Characterizing anomalous diffusion in crowded polymer solutions and gels over five decades in time with variable-lengthscale fluorescence correlation spectroscopy (original) (raw)
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Physical Review E, 2005
The direct observation of a spatiotemporal behavior of anomalous diffusion in aqueous polymer ͓hyaluronan ͑HA͔͒ solution was achieved by fluorescence correlation spectroscopy ͑FCS͒ using a modified instrument, enabling continuous change of the confocal volume of a microscope, namely, sampling-volume-controlled ͑SVC͒ FCS ͑SVC-FCS͒. Since HA chains form a mesh structure with a pore size of about 10-40 nm, the observed diffusion coefficient ͑D obs ͒ is markedly dependent on the diffusion distance ͑L͒. By SVC-FCS, the curve of the distance dependence of diffusion coefficient was directly obtained as a continuous profile in L = 245-600 nm showing evidence of anomalous diffusion. On plotting D obs against either of the sampling time ͑ obs ͒ or the diffusion distance ͑L͒, D obs turnover was observed near the anomalous diffusion area. The appearance of this turnover is attributed to the nonuniform mesh structure that can be observed only by a fast observation and that should be dynamically averaged by polymer motions with large obs. This behavior is similar to that revealed in glass, colloidal systems, and gel solutions using dynamic light scattering, neutron scattering, and other techniques.
Anomalous Diffusion in Inverted Variable-Lengthscale Fluorescence Correlation Spectroscopy
Biophysical Journal, 2019
Using fluorescence correlation spectroscopy (FCS) to distinguish between different types of diffusion processes is often a perilous undertaking because the analysis of the resulting autocorrelation data is model dependant. Two recently introduced strategies, however, can help move toward a model-independent interpretation of FCS experiments: 1) the obtention of correlation data at different length scales and 2) their inversion to retrieve the mean-squared displacement associated with the process under study. We use computer simulations to examine the signature of several biologically relevant diffusion processes (simple diffusion, continuous-time random walk, caged diffusion, obstructed diffusion, two-state diffusion, and diffusing diffusivity) in variable-length-scale FCS. We show that, when used in concert, length-scale variation and data inversion permit us to identify non-Gaussian processes and, regardless of Gaussianity, to retrieve their mean-squared displacement over several orders of magnitude in time. This makes unbiased discrimination between different classes of diffusion models possible.
ACS Omega
The diffusion of molecules and particles inside the aqueous suspension of soft colloids (polymer microgels) is investigated using variable length scale fluorescence correlation spectroscopy (VLS-FCS). Carbopol 940 is chosen as the model matrix system, and two factors affecting diffusion are investigated: the spatial hindrance and the diffusant−matrix interaction. By studying diffusion of molecules and particles with different sizes inside the suspension, VLS-FCS reveals the restricted motion at a short length scale, that is, in the gaps between the microgels, and normal diffusion at a larger length scale. The information on the gap's length scale is also accessed. On the other hand, by tuning the pH value, the diffusant−matrix electrostatic attraction is adjusted and the results expose a short-time fast diffusion of probe molecules inside the gaps and a long-time restricted diffusion because of trapping inside the microgels. It is proved that VLS-FCS is a powerful method, investigating anomalous diffusion at different length scales and it is a promising approach to investigate diffusion in complex soft matter systems.
From free to effective diffusion coefficients in fluorescence correlation spectroscopy experiments
Physical Review E, 2013
Diffusion is one of the main transport processes that occur inside cells determining the spatial and time distribution of relevant action molecules. In most cases these molecules not only diffuse but also interact with others as they get transported. When these interactions occur faster than diffusion the resulting transport can be characterized by "effective diffusion coefficients" that depend on both the reaction rates and the "free" diffusion coefficients. Fluorescence correlation spectroscopy (FCS) gives information on effective rather than free diffusion coefficients under this condition. In the present paper we investigate what coefficients can be drawn from FCS experiments for a wide range of values of the ratio of reaction to diffusion time scales, using different fitting functions. We find that the effective coefficients can be inferred with relatively small errors even when the condition of fast reactions does not exactly hold. Since the diffusion time scale depends on the size of the observation volume and the reaction time scale depends on concentrations, we also discuss how by changing either one or the other property one can switch between the two limits and extract more information on the system under study.
Journal of Biomedical Optics, 2013
Fluorescence recovery after photobleaching (FRAP) is a common technique to probe mobility of fluorescently labeled proteins in biological membranes by monitoring the time-dependence of the spatially integrated fluorescence signals after a bleaching pulse. Discrimination by FRAP between free diffusion with an immobile fraction (FDIM) and the phenomenological model for anomalous diffusion based on the time-dependent diffusion coefficient (TDDC) is a challenging problem, requiring extremely long observation times for differentiation. Recently, rectangular FRAP (rFRAP) has been introduced for normal diffusion by considering not only the temporal but also spatial information, taking the effective point spread function of the optical system into account. In this work we provide an extension of rFRAP toward anomalous diffusion according to the continuous time random walk (CTRW). We explore whether the spatial information in rFRAP allows for enhanced discrimination between FDIM, TDDC, and CTRW in a single experiment within a feasible time window. Simulations indicate that rFRAP can indeed differentiate the different models by evaluating the spatial autocorrelation of the differences between the measured and fitted pixel values. Hence, rFRAP offers a tool that is capable of discriminating different types of diffusion at shorter time scales than in the case where spatial information is discarded.
Quantitative methods for diffusion measurements in fluorescence microscopy
2019
In this work, statistical methods are developed for mapping mass transport locally based on images collected using a confocal laser scanning microscope. Besides presenting raster image correlation spectroscopy as an established method in fluorescence microscopy, we introduce a single particle tracking method which takes advantage of the raster scanning of the image in a confocal microscope. In single particle tracking, particles are identified and followed in consecutive frames of a video to measure their diffusive mobility. Both a maximum likelihood and a centroid-based method have been developed to locate the particles and hence to estimate the diffusion coefficient. The method is generalized to analyse mixtures of particles having different diffusion coefficients. The proposed method allows us to study the entire distribution of diffusion coefficients, enabling the characterization of heterogeneous systems. Motivated by experiments with particle mixtures, we investigate the use o...
Statistical Analysis of Diffusion Coefficient Determination by Fluorescence Correlation Spectroscopy
Journal of Fluorescence, 2005
Fluorescence correlation spectroscopy (FCS) has become an important and widely used technique for many applications in physics, chemistry, and biology. The parameter most frequently addressed by FCS is the diffusion of molecules in solution. Due to the highly non-linear connection between the diffusion coefficient and a measured autocorrelation function, it is extremely difficult to analyse the accuracy of the diffusion-coefficient determination in a FCS experiment. Here, we present a simplified analysis based on some general maximum-likelihood considerations, and numerical result are given for the dependence of the accuracy of the diffusion-coefficient determination on sample concentration, brightness, and measurement time. Optimal concentration values for performing FCS are found.
Precise measurement of diffusion by multi-color dual-focus fluorescence correlation spectroscopy
EPL (Europhysics Letters), 2008
Dual-focus fluorescence correlation spectroscopy is a method for precisely measuring the diffusion coefficient of fluorescing molecules close to the infinite dilution limit in a referencefree and absolute manner. We apply the method to determine the diffusion coefficients of three fluorescent dyes across the visible spectrum. These values can be used as absolute reference standards for fluorescence correlation spectroscopy. In particular, it is found that the diffusion coefficient of the widely used reference dye Rhodamine 6G is by 37% larger than the value used in most publications on fluorescence correlation spectroscopy over the last three decades.
Macromolecules, 2009
We present a comprehensive investigation of polymer diffusion in the semidilute regime by fluorescence correlation spectroscopy (FCS) and dynamic light scattering (DLS). Using single-labeled polystyrene chains, FCS leads to the self-diffusion coefficient while DLS gives the cooperative diffusion coefficient for exactly the same molecular weights and concentrations. Using FCS we observe a new fast mode in the semidilute entangled concentration regime beyond the slower mode which is due to self-diffusion. Comparison of FCS data with data obtained by DLS on the same polymers shows that the second mode observed in FCS is identical to the cooperative diffusion coefficient measured with DLS. An in-depth analysis and a comparison with current theoretical models demonstrates that the new cooperative mode observed in FCS is due to the effective long-range interaction of the chains through the transient entanglement network.