Biomedical subjects

Jianshu Cao

Publications and source records attributed to Jianshu Cao.

At least 19 recordsLinked to original sources

PubMed2006

Aging correlation functions of the interrupted fractional Fokker-Planck propagator.

The authors explore aging in a general semi-Markov process with arbitrary waiting time distributions and discuss the role of trapping phenomenon in glasses in determining the waiting time distributions. In certain limits, they obtain a two-time propagator for the fractional Fokker-Planck equation through coordination, but one can generalize the construction to incorporate cutoffs in the aging of the system, i.e., the interrupted aging. The construction allows the incorporation of cutoffs in the aging of the system, and the exploration of signatures of aging effects in systems that eventually achieve equilibrium. Cutoffs in aging effects are illustrated for interrupted fractional diffusion in a harmonic potential and for the on-time probability of a quantum dot system.

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PubMed2006

Correlations in single molecule photon statistics: renewal indicator.

Multiple time scales are the intrinsic nature of complex systems and can be revealed through single molecule photon statistical analysis. The standard Poisson indicator defined by the time-averaged initial condition measures photon bunching and antibunching but cannot be directly related to multiple time scales. A new indicator defined by the event-averaged initial condition is proposed to detect the deviation from the renewal behavior and to directly probe the effects of conformational fluctuations. Detailed calculations of modulated two-level systems are carried out using the transfer matrix method to demonstrate the difference between the two indicators. The relationship between ensemble-averaged survival probabilities and photon statistics is also explored in the context of single molecule measurements.

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PubMed2006

Testing for renewal and detailed balance violations in single-molecule blinking processes.

This paper examines methods to test one- and two-dimensional histograms for several features including the renewal properties, detailed balance violations, and experimental condition dependences. The tests are simple to implement and allow rigorous statistical determination of the existence of these kinetic features. The tests are used to determine the lower bound on the number of measurements necessary to differentiate underlying kinetic models.

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PubMed2006

Classical divergence of nonlinear response functions.

The time divergence of classical nonlinear response functions reveals the fundamental difficulty of dynamic perturbation based on classical mechanics. The nature of the divergence is established for systems in regular motions using asymptotic decomposition of Fourier integrals. The asymptotic analysis shows that the divergence cannot be removed by phase-space averaging such as the Boltzmann distribution function. The implications of this study are discussed in the context of the conceptual development of quantum-classical correspondence in dynamic response.

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PubMed2006

Description of the fluorescence intensity time trace of collections of CdSe nanocrystal quantum dots based on single quantum dot fluorescence blinking statistics.

This paper analyzes the observed phenomenology of the fluorescence time trace of collections of quantum dots (QDs) in terms of the model parameters that characterize the fluorescence blinking statistics of single QDs. We demonstrate that the non-universal dynamics that appear in fluorescence time traces of collections of QDs at short time scales are related to the universal dynamics that appear at longer time scales. We explore how the extent of time separation between the short and long dynamics affects the transition region and the dynamics at longer time scales. We suggest a methodology to extract single QD statistical model parameters from experimental fluorescence time traces of collections of QDs. We explore theoretical time traces and their experimental analogs for three different cases that span the diverse nonuniversal dynamics that appear at short time scales.

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PubMed2005

Stability analysis of three-dimensional colloidal domains: quadratic fluctuations.

Three-dimensional domain patterns can self-assemble in a charged colloidal suspension with competing short-range attraction and long-range Yukawa repulsion. Following the investigation of the ground-state domain shapes in our previous paper, we study the stability of isolated spherical, cylindrical, and lamellar domains with respect to shape fluctuations on boundaries. In the framework of the continuum model, we expand the free energy variation to quadratic terms under the constraint of constant volume. For the three shapes (sphere, cylinder, and lamella) discussed, domains with equilibrium sizes are stable with respect to shape fluctuations, and the stability of domains decreases as the spatial symmetry decreases.

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PubMed2005

Quantum-classical correspondence in response theory.

The correspondence principle between the quantum commutator [A, B] and the classical Poisson brackets iota h{A, B} is examined in the context of response theory. The classical response function is obtained as the leading term of the expansion of the phase space representation of the response function in terms of Weyl-Wigner transformations and is shown to increase without bound at long times as a result of ignoring divergent higher-order contributions. Systematical inclusion of higher-order contributions improves the accuracy of the h expansion at finite times. Resummation of all the higher-order terms establishes the classical-quantum correspondence <--> alpha n e iota n omega t|Jv + nh/2. The time interval of the validity of the simple classical limit [A(t), B(0)] --> iota h{A(t), B(0)} is estimated for quasiperiodic dynamics and is shown to be inversely proportional to anharmonicity.

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PubMed2005

High-order mode-coupling theory for the colloidal glass transition.

A theoretical approach is developed to derive a hierarchy of mode-coupling equations for the dynamics of concentrated colloidal suspensions, which improves the prediction of the colloidal glass transition. Our derivation is based on a matrix formalism for stochastic dynamics and the resulting recursive expressions for irreducible memory functions. The 1st order truncation of the generalized mode-coupling closure recovers mode-coupling theory, whereas its 2nd and 3rd order truncations provide corrections. The predictions of the transition volume fraction and Debye-Waller parameter for the hard-sphere colloidal system improve with the increasing mode-coupling order and compare favorably with experimental measurements.

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PubMed2005

Stationary phase evaluations of quantum rate constants.

We compute the quantum rate constant based on two extended stationary phase approximations to the imaginary-time formulation of the quantum rate theory. The optimized stationary phase approximation to the imaginary-time flux-flux correlation function employs the optimized quadratic reference system to overcome the inaccuracy of the quadratic expansion in the standard stationary phase approximation, and yields favorable agreements with instanton results for both adiabatic and nonadiabatic processes in dissipative and nondissipative systems. The integrated stationary phase approximation to the two-dimensional barrier free energy is particularly useful for adiabatic processes and demonstrates consistent results with the imaginary-time flux-flux correlation function approach. Our stationary phase methods do not require calculation of tunneling paths or stability matrices, and work equally well in the high-temperature and the low-temperature regimes. The numerical results suggest their general applicability for calibration of imaginary-time methods and for the calculation of quantum rate constants in systems with a large number of degrees of freedom.

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PubMed2005

Nondivergent classical response functions from uncertainty principle: quasiperiodic systems.

Time-divergence in linear and nonlinear classical response functions can be removed by taking a phase-space average within the quantized uncertainty volume O(hn) around the microcanonical energy surface. For a quasiperiodic system, the replacement of the microcanonical distribution density in the classical response function with the quantized uniform distribution density results in agreement of quantum and classical expressions through Heisenberg's correspondence principle: each matrix element (u/alpha(t)/v) corresponds to the (u-v)th Fourier component of alpha(t) evaluated along the classical trajectory with mean action (Ju+Jv)/2. Numerical calculations for one- and two-dimensional systems show good agreement between quantum and classical results. The generalization to the case of N degrees of freedom is made. Thus, phase-space averaging within the quantized uncertainty volume provides a useful way to establish the classical-quantum correspondence for the linear and nonlinear response functions of a quasiperiodic system.

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PubMed2004

Nonperturbative vibrational energy relaxation effects on vibrational line shapes.

A general formulation of nonperturbative quantum dynamics of solutes in a condensed phase is proposed to calculate linear and nonlinear vibrational line shapes. In the weak solute-solvent interaction limit, the temporal absorption profile can be approximately factorized into the population relaxation profile from the off-diagonal coupling and the pure-dephasing profile from the diagonal coupling. The strength of dissipation and the anharmonicity-induced dephasing rate are derived in Appendix A. The vibrational energy relaxation (VER) rate is negligible for slow solvent fluctuations, yet it does not justify the Markovian treatment of off-diagonal contributions to vibrational line shapes. Non-Markovian VER effects are manifested as asymmetric envelops in the temporal absorption profile, or equivalently as side bands in the frequency domain absorption spectrum. The side bands are solvent-induced multiple-photon effects which are absent in the Markovian VER treatment. Exact path integral calculations yield non-Lorentzian central peaks in absorption spectrum resulting from couplings between population relaxations of different vibrational states. These predictions cannot be reproduced by the perturbative or the Markovian approximations. For anharmonic potentials, the absorption spectrum shows asymmetric central peaks and the asymmetry increases with anharmonicity. At large anharmonicities, all the approximation schemes break down and a full nonperturbative path integral calculation that explicitly accounts for the exact VER effects is needed. A numerical analysis of the O-H stretch of HOD in D(2)O solvent reveals that the non-Markovian VER effects generate a small recurrence of the echo peak shift around 200 fs, which cannot be reproduced with a Markovian VER rate. In general, the nonperturbative and non-Markovian VER contributions have a stronger effect on nonlinear vibrational line shapes than on linear absorption.

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PubMed2004

Structural arrest transitions in fluids described by two Yukawa potentials.

We study a model colloidal system where particles interact via short-range attractive and long-range repulsive Yukawa potentials. Using the structure factor calculated from the mean-spherical approximation as the input, the kinetic phase diagrams as functions of the attraction depth and the volume fraction are obtained by calculating the Debye-Waller factors in the framework of the mode-coupling theory for three different heights of the repulsive barrier. The glass-glass reentrance phenomenon in the attractive colloidal case is also observed in the presence of the long-range repulsive barrier, which results in the lower and upper glass regimes. Competition between the short-range attraction and the long-range repulsion gives rise to new regimes associated with clusters such as "static cluster glass" and "dynamic cluster glass," which appear in the lower glass regime. Along the liquid-glass transition line between the liquid regime and the lower glass regime, crossover points separating different glass states are identified.

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PubMed2004

A semiclassical study of wave packet dynamics in anharmonic potentials.

Classical and semiclassical methods are developed to calculate and invert the wave packet motion measured in pump-probe experiments. With classical propagation of the Wigner distribution of the initial wave packet created by the pump pulse, we predict the approximate probe signal with slightly displaced recurrence peaks, and derive a set of first-order canonical perturbation expressions to relate the temporal features of the signal to the characteristics of the potential surface. A reduced dynamics scheme based on the Gaussian assumption leads to the correct center of mass motion but does not describe the evolution of the shape of the wave packet accurately. To incorporate the quantum interference into classical trajectories, we propose a final-value representation semiclassical method, specifically designed for the purpose of computing pump-probe signals, and demonstrate its efficiency and accuracy with a Morse oscillator and two kinetically coupled Morse oscillators. For the case of one-color pump probe, a simple phase-space quantization scheme is devised to reproduce the temporal profile at the left-turning point without actual wave packet propagation, revealing a quantum mechanical perspective of the nearly classical pump-probe signal.

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PubMed2004

Single molecule kinetics. I. Theoretical analysis of indicators.

Single molecule experiments reveal intriguing phenomenon in chemical and biological systems. Several indicators of complex dynamics, including "intensity" correlations, "event" correlations, and characteristic functions have been proposed, but extraction of information from these indicators can be difficult since these indicators only observe certain characteristics of the system. Generally, for systems that follow Poisson kinetics, all of these indicators contain similar information about the relaxation times of the system and the connections between different relaxation times, but the information is convoluted in different ways so the strength of various indicators is system specific. The paper discusses the theoretical implications and information content of various data analysis methods for single molecule experiments and demonstrates the relationships between indicators. Under certain conditions, common indicators contain all available information about systems with Poisson kinetics between degenerate states, but extraction of this information is generally not numerically feasible. The paper also discusses practical issues associated with these analyses, which motivates a numerical study based on Bayes' formula in the companion paper [J. Witkoskie and J. S. Cao, J. Chem. Phys. 121, 6373 (2004), following paper].

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PubMed2004

Single molecule kinetics. II. Numerical Bayesian approach.

As discussed in the companion paper [J. B. Witkoskie and J. S. Cao, J. Chem. Phys. 121, 6361 (2004), preceding paper], quantitative extraction of information from single molecule experiments by several proposed indicators is difficult since the experiments only observe certain characteristics of the system, even though the indicators can contain all available information. This paper shows how one can circumvent the shortcomings of these indicators by combining information extracted from indicators with a numerical Bayesian statistical approach. The Bayesian approach determines the relative probability of various models reproducing the entire sequence of the single molecules trajectory, instead of binning and averaging over the data, which removes much of this information.

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PubMed2004

Theoretical analysis and computer simulation of fluorescence lifetime measurements. I. Kinetic regimes and experimental time scales.

The configuration-controlled regime and the diffusion-controlled regime of conformation-modulated fluorescence emission are systematically studied for Markovian and non-Markovian dynamics of the reaction coordinate. A path integral simulation is used to model fluorescence quenching processes on a semiflexible chain. First-order inhomogeneous cumulant expansion in the configuration-controlled regime defines a lower bound for the survival probability, while the Wilemski-Fixman approximation in the diffusion-controlled regime defines an upper bound. Inclusion of the experimental time window of the fluorescence measurement adds another dimension to the two kinetic regimes and provides a unified perspective for theoretical analysis and experimental investigation. We derive a rigorous generalization of the Wilemski-Fixman approximation [G. Wilemski and M. Fixman, J. Chem. Phys. 60, 866 (1974)] and recover the 1/D expansion of the average lifetime derived by Weiss [G. H. Weiss, J. Chem. Phys. 80, 2880 (1984)].

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PubMed2004

Theoretical analysis and computer simulation of fluorescence lifetime measurements. II. Contour length dependence of single polymers.

Fluorescence lifetime measurements in a polymer chain are modeled using a memory function expansion, computer simulations, and simple scaling arguments. Unless the quenching rate is localized and infinitely fast, the fluorescence lifetime is generally not equivalent to the first passage time. The fluorescence lifetime distribution is decomposed into memory functions that can be measured separately in single-molecule experiments. The leading order of the expansion gives the Wilemski-Fixman (WF) approximation, and the convergence of higher order terms determines its validity. Simulations of the fluorescence quenching on a Rouse chain verify the accuracy of the WF approximation at small contact radii, short contour lengths, and small quenching rates. Detailed investigation of the average fluorescence lifetime reveals two competing mechanisms: the independent motion of end-to-end vector, which dominates at small contact radius, and the slowest relaxation of polymer, which dominates at large contact radius. The Wilemski-Fixman rate is used in combination with scaling arguments to predict the dependence of fluorescence lifetime on the contour length. Our predictions for the scaling of the average lifetime with the contour length are in good agreement with both simulations and recent experiments by Eaton and his group [L. J. Lapidus, W. A. Eaton, and J. Hofrichter, Proc. Natl. Acad. Sci. U.S.A. 97, 7220 (2000)].

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PubMed2004

Scaling and universality of inherent structure simulations.

In this paper we explore the inherent structures (IS) approach to the dynamics of the East constrained kinetic Ising model. The inherent structures do not capture the nature of the dynamics of many quantities, including the spin autocorrelation function. Simply monitoring the quenched energy fluctuations, i.e., IS energy, results in an oversimplified single order-parameter description of the system's dynamics, but examining other features, such as domain dynamics or normal modes, may give a more complete and useful picture of the dynamics. The universality in the behavior of the IS energy of this model does not reveal nonuniversal features of the kinetics that determine long-time relaxation of the system. As a result, popular functional forms, such as the stretched exponential relaxation or Gaussian distribution of energies, may be a numerical fit to data with little physical justification. Filtering data can be shown to erase features of the system and the resulting quantities resemble more universal functional forms that lack physical insight. These results for the East model have implications for IS simulations of realistic systems and suggest careful analysis including the examination of other potential order parameters is necessary to evaluate the validity of applications of universal and scaling arguments to IS simulations.

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