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Ophir Flomenbom

Publications and source records attributed to Ophir Flomenbom.

6 recordsLinked to original sources
PubMed2006

Utilizing the information content in two-state trajectories.

The signal from many single-molecule experiments monitoring molecular processes, such as enzyme turnover by means of fluorescence and opening and closing of ion channel through 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 multisubstate on-off kinetic scheme (KS) of the process. The determination of the underlying KS is difficult and sometimes even impossible because of the loss of information in the mapping of the multidimensional KS onto two dimensions. Here we introduce a previously undescribed procedure that efficiently and optimally relates the signal to all equivalent underlying KS. This procedure partitions the space of KS 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 KS. Based on our approach, the upper bound on the information content in two-state trajectories is determined.

Ion Channel Gating↗
PubMed2005

Closed-form solutions for continuous time random walks on finite chains.

Continuous time random walks (CTRWs) on finite arbitrarily inhomogeneous chains are studied. By introducing a technique of counting all possible trajectories, we derive closed-form solutions in Laplace space for the Green's function (propagator) and for the first passage time probability density function (PDF) for nearest neighbor CTRWs in terms of the input waiting time PDFs. These solutions are also the Laplace space solutions of the generalized master equation. Moreover, based on our counting technique, we introduce the adaptor function for expressing higher order propagators (joint PDFs of time-position variables) for CTRWs in terms of Green's functions. Using the derived formula, an escape problem from a biased chain is considered.

DNA-Directed RNA Polymerases↗
PubMed2005

On the relationships between kinetic schemes and two-state single molecule trajectories.

Trajectories of a signal that fluctuates between two states which originate from single molecule activities have become ubiquitous. Common examples are trajectories of ionic flux through individual membrane channels and of photon counts collected from diffusion, activity, and conformational changes of biopolymers. By analyzing the trajectory, one wishes to deduce the underlying mechanism, which is usually described by a multisubstate kinetic scheme. In previous works [O. Flomenborn, J. Klafter, and A. Szabo, Biophys. J. 88, 3780 (2005); O. Flomenbom and J. Klafter, Acta Phys. Pol. B 36, 1527 (2005)], we divided kinetic schemes that generate two-state trajectories into two types: reducible schemes and irreducible schemes. A full characterization of the reducible ones was given. We showed that all the information in trajectories generated from reducible schemes is contained in the waiting time probability density functions (PDFs) of the two states. It follows that reducible schemes with the same waiting time PDFs are not distinguishable; namely, such schemes lead to identical two-state trajectories in the statistical sense. In this work, we further characterize the topologies of kinetic schemes, now of irreducible schemes, and further study two-state trajectories from the two types of scheme. We suggest various methods for extracting information about the underlying kinetic scheme from the trajectory (e.g., calculate the binned successive waiting times PDFs and analyze the ordered waiting time trajectories), and point out the advantages and disadvantages of each. We show that the binned successive waiting times PDFs are not only more robust than other functions when analyzing finite trajectories, but contain, in most cases, more information about the underlying kinetic scheme than other functions in the limit of infinitely long trajectories. For some cases, however, analyzing the ordered waiting times trajectory may supply unique information about the underlying kinetic scheme.

Journal Article↗
PubMed2005

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 multisubstate 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 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, and cannot be differentiated 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.

Biophysical Phenomena↗
PubMed2005

Stretched exponential decay and correlations in the catalytic activity of fluctuating single lipase molecules.

Single-molecule techniques offer a unique tool for studying the dynamical behavior of individual molecules and provide the possibility to construct distributions from individual events rather than from a signal stemming from an ensemble of molecules. In biological systems, known for their complexity, these techniques make it possible to gain insights into the detailed spectrum of molecular conformational changes and activities. Here, we report on the direct observation of a single lipase-catalyzed reaction for extended periods of time (hours), by using confocal fluorescence microscopy. When adding a profluorescent substrate, the monitored enzymatic activity appears as a trajectory of "on-state" and "off-state" events. The waiting time probability density function of the off state and the state-correlation function fit stretched exponentials, independent of the substrate concentration in a certain range. The data analysis unravels oscillations in the logarithmic derivative of the off-state waiting time probability density function and correlations between off-state events. These findings imply that the fluctuating enzyme model, which involves a spectrum of enzymatic conformations that interconvert on the time scale of the catalytic activity, best describes the observed enzymatic activity. Based on this model, values for the coupling and reaction rates are extracted.

Biophysical Phenomena↗