Biomedical subjects

E Barkai

Publications and source records attributed to E Barkai.

At least 19 recordsLinked to original sources

PubMed2006

Photon counting statistics for blinking CdSe-ZnS quantum dots: a Lévy walk process.

We analyze photon statistics of blinking CdSe-ZnS nanocrystals interacting with a continuous wave laser field, showing that the process is described by a ballistic Lévy walk. In particular, we show that Mandel's Q parameter, describing the fluctuations of the photon counts, is increasing with time even in the limit of long time. This behavior is in agreement with the theory of Silbey and co-workers (Jung et al. Chem. Phys. 2002, 284, 181), and in contrast to all existing examples where Q approaches a constant, independent of time in the long time limit. We then analyze the distribution of the time averaged intensities, showing that they exhibit a nonergodic behavior, namely, the time averages remain random even in the limit of a long measurement time. In particular, the distribution of occupation times in the on-state compares favorably to a theory of weak ergodicity breaking of blinking nanocrystals. We show how our data analysis yields information on the amplitudes of power-law decaying on and off time distributions, information not available using standard data analysis of on and off time histograms. Photon statistics reveals fluctuations in the intensity of the bright state indicating that it is composed of several states. Photon statistics exhibits a Lévy walk behavior also when an ensemble of 100 dots is investigated, indicating that the strange kinetics can be observed already at the level of small ensembles.

Journal Article↗

PubMed2006

Random walk to a nonergodic equilibrium concept.

Random walk models, such as the trap model, continuous time random walks, and comb models, exhibit weak ergodicity breaking, when the average waiting time is infinite. The open question is, what statistical mechanical theory replaces the canonical Boltzmann-Gibbs theory for such systems? In this paper a nonergodic equilibrium concept is investigated, for a continuous time random walk model in a potential field. In particular we show that in the nonergodic phase the distribution of the occupation time of the particle in a finite region of space approaches U- or W-shaped distributions related to the arcsine law. We show that when conditions of detailed balance are applied, these distributions depend on the partition function of the problem, thus establishing a relation between the nonergodic dynamics and canonical statistical mechanics. In the ergodic phase the distribution function of the occupation times approaches a delta function centered on the value predicted based on standard Boltzmann-Gibbs statistics. The relation of our work to single-molecule experiments is briefly discussed.

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PubMed2005

Photon emission from a driven single-molecule source: a renormalization group approach.

The photon emission from a single molecule driven simultaneously by a laser and a slow electric radio frequency (rf) field is studied. We use a non-Hermitian Hamiltonian approach which accounts for the radiative decay of a two-level system modeling the single-molecule source. We apply the renormalization group method for differential equations to obtain long time solution of the corresponding Schrodinger equation, which allows us to calculate the average waiting time for the first photon emission. Then, we analyze the conditions for suppression and enhancement of photon emission in this dissipative two-level system. In particular we derive a transcendental equation, which yields the nontrivial rf field control parameters, for which enhancement and suppression of photon emission occurs. For finite values of radiative decay rate an abrupt transition to the state when both situations are indistinguishable is found for certain values of the rf field parameters. Our results are shown to be in agreement with the available experiments [Ch. Brunel et al., Phys. Rev. Lett. 81, 2679 (1998)].

Journal Article↗

PubMed2005

Single-molecule chemical reactions: reexamination of the Kramers approach.

Single-molecule chemical reactions yield insight into fluctuation phenomena that are obscured in the measurement of the ensemble of molecules. Kramers escape problem is investigated here in a framework suitable for single-molecule reactions. In particular we obtain distributions of escape times in simple limiting cases, rather than their mean, and investigate their sensitivity on initial conditions. Rich physical behaviors are observed: sub-Poissonian statistics when the dynamics is only slightly deviating from the Newtonian, super-Poissonian behavior when diffusion is dominating, and Poissonian behavior when Kramers original conditions hold. By varying initial conditions escape time distributions can follow a (usual) exponential or a tau(-3/2) decay, due to regular diffusion. We briefly address experimental results that yield the tau(-3/2) behavior (with cutoffs) and propose that this behavior is universal.

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PubMed2005

Nonergodicity of blinking nanocrystals and other Lévy-walk processes.

We investigate the nonergodic properties of blinking nanocrystals modeled by a Lévy-walk stochastic process. Using a nonergodic mean field approach we calculate the distribution functions of the time averaged intensity correlation function. We show that these distributions are not delta peaked on the ensemble average correlation function values; instead they are W or U shaped. Beyond blinking nanocrystals our results describe ergodicity breaking in systems modeled by Lévy walks , for example, certain types of chaotic maps and spin dynamics to name a few.

Journal Article↗

PubMed2004

Influence of spectral diffusion on single-molecule photon statistics.

We investigate the distribution of the number of photons emitted by a single molecule undergoing a spectral diffusion process and interacting with a continuous wave field. Using a generating function formalism an exact analytical formula for Mandel's Q parameter is obtained. The solution, which is valid for weak and strong excitation fields, exhibits transitions between (i) quantum sub-Poissonian and classical super-Poissonian behaviors, and (ii) fast to slow modulation limits.

Algorithms↗

PubMed2004

Aging correlation functions for blinking nanocrystals, and other on-off stochastic processes.

Following recent experiments on power law blinking behavior of single nanocrystals, we calculate two-time intensity correlation functions I(t)I(t+t') for these systems. We use a simple two state (on and off) stochastic model to describe the dynamics. We classify possible behaviors of the correlation function and show that aging, e.g., dependence of the correlation function on age of process t, is obtained for classes of the on time and off time distributions relevant to experimental situation. Analytical asymptotic scaling behaviors of the intensity correlation in the double time t and t' domain are obtained. In the scaling limit I(t)I(t+t('))-->h(x), where four classes of behaviors are found: (i) finite averaged on and off times x=t' (standard behavior); (ii) on and off times with identical power law behaviors x=t/t' (case relevant for capped nanocrystals); (iii) exponential on times and power law off times x=tt' (case relevant for uncapped nanocrystals); (iv) for defected off time distribution we also find x=t+t'. Origin of aging behavior is explained based on simple diffusion model. We argue that the diffusion controlled reaction A+B <==>AB, when followed on a single particle level exhibits aging behavior.

Journal Article↗

PubMed2003

Lévy statistics for random single-molecule line shapes in a glass.

We demonstrate that the statistical behavior of random line shapes of single tetra-tert-butylterrylene chromophores embedded in an amorphous polyisobutylene matrix at T=2 K is described by Lévy statistics as predicted theoretically by Barkai, Silbey, and Zumofen [Phys. Rev. Lett. 84, 5339 (2000)]. This behavior is a manifestation of the long-range interaction between two-level systems in the glass and the single molecule. A universal amplitude ratio is investigated, which shows that the standard tunneling model assumptions are compatible with the experimental data.

Journal Article↗

PubMed2001

Time-dependent fluctuations in single molecule spectroscopy: a generalized Wiener-Khintchine approach.

We consider the theory of time-dependent fluctuations in single molecule spectroscopy. In particular, the relation between stationary spectral diffusion processes and photon counting statistics is investigated. Within linear response theory, a general relation between Mandel's Q parameter and a three time dipole correlation function is obtained. For a prototype spectral diffusion process, an exact solution of Q is found which exhibits rich types of physical behaviors.

Journal Article↗

PubMed2001

Fractional Fokker-Planck equation, solution, and application.

Recently, Metzler et al. [Phys. Rev. Lett. 82, 3563 (1999)], introduced a fractional Fokker-Planck equation (FFPE) describing a subdiffusive behavior of a particle under the combined influence of external nonlinear force field, and a Boltzmann thermal heat bath. In this paper we present the solution of the FFPE in terms of an integral transformation. The transformation maps the solution of ordinary Fokker-Planck equation onto the solution of the FFPE, and is based on Lévy's generalized central limit theorem. The meaning of the transformation is explained based on the known asymptotic solution of the continuous time random walk (CTRW). We investigate in detail (i) a force-free particle, (ii) a particle in a uniform field, and (iii) a particle in a harmonic field. We also find an exact solution of the CTRW, and compare the CTRW result with the corresponding solution of the FFPE. The relation between the fractional first passage time problem in an external nonlinear field and the corresponding integer first passage time is given. An example of the one-dimensional fractional first passage time in an external linear field is investigated in detail. The FFPE is shown to be compatible with the Scher-Montroll approach for dispersive transport, and thus is applicable in a large variety of disordered systems. The simple FFPE approach can be used as a practical tool for a phenomenological description of certain types of complicated transport phenomena.

Journal Article↗

PubMed2001

Long-lasting cholinergic modulation underlies rule learning in rats.

We studied the role of acetylcholine (ACh) in creating learning-related long-lasting modifications in the rat cortex. Rats were trained to discriminate positive and negative cues in pairs of odors, until they demonstrated rule learning and entered a mode of high capability for learning of additional odors. We have previously reported that pyramidal neurons in olfactory (piriform) cortex from trained rats had reduced spike afterhyperpolarization (AHP) for 3 d after rule learning. In the present study we examined the mechanism underlying this long-lasting modification. The cholinergic agonist carbachol reduced both slow AHP and firing adaptation in neurons from pseudotrained rats, but had no effect on neurons from trained rats, suggesting pre-existing cholinergic effect. Intracellular application of the calcium chelator BAPTA abolished the difference in slow AHP and in adaptation between groups, suggesting that the difference resulted from reduction in the ACh-sensitive, Ca(2+)-dependent potassium current, I(AHP). At the behavioral level, application of the muscarinic blocker scopolamine before each training session delayed rule learning but had no effect on further acquisition of odor memory. We suggest that intense ACh activity during rule learning enhances neuronal excitability in the piriform cortex by reducing I(AHP) and that the effect outlasts the stage of rule learning, so that ACh activity is not crucial for further odor learning.

Acetylcholine↗

PubMed2001

Olfactory learning is associated with increased spine density along apical dendrites of pyramidal neurons in the rat piriform cortex.

We studied the effect of olfactory learning on the dendritic spine density of pyramidal neurons in the rat piriform (olfactory) cortex. Rats were trained to distinguish between two pairs of odours in an olfactory discrimination task. Three days after training completion, rats were killed and layer II pyramidal neurons identified by Golgi impregnation were examined with a light microscope. Counts of visible spines were performed along the secondary and tertiary branches of both the apical dendrites and the basal dendrites, which are the sites of intracortical synaptic inputs. An estimate of the true spine density was obtained using Feldman and Peters' method (1979, The Journal of Comparative Neurology, 188, 527--542). The estimated true spine density along apical dendrites was higher in neurons from trained rats than those in pseudotrained and naive rats by 15%. As length of spiny dendrites did not change significantly after learning, the learning-related increase in spine density in neurons from trained rats may indicate on an increased number of excitatory synapses interconnecting pyramidal neurons in the piriform cortex, following olfactory learning.

Animals↗

PubMed2001

Olfactory learning modifies predisposition for long-term potentiation and long-term depression induction in the rat piriform (olfactory) cortex.

Learning-related modifications in predisposition for long-term potentiation (LTP) and long-term depression (LTD) were studied in brain slices of the rat piriform cortex following olfactory learning. Rats were trained to discriminate between pairs of odors until they demonstrated rule learning. We have previously shown that such training is accompanied by enhanced neuronal excitability and increased synaptic transmission in the intrinsic synaptic pathway. Here we show that the susceptibility for further enhancing synaptic connectivity by inducing LTP in slices from trained rats is markedly reduced after training, compared with slices from pseudo-trained and naive rats. Accordingly, while 900 stimuli at 1 Hz did not induce LTD in slices from control rats, it induced significant LTD in slices from trained rats. Post-tetanic potentiation (PTP) was also reduced after training, indicating that synaptic release is enhanced after odor learning, as previously suggested. We suggest that learning-related cellular modifications and activity-dependent synaptic plasticity share a common mechanism in the primary olfactory cortex. Our data also support the prediction generated according to the sliding modification threshold theory that learning should be accompanied by reduced capability of inducing LTP and increased susceptibility for LTD induction.

Animals↗

PubMed2001

Cellular correlates of olfactory learning in the rat piriform cortex.

This review describes research that combines cellular physiology with behavioral neuroscience, to study the cellular mechanisms underlying learning and memory in the mammalian brain. Rats were trained with an olfactory conditioning paradigm, in which they had to memorize odors in order to be rewarded with drinking water. Such training results in rule learning, which enables enhanced acquisition of odor memory. Training results in the following learning-related physiological modifications in intrinsic and synaptic properties in olfactory (piriform) cortex pyramidal neurons: 1. increased neuronal excitability, indicated by reduced afterhyperpolarization, and 2. increased synaptic transmission, indicated by reduced paired-pulse facilitation. These modifications are correlated to enhanced learning capability rather than to storage of memory for specific odors. In addition, using a different paradigm of odor-training, it is shown that NMDA and betra-adrenergic receptors are involved at different stages of long-term memory consolidation.

Animals↗

PubMed2000

Levy distribution of single molecule line shape cumulants in glasses

We investigate the distribution of single molecule line shape cumulants, kappa(1),kappa(2),ellipsis, in low temperature glasses based on the sudden jump, standard tunneling model. We find that the cumulants are described by Levy stable laws, thus the generalized central limit theorem is applicable for this problem.

Journal Article↗

PubMed2000

One-dimensional stochastic Levy-lorentz gas

We introduce a Levy-Lorentz gas in which a light particle is scattered by static point scatterers arranged on a line. We investigate the case where the intervals between scatterers xi(i) are independent random variables identically distributed according to the probability density function &mgr;(xi) approximately xi(-(1+gamma)). We show that under certain conditions the mean square displacement of the particle obeys >/=Ct3-gamma for 1<gamma<2. This behavior is compatible with a renewal Levy walk scheme. We discuss the importance of rare events in the proper characterization of the diffusion process.

Journal Article↗

PubMed2000

From continuous time random walks to the fractional fokker-planck equation

We generalize the continuous time random walk (CTRW) to include the effect of space dependent jump probabilities. When the mean waiting time diverges we derive a fractional Fokker-Planck equation (FFPE). This equation describes anomalous diffusion in an external force field and close to thermal equilibrium. We discuss the domain of validity of the fractional kinetic equation. For the force free case we compare between the CTRW solution and that of the FFPE.

Journal Article↗

PubMed1999

Reduced synaptic facilitation between pyramidal neurons in the piriform cortex after odor learning.

Learning-related cellular modifications were studied in the rat piriform cortex after operand conditioning. Rats were trained to discriminate positive cues in pairs of odors. In one experimental paradigm, rats were trained to memorize 35-50 pairs of odors ("extensive training"). In another paradigm, training was continued only until rats acquired the rule of the task, usually after learning the first two pairs of odors ("short training"). "Pseudotrained" and "naive" rats served as controls. We have previously shown that "rule learning" of this task was accompanied by reduced spike afterhyperpolarization in pyramidal neurons in brain slices of the piriform cortex. In the present study, synaptic inputs to the same cells were examined. Pairs of electrical stimuli applied to the intrinsic fibers that interconnect layer II pyramidal neurons revealed significant reduction in paired-pulse facilitation (PPF) in this pathway even after short training. PPF in shortly trained rats was reduced to the same extent as in extensively trained rats. PPF reduction did not result from modification of membrane properties in the postsynaptic cells, change in postsynaptic inhibition, or impairment of the facilitation mechanism. Extracellular field potential recordings showed enhanced synaptic transmission in these synapses. The reduction in PPF became apparent only 3 d after task acquisition and returned to control value 5 d later. PPF evoked by stimulating the afferent fibers to the same neurons was increased 1 d after training for 2 d. We suggest that the transient enhancement in connectivity in the intrinsic pathway is related to the enhanced learning capability and not to memory for specific odors, which lasts for weeks.

Afferent Pathways↗