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...

This paper presents a protocol using theoretical methods and free software to design and analyze multivolume digital PCR (MV digital PCR) devices; the theory and software are also applicable to design and analysis of dilution series in digital PCR. MV digital PCR minimizes the total number of wells required for “digital” (single molecule) measurements while maintaining high dynamic range and high resolution. In some examples, multivolume designs with fewer than 200 total wells are predicted to provide dynamic range with 5-fold resolution similar to that of single-volume designs requiring 12,000 wells. Mathematical techniques were utilized and expanded to maximize the information obtained from each experiment and to quantify performance of devices, and were experimentally validated using the SlipChip platform. MV digital PCR was demonstrated to perform reliably, and results from wells of different volumes agreed with one another. No artifacts due to different surface-to-volume ratios were observed, and single molecule amplification in volumes ranging from 1 to 125 nL was self-consistent. The device presented here was designed to meet the testing requirements for measuring clinically-relevant levels of HIV viral load at the point-of-care (in plasma, <500 molecules/mL to >1,000,000 molecules/mL), and the predicted resolution and dynamic range was experimentally validated using a control sequence of DNA. This approach simplifies digital PCR experiments, saves space and thus enables multiplexing by using separate areas for each sample on one chip, and facilitates the development of new high-performance diagnostic tools for resource-limited applications. The theory and software presented here are general, and are applicable to designing and analyzing other digital analytical platforms including digital immunoassays and digital bacterial analysis. It is not limited to SlipChip, and could also be useful for the design of systems on platforms including valve-based and droplet-based platforms. In the accompanying paper by Shen et al. (JACS 2011), this approach is used to design and test digital RT-PCT devices for quantifying RNA.

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...

Although the incidence of pneumonia was not influenced by gender, female trauma patients had better outcomes than male patients in the younger age group. Outcome in the older age group was not gender-related. Our data support a gender-based difference in outcome after traumatic injuries in younger patients.

We develop a method for achieving scalable transmission stabilization and switching of N colliding soliton sequences in optical waveguides with broadband delayed Raman response and narrowband nonlinear gain-loss. We show that dynamics of soliton amplitudes in N -sequence transmission is described by a generalized N -dimensional predator-prey model. Stability and bifurcation analysis for the predator-prey model are used to obtain simple conditions on the physical parameters for robust transmission stabilization as well as on-off and off-on switching of M out of N soliton sequences. Numerical simulations for single-waveguide transmission with a system of N coupled nonlinear Schrödinger equations with 2 ≤ N ≤ 4 show excellent agreement with the predator-prey model's predictions and stable propagation over significantly larger distances compared with other broadband nonlinear single-waveguide systems. Moreover, stable on-off and off-on switching of multiple soliton sequences and stable multiple transmission switching events are demonstrated by the simulations. We discuss the reasons for the robustness and scalability of transmission stabilization and switching in waveguides with broadband delayed Raman response and narrowband nonlinear gain-loss, and explain their advantages compared with other broadband nonlinear waveguides.