Kinetic lattice Monte Carlo simulation of viscoelastic subdiffusion

Microtubules Regulate Localization and Availability of Insulin Granules in Pancreatic Beta Cells

Two key prerequisites for glucose-stimulated insulin secretion (GSIS) in β cells are the proximity of insulin granules to the plasma membrane and their anchoring or docking to the plasma membrane (PM). Although recent evidence has indicated that both of these factors are altered in the context of diabetes, it is unclear what regulates localization of insulin granules and their interactions with the PM within single cells. Here, we demonstrate that microtubule (MT)-motor-mediated transport dynamics have a critical role in regulating both factors. Super-resolution imaging shows that whereas the MT cytoskeleton resembles a random meshwork in the cells' interior, MTs near the cell surface are preferentially aligned with the PM. Computational modeling suggests two consequences of this alignment. First, this structured MT network preferentially withdraws granules from the PM. Second, the binding and transport of insulin granules by MT motors prevents their stable anchoring to the PM. These findings suggest the MT cytoskeleton may negatively regulate GSIS by both limiting the amount of insulin proximal to the PM and preventing or breaking interactions between the PM and the remaining nearby insulin granules. These results predict that altering MT network structure in β cells can be used to tune GSIS. Thus, our study points to the potential of an alternative therapeutic strategy for diabetes by targeting specific MT regulators.

Subdiffusive Dynamics Lead to Depleted Particle Densities near Cellular Borders

It has long been known that the complex cellular environment leads to anomalous motion of intracellular particles. At a gross level, this is characterized by mean-squared displacements that deviate from the standard linear profile. Statistical analysis of particle trajectories has helped further elucidate how different characteristics of the cellular environment can introduce different types of anomalousness. A significant majority of this literature has, however, focused on characterizing the properties of trajectories that do not interact with cell borders (e.g., cell membrane or nucleus). Numerous biological processes ranging from protein activation to exocytosis, however, require particles to be near a membrane. This study investigates the consequences of a canonical type of subdiffusive motion, fractional Brownian motion, and its physical analog, generalized Langevin equation dynamics, on the spatial localization of particles near reflecting boundaries. Results show that this type of subdiffusive motion leads to the formation of significant zones of depleted particle density near boundaries and that this effect is independent of the specific model details encoding those dynamics. Rather, these depletion layers are a natural and robust consequence of the anticorrelated nature of motion increments that is at the core of fractional Brownian motion (or alternatively generalized Langevin equation) dynamics. If such depletion zones are present, it would be of profound importance given the wide array of signaling and transport processes that occur near membranes. If not, that would suggest our understanding of this type of anomalous motion may be flawed. Either way, this result points to the need to further investigate the consequences of anomalous particle motions near cell borders from both theoretical and experimental perspectives.

Time averages and their statistical variation for the Ornstein-Uhlenbeck process: Role of initial particle distributions and relaxation to stationarity

How ergodic is diffusion under harmonic confinements? How strongly do ensemble- and time-averaged displacements differ for a thermally-agitated particle performing confined motion for different initial conditions? We here study these questions for the generic Ornstein-Uhlenbeck (OU) process and derive the analytical expressions for the second and fourth moment. These quantifiers are particularly relevant for the increasing number of single-particle tracking experiments using optical traps. For a fixed starting position, we discuss the definitions underlying the ensemble averages. We also quantify effects of equilibrium and nonequilibrium initial particle distributions onto the relaxation properties and emerging nonequivalence of the ensemble- and time-averaged displacements (even in the limit of long trajectories). We derive analytical expressions for the ergodicity breaking parameter quantifying the amplitude scatter of individual time-averaged trajectories, both for equilibrium and out-of-equilibrium initial particle positions, in the entire range of lag times. Our analytical predictions are in excellent agreement with results of computer simulations of the Langevin equation in a parabolic potential. We also examine the validity of the Einstein relation for the ensemble- and time-averaged moments of the OU-particle. Some physical systems, in which the relaxation and nonergodic features we unveiled may be observable, are discussed.

Ergodicity testing for anomalous diffusion: small sample statistics

The analysis of trajectories recorded in experiments often requires calculating time averages instead of ensemble averages. According to the Boltzmann hypothesis, they are equivalent only under the assumption of ergodicity. In this paper, we implement tools that allow to study ergodic properties. This analysis is conducted in two classes of anomalous diffusion processes: fractional Brownian motion and subordinated Ornstein-Uhlenbeck process. We show that only first of them is ergodic. We demonstrate this by applying rigorous statistical methods: mean square displacement, confidence intervals, and dynamical functional test. Our methodology is universal and can be implemented for analysis of many experimental data not only if a large sample is available but also when there are only few trajectories recorded.

A generalization of the bond fluctuation model to viscoelastic environments

A lattice-based simulation method for polymer diffusion in a viscoelastic medium is presented. This method combines the eight-site bond fluctuation model with an algorithm for the simulation of fractional Brownian motion on the lattice. The method applies to unentangled self-avoiding chains and is probed for anomalous diffusion exponents α between 0.7 and 1.0. The simulation results are in very good agreement with the predictions of the generalized Rouse model of a self-avoiding chain polymer in a viscoelastic medium.

Universal algorithm for identification of fractional Brownian motion. A case of telomere subdiffusion

We present a systematic statistical analysis of the recently measured individual trajectories of fluorescently labeled telomeres in the nucleus of living human cells. The experiments were performed in the U2OS cancer cell line. We propose an algorithm for identification of the telomere motion. By expanding the previously published data set, we are able to explore the dynamics in six time orders, a task not possible earlier. As a result, we establish a rigorous mathematical characterization of the stochastic process and identify the basic mathematical mechanisms behind the telomere motion. We find that the increments of the motion are stationary, Gaussian, ergodic, and even more chaotic--mixing. Moreover, the obtained memory parameter estimates, as well as the ensemble average mean square displacement reveal subdiffusive behavior at all time spans. All these findings statistically prove a fractional Brownian motion for the telomere trajectories, which is confirmed by a generalized p-variation test. Taking into account the biophysical nature of telomeres as monomers in the chromatin chain, we suggest polymer dynamics as a sufficient framework for their motion with no influence of other models. In addition, these results shed light on other studies of telomere motion and the alternative telomere lengthening mechanism. We hope that identification of these mechanisms will allow the development of a proper physical and biological model for telomere subdynamics. This array of tests can be easily implemented to other data sets to enable quick and accurate analysis of their statistical characteristics.

Fractional process as a unified model for subdiffusive dynamics in experimental data

We show how to use a fractional autoregressive integrated moving average (FARIMA) model to a statistical analysis of the subdiffusive dynamics. The discrete time FARIMA(1,d,1) model is applied in this paper to the random motion of an individual fluorescently labeled mRNA molecule inside live E. coli cells in the experiment described in detail by Golding and Cox [Phys. Rev. Lett. 96, 098102 (2006)] as well as to the motion of fluorescently labeled telomeres in the nucleus of live human cells (U2OS cancer) in the experiment performed by Bronstein et al. [Phys. Rev. Lett. 103, 018102 (2009)]. It is found that only the memory parameter d of the FARIMA model completely detects an anomalous dynamics of the experimental data in both cases independently of the observed distribution of random noises.