We quantitatively analyzed particle tracking data on insulin granules expressing fluorescent fusion proteins in MIN6 cells to better understand the motions contributing to intracellular transport and, more generally, the means for characterizing systems far from equilibrium. Care was taken to ensure that the statistics reflected intrinsic features of the individual granules rather than details of the measurement and overall cell state. We find anomalous diffusion. Interpreting such data conventionally requires assuming that a process is either ergodic with particles working against fluctuating obstacles (fractional Brownian motion) or nonergodic with a broad distribution of dwell times for traps (continuous-time random walk). However, we find that statistical tests based on these two models give conflicting results. We resolve this issue by introducing a subordinated scheme in which particles in cages with random dwell times undergo correlated motions owing to interactions with a fluctuating environment. We relate this picture to the underlying microtubule structure by imaging in the presence of vinblastine. Our results provide a simple physical picture for how diverse pools of insulin granules and, in turn, biphasic secretion could arise. Eukaryotic cells package proteins into vesicles for trafficking and spatially localized secretion. These essential functions are highly regulated, and defects in them can lead to disease (1, 2). Although optical microscopy, combined with molecular and cellular biology, can provide important insight into intracellular dynamics, in the past, most measurements detected variations in intensities from many molecular events and thus averaged in some way. These include fluorescence correlation spectroscopy (FCS) (3), fluorescence recovery after photobleaching (FRAP) (4), and image correlation spectroscopy (5). Recent advances in experimental methods now enable tracking single particles in cells (6). Although these measurements still involve a degree of time averaging (7), the resulting individual time trajectories contain more information than the mean values extracted from the aforementioned approaches.Qualitatively, the time trajectories reveal complex behaviors: combinations of random, directed, transiently stalled and constrained motions (e.g., refs. 7, 8). These different types of motion reflect the interplay of various molecular components in crowded environments. Quantifying their relative importance can constrain mechanisms, but extracting this information from the particle tracking data requires new theoretical tools. Operationally, one strategy is to classify segments of trajectories according to their motions (e.g., active and passive) (9, 10), but this requires long trajectories. A less data-demanding approach is to identify different types of anomalous diffusion (11).What features can give rise to the observed anomalous behavior? Simple crowding is insufficient, as it results in standard Brownian motion but with a reduced diffusion coefficient (12). Instead, anomalous b...

Replication protein A (RPA) coordinates important DNA metabolic events by stabilizing single-strand DNA (ssDNA) intermediates, activating the DNA damage response and handing off ssDNA to appropriate downstream players. Six DNA binding domains (DBDs) in RPA promote high affinity binding to ssDNA yet also allow RPA displacement by lower affinity proteins. We generated fluorescent versions of Saccharomyces cerevisiae RPA and visualized the conformational dynamics of individual DBDs in the context of the full-length protein. We show that both DBD-A and DBD-D rapidly bind to and dissociate from ssDNA while RPA remains bound to ssDNA. The recombination mediator protein Rad52 selectively modulates the dynamics of DBD-D. These findings reveal how RPA interacting proteins with lower ssDNA binding affinities can access the occluded ssDNA and remodel individual DBDs to replace RPA.

Robust methods for identifying patterns of expression in genome-wide data are important for generating hypotheses regarding gene function. To this end, several analytic methods have been developed for detecting periodic patterns. We improve one such method, JTK_CYCLE, by explicitly calculating the null distribution such that it accounts for multiple hypothesis testing and by including non-sinusoidal reference waveforms. We term this method empirical JTK_CYCLE with asymmetry search, and we compare its performance to JTK_CYCLE with Bonferroni and Benjamini-Hochberg multiple hypothesis testing correction, as well as to five other methods: cyclohedron test, address reduction, stable persistence, ANOVA, and F24. We find that ANOVA, F24, and JTK_CYCLE consistently outperform the other three methods when data are limited and noisy; empirical JTK_CYCLE with asymmetry search gives the greatest sensitivity while controlling for the false discovery rate. Our analysis also provides insight into experimental design and we find that, for a fixed number of samples, better sensitivity and specificity are achieved with higher numbers of replicates than with higher sampling density. Application of the methods to detecting circadian rhythms in a metadataset of microarrays that quantify time-dependent gene expression in whole heads of Drosophila melanogaster reveals annotations that are enriched among genes with highly asymmetric waveforms. These include a wide range of oxidation reduction and metabolic genes, as well as genes with transcripts that have multiple splice forms.

The LiHoxY1-xF4 magnetic material in a transverse magnetic field Bx x perpendicular to the Ising spin direction has long been used to study tunable quantum phase transitions in a random disordered system. We show that the Bx-induced magnetization along the x direction, combined with the local random dilution-induced destruction of crystalline symmetries, generates, via the predominant dipolar interactions between Ho3+ ions, random fields along the Ising z direction. This identifies LiHoxY1-xF4 in Bx as a new random field Ising system. The random fields explain the rapid decrease of the critical temperature in the diluted ferromagnetic regime and the smearing of the nonlinear susceptibility at the spin-glass transition with increasing Bx and render the Bx-induced quantum criticality in LiHoxY1-xF4 likely inaccessible.

Analyses of random walks traditionally use the mean square displacement (MSD) as an order parameter characterizing dynamics. We show that the distribution of relative angles of motion between successive time intervals of random walks in two or more dimensions provides information about stochastic processes beyond the MSD. We illustrate the behavior of this measure for common models and apply it to experimental particle tracking data. For a colloidal system, the distribution of relative angles reports sensitively on caging as the density varies. For transport mediated by molecular motors on filament networks in vitro and in vivo, we discover self-similar properties that cannot be described by existing models and discuss possible scenarios that can lead to the elucidated statistical features.random walks | angular correlation | cytoskeleton C omplex dynamics often emerge from ensembles of interacting constituents. Trajectories that are obtained by tracking individual constituents contain information beyond the evolution of ensemble properties, and these data can thus reveal new mechanistic features of the system studied. Examples cut across disciplines and include quantum dots (1), colloidal beads (2), features in cells (3, 4), fish in schools (5), birds in flocks (6), and primates in social groups (7,8). These data (individual trajectories) demand theoretical frameworks for characterizing and interpreting them.The standard reporter for different forms of motion is the mean square displacement (MSD)where brackets and overlines denote ensemble and time averages, respectively. In simple Brownian motion (9), the MSD grows linearly with the separation in time between two observation points (the lag time, Δ) and does not depend on the amount of data included in averages (the measurement time, T)-i.e., there is ergodicity. Anomalous (i.e., non-Brownian) dynamics can arise from correlations in the walk steps. Correlations in the step sizes [e.g., as in fractional Brownian motion (FBM)] (10) give rise to nonlinear scaling of the MSD with lag time, retaining ergodicity (11). By contrast, a power-law distribution of dwell times [e.g., as in a continuous time random walk (CTRW)] (12) is associated with linear scaling with lag time but nonergodicity (13, 14). The two types of correlations can exist together (4, 15). Despite the success of the MSD as an order parameter for dynamics, it is essentially a 1D measure. We expect random walks in two and more dimensions to contain information beyond the MSD, and various alternative analyses have been suggested (16) (Conclusions). In this paper, we introduce a statistical measure of such information. Specifically, we consider the relative angle, which quantifies the direction of motion over successive time intervals. We show that different models of stochastic processes give rise to different distributions of relative angles and how the intervals can be varied to probe contributing time scales. We apply our order parameter to 2D experimental data obtained for mesoscopic systems. We ex...