  Deducing an underlying multi-substate on-off kinetic scheme (KS) from the
statistical properties of a two-state trajectory is the aim from 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 multi-exponential
waiting time probability density functions (WT-PDFs). A RD form has the
simplest toplogy 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 develped 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.
