Making it possible: constructing a reliable mechanism from a finite trajectory

Deducing an underlying multi-substate on-off kinetic scheme (KS) from the statistical properties of a two-state trajectory is the aim of many experiments in biophysics and chemistry, such as, ion-channel recordings, enzymatic activity and structural dynamics of bio-molecules. Doing so is almost always impossible, as the mapping of a KS into a two-state trajectory leads to the loss of information about the KS (almost always). Here, we present the optimal way to solve this problem. It is based on unique forms of reduced dimensions (RD). RD forms are on-off networks with connections only between substates of different states, where the connections can have multiexponential waiting time probability density functions (WT-PDFs). A RD form has the simplest topology that can reproduce a given data. In theory, only a single RD form can be constructed from the full data (hence its uniqueness), still this task is not easy when dealing with finite data. For doing so, a toolbox made of known statistical methods in data analysis and new statistical methods and numerical algorithms developed for this problem is presented. Our toolbox is self-contained: it builds a mechanism based only on the information it extracts from the data. The implementation of the toolbox on the data is fast. The toolbox is automated and is available for academic research upon electronic request.