Large-Scale, Wavelet-Based Analysis of Lysosomal Trajectories and Co-Movements of Lysosomes with Nanoparticle Cargos

Lysosomes—that is, acidic organelles known for degradation/recycling—move through the cytoplasm alternating between bursts of active transport and short, diffusive motions or even pauses. While their mobility is essential for lysosomes’ fusogenic and non-fusogenic interactions with target organelles, their movements have not been characterized in adequate detail. Here, large-scale statistical analysis of lysosomal movement trajectories reveals that lysosome trajectories in all examined cell types—both cancer and noncancerous ones—are superdiffusive and characterized by heavy-tailed distributions of run and flight lengths. Consideration of Akaike weights for various potential models (lognormal, power law, truncated power law, stretched exponential, and exponential) indicates that the experimental data are best described by the lognormal distribution, which, in turn, can be related to one of the space-search strategies particularly effective when “thorough” search needs to balance search for rare target(s) (organelles). In addition, automated, wavelet-based analysis allows for co-tracking the motions of lysosomes and the cargos they carry—particularly the nanoparticle aggregates known to cause selective lysosome disruption in cancerous cells. The methods we describe here could help study nanoparticle assemblies, viruses, and other objects transported inside various vesicle types, as well as coordinated movements of organelles/particles in the cytoplasm. Custom-written code that includes integrated workflow for our analyses is made available for academic use.

Information encoded in volumes and areas of dendritic spines is nearly maximal across mammalian brains

Long-term information associated with neuronal memory resides in dendritic spines. However, spines can have a limited size due to metabolic and neuroanatomical constraints, which should effectively limit the amount of encoded information in excitatory synapses. This study investigates how much information can be stored in the sizes of dendritic spines, and whether is it optimal in any sense? It is shown here, using empirical data for several mammalian brains across different regions and physiological conditions, that dendritic spines nearly maximize entropy contained in their volumes and surface areas for a given mean size. This result is essentially independent of the type of a fitting distribution to size data, as both short- and heavy-tailed distributions yield similar nearly 100 % information efficiency in the majority of cases, although heavy-tailed distributions slightly better fit the data. On average, the highest information is contained in spine volume, and the lowest in spine length or spine head diameter. Depending on a species and brain region, a typical spine can encode between 6.1 and 10.8 bits of information in its volume, and 3.1-8.1 bits in its surface area. Our results suggest a universality of entropy maximization in spine volumes and areas, which can be a new principle of memory storing in synapses.

Ruin Probabilities and Complex Analysis

This paper considers the solution of the equations for ruin probabilities in infinite continuous time. Using the Fourier Transform and certain results from the theory of complex functions, these solutions are obtained as com- plex integrals in a form which may be evaluated numerically by means of the inverse Fourier Transform. In addition the relationship between the re- sults obtained for the continuous time cases, and those in the literature, are compared. Closed form ruin probabilities for the heavy tailed distributions: mixed exponential; Gamma (including Erlang); Lognormal; Weillbull; and Pareto, are derived as a result (or computed to any degree of accuracy, and without the use of simulations).

Taylor’s law of fluctuation scaling for semivariances and higher moments of heavy-tailed data

We generalize Taylor’s law for the variance of light-tailed distributions to many sample statistics of heavy-tailed distributions with tail index α in (0, 1), which have infinite mean. We show that, as the sample size increases, the sample upper and lower semivariances, the sample higher moments, the skewness, and the kurtosis of a random sample from such a law increase asymptotically in direct proportion to a power of the sample mean. Specifically, the lower sample semivariance asymptotically scales in proportion to the sample mean raised to the power 2, while the upper sample semivariance asymptotically scales in proportion to the sample mean raised to the power (2−α)/(1−α)>2. The local upper sample semivariance (counting only observations that exceed the sample mean) asymptotically scales in proportion to the sample mean raised to the power (2−α2)/(1−α). These and additional scaling laws characterize the asymptotic behavior of commonly used measures of the risk-adjusted performance of investments, such as the Sortino ratio, the Sharpe ratio, the Omega index, the upside potential ratio, and the Farinelli–Tibiletti ratio, when returns follow a heavy-tailed nonnegative distribution. Such power-law scaling relationships are known in ecology as Taylor’s law and in physics as fluctuation scaling. We find the asymptotic distribution and moments of the number of observations exceeding the sample mean. We propose estimators of α based on these scaling laws and the number of observations exceeding the sample mean and compare these estimators with some prior estimators of α.

Cascade events in geographical space

In this paper, we present a simple discrete model of cascade behavior in an actual geographical space with built environments. By simultaneously triggering and relaxing random locations in a network of Voronoi cells interacting via the gravity model, we observe nontrivial statistics with heavy-tailed distributions of cells and actual area extents involved in the cascade. The distributions of these affected areas follow unimodal statistics, unlike the other externally-driven models operating over uniform neighborhoods that exhibit power-laws. Majority of the cascades are limited within the immediate neighborhoods of adjacent Voronoi cells, even for sufficiently large triggering magnitudes. The results are viewed from the perspective of inhomogeneous driving in sandpile-based models, and benchmarked with distributions obtained in other geographic datasets. The method offers a complexity perspective into the generation of large-scale events in physical and intangible flows, and explains their origins from cascaded accumulations of slow, random, and intermittent processes.