Modeling and analysis of single-molecule experiments

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemistry, 2005.Vita.Includes bibliographical references (p. 281-311).Single molecule experiments offer a unique window into the molecular world. This window allows us to distinguish the behaviors of individual molecules from the behavior of bulk by observing rare events and heterogeneity in the dynamics. This thesis discusses both models for single molecule experiments, including the stretching of DNA in hydrodynamic flows and the diffusion of tracer particles in heterogeneous environments, and methods to analyze single molecule data to allow determination of properties and models for single molecule experiments. These methods of analysis are based on combining information theory and Bayesian methods with physical insight and are applied to several experimental situations.by James B. Witkoskie.Ph.D

What can one learn from two-state single molecule trajectories?

A time trajectory of an observable that fluctuates between two values (say, on and off), stemming from some unknown multi-substate kinetic scheme, is the output of many single molecule experiments. Here we show that when all successive waiting times along the trajectory are uncorrelated the on and the off waiting time probability density functions (PDFs) contain all the information. By relating the lack of correlation in the trajectory to the topology of kinetic schemes, we can immediately specify those kinetic schemes that are equally consistent with experiment, which means that it is impossible to differentiate between them by any sophisticated analyses of the trajectory. Correlated trajectories, however, contain additional information about the underlying kinetic scheme, and we consider the strategy that one should use to extract it. An example is given on correlations in the activity of individual lipase molecules.Comment: Biophys. J., in press (2005

Utilizing the information content in two-state trajectories

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.Comment: The file contains: main text (+4 figures), supporting information (+9 figures), poster (1 page

Correctly validating results from single molecule data: the case of stretched exponential decay in the catalytic activity of single lipase B molecules

The question of how to validate and interpret correctly the waiting time probability density functions (WT-PDFs) from single molecule data is addressed. It is shown by simulation that when a stretched exponential WT-PDF, with a stretched exponent alfa and a time scale parameter tau, generates the off periods of a two-state trajectory, a reliable recovery of the input WT-PDF from the trajectory is obtained even when the bin size used to define the trajectory, dt, is much larger than the parameter tau. This holds true as long as the first moment of the WT-PDF is much larger than dt. Our results validate the results in an earlier study of the activity of single Lipase B molecules and disprove recent related critique

Random Set Tracker Experiment on a Road Constrained Network with Resource Management

Abstract -This paper describes the application of finite set statistics (FISST) to real-time multiple target road constrained tracking problems. We studied specific test problems where multiple modality wireless sensor networks monitored road networks of interest. Acoustic and radar detections updated a global density that tracked the number and positions of targets. The global density determines "information states" that form the basis of a closed-loop Markov Decision Process resource management procedure that controls sensor operation

Construction of effective free energy landscape from single-molecule time series

A scheme for extracting an effective free energy landscape from single-molecule time series is presented. This procedure uniquely identifies a non-Gaussian distribution of the observable associated with each local equilibrium state (LES). Both the number of LESs and the shape of the non-Gaussian distributions depend on the time scale of observation. By assessing how often the system visits and resides in a chosen LES and escapes from one LES to another (with checking whether the local detailed balance is satisfied), our scheme naturally leads to an effective free energy landscape whose topography depends on in which time scale the system experiences the underlying landscape. For example, two metastable states are unified as one if the time scale of observation is longer than the escape time scale for which the system can visit mutually these two states. As an illustrative example, we present the application of extracting the effective free energy landscapes from time series of the end-to-end distance of a three-color, 46-bead model protein. It indicates that the time scales to attain the local equilibrium tend to be longer in the unfolded state than those in the compact collapsed state

Multiscale complex network of protein conformational fluctuations in single-molecule time series

Conformational dynamics of proteins can be interpreted as itinerant motions as the protein traverses from one state to another on a complex network in conformational space or, more generally, in state space. Here we present a scheme to extract a multiscale state space network (SSN) from a single-molecule time series. Analysis by this method enables us to lift degeneracy—different physical states having the same value for a measured observable—as much as possible. A state or node in the network is defined not by the value of the observable at each time but by a set of subsequences of the observable over time. The length of the subsequence can tell us the extent to which the memory of the system is able to predict the next state. As an illustration, we investigate the conformational fluctutation dynamics probed by single-molecule electron transfer (ET), detected on a photon-by-photon basis. We show that the topographical features of the SSNs depend on the time scale of observation; the longer the time scale, the simpler the underlying SSN becomes, leading to a transition of the dynamics from anomalous diffusion to normal Brownian diffusion