Superdiffusion in a model for diffusion in a molecularly crowded environment

Fast and precise inference on diffusivity in interacting particle systems

Particle systems made up of interacting agents is a popular model used in a vast array of applications, not the least in biology where the agents can represent everything from single cells to animals in a herd. Usually, the particles are assumed to undergo some type of random movements, and a popular way to model this is by using Brownian motion. The magnitude of random motion is often quantified using mean squared displacement, which provides a simple estimate of the diffusion coefficient. However, this method often fails when data is sparse or interactions between agents frequent. In order to address this, we derive a conjugate relationship in the diffusion term for large interacting particle systems undergoing isotropic diffusion, giving us an efficient inference method. The method accurately accounts for emerging effects such as anomalous diffusion stemming from mechanical interactions. We apply our method to an agent-based model with a large number of interacting particles, and the results are contrasted with a naive mean square displacement-based approach. We find a significant improvement in performance when using the higher-order method over the naive approach. This method can be applied to any system where agents undergo Brownian motion and will lead to improved estimates of diffusion coefficients compared to existing methods.

A quantitative modelling approach for DNA repair on a population scale

The great advances of sequencing technologies allow the in vivo measurement of nuclear processes-such as DNA repair after UV exposure-over entire cell populations. However, data sets usually contain only a few samples over several hours, missing possibly important information in between time points. We developed a data-driven approach to analyse CPD repair kinetics over time in Saccharomyces cerevisiae. In contrast to other studies that consider sequencing signals as an average behaviour, we understand them as the superposition of signals from independent cells. By motivating repair as a stochastic process, we derive a minimal model for which the parameters can be conveniently estimated. We correlate repair parameters to a variety of genomic features that are assumed to influence repair, including transcription rate and nucleosome density. The clearest link was found for the transcription unit length, which has been unreported for budding yeast to our knowledge. The framework hence allows a comprehensive analysis of nuclear processes on a population scale.

Behavior analysis of virtual-item gambling

From the gambling logs of an online lottery game we extract the probability distribution of various quantities (e.g., bet value, total pool size, waiting time between successive gambles) as well as related correlation coefficients. We view the net change of income of each player as a random walk. The mean-squared displacement of these net income random walks exhibits a transition between a superdiffusive and a normal diffusive regime. We discuss different random-walk models with truncated power-law step lengths distributions that allow us to reproduce some of the properties extracted from the gambling logs. Analyzing the mean-squared displacement and the first-passage time distribution for these models allows us to identify the key features needed for observing this crossover from superdiffusion to normal diffusion.

Cell-size confinement effect on protein diffusion in crowded poly(ethylene)glycol solution

Micrometric membrane confinements and macromolecular crowding of cytoplasm are key factors that regulate molecular diffusion in live cells. Previous studies have shown that macromolecular crowding delays molecular diffusion. However, the effect of cell-size confinement on diffusion in the crowding environment is yet to be elucidated. Using fluorescence correlation spectroscopy (FCS), we analyzed protein diffusion in microdroplets containing polymer solution covered with lipid membranes that mimic cells. As a result, we found that a synergistic condition of crowding and micrometric confinement results in accelerated protein diffusion on a sub-millisecond time scale. This acceleration rate strongly depended on the size of the confined space and the degree of crowding. These findings indicate that cell-size confinement supports protein diffusion in highly crowded cytoplasm.

Macromolecular crowding directs the motion of small molecules inside cells

It is now well established that cell interiors are significantly crowded by macromolecules, which impede diffusion and enhance binding rates. However, it is not fully appreciated that levels of crowding are heterogeneous, and can vary substantially between subcellular regions. In this article, starting from a microscopic model, we derive coupled nonlinear partial differential equations for the concentrations of two populations of large and small spherical particles with steric volume exclusion. By performing an expansion in the ratio of the particle sizes, we find that the diffusion of a small particle in the presence of large particles obeys an advection–diffusion equation, with a reduced diffusion coefficient and a velocity directed towards less crowded regions. The interplay between advection and diffusion leads to behaviour that differs significantly from Brownian diffusion. We show that biologically plausible distributions of macromolecules can lead to highly non-Gaussian probability densities for the small particle position, including asymmetrical and multimodal densities. We confirm all our results using hard-sphere Brownian dynamics simulations.

Diffusing diffusivity: Rotational diffusion in two and three dimensions

We consider the problem of calculating the probability distribution function (pdf) of angular displacement for rotational diffusion in a crowded, rearranging medium. We use the diffusing diffusivity model and following our previous work on translational diffusion [R. Jain and K. L. Sebastian, J. Phys. Chem. B 120, 3988 (2016)], we show that the problem can be reduced to that of calculating the survival probability of a particle undergoing Brownian motion, in the presence of a sink. We use the approach to calculate the pdf for the rotational motion in two and three dimensions. We also propose new dimensionless, time dependent parameters, αrot,2D and αrot,3D, which can be used to analyze the experimental/simulation data to find the extent of deviation from the normal behavior, i.e., constant diffusivity, and obtain explicit analytical expressions for them, within our model.

Lévy flight with absorption: A model for diffusing diffusivity with long tails

We consider diffusion of a particle in rearranging environment, so that the diffusivity of the particle is a stochastic function of time. In our previous model of "diffusing diffusivity" [Jain and Sebastian, J. Phys. Chem. B 120, 3988 (2016)JPCBFK1520-610610.1021/acs.jpcb.6b01527], it was shown that the mean square displacement of particle remains Fickian, i.e., 〈x^{2}(T)〉∝T at all times, but the probability distribution of particle displacement is not Gaussian at all times. It is exponential at short times and crosses over to become Gaussian only in a large time limit in the case where the distribution of D in that model has a steady state limit which is exponential, i.e., π_{e}(D)∼e^{-D/D_{0}}. In the present study, we model the diffusivity of a particle as a Lévy flight process so that D has a power-law tailed distribution, viz., π_{e}(D)∼D^{-1-α} with 0<α<1. We find that in the short time limit, the width of displacement distribution is proportional to sqrt[T], implying that the diffusion is Fickian. But for long times, the width is proportional to T^{1/2α} which is a characteristic of anomalous diffusion. The distribution function for the displacement of the particle is found to be a symmetric stable distribution with a stability index 2α which preserves its shape at all times.

Fractal model of anomalous diffusion

An equation of motion is derived from fractal analysis of the Brownian particle trajectory in which the asymptotic fractal dimension of the trajectory has a required value. The formula makes it possible to calculate the time dependence of the mean square displacement for both short and long periods when the molecule diffuses anomalously. The anomalous diffusion which occurs after long periods is characterized by two variables, the transport coefficient and the anomalous diffusion exponent. An explicit formula is derived for the transport coefficient, which is related to the diffusion constant, as dependent on the Brownian step time, and the anomalous diffusion exponent. The model makes it possible to deduce anomalous diffusion properties from experimental data obtained even for short time periods and to estimate the transport coefficient in systems for which the diffusion behavior has been investigated. The results were confirmed for both sub and super-diffusion.

Nonextensivity and self-affinity in the mammalian neuromuscular junction

We study time series and the spontaneous miniature end-plate potentials (MEPPs) of mammals recorded at neuromuscular junctions using two different approaches: generalized thermostatistics and detrended fluctuation analysis (DFA). Classical concepts establish that the magnitude of these potentials is characterized by Gaussian statistics and that their intervals are randomly displayed. First we show that MEPP distributions adequately satisfy the q-Gaussian distributions that maximize the Tsallis entropy, indicating their nonextensive and nonequilibrium behavior. We then examine the intervals between the miniature potentials via DFA, where the profile of the intervals between events configures a deviation from the expected random behavior. Some possible physiological substrates for these findings are discussed.

Impact of external stimuli and cell micro-architecture on intracellular transport states

A living cell is a complex out-of-equilibrium system, in which a great variety of biochemical and physical processes have to be coordinated to ensure viability. We investigate properties of intracellular transport in single cells of the amoeba Dictyostelium discoideum, a relevant model organism due to its cytoskeleton simplicity. In the cells, vesicles undergo two types of motion: directed transport, driven by molecular motors on filaments, or thermal diffusion in a crowded active medium. We present results obtained with our recently developed TRAnSpORT algorithm, which performs a high-resolution temporal analysis of the track of endosomal superparamagnetic particles and splits intracellular transport into different motion states. It results in a two-state model, distinguishing active and passive transport phenomena. We can extract the precise effect of cellular micro- and nanoarchitecture on endosomal transport by disturbing the cytoskeleton through the use of depolymerizing drugs (Benomyl for microtubules, and Latrunculin A for F-actin). Further, we investigate how cytoskeleton filaments act together in order to maintain cell integrity, by applying external mechanical force on the magnetic particle and influencing its motion.

Fluctuation relation and heterogeneous superdiffusion in glassy transport

Current fluctuations and related steady-state fluctuation relation are investigated in simple coarse-grained lattice-gas analogs of a non-Newtonian fluid driven by a constant and uniform force field in two regimes of small entropy production. Non-Gaussian current fluctuations and deviations from fluctuation relation are observed and related to the existence of growing amorphous correlations and heterogeneous anomalous diffusion regimes.