S. M. Ali Tabei

Intracellular transport of insulin granules is a subordinated random walk

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.

Modeling bistable cell-fate choices in the Drosophila eye: qualitative and quantitative perspectives

A major goal of developmental biology is to understand the molecular mechanisms whereby genetic signaling networks establish and maintain distinct cell types within multicellular organisms. Here, we review cell-fate decisions in the developing eye of Drosophila melanogaster and the experimental results that have revealed the topology of the underlying signaling circuitries. We then propose that switch-like network motifs based on positive feedback play a central role in cell-fate choice, and discuss how mathematical modeling can be used to understand and predict the bistable or multistable behavior of such networks.

Distribution of directional change as a signature of complex dynamics

Significance Since Einstein’s seminal work in 1905, the main means of characterizing stochastic processes has been the mean square displacement (MSD). However, this order parameter fails to capture many features of dynamics at the forefront of science today, ranging from glassy relaxation to active transport in biological cells. Although there have been several studies seeking to go beyond the MSD, such studies have not made full use of the information available in individual trajectories in two (or more) dimensions, as are now commonly obtained in particle tracking experiments. Here, we introduce an approach that quantifies directional properties of complex motions and discover striking correlations in a number of condensed phase systems. 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.

Improved Statistical Methods Enable Greater Sensitivity in Rhythm Detection for Genome-Wide Data

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.

Model for competition from self during passive immunization, with application to broadly neutralizing antibodies for HIV

We propose a mathematical model to interpret observations concerning the behavior of broadly neutralizing antibodies for chronic HIV in vivo. The model enables us to identify a threshold antibody level that must be achieved to decrease the viral load effectively. Although this threshold has not been reached in existing passive immunization studies, it is within range of humoral immune responses, suggesting that therapeutic vaccines are feasible. In an appendix, we develop a model of passive immunization against influenza, and acute infection.

Understanding Non Brownian Dynamics of Intracellular Transport

Understanding insulin granule transport in live beta cells is a complicated task. Traditionally, the diffusion coefficients and the velocity of insulin granules measured via particle tracking techniques are used to characterize the dynamics, which requires the assumption that the dynamics to be either purely diffusive or ballistic. This is not the case for insulin granules. We use a variety of statistical data analysis, to show that insulin granule vesicles in their pathway, which leads to exocytosis performs a subordinated intercellular transport mechanisms, which leads to a statistical anomalous dynamics.