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تسجيل مستخدم جديدUtilizing the information content in two-state trajectories
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The signal from many single molecule experiments monitoring molecular processes, such as enzyme turnover via fluorescence and opening and closing of ion channel via the flux of ions, consists of a time series of stochastic on and off (or open and closed) periods, termed a two-state trajectory. This signal reflects the dynamics in the underlying multi-substate on-off kinetic scheme (KS) of the process. 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. Here we introduce a new procedure that efficiently and optimally relates the signal to all equivalent underlying KSs. This procedure partitions the space of KSs into canonical (unique) forms that can handle any KS, and obtains the topology and other details of the canonical form from the data without the need for fitting. Also established are relationships between the data and the topology of the canonical form to the on-off connectivity of a KS. The suggested canonical forms constitute a powerful tool in discriminating between KSs. Based on our approach, the upper bound on the information content in two state trajectories is determined.
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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 abo
ut 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.
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 mul
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