanisms from finite two-state trajectories

TL;DR

This paper introduces canonical forms of reduced dimensions for finite two-state trajectories, enabling the discrimination of underlying kinetic schemes despite data limitations and complex transition structures.

Contribution

It presents a novel method to construct canonical forms from finite data, handling complex and irreversible kinetic schemes, improving analysis of single molecule on-off data.

Findings

Canonical forms can distinguish different kinetic schemes.

Method handles symmetry and irreversible transitions.

Applicable to finite and noisy data.

Abstract

Single molecule data made of on and off events are ubiquitous. Famous examples include enzyme turnover, probed via fluorescence, and opening and closing of ion-channel, probed via the flux of ions. The data reflects the dynamics in the underlying multi-substate on-off kinetic scheme (KS) of the process, but the determination of the underlying KS is difficult, and sometimes even impossible, due to the loss of information in the mapping of the mutli-dimensional KS onto two dimensions. A way to deal with this problem considers canonical (unique) forms. (Unique canonical form is constructed from an infinitely long trajectory, but many KSs.) Here we introduce canonical forms of reduced dimensions that can handle any KS (i.e. also KSs with symmetry and irreversible transitions). We give the mapping of KSs into reduced dimensions forms, which is based on topology of KSs, and the tools for extracting the reduced dimensions form from finite data. The canonical forms of reduced dimensions constitute a powerful tool in discriminating between KSs.