Search PubMed⌕ Search

Biomedical subjects

Joseph Klafter

Publications and source records attributed to Joseph Klafter.

13 recordsLinked to original sources
PubMed2005

On the nonlinear modeling of shot noise.

We introduced a nonlinear shot-noise model, a natural generalization of the "classic" shot-noise model, which differs markedly from the existing linear shot-noise models. This model produces a wide spectrum of stationary noise processes. Because of its intrinsic nonlinearity, the model's resulting noise processes are capable of displaying a rich variety of both amplitudal and temporal statistical behaviors. Surprisingly, the nonlinear model is amenable to mathematical analysis and yields closed-form formulae for the characterizing statistics of its resulting noise processes.

Journal Article↗
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

Fractons in proteins: can they lead to anomalously decaying time autocorrelations?

Motivated by recent studies on the fractal nature of folded proteins, we analyze the time-dependent autocorrelation function < x (-->)(t).x(-->)(0) >of the distance between two points on a thermally vibrating fractal. Using fractons, the vibrational excitations of a fractal, we show that for both strongly underdamped and overdamped vibrations this correlation function decays anomalously, displaying a crossover from a nearly stretched exponential decay at short times to a slow algebraic decay at long times. Relationship to single molecule experiments is discussed.

Fractals↗
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

Nuclear localization signal peptides induce molecular delivery along microtubules.

Many essential processes in eukaryotic cells depend on regulated molecular exchange between its two major compartments, the cytoplasm and the nucleus. In general, nuclear import of macromolecular complexes is dependent on specific peptide signals and their recognition by receptors that mediate translocation through the nuclear pores. Here we address the question of how protein products bearing such nuclear localization signals arrive at the nuclear membrane before import, i.e., by simple diffusion or perhaps with assistance of cytoskeletal elements or cytoskeleton-associated motor proteins. Using direct single-particle tracking and detailed statistical analysis, we show that the presence of nuclear localization signals invokes active transport along microtubules in a cell-free Xenopus egg extract. Chemical and antibody inhibition of minus-end directed cytoplasmic dynein blocks this active movement. In the intact cell, where microtubules project radially from the centrosome, such an interaction would effectively deliver nuclear-targeted cargo to the nuclear envelope in preparation for import.

Actins↗
PubMed2005

Natural cutoff in Lévy flights caused by dissipative nonlinearity.

Lévy flight models are often used to describe stochastic processes in complex systems. However, due to the occurrence of diverging position and/or velocity fluctuations Lévy flights are physically problematic if describing the dynamics of a particle of finite mass. Here we show that the velocity distribution of a random walker subject to Lévy noise can be regularized by nonlinear friction, leading to a natural cutoff in the velocity distribution and finite velocity variance.

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↗
PubMed2004

The nonlinear nature of friction.

Tribology is the study of adhesion, friction, lubrication and wear of surfaces in relative motion. It remains as important today as it was in ancient times, arising in the fields of physics, chemistry, geology, biology and engineering. The more we learn about tribology the more complex it appears. Nevertheless, recent experiments coupled to theoretical modelling have made great advances in unifying apparently diverse phenomena and revealed many subtle and often non-intuitive aspects of matter in motion, which stem from the nonlinear nature of the problem.

Animals↗
PubMed2003

Bifurcation, bimodality, and finite variance in confined Lévy flights.

We investigate the statistical behavior of Lévy flights confined in a symmetric, quartic potential well U(x) proportional, variant x(4). At stationarity, the probability density function features a distinct bimodal shape and decays with power-law tails which are steep enough to give rise to a finite variance, in contrast to free Lévy flights. From a delta-initial condition, a bifurcation of the unimodal state is observed at t(c)>0. The nonlinear oscillator with potential U(x)=ax(2)/2+bx(4)/4, a,b>0, shows a crossover from unimodal to bimodal behavior at stationarity, depending on the ratio a/b.

Journal Article↗
PubMed2001

Hopping motion of interacting particles: from time-dependent interaction to directed transport.

The hopping motion of three or more pairwise interacting particles on a linear equipotential chain is investigated. It is shown that a directed transport of the particle array can be obtained by introducing time-dependent interactions such as switching the interaction strength periodically between two values. The direction and mean velocity of the motion are determined by the nature of the imposed time dependence and can, hence, be chosen dynamically. The possibility of transporting a passive cargo and some other applications are discussed.

Journal Article↗