Viscoelasticity in Homogeneous Protein Solutions

Pan, Weichun; Filobelo, Luis; Pham, Ngoc; Galkin, Oleg; Uzunova, Veselina; Vekilov, Peter G.

doi:10.1103/physrevlett.102.058101

Cited by 126 publications

(132 citation statements)

References 38 publications

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“…Other studies in similar systems have also suggested that protein diffusion in crowded marginally entangled polymer solutions deviates from simple Fickian diffusion 15,24,[50][51][52][53] . This, however, remains somewhat controversial, as mobile obstacles are not expected to produce anomalous diffusion 23 .…”

Section: Introductionmentioning

confidence: 99%

Characterizing anomalous diffusion in crowded polymer solutions and gels over five decades in time with variable-lengthscale fluorescence correlation spectroscopy

et al. 2016

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The diffusion of macromolecules in cells and in complex fluids is often found to deviate from simple Fickian diffusion. One explanation offered for this behavior is that molecular crowding renders diffusion anomalous, where the mean-squared displacement of the particles scales as r 2 ∝ t α with α < 1. Unfortunately, methods such as fluorescence correlation spectroscopy (FCS) or fluorescence recovery after photobleaching (FRAP) probe diffusion only over a narrow range of lengthscales and cannot directly test the dependence of the mean-squared displacement (MSD) on time. Here we show that variable-lengthscale FCS (VLS-FCS), where the volume of observation is varied over several orders of magnitude, combined with a numerical inversion procedure of the correlation data, allows retrieving the MSD for up to five decades in time, bridging the gap between diffusion experiments performed at different lengthscales. In addition, we show that VLS-FCS provides a way to assess whether the propagator associated with the diffusion is Gaussian or non-Gaussian. We used VLS-FCS to investigate two systems where anomalous diffusion had been previously reported. In the case of dense cross-linked agarose gels, the measured MSD confirmed that the diffusion of small beads was anomalous at short lengthscales, with a cross-over to simple diffusion around ≈ 1 µm, consistent with a caged diffusion process. On the other hand, for solutions crowded with marginally entangled dextran molecules, we uncovered an apparent discrepancy between the MSD, found to be linear, and the propagators at short lengthscales, found to be non-Gaussian. These contradicting features call to mind the "anomalous, yet Brownian" diffusion observed in several biological systems, and the recently proposed "diffusing diffusivity" model.

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Section: Introductionmentioning

confidence: 99%

Characterizing anomalous diffusion in crowded polymer solutions and gels over five decades in time with variable-lengthscale fluorescence correlation spectroscopy

et al. 2016

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“…For instance, they include blinking quantum dots (20)(21)(22)(23), or biologically relevant systems. The latter include subdiffusion of tracer particles in living biological cells (24)(25)(26)(27)(28)(29) or reconstituted crowding systems (30)(31)(32)(33), protein conformational dynamics (34), or the motion of bacteria in a biofilm (35). Here we show how the knowledge of the aging correlation function allows us to quantify the nonergodic behavior of the underlying process.…”

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confidence: 99%

Aging and nonergodicity beyond the Khinchin theorem

Burov¹,

Metzler

Barkai

2010

Proc. Natl. Acad. Sci. U.S.A.

165

145

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The Khinchin theorem provides the condition that a stationary process is ergodic, in terms of the behavior of the corresponding correlation function. Many physical systems are governed by nonstationary processes in which correlation functions exhibit aging. We classify the ergodic behavior of such systems and suggest a possible generalization of Khinchin's theorem. Our work also quantifies deviations from ergodicity in terms of aging correlation functions. Using the framework of the fractional Fokker-Planck equation, we obtain a simple analytical expression for the two-time correlation function of the particle displacement in a general binding potential, revealing universality in the sense that the binding potential only enters into the prefactor through the first two moments of the corresponding Boltzmann distribution. We discuss applications to experimental data from systems exhibiting anomalous dynamics.anomalous diffusion | ergodicity breaking | single particle trajectories | continuous time random walk | irreversibility I mportant tools for analyzing the generally complicated dynamics of physical observables O are their two-time correlation functions C O ðt 2 ;t 1 Þ. These are pair products of dynamic observables that are averaged over an ensemble, as defined below. When such a correlation function describes a stationary process, C O ðt 2 ;t 1 Þ is a function of the time difference only; that is, C O ðt 2 ;t 1 Þ ¼Ĉ O ðjt 2 − t 1 jÞ. For such processes the correlation function contains the dynamical information on other physical observables via fundamental theorems (1). For instance, the Wiener-Khinchin theorem relates the power spectrum to the correlation function, or the fluctuation-dissipation theorem connects correlation functions to linear response functions. Another well-known example is Khinchin's theorem (2), which provides a criterion for ergodicity of a process in terms of the corresponding stationary correlation function. However, the stationarity property is found to be violated in numerous systems (see below). These systems exhibit aging properties that are intimately connected to the nonstationary behavior. Correlation functions in aging systems behave very differently from their stationary counterparts (3-6). For instance, systems may be characterized by correlation functions of the type C O ðt 2 ;t 1 Þ ¼ h O ðt 1 ∕t 2 Þ (if t 2 ≥ t 1 ); i.e., the two times enter as a quotient rather than their difference. This nonstationary behavior is also connected to a breaking of ergodicity in the sense that long-time averages differ from ensemble averages of the same quantities (3, 7-10). The relation between correlation functions and ergodicity breaking can be quantified by the Edwards-Anderson parameter (3); see below.We here present a possible generalization of the Khinchin theorem for aging systems, namely, provide the condition for ergodicity for systems exhibiting aging. Moreover, for systems with broken ergodicity we relate fluctuations of time averages to the corresponding correlation function. I...

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“…It is seen from (2) that the damping force at time t is only relative with the damping coefficient and instantaneous velocity at time t. But in some viscoelastic mediums [29][30][31][32][33][34], the damping force shows the property of ''fading memory'' [27], that is, the nearest velocity gives the highest impact on damping force, and the farthest is nearly close to zero. Here, the memory kernel of viscoelasticity [29,53] is given by…”

Section: Langevin Equationmentioning

confidence: 95%

“…Whereas in some complex viscoelastic mediums [29][30][31][32][33][34], such as actin filament networks [29], protein solutions [30][31][32], interiors of biological cells [33,34], anomalous diffusions have been widely observed, and it is characterized by the mean-square displacement satisfying ⟨x 2 (t)⟩ ∼ t α , where the diffusion exponents 0 < α < 1.0 and α > 1.0 respectively indicate subdiffusion [29][30][31][32][33][34][35][36][37][38] and super-diffusion [39], and α = 1.0 recovers the normal diffusion. Especially, the subdiffusion is experimentally firmly established in various mediums with different α in the range of 0.25 ∼ 1.0 [30][31][32][33][34]40,41]. It is found that the traditional coupled Brownian motors expressed by the integer order stochastic differential equations could not describe the complex transport behaviors of coupled particles under the background of anomalous diffusion.…”

Section: Introductionmentioning

confidence: 99%